Teoria da Ligacao de Valencia - Origem, Conflitos com a Teoria do Orbital Molecular, Estado Atual e Perspectivas Futuras

Review Valence Bond TheoryIts Birth Struggles with Molecular Orbital Theory Its Present State and Future Prospects Sason Shaik 1 David Danovich 1 and Philippe C Hiberty 2 1 Institute of Chemistry The Hebrew University of Jerusalem Jerusalem 9190401 Israel daviddanovichgmailcom 2 CNRS Institut de Chimie Physique UMR8000 Université ParisSaclay 91405 Orsay France Correspondence sasonshaikgmailcom SS philippehibertyuniversiteparissaclayfr PCH Abstract This essay describes the successive births of valence bond VB theory during 19161931 The alternative molecular orbital MO theory was born in the late 1920s The presence of two seemingly different descriptions of molecules by the two theories led to struggles between the main proponents Linus Pauling and Robert Mulliken and their supporters Until the 1950s VB theory was dominant and then it was eclipsed by MO theory The struggles will be discussed as well as the new dawn of VB theory and its future Keywords valence bond molecular orbital Lewis electronpair bonds Pauling Mulliken Hund Hückel 1 Introduction This essay tells briefly a story of the emerging two major quantum mechanical theories valence bond VB theory and molecular orbital MO theory which look as two different descriptions of the same reality but are actually not We discuss the struggles between the two main groups of followers of Pauling and Mulliken and the ups and downs in the popularity of the two methods among chemists and then the fall of VB theory only to be revived and to flourish We end the story with the description of the renaissance in modern VB theory its current state and its future outlook The grassroots of Valence Bond VB theory date back to the second decade of the 20th century when Lewis published his seminal paper entitled The Atom and The Molecule 1 Lewis made use of the discovery of the electron as a fundamental particle of matter while interjecting his command of chemical facts These led him to conclude that the most abundant compounds are those which possess an even number of electrons He therefore formulated the quantum unit of chemical bonding an electron pair that glues atoms of most known molecular matter In so doing he was brilliantly able to derive electronic structure cartoons that are used to this day and age for teaching and as means of communication among chemists Lewis further distinguished between shared covalent ionic bonds and polar bonds He also laid foundations for resonance theory and used it to explain for the first time color in molecules He even discussed geometry in terms akin to the valenceshell electron pair repulsion VSEPR approach 2 The contribution of Lewis and its implementation in 19271928 into quantum mechanics by Heitler and London 35 reached Pauling who was then in Europe in a mission to learn the new quantum mechanics and bring it back to the USA Pauling was excited He dropped all the previous mechanical models which he used to teach 6 and began a wideranging program of this theory which he called valence bond theory and which he summarized in his monograph 7 Paulings work translated Lewis ideas to quantum mechanics and the work received very high attention and became extremely popular among chemists Citation Shaik S Danovich D Hiberty PC Valence Bond TheoryIts Birth Struggles with Molecular Orbital Theory Its Present State and Future Prospects Molecules 2021 26 1624 httpsdoiorg103390molecules26061624 Academic Editor Steve Scheiner Received 19 February 2021 Accepted 10 March 2021 Published 15 March 2021 Publishers Note MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations Copyright 2021 by the authors Licensee MDPI Basel Switzerland This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution CC BY license httpscreativecommonsorglicensesby40 Molecules 2021 26 1624 httpsdoiorg103390molecules26061624 httpswwwmdpicomjournalmolecules Molecules 2021 26 1624 2 of 24 Molecular orbital MO theory was developed at the same time by Hund and Mul liken 813 and served initially as a conceptual framework in spectroscopy Some what later LennardJones and Hückel applied MO theory to electronic structures of molecules 1417 Soon enough the two theories and their major proponents started a struggle to domi nate the conceptual frame of chemistry Initially MO theory was not accepted too easily by chemists and until the late 1950s VB theory which used a chemical language was up Subsequently MO theory was implemented in useful semiempirical programs and was gradually popularized by eloquent proponents like Coulson 18 Dewar 19 and others These developments and the consequences of the VBMO struggle on the reputation of VB theory determined its gradual downfall However with the developments of new conceptual frames and new computational methods during the 1970s onwards VB theory began to enjoy a renaissance and reoccupy its place alongside MO theory and DFT 2 The Roots and Development of VB Theory Lewis formulation of the nature of the chemical bond is in many ways the precursor of VB theory Lewis paper The Atom and The Molecule 1 contains plenty of ideas some of which were later embedded into VB theory His electronpair model and its dynamic nature regarding polarity was formulated 11 years before the onset of VB theory in physics 2 Moreover his work was portable and instrumental for the emergence of the new VB theory of bonding in the hands of Pauling and Slater 2 It is appropriate therefore to begin this section by briefly describing Lewis contribution to the nature of the chemical bond 21 The Lewis Electronic Cubes and Electron Pair Bonds While Lewis formulated the electronpair bonds he also tried to relate these bonds to the experience of the practicing chemists in the communities of inorganic and organic chemistries 120 In broad terms the inorganic chemists were observing chemistry of charged species ions in todays language or molecules undergoing dissociation to ions like acids while the organic chemists did not observe much of an ionic chemistry and were interested in the structure of their compounds 22122 The term structure was abstract in those early days mid 19th century and its representations lumped together groups of atom which appear in many molecules and were oddlooking in modern terms eg the initial sausages model of benzene by Kekulé 2123 Nevertheless this was the chemical landscape which Lewis tried to describe in terms of bonds between atoms The first model in the key Lewis paper 1 is itself quite cumbersome and is based on his representation of the atom as a cube with a valenceshell that may contain up to eight electrons later to be called the Octet Rule placed at the corners of the cubea model he had developed already in 1902 24 Figure 1 describes how Lewis viewed the three putative states of a single bond in the molecule like dihalogen under different conditions using the cubic model His view of the bond is dynamic and he is aware that a bond can change its character in different environments and depending on the nature of the atoms Molecules 2021 26 x FOR PEER REVIEW 2 of 24 Molecular orbital MO theory was developed at the same time by Hund and Mulli ken 813 and served initially as a conceptual framework in spectroscopy Somewhat later LennardJones and Hückel applied MO theory to electronic structures of molecules 1417 Soon enough the two theories and their major proponents started a struggle to dom inate the conceptual frame of chemistry Initially MO theory was not accepted too easily by chemists and until the late 1950s VB theory which used a chemical language was up Subsequently MO theory was implemented in useful semiempirical programs and was gradually popularized by eloquent proponents like Coulson 18 Dewar 19 and others These developments and the consequences of the VBMO struggle on the reputation of VB theory determined its gradual downfall However with the developments of new conceptual frames and new computational methods during the 1970s onwards VB theory began to enjoy a renaissance and reoccupy its place alongside MO theory and DFT 2 The Roots and Development of VB Theory Lewis formulation of the nature of the chemical bond is in many ways the precursor of VB theory Lewis paper The Atom and The Molecule 1 contains plenty of ideas some of which were later embedded into VB theory His electronpair model and its dynamic nature regarding polarity was formulated 11 years before the onset of VB theory in phys ics 2 Moreover his work was portable and instrumental for the emergence of the new VB theory of bonding in the hands of Pauling and Slater 2 It is appropriate therefore to begin this section by briefly describing Lewis contribution to the nature of the chemical bond 21 The Lewis Electronic Cubes and Electron Pair Bonds While Lewis formulated the electronpair bonds he also tried to relate these bonds to the experience of the practicing chemists in the communities of inorganic and organic chemistries 120 In broad terms the inorganic chemists were observing chemistry of charged species ions in todays language or molecules undergoing dissociation to ions like acids while the organic chemists did not observe much of an ionic chemistry and were interested in the structure of their compounds 22122 The term structure was abstract in those early days mid 19th century and its representations lumped together groups of atom which appear in many molecules and were oddlooking in modern terms eg the initial sausages model of benzene by Kekulé 2123 Nevertheless this was the chemical landscape which Lewis tried to describe in terms of bonds between atoms The first model in the key Lewis paper 1 is itself quite cumbersome and is based on his representation of the atom as a cube with a valenceshell that may contain up to eight electrons later to be called the Octet Rule placed at the corners of the cubea model he had developed already in 1902 24 Figure 1 describes how Lewis viewed the three puta tive states of a single bond in the molecule like dihalogen under different conditions using the cubic model His view of the bond is dynamic and he is aware that a bond can change its character in different environments and depending on the nature of the atoms Figure 1 Bonding situations in dihalides described through the cubic model Adapted with ACS permission from Ref 1 Copyright 1916 It is seen that the doublecube in C represents a shared electronpair bond between the two halogen atoms which Lewis views as the predominant and characteristic struc ture of the dihalogens In addition both atoms satisfy the octet rule in their valence shell Figure 1 Bonding situations in dihalides described through the cubic model Adapted with ACS permission from Ref 1 Copyright 1916 It is seen that the doublecube in C represents a shared electronpair bond between the two halogen atoms which Lewis views as the predominant and characteristic structure of the dihalogens In addition both atoms satisfy the octet rule in their valence shell by Molecules 2021 26 1624 3 of 24 sharing an edge which involves an electron pair This shared bond will later be called by Langmuir 2526 a covalent bond On the other hand the two cubes in A represent an ionic bond which for Lewis accounted to a certain extent for the state of I2 in liquid iodine In the middle in B Lewis describes a case in which one of the electrons of one ion fits into the outer shell of the second ion 1 Reading the Lewis text it is apparent that he is describing dynamic situations occurring from the covalent form C to the ionic one A and passing through B which represents a case of intermediate ionicity ie a polar bond note that the cartoon B maybe viewed also as a one electron bond though Lewis does not say so Within his general idea of dynamic bonds Lewis discusses this dynamic electronic structure as tautomerism between polar and nonpolar 20 and writes However we must assume these forms represent two limiting types and that the individual molecules range all the way from one limit to the other 1 It is clear that Lewis is thinking about a polarnonpolar superposition in bonding which in a modern dress is Paulings covalent ionic superposition of the electron pair bond 7 pp 127 73100 and in an altered dress will become the mesomerism theory of Ingold 2728 pp 194 199 202207 In the same discussion Lewis considers intermediate cases in between the extremesthis is a seminal notion of the resonance theory 129 p 135 Lewis further uses this mechanism of the dynamic position of the electron pair to allude to heterolysis in solution when an electron pair moves to one of the atoms This idea will be fleshed out in the curved arrow invented by Robinson 28 p 191 to describe the reaction mechanism and later by Ingold and Hughes to describe heterolytic processes in organic molecules 28 pp 158 199 216220 Using the cubic model Lewis tries to describe double and triple bonds between atoms 1 For a double bond he describes two cubes sharing a face such that the two atoms share four electrons ergo a double bond However when Lewis moves on to triple bonds eg in acetylene he finds the cubic model to be useless Very soon Lewis recalls the fact that the helium atom possesses an electron pair Moselys work and all of a sudden he changes the cumbersome cubic model in Figure 1 and decides that electronpair bonding is the fundamental nature of the chemical bond He then uses the electrondot structure as shown in the cartoon in Figure 2 Molecules 2021 26 x FOR PEER REVIEW 3 of 24 by sharing an edge which involves an electron pair This shared bond will later be called by Langmuir 2526 a covalent bond On the other hand the two cubes in A represent an ionic bond which for Lewis accounted to a certain extent for the state of I2 in liquid iodine In the middle in B Lewis describes a case in which one of the electrons of one ion fits into the outer shell of the second ion 1 Reading the Lewis text it is apparent that he is describing dynamic situations occurring from the covalent form C to the ionic one A and passing through B which represents a case of intermediate ionicity ie a polar bond note that the cartoon B maybe viewed also as a one electron bond though Lewis does not say so Within his general idea of dynamic bonds Lewis discusses this dynamic electronic structure as tautomerism between polar and nonpolar 20 and writes However we must assume these forms represent two limiting types and that the individual molecules range all the way from one limit to the other 1 It is clear that Lewis is thinking about a polarnonpolar superposition in bonding which in a modern dress is Paulings cova lentionic superposition of the electron pair bond 7 pp 127 73100 and in an altered dress will become the mesomerism theory of Ingold 2728 pp 194 199 202207 In the same discussion Lewis considers intermediate cases in between the extremesthis is a seminal notion of the resonance theory 129 p 135 Lewis further uses this mechanism of the dynamic position of the electron pair to allude to heterolysis in solution when an electron pair moves to one of the atoms This idea will be fleshed out in the curved arrow invented by Robinson 28 p 191 to describe the reaction mechanism and later by Ingold and Hughes to describe heterolytic processes in organic molecules 28 pp 158 199 216220 Using the cubic model Lewis tries to describe double and triple bonds between at oms 1 For a double bond he describes two cubes sharing a face such that the two atoms share four electrons ergo a double bond However when Lewis moves on to triple bonds eg in acetylene he finds the cubic model to be useless Very soon Lewis recalls the fact that the helium atom possesses an electron pair Moselys work and all of a sudden he changes the cumbersome cubic model in Figure 1 and decides that electronpair bonding is the fundamental nature of the chemical bond He then uses the electrondot structure as shown in the cartoon in Figure 2 Figure 2 A cartoon of Lewis showing his electron dot model for the electronpair holding Cl2 Adapted by permission of the creator of the cartoon WB Jensen Subsequently all the molecular drawings are presented in the electron dot structures 1 whereas in his book there are also modern representations in which a line connecting the atom replaces the pair of dots 24 eg p 91 Nevertheless Lewis goes back to the arrangement of the group of eight electrons which atoms assume in a shared bond 1 and in his Figure 5 in 1 he arranges these four pairs in the middle of the cubes edges in a tetrahedral fashion As such he makes a connection to the organic chemists who have been using tetrahedral models for carbon atoms in molecules eg Kekulé in his lectures and Va not Hoff in his landmark contribution to 3D structure 21 He further shows that two tetrahedra attached by one two or three centers of each represents respectively the single the double and the triple bond His paper is amazing in this respect since it reads like a streama symphonyof thoughts and ideas 1 very different to contemporary papers Lewis is aware that others like Abegg Kossell Stark Thomson and Parson may have priority claims on various aspects of his theory 30 He therefore emphasizes that he Figure 2 A cartoon of Lewis showing his electron dot model for the electronpair holding Cl2 Adapted by permission of the creator of the cartoon WB Jensen Subsequently all the molecular drawings are presented in the electron dot struc tures 1 whereas in his book there are also modern representations in which a line connecting the atom replaces the pair of dots 24 eg p 91 Nevertheless Lewis goes back to the arrangement of the group of eight electrons which atoms assume in a shared bond 1 and in his Figure 5 in 1 he arranges these four pairs in the middle of the cubes edges in a tetrahedral fashion As such he makes a connection to the organic chemists who have been using tetrahedral models for carbon atoms in molecules eg Kekulé in his lectures and Vant Hoff in his landmark contribution to 3D structure 21 He further shows that two tetrahedra attached by one two or three centers of each represents respectively the single the double and the triple bond His paper is amazing in this respect since it reads like a streama symphonyof thoughts and ideas 1 very different to contemporary papers Molecules 2021 26 1624 4 of 24 Lewis is aware that others like Abegg Kossell Stark Thomson and Parson may have priority claims on various aspects of his theory 30 He therefore emphasizes that he came up with this idea in 1902 and writes 1 The date of origin 1902 of this theory is mentioned because the fact that similar theories have been developed independently adds to the probability that all possess some characteristics of fundamental reality Indeed as with any great concept Lewis may have not been the only one to come up with the ideas of electronpair bonding or the octet rule see Box 1 Furthermore Langmuir followed him 25 and articulated his model further than he did see Box 1 At the same time Lewis stayed aloof and did not make special efforts to popularize his model within the chemical community eg by giving talks andor writing more about it On the other hand the more articulate Langmuir contributed a great deal to the dissemination of the Lewis model 30 Despite of all this and in retrospect it is clear that the Lewis approach has prevailed over all others and has become the bread and butter of chemical education and communication amongst chemists Additionally further it constitutes the grassroot of VB theory Box 1 Lewis and others Lewis may have been preceded by Stark Parson Thomson and Bohr Being aware of these publications and likely being challenged by colleagues he made a point to establish priority 1 and he writes on his cubic model A number of years ago to account for the striking fact I designed what may be called the theory of the cubical atom This theory while it has become familiar to my colleagues has never been published and he adds a footnote These figures are taken from a memorandum dated March 28 1902 and then he explains his reasons for exacting this date The date of origin of this theory is mentioned because the fact that similar theories have been developed independently adds to the probability that all possess some characteristics of fundamental reality There exists a very interesting correspondence between Langmuir and Lewis which is a highly recommended reading 30 In this correspondence Langmuir mentions the Bohr model of CH4 in which Bohr used four elliptical 2electron orbits pointing in a tetrahedral arrangement He further suggests to rename the model as the ThomsonStarkRutherfordBohrParsonKosselLewisLangmuir theory Factually it is known today as the Lewis model 22 Heitler London Pauling and Slater and the Development of VB Theory Heitler and Londons Study and FollowUps The chemical support of Lewis idea presented an agenda for research directed at understanding the mechanism whereby an electron pair could constitute a bond To physicists this was not obvious that two negatively charged particles could be paired Indeed electron pairing remained a mystery until 1927 when Heitler and London HL went to Zurich to work with Schrödinger Schrödinger was not interested in the chemical bond but they were In the summer of 1927 HL published a seminal paper Interaction Between Neutral Atoms and Homopolar Binding 3 in which they showed that the bonding in H2 originates in the quantum mechanical resonance interaction which transpires as the two electrons are allowed to exchange their positions between the two atoms This wave function and the notion of resonance were based on the work of Heisenberg 31 Thus since electrons are indistinguishable particles for twoelectron systems with two quantum numbers n and m there exist two wave functions which are linear combinations of the two possibilities of arranging these electrons as shown Equations 1 and 2 ΨA 12ϕn1ϕm2 ϕn2ϕm1 1 ΨB 12ϕn1ϕm2 ϕn2ϕm1 2 As demonstrated by Heisenberg the interference mixing of ϕn1ϕm2 and ϕn2ϕm1 led to a new energy term which splits the energy of the two wave functions ΨA and ΨB He called this term resonance using a classical analogy of two oscillators that by virtue of possessing the same frequency form a resonating situation with characteristic exchange energy Molecules 2021 26 1624 5 of 24 In modern terms and pictorially the bonding in H2 can be accounted for by the wave function drawn in Scheme 1 This wave function is expressed as a superposition of two covalent situations wherein in form a one electron has a spinup α spin while the other spindown β spin and vice versa in form b Molecules 2021 26 x FOR PEER REVIEW 5 of 24 As demonstrated by Heisenberg the interference mixing of φn1φm2 and φn2φm1 led to a new energy term which splits the energy of the two wave functions ΨA and ΨB He called this term resonance using a classical analogy of two oscillators that by virtue of possessing the same frequency form a resonating situation with charac teristic exchange energy In modern terms and pictorially the bonding in H2 can be accounted for by the wave function drawn in Scheme 1 This wave function is expressed as a superposition of two covalent situations wherein in form a one electron has a spinup α spin while the other spindown β spin and vice versa in form b Scheme 1 A pictorial representation of the HL covalent form of the H2 bond with spins shown by arrows On the right side are photos of Heitler and London from left to right respectively Photos of Heitler and London were taken from httpvintagefhhujiacilroiblecturenoteshtm ac cessed on 11 March 2021 Thus the bonding in H2 arises due to the quantum mechanical resonance interac tion between the two patterns of spin arrangements that are required in order to form a singlet electron pair This resonance energy accounted for about 75 of the total bond ing of the molecule in the HL calculations in modern treatments 32 this is 90 As such the HL wave function in Scheme 1 describes the chemical bonding of H2 in a satis factory manner This resonance origin of the bonding was a remarkable feat of the new quantum theory since until then it was not obvious how two neutral species could be at all bonded In 1928 London extended the HL wave function and drew the general principles of the covalent bonding in terms of the resonance interaction between the forms that allow interchange of the spin paired electrons between the two atoms 4 In both treatments 34 Heitler and London considered ionic structures for homopolar bonds but discarded this covalentionic mixing as being too small In 1929 London extended the HL method to a full potential energy surface for the reaction of H H2 5 In so doing he founded a basis for a VBbased approach to chemical reactivity and molecular dynamics MD His method created an uninterrupted chain of VB usage from London through Eyring M Polanyi and all the way to Wyatt Truhlar and others In essence the HL theory was a quantum mechanically dressed version of Lewis electronpair theory Thus even though Heitler and London did their work independently and perhaps unknowingly of the Lewis model still the HL wave function described pre cisely the sharedpair bond of Lewis As written above this issue was forcefully raised by Pauling The HL wave function formed the basis for the version of VB theory that became very popular later and which was behind some of the failings that were to be attributed to VB theory In 1929 Slater presented his determinantbased method 33 and in 1931 he gen eralized the HL model to nelectrons by expressing the total wave function as a product of n2 bond wave functions of the HL type 34 In 1932 Rumer 35 showed how to write down all the possible bond pairing schemes for nelectrons and avoid linear dependencies among the forms in order to obtain canon ical structures This level of VB theory which considers only covalent structures is re ferred to as HLVB theory Scheme 1 A pictorial representation of the HL covalent form of the H2 bond with spins shown by arrows On the right side are photos of Heitler and London from left to right respectively Photos of Heitler and London were taken from httpvintagefhhujiacilroiblecturenoteshtm accessed on 11 March 2021 Thus the bonding in H2 arises due to the quantum mechanical resonance interaction between the two patterns of spin arrangements that are required in order to form a singlet electron pair This resonance energy accounted for about 75 of the total bonding of the molecule in the HL calculations in modern treatments 32 this is 90 As such the HL wave function in Scheme 1 describes the chemical bonding of H2 in a satisfactory manner This resonance origin of the bonding was a remarkable feat of the new quantum theory since until then it was not obvious how two neutral species could be at all bonded In 1928 London extended the HL wave function and drew the general principles of the covalent bonding in terms of the resonance interaction between the forms that allow interchange of the spin paired electrons between the two atoms 4 In both treatments 34 Heitler and London considered ionic structures for homopolar bonds but discarded this covalentionic mixing as being too small In 1929 London extended the HL method to a full potential energy surface for the reaction of H H2 5 In so doing he founded a basis for a VBbased approach to chemical reactivity and molecular dynamics MD His method created an uninterrupted chain of VB usage from London through Eyring M Polanyi and all the way to Wyatt Truhlar and others In essence the HL theory was a quantum mechanically dressed version of Lewis electronpair theory Thus even though Heitler and London did their work independently and perhaps unknowingly of the Lewis model still the HL wave function described precisely the sharedpair bond of Lewis As written above this issue was forcefully raised by Pauling The HL wave function formed the basis for the version of VB theory that became very popular later and which was behind some of the failings that were to be attributed to VB theory In 1929 Slater presented his determinantbased method 33 and in 1931 he generalized the HL model to nelectrons by expressing the total wave function as a product of n2 bond wave functions of the HL type 34 In 1932 Rumer 35 showed how to write down all the possible bond pairing schemes for nelectrons and avoid linear dependencies among the forms in order to obtain canonical structures This level of VB theory which considers only covalent structures is referred to as HLVB theory Further refinements of VBT 36 between 1928 and 1933 were mostly quantitative focusing on improvement of the exponents of the atomic orbitals by Wang 37 and on the inclusion of polarization function and ionic terms by Rosen 38 and Weinbaum 39 Almost two decades later in 1949 Coulson and Fischer introduced a new method for calculating covalent bonds Using H2 40 they showed that by writing the HL wave function and allowing the orbitals to be optimized and delocalized these atomic orbitals Molecules 2021 26 1624 6 of 24 AOs developed small delocalization tails on the other hydrogen atom as shown in Figure 3 and this improves the energy of the molecule This wave function with AOs having tails on adjacent atoms forms the basis for the modern Generalized VB method GVB 4144 which will be further discussed later Molecules 2021 26 x FOR PEER REVIEW 6 of 24 Further refinements of VBT 36 between 1928 and 1933 were mostly quantitative focusing on improvement of the exponents of the atomic orbitals by Wang 37 and on the inclusion of polarization function and ionic terms by Rosen 38 and Weinbaum 39 Almost two decades later in 1949 Coulson and Fischer introduced a new method for calculating covalent bonds Using H2 40 they showed that by writing the HL wave func tion and allowing the orbitals to be optimized and delocalized these atomic orbitals AOs developed small delocalization tails on the other hydrogen atom as shown in Figure 3 and this improves the energy of the molecule This wave function with AOs having tails on adjacent atoms forms the basis for the modern Generalized VB method GVB 4144 which will be further discussed later Figure 3 The two CoulsonFischer AOs for the H2 molecule using STO3G for simplicity On the right are photos of Coulson and Fischer Coulsons photo was taken from httpsiaqmsorgde ceasedcoulsonphp accessed on 11 March 2021 Fischers photo was taken from httpwwwquan tumchemistryhistorycomFiHjal1htm accessed on 11 March 2021 23 Pauling and Slater At the time when the HL paper was published Pauling was in Europe learning the new quantum mechanics QM where it originated He was very excited to see a QM for mulation of the Lewis sharedcovalent bond He was already aware of and excited about the Lewis paper In a landmark paper 45 Pauling pointed out that the HL treat ments were entirely equivalent to GN Lewis successful theory of shared electron pair Thus although the final formulation of the chemical bond has a physicists dress the origin is clearly the chemical theory of Lewis The success of the HL model and its affinity to the Lewis chemical model posed a great opportunity for Pauling and Slater to construct a general quantum chemical theory for polyatomic molecules In the same year 1931 they both published groundbreaking papers in which they developed the notion of hybridization the covalentionic superpo sition and the resonating benzene picture 344649 In so doing they formulated thereby a link between the new theory of valence and the nature and 3D structure of key molecular types Pauling called this new theory Valence Bond Theory VBT Especially effective in chemistry were Paulings papers First and foremost Pauling was a crystallographer and had a command of the huge structural nuances of molecules As such he applied the VB ideas as close as possible to the intuition of chemists In the first paper 48 Pauling presented the electron pair bond as a superposition of the covalent HL form and the two possible ionic forms of the bond as shown in Scheme 2 and dis cussed the transition from a covalent to ionic bonding In this Scheme which is analogous to the Lewis Scheme bonding can change from being mostly covalent through different degrees of polarity due to mixing of the ionic structures and all the way to an ionic bond AB assuming this to be the lower ionic structure Figure 3 The two CoulsonFischer AOs for the H2 molecule using STO3G for simplicity On the right are photos of Coulson and Fischer Coulsons photo was taken from httpsiaqmsorgdeceasedcoulsonphp accessed on 11 March 2021 Fischers photo was taken from httpwwwquantumchemistryhistorycomFiHjal1htm accessed on 11 March 2021 23 Pauling and Slater At the time when the HL paper was published Pauling was in Europe learning the new quantum mechanics QM where it originated He was very excited to see a QM formulation of the Lewis sharedcovalent bond He was already aware of and excited about the Lewis paper In a landmark paper 45 Pauling pointed out that the HL treatments were entirely equivalent to GN Lewis successful theory of shared electron pair Thus although the final formulation of the chemical bond has a physicists dress the origin is clearly the chemical theory of Lewis The success of the HL model and its affinity to the Lewis chemical model posed a great opportunity for Pauling and Slater to construct a general quantum chemical theory for polyatomic molecules In the same year 1931 they both published groundbreaking papers in which they developed the notion of hybridization the covalentionic superposition and the resonating benzene picture 344649 In so doing they formulated thereby a link between the new theory of valence and the nature and 3D structure of key molecular types Pauling called this new theory Valence Bond Theory VBT Especially effective in chemistry were Paulings papers First and foremost Pauling was a crystallographer and had a command of the huge structural nuances of molecules As such he applied the VB ideas as close as possible to the intuition of chemists In the first paper 48 Pauling presented the electron pair bond as a superposition of the covalent HL form and the two possible ionic forms of the bond as shown in Scheme 2 and discussed the transition from a covalent to ionic bonding In this Scheme which is analogous to the Lewis Scheme bonding can change from being mostly covalent through different degrees of polarity due to mixing of the ionic structures and all the way to an ionic bond AB assuming this to be the lower ionic structure Molecules 2021 26 x FOR PEER REVIEW 7 of 24 Scheme 2 The wave function of a single bond AB expressed as a resonance hybrid of the covalent HL form and the two possible ionic forms Shown on the right is the photo of Pauling taken from httpsenwikipediaorgwikiLinusPauling accessed on 11 March 2021 Later in his book 7 footnote 13 on p 73 when he referred to homonuclear bonds AA Pauling stated clearly that the covalentionic resonance in such a bond is negligible and assumed to be zero The covalentionic resonance was ascribed only to heteronuclear bonds As such Pauling could estimate the covalent bond energy as a geometric mean of the AA and BB bond strengths Equation 3 while the covalentionic resonance was scaled to be proportional to the electronegativity difference χA χB of the atoms A and B in Equation 4 In so doing Pauling was able to generate a continuous bond ionicity scale δ as a function of the electronegativity difference of the atoms Equation 5 5051 The δ scale is seen to vary from zero for homonuclear bonds continuously to 1 full ionicity for AB bonds with a very large electronegativity difference We shall come back to this clever scheme and see its shortcomings DABcov DAADBB12 3 REcovion DAB DABcov 23χA χB2 in kcal mol1 4 δ 1 exp 025χA χB2 5 Pauling and Slater subsequently developed the creative notion of hybridization which forms localized bonds which determine the molecular geometry The angles of these hybrids follow the observed bond angles Thus for example sp is the hybridization for colinear bonds sp2 for three trigonal bonds sp3 for tetrahedral bonds while sp3d and sp3d2 are for bonds directed to the corners of a trigonal bipyramid and octahedron respec tively As such these hybridizations allowed a modern discussion of molecular geome tries in a variety of molecules ranging from organic to transition metal compounds These hybrids have become very efficient chemistryteaching tools that allow young students to figure out the geometry of molecules and in some crude way also their bonding Again this clever scheme will be reexamined later and its shortcomings will be clarified In a subsequent paper 49 Pauling addressed bonding in molecules like diborane and oddelectron bonds as in the ion molecule H2 and in dioxygen O2 which Pauling represented as having two threeelectron bonds as shown in Scheme 3 A threeelectron bond has two dominant πresonance structures 1e 2e 2e1e with two unpaired elec trons in the two perpendicular plans of the molecule having the same spins and hence the molecule has a triplet ground state This Pauling cartoon should surprise any chemist who still holds the opinion that VBT fails and makes a wrong prediction of the electronic structure for the ground state of O2 Unfortunately a close inspection of introductory chemistry textbooks shows that the allegation of failure of VBT for O2 is being actively taught Scheme 2 The wave function of a single bond AB expressed as a resonance hybrid of the covalent HL form and the two possible ionic forms Shown on the right is the photo of Pauling taken from httpsenwikipediaorgwikiLinusPauling accessed on 11 March 2021 Molecules 2021 26 1624 7 of 24 Later in his book 7 footnote 13 on p 73 when he referred to homonuclear bonds AA Pauling stated clearly that the covalentionic resonance in such a bond is negligible and assumed to be zero The covalentionic resonance was ascribed only to heteronuclear bonds As such Pauling could estimate the covalent bond energy as a geometric mean of the AA and BB bond strengths Equation 3 while the covalentionic resonance was scaled to be proportional to the electronegativity difference χA χB of the atoms A and B in Equation 4 In so doing Pauling was able to generate a continuous bond ionicity scale δ as a function of the electronegativity difference of the atoms Equation 5 5051 The δ scale is seen to vary from zero for homonuclear bonds continuously to 1 full ionicity for AB bonds with a very large electronegativity difference We shall come back to this clever scheme and see its shortcomings DABcov DAADBB12 3 REcovion DAB DABcov 23χA χB2 in kcal mol1 4 δ 1 exp 025χA χB2 5 Pauling and Slater subsequently developed the creative notion of hybridization which forms localized bonds which determine the molecular geometry The angles of these hybrids follow the observed bond angles Thus for example sp is the hybridization for co linear bonds sp2 for three trigonal bonds sp3 for tetrahedral bonds while sp3d and sp3d2 are for bonds directed to the corners of a trigonal bipyramid and octahedron respectively As such these hybridizations allowed a modern discussion of molecular geometries in a variety of molecules ranging from organic to transition metal compounds These hybrids have become very efficient chemistryteaching tools that allow young students to figure out the geometry of molecules and in some crude way also their bonding Again this clever scheme will be reexamined later and its shortcomings will be clarified In a subsequent paper 49 Pauling addressed bonding in molecules like diborane and oddelectron bonds as in the ion molecule H2 and in dioxygen O2 which Pauling represented as having two threeelectron bonds as shown in Scheme 3 A threeelectron bond has two dominant πresonance structures 1e 2e 2e1e with two unpaired elec trons in the two perpendicular plans of the molecule having the same spins and hence the molecule has a triplet ground state This Pauling cartoon should surprise any chemist who still holds the opinion that VBT fails and makes a wrong prediction of the electronic struc ture for the ground state of O2 Unfortunately a close inspection of introductory chemistry textbooks shows that the allegation of failure of VBT for O2 is being actively taught Molecules 2021 26 x FOR PEER REVIEW 8 of 24 Scheme 3 The electronic structure of O2 according to Pauling involving two threeelectron πbonds in two perpendicular planes These are shown in the right drawings using two resonance structures 1e 2e 2e1e The description of benzene in terms of a superposition resonance of two Kekulé structures appeared for the first time in the work of Slater as a case belonging to a class of species in which each atom possesses more neighbors than electrons it can share much like in metals 46 Two years later Pauling and Wheland 52 applied the HLVB theory to benzene As shown in Scheme 4 they used the five Rumer structures of benzene two Kekulé and three Dewar structures They further approximated the matrix elements be tween the structures by retaining only close neighbor resonance interactions Scheme 4 The VB structures Rumer structures for describing the πelectronic system of ben zene two Kekulé structures K1 and K2 and three Dewar Structures D1D3 K1 K2 dominate the wave function The corresponding wave function is shown in Scheme 4 below the drawings of the resonance structures and one can see that the wave function is dominated by the two Kekulé structures which together form circularly delocalized 6π electrons This resonance between the two Kekulé structures was calculated to lower the energy of benzene with respect to a single Kekulé structure Incidentally the circularly delocalized 6π benzene pretty much resembles Kekulés dream 53 which he had one day in 18611862 when he dozed in front of the fire at his home in Ghent There he saw this molecule as a self devouring snake writhing on the hexagon periphery Again we see Pauling linking his theoretical objects to the chemical graphs of Lewis and his predecessors The PaulingWheland approach allowed the extension of the treatment to naphtha lene and to a great variety of other species In his book published for the first time in 1944 Wheland explains the resonance hybrid with the biological analogy of mule donkey horse 54 The pictorial representation of the wave function the link to Kekulés oscilla tion hypothesis and to Ingolds mesomerism which were common knowledge for chem ists made the HLVB representation rather popular among practicing chemists While the description of benzene fitted its known excess stability and the ubiquity of its motif in natural products a similar description of cyclobutadiene in terms of two HLVB structures led to a molecule with a more stable πelectronic system than that of benzene Clearly this prediction was obviously incorrect and we have to revisit it when we discuss the MOVB wars Scheme 3 The electronic structure of O2 according to Pauling involving two threeelectron π bonds in two perpendicular planes These are shown in the right drawings using two resonance structures 1e 2e 2e1e The description of benzene in terms of a superposition resonance of two Kekulé structures appeared for the first time in the work of Slater as a case belonging to a class of species in which each atom possesses more neighbors than electrons it can share much like in metals 46 Two years later Pauling and Wheland 52 applied the HLVB theory to benzene As shown in Scheme 4 they used the five Rumer structures of benzene two Kekulé and three Dewar structures They further approximated the matrix elements between the structures by retaining only close neighbor resonance interactions Molecules 2021 26 1624 8 of 24 Molecules 2021 26 x FOR PEER REVIEW 8 of 24 Scheme 3 The electronic structure of O2 according to Pauling involving two threeelectron πbonds in two perpendicular planes These are shown in the right drawings using two resonance structures 1e 2e 2e1e The description of benzene in terms of a superposition resonance of two Kekulé structures appeared for the first time in the work of Slater as a case belonging to a class of species in which each atom possesses more neighbors than electrons it can share much like in metals 46 Two years later Pauling and Wheland 52 applied the HLVB theory to benzene As shown in Scheme 4 they used the five Rumer structures of benzene two Kekulé and three Dewar structures They further approximated the matrix elements be tween the structures by retaining only close neighbor resonance interactions Scheme 4 The VB structures Rumer structures for describing the πelectronic system of ben zene two Kekulé structures K1 and K2 and three Dewar Structures D1D3 K1 K2 dominate the wave function The corresponding wave function is shown in Scheme 4 below the drawings of the resonance structures and one can see that the wave function is dominated by the two Kekulé structures which together form circularly delocalized 6π electrons This resonance between the two Kekulé structures was calculated to lower the energy of benzene with respect to a single Kekulé structure Incidentally the circularly delocalized 6π benzene pretty much resembles Kekulés dream 53 which he had one day in 18611862 when he dozed in front of the fire at his home in Ghent There he saw this molecule as a self devouring snake writhing on the hexagon periphery Again we see Pauling linking his theoretical objects to the chemical graphs of Lewis and his predecessors The PaulingWheland approach allowed the extension of the treatment to naphtha lene and to a great variety of other species In his book published for the first time in 1944 Wheland explains the resonance hybrid with the biological analogy of mule donkey horse 54 The pictorial representation of the wave function the link to Kekulés oscilla tion hypothesis and to Ingolds mesomerism which were common knowledge for chem ists made the HLVB representation rather popular among practicing chemists While the description of benzene fitted its known excess stability and the ubiquity of its motif in natural products a similar description of cyclobutadiene in terms of two HLVB structures led to a molecule with a more stable πelectronic system than that of benzene Clearly this prediction was obviously incorrect and we have to revisit it when we discuss the MOVB wars Scheme 4 The VB structures Rumer structures for describing the πelectronic system of benzene two Kekulé structures K1 and K2 and three Dewar Structures D1D3 K1 K2 dominate the wave function The corresponding wave function is shown in Scheme 4 below the drawings of the resonance structures and one can see that the wave function is dominated by the two Kekulé structures which together form circularly delocalized 6π electrons This resonance between the two Kekulé structures was calculated to lower the energy of benzene with respect to a single Kekulé structure Incidentally the circularly delocalized 6π benzene pretty much resembles Kekulés dream 53 which he had one day in 18611862 when he dozed in front of the fire at his home in Ghent There he saw this molecule as a self devouring snake writhing on the hexagon periphery Again we see Pauling linking his theoretical objects to the chemical graphs of Lewis and his predecessors The PaulingWheland approach allowed the extension of the treatment to naph thalene and to a great variety of other species In his book published for the first time in 1944 Wheland explains the resonance hybrid with the biological analogy of mule donkey horse 54 The pictorial representation of the wave function the link to Kekulés oscillation hypothesis and to Ingolds mesomerism which were common knowledge for chemists made the HLVB representation rather popular among practic ing chemists While the description of benzene fitted its known excess stability and the ubiquity of its motif in natural products a similar description of cyclobutadiene in terms of two HLVB structures led to a molecule with a more stable πelectronic system than that of benzene Clearly this prediction was obviously incorrect and we have to revisit it when we discuss the MOVB wars The above 1931 Pauling papers 4849 were followed by a stream of five papers published during 19311933 in Journal of the American Chemical Society and entitled The Nature of the Chemical Bond This series of papers enabled the description of any bond in any molecule and culminated in the famous monograph in which all the structural chemistry of the time was treated in terms of the covalentionic superposition theory resonance theory and hybridization theory The book 7 which was published in 1939 is dedicated to GN Lewis and the 1916 paper of Lewis is the only reference cited in the preface to the first edition VB theory in Paulings view is a quantum chemical version of Lewis theory of valence In Paulings work the long sought for basis for the Allgemeine Chemie unified chemistry of Ostwald the father of physical chemistry was finally found 29 p 135 3 Origins of MO Theory At the same time that Slater and Pauling were developing their VB theory 36 Mul liken 1013 and Hund 89 were developing an alternative approach called molecular orbital MO theory The term MO theory MOT appears only in 1932 but the roots of the method can be traced back to earlier papers from 1928 911 in which both Hund and Mulliken made spectral and quantum number assignments of electrons in molecules based Molecules 2021 26 1624 9 of 24 on correlation diagrams tracing the energies from separated to united atoms According to Brush 5556 LennardJones was the first who has expressed in 1929 a wave function for a molecular orbital wave function in his treatment of diatomic molecules In this paper LennardJones showed with facility that the O2 molecule is paramagnetic and mentions that the HLVB method runs into difficulties with this molecule 14 The authors of this essay do not really agree with this conclusion since it is very easy to show that the simplest VB theory gets O2 correct 22 pp 9497 57 Additionally as we wrote above there was no obvious reasons for this statement since VB theory always described this molecule as a diradical with two threeelectron bonds Scheme 3 Nevertheless this molecule would eventually become a symbol for the alleged failings of VB theory In MO theory the electrons in a molecule occupy delocalized orbitals made from linear combination of atomic orbitals Scheme 5 shows the molecular orbitals of the H2 molecule At the simplest level the electron pair of H2 occupies a delocalized σg MO Already with this little molecule one can see an apparent difference with the HL structures in Scheme 1 and with the more detailed description of an electron pair AB in Scheme 2 These two cartoons look as though they are describing bonds in alternative universes Despite the many demonstrations 22 pp 4041 of a subsequent configuration interaction CI which includes that the σu2 configuration creates a complete equivalence between the VB and MO descriptions of the bond the pictorial difference has been stamped in the minds of many chemists that VBT and MOT are very different and mutually exclusive theories Molecules 2021 26 x FOR PEER REVIEW 9 of 24 The above 1931 Pauling papers 4849 were followed by a stream of five papers pub lished during 19311933 in Journal of the American Chemical Society and entitled The Na ture of the Chemical Bond This series of papers enabled the description of any bond in any molecule and culminated in the famous monograph in which all the structural chemistry of the time was treated in terms of the covalentionic superposition theory resonance theory and hybridization theory The book 7 which was published in 1939 is dedicated to GN Lewis and the 1916 paper of Lewis is the only reference cited in the preface to the first edition VB theory in Paulings view is a quantum chemical version of Lewis theory of valence In Paulings work the long sought for basis for the Allgemeine Chemie uni fied chemistry of Ostwald the father of physical chemistry was finally found 29 p 135 3 Origins of MO Theory At the same time that Slater and Pauling were developing their VB theory 36 Mul liken 1013 and Hund 89 were developing an alternative approach called molecular orbital MO theory The term MO theory MOT appears only in 1932 but the roots of the method can be traced back to earlier papers from 1928 911 in which both Hund and Mulliken made spectral and quantum number assignments of electrons in molecules based on correlation diagrams tracing the energies from separated to united atoms Ac cording to Brush 5556 LennardJones was the first who has expressed in 1929 a wave function for a molecular orbital wave function in his treatment of diatomic molecules In this paper LennardJones showed with facility that the O2 molecule is paramagnetic and mentions that the HLVB method runs into difficulties with this molecule 14 The authors of this essay do not really agree with this conclusion since it is very easy to show that the simplest VB theory gets O2 correct 22 pp 9497 57 Additionally as we wrote above there was no obvious reasons for this statement since VB theory always described this molecule as a diradical with two threeelectron bonds Scheme 3 Nevertheless this mol ecule would eventually become a symbol for the alleged failings of VB theory In MO theory the electrons in a molecule occupy delocalized orbitals made from linear combination of atomic orbitals Scheme 5 shows the molecular orbitals of the H2 molecule At the simplest level the electron pair of H2 occupies a delocalized σg MO Al ready with this little molecule one can see an apparent difference with the HL structures in Scheme 1 and with the more detailed description of an electron pair AB in Scheme 2 These two cartoons look as though they are describing bonds in alternative universes Despite the many demonstrations 22 pp 4041 of a subsequent configuration interac tion CI which includes that the σu2 configuration creates a complete equivalence be tween the VB and MO descriptions of the bond the pictorial difference has been stamped in the minds of many chemists that VBT and MOT are very different and mutually exclu sive theories Scheme 5 The MO description of the H2 molecule At the simplest level the bond is an electron pair with opposite spins occupying a delocalized MO σg On the right side are photos of Mulli ken and Hund respectively Mullikens was taken from httpswwwnobelprizeorgprizeschem istry1966mullikenbiographical accessed on 11 March 2021 Hunds was taken from httpsenwikipediaorgwikiFriedrichHund accessed on 11 March 2021 Scheme 5 The MO description of the H2 molecule At the simplest level the bond is an electron pair with opposite spins occupying a delocalized MO σg On the right side are photos of Mulliken and Hund respectively Mullikens was taken from httpswwwnobelprizeorgprizeschemistry1966 mullikenbiographical accessed on 11 March 2021 Hunds was taken from httpsenwikipedia orgwikiFriedrichHund accessed on 11 March 2021 Eventually it would be the work of Hückel that would usher MO theory into main stream chemistry Hückels MO theory had initially in the early 1930s a chilly reception 58 but eventually it gave MOT an impetus and formed a successful and widely applicable tool In 1930 Hückel used LennardJones MO ideas on O2 applied it to CX X C N O double bonds and suggested the σπ separation 15 With this approximation Hückel ascribed the restricted rotation in ethylene to the πtype orbital Using σπ separability Hückel turned to solve the electronic structure of benzene 16 by comparing HLVB theory and his new HückelMO HMO approach He argued that HMO was preferred since it gave better quantitative results a statement that remains somewhat unclear to the two authors The πMO picture inScheme 6 was quite unique in the sense that it viewed the molecule as a whole with a σframe dressed by πelectrons that occupy three completely delocalized πorbitals Comparison of these MO pictures to the five Rumer structures in Paulings model Scheme 4 for benzene underscores the feeling that these theories are describing benzene in alternative universes Molecules 2021 26 1624 10 of 24 Molecules 2021 26 x FOR PEER REVIEW 10 of 24 Eventually it would be the work of Hückel that would usher MO theory into main stream chemistry Hückels MO theory had initially in the early 1930s a chilly reception 58 but eventually it gave MOT an impetus and formed a successful and widely appli cable tool In 1930 Hückel used LennardJones MO ideas on O2 applied it to CX X C N O double bonds and suggested the σπ separation 15 With this approximation Hückel ascribed the restricted rotation in ethylene to the πtype orbital Using σπ separability Hückel turned to solve the electronic structure of benzene 16 by comparing HLVB theory and his new HückelMO HMO approach He argued that HMO was preferred since it gave better quantitative results a statement that re mains somewhat unclear to the two authors The πMO picture in Scheme 6 was quite unique in the sense that it viewed the molecule as a whole with a σframe dressed by π electrons that occupy three completely delocalized πorbitals Comparison of these MO pictures to the five Rumer structures in Paulings model Scheme 4 for benzene under scores the feeling that these theories are describing benzene in alternative universes Scheme 6 The πelectronic system of benzene by Hückel On the right is Hückels photo taken from httpsenwikipediaorgwikiErichHC3BCckel accessed on 11 March 2021 The HMO picture also allowed Hückel to understand the special stability of benzene Thus the molecule was found to have a closedshell πcomponent and its energy was calculated to be lower relative to that of three isolated πbonds as in ethylene In the same paper Hückel treated the ion molecules of C5H5 and C7H7 as well as the molecules C4H4 CBD and C8H8 COT This enabled him to comprehend the special stability of molecules with six πelectrons and why molecules like COT or CBD either did not possess this sta bility ie COT or had not yet been made ie CBD Already in this paper and in a sub sequent one 17 Hückel laid the foundations for what will become later known as the HückelRule regarding the special stability of aromatic molecules with 4n2 πelec trons 55 This rule its extension to antiaromaticity 4n electrons and its experimental articulation by organic chemists in the 19501970s will constitute a major cause for the acceptance of MO theory and the rejection of VB theory 55 4 The MOVB Wars With these two seemingly different treatments of benzene the chemical community was faced with two alternative descriptions of one of its molecular icons and this began the VBMO rivalry that seems to accompany chemistry to the 21st Century 59 This ri valry involved most of the prominent chemists of these times to mention but a few names Mulliken Pauling Hückel J Mayer Robinson Lapworth Ingold Sidgwick Lucas Bart lett Dewar LonguetHiggins Coulson Roberts Winstein Brown etc and so forth A detailed and interesting account of the nature of this rivalry and the major players can be found in the treatment by Brush 5556 Interestingly already back in the 1930s Slater 47 and van Vleck and Sherman 60 stated that since the two methods ultimately converge it is senseless to quibble on the issue of which one is better Unfortunately however this more rational attitude does not seem to have made much of an impression on this religious warlike rivalry This rivalry persisted many years afterwards even though Hiberty and Ohanessian 61 showed that applying the MO VB expansion method 62 to the MOCI wave function of benzene Scheme 6 The πelectronic system of benzene by Hückel On the right is Hückels photo taken from httpsenwikipediaorgwikiErichHC3BCckel accessed on 11 March 2021 The HMO picture also allowed Hückel to understand the special stability of benzene Thus the molecule was found to have a closedshell πcomponent and its energy was calculated to be lower relative to that of three isolated πbonds as in ethylene In the same paper Hückel treated the ion molecules of C5H5 and C7H7 as well as the molecules C4H4 CBD and C8H8 COT This enabled him to comprehend the special stability of molecules with six πelectrons and why molecules like COT or CBD either did not possess this stability ie COT or had not yet been made ie CBD Already in this paper and in a subsequent one 17 Hückel laid the foundations for what will become later known as the HückelRule regarding the special stability of aromatic molecules with 4n2 πelectrons 55 This rule its extension to antiaromaticity 4n electrons and its experimental articulation by organic chemists in the 19501970s will constitute a major cause for the acceptance of MO theory and the rejection of VB theory 55 4 The MOVB Wars With these two seemingly different treatments of benzene the chemical community was faced with two alternative descriptions of one of its molecular icons and this began the VBMO rivalry that seems to accompany chemistry to the 21st Century 59 This rivalry involved most of the prominent chemists of these times to mention but a few names Mulliken Pauling Hückel J Mayer Robinson Lapworth Ingold Sidgwick Lucas Bartlett Dewar LonguetHiggins Coulson Roberts Winstein Brown etc and so forth A detailed and interesting account of the nature of this rivalry and the major players can be found in the treatment by Brush 5556 Interestingly already back in the 1930s Slater 47 and van Vleck and Sherman 60 stated that since the two methods ultimately converge it is senseless to quibble on the issue of which one is better Unfortunately however this more rational attitude does not seem to have made much of an impression on this religious warlike rivalry This rivalry persisted many years afterwards even though Hiberty and Ohanessian 61 showed that applying the MO VB expansion method 62 to the MOCI wave function of benzene gave rise to the full VB wave function strictly identical to the directly calculated VB wave function 63 and proved the identity of the two methods Pauling and Mulliken were the leading figures in this duality that has become sort of a never ending rivalry in the generations to come 59 At times this rivalry seemed to be personal and even bitter so much so that in one of the reports of the Löwdin Summer Schools in Vålådalen 1958 the writer still a student then who did not reveal hisher name of the report described the relationship between these two great scientists by the orthogonality symbol MullikenPauling 0 For a while the tide was in favor of VBT because Pauling was very eloquent and persuasive and because VBT is a chemical language and hence it was easier for chemists to grasp it Furthermore the condensation of VBT to resonance theory by Pauling made the method so easy to use and this enhanced its huge popularity However this was temporary The struggle between the Pauling camp and Mullikens growing group of followers started to shift in favor of MO theory by the late 1950s onwards when successful Molecules 2021 26 1624 11 of 24 semiempirical methods 5556 started to be implemented and could be widely used eg 6465 Furthermore MOT started to have its own eloquent proponents like Coulson Dewar LonguetHiggins Hoffmann etc The PaulingMulliken rivalry and the avoidance of Pauling to include in his book even a single MO diagram had its share in the eventual branding of VB theory as a failed theory among the growing number of supporters of the MO approach 59 However other major factors combined to make this happen the fast development of efficient molecular orbital MObased software the GAUSSIAN suit of programs 66 and others the synthesis of aromatic and antiaromatic molecules a dichotomy that initially evaded VB theory and the formulation of attractive qualitative concepts like Walsh diagrams Fukuis frontier molecular orbital theory the WoodwardHoffmann rules of conservation of orbital symmetry 67 and the synthesis of molecules like ferrocene and the elegant interpretation of its unusual bonding by MO theory 59 The fact that MOT described excited states pictorially and simply with excitations from bonding to antibonding MOs made it attractive to spectroscopists Finally the entrance of density functional theory into chemistry and its formulation in terms of KohnSham MOs 68 which looked like simple Extended Hückel MOs thus developing the same MO interaction diagram types 69 which made MO theory attractive to chemists 67 At the same time VB theory seemed to have stagnated conceptually and its implementation into an efficient computer code proved to be less successful than that of MO theory The theory VBT ceased to guide chemists to new experiments though it remained the lingua franca of chemists However conceptually it was cast aside and branded with mythical failures 22 Chapters 1 and 5 5 Hybridization Is Being Called into Doubt Ever since hybridization was introduced by Pauling 48 and Slater 46 in 1931 the idea proved extremely insightful and has been extensively used by chemists throughout decades of sustained applications and teaching Three main categories of hybrid atomic orbitals HAOs were defined the tetrahedral HAOs directed to the corners of a regular tetrahedron the trigonal ones lying in the same plane with angles of 120 between them and the linear hybrids with an angle of 180 It is well known that the above three hy bridization types take place in the prototypical molecules CH4 BH3 and BeH2 respectively and account faithfully for the bond angles in these systems More generally the HAOs show remarkable portability from one molecule to many others This portability of HAOs in organic molecules is not restricted to bond angles but it also applies to bonding energies bond lengths and force constants as exemplified in eg alkanes whose CH bonds display practically identical properties different from those of alkenes and alkynes Despite its popularity the hybridization concept has often been criticized partly for its supposed inability to account for the photoelectron spectroscopy of eg CH4 and H2O we will return to this point below but not only this The hybridization model was also deemed by some to be useless and inappropriate for the description of electron density within a molecule 70 More recently the sheer legitimacy of hybridization was denied by Brion who wrote that hybrid orbitals were simply chosen initially by Pauling and later on implicitly by others so as to correspond to the supposed localized electron pair chemical bonds as defined in the classical prequantum GN Lewis purely empirical localized view of the behavior of electrons In contrast canonical molecular orbitals CMOs result directly from the HartreeFock procedures without any such additional assumptions 71 Owing to the diversity of rigorous ab initio calculations there are several levels of answers to the above negation of HAOs At the HartreeFock level a wellknown property of the singledeterminant wave function is that applying unitary transformations eg rotations on the CMOs does not change the expectation values eg density energy etc of the determinant There is an infinity of such unitary transformations but one is physically more sensible it is the one that maximizes the distance between the electron pairs that reside in the orbitals 7274 Molecules 2021 26 1624 12 of 24 Such orbital transformations for methane generate a set of localized molecular or bond orbitals LMOsLBOs transformed into one another by the symmetry operations of the Td point group and each containing a tetrahedral HAO pointing precisely toward one of the hydrogen atoms Two points are noteworthy i the polyelectronic single determinant wave function made of LMOs involving the HAOs is exactly equivalent to the one made of CMOs It follows that the two Slater determinants yield the same electronic density the same energy and the same molecular properties Therefore the abovementioned statement that HAOs are inappropriate for the description of electronic density is unfounded by theory and is strictly wrong ii The tetrahedral hybridization of methane is uniquely determined and arises from the HartreeFock calculation without any a priori assumption as being entirely based on a physical criterion that is nothing else than the VSEPR 75 principle of minimizing the Pauli repulsions between electron pairs It follows therefore that at the HartreeFock level the delocalized CMOs and the localized orbitals in terms of HAOs are equally appropriate for the description of chemical bonding Furthermore hybrid orbitals emerge naturally from higher ab initio levels without any assumptions The highest level of theory that retains the orbital approximation with fixed orbital occupancies and uses a single configuration for expressing the total molecular wave function is provided by the SpinCoupled Generalized Valence Bond SCGVB method 76 Relative to the HartreeFock level the SCGVB wave function releases the constraint of double orbital occupancy the orbitals are free to remain doubly occupied or to split into pairs of singly occupied orbitals and it also releases the constraint of orthogonality between orbitals Penotti et al have shown in 1988 that the SCGVB wave function of methane yields four atomic orbitals localized on the hydrogens and four tetrahedral HAOs each pointing to a hydrogen atomic orbital 77 Furthermore these authors took into account all the possible ways to perform spincoupling and demonstrated that the perfectpairing way is by far the major wave function of methane and each of its HAOs is singletcoupled with the hydrogen AO toward which it is directed In addition the tetrahedral molecular geometry is a global minimum on the potential surface at this level of theory and was therefore not preassumed As such the shapes of the HAOs arose uniquely in a variational calculation where all constraints are released and where the only preliminary assumption is that one is dealing with a carbon atom surrounded by four hydrogens On the other hand there is a logical sequence of constraints that could be placed on SCGVB wave functions to yield the corresponding HartreeFock HF wave functions 78 As expected the SCGVB wave function lies well below the HartreeFock one by some 41 kcal mol1 and only 75 kcal mol1 above the fullvalence CASSCF It follows that at the highest possible level of singleconfiguration methods the description of methane in terms of localized orbitals made of HAOs is not merely just as good as the one in terms of CMOs but definitely better Another key feature of these variational hybrids is their ps ratios which reflects the tendency to minimize the costly hybridization 7879 of the central atom eg more than 90 kcalmol for an sp3 hybridization in CH4 and afford at the same time the maximum overlap with the ligand atom H in CH4 As such these variational hybrids deviate from the ideal PaulingSlater ratios and variationally depend on the location of the central atom in the Periodic Table For example the perfectly tetrahedral hybrids in BH4 CH4 and NH4 possess ps ratios of 238 176 and 139 respectively 79 as calculated by multi structure VB calculations involving the full space of 1764 covalent and ionic structures As such directional hybrids are perfectly correct and perfectly reflecting the geometry of the molecules eg tetrahedral for methane trigonal for BH3 and linear for BeH2 but their compositions are determined variationally by the promotion energy of the central atom which varies with its electronegativity The hybrids behave physically sensible by all means and measures Molecules 2021 26 1624 13 of 24 6 Conceptual Errors Made during the Early Development of VB Theory Of course like any new theory VBT too made some errors in its initial applications to chemical problems These were however errors due to the need for approximations during the calculations or simplifications that generate useful models which could not be tested computationally due to the limitations of VB computations at the time of conception 61 Assessment of the CovalentIonic Bond Scheme The very clever scheme of Pauling for describing electron pair bonds AB in Equation 3 is partly based on a wrong assumption Thus as we showed using mod ern VB calculations 3250518081 the central assumption for the elegant empirical scheme was that REcovionAA REcovionBB 0 while this assumption is not too bad for HH it is extremely poor for FF In this bond and others alike ClCl OO SS etc the covalent structure is repulsive and the entire bond energy is contributed by the covalentionic resonance energy REcovion As we showed many a time this Paulings assumption has caused the community to ignore a whole family of bonds in which the bond energy is dominated by the covalentionic energy socalled the chargeshift bond CSB family 3250518081 62 Missing the Antiaromatic Character of C4H4 The early HLVB treatment of benzene and cyclobutadiene CBD by Pauling and Wheland led to a correct prediction that benzene is stabilized by resonance of the two Kekulé structures However the resonance energy for CBD came out larger than that of benzene This was a problem because unlike the ubiquity of benzene and its motif in many natural compounds CBD could be made only after a great synthetic effort and strategies to protect the molecule against its high reactivity Wheland analyzed the problem 5254578283 and reached the conclusion that inclusion of the ionic structures to the HLVB method should give a correct prediction This was an early hint that the neglect of ionic structures in the early VB developments was responsible for the unawareness of the fundamental difference between the 4n2 and 4nelectronic systems Furthermore the importance of ionic VB structures in conjugated rings was later quantitatively demonstrated by Tantardini et al 63 who showed that the summed contributions of the two purely covalent Kekulé structures of benzene amount to only 22 vs 68 for the ionic structures Subsequently Shurki et al demonstrated the key role played by the ionic structures in the aromaticantiaromatic characters of conjugated rings 84 She showed elegantly during her PhD with one of us SS that the 4n24n difference is controlled by symmetry the diionic structures which mixed efficiently with the covalent ones in benzene do not do so in CBD due to symmetry mismatch 84 Of course the ionic structures may be included either explicitly in the VB wave function or implicitly through the definition of formally covalent structures with CoulsonFischer orbitals vide supra as in the GVB method Thus the GVB treatment of Goddard and Voter 85 showed that CBD has indeed a smaller resonance energy than benzene This calculation also correctly predicted the singlet nature of the ground state its tendency to distort to a rectangular geometry and even the sequence of the excited states It is also important to note that Hückel theory made a correct prediction for the wrong reason Thus as shown by Wheland the HMO wave function used by Hückel for the singlet state of CBD is equivalent to a single VB structure with two isolated double bonds 82 which is not the correct wave function for CBD in the square geometry While this orbital choice gave a wrong description of CBD it accidentally was on the side of experimental facts that the species is highly reactive Furthermore in the early 1950s Craig showed that the monodeterminantal MO theory makes a wrong assignment of the ground state of CBD as the triplet 3A2g state 8687 while HLVB gives the correct ground state 1B1g Therefore the belief that HMO correctly described CBD whereas VB failed is incorrect In reality finding the right answer for CBD requires adding the ionic structures to the HLVB treatment 84 or using CoulsonFischer AOs 85 whereas the MO treatment requires CI 87 Molecules 2021 26 1624 14 of 24 7 Myths about VB Failures Some of the myths that stuck to VBT are discussed in this section which shows how some myths that were proven wrong time and again nevertheless have lives of their own 71 The O2 Myth and Mystery One of the first myths about VB theory is its alleged failure to predict the triplet ground state of O2 LennardJones stated in his paper that HLVB theory fails to predict the triplet state of O2 It is very clear from Scheme 3 that already early on Pauling discussed the ground state of O2 as a triplet state 49 so did Heitler and Pöschl in 1934 when they discussed the electronic structures of O2 and C2 88 Later Wheland wrote the same on page 39 of his book 54 In the 1970s onwards Goddard et al 41 Harcourt 89 p 50 and the present two authors 2257 pp 9497 showed again that VB correctly predicts the ground state of O2 not only at the ab initio level but already at a simple qualitative level in terms of β integrals and overlaps between atomic orbitals Nevertheless this myth still appears even these days in textbooks and papers as evidenced by a very recent paper on this issue by Corry and OMalley who try to dispel this myth 90 What could be the key to the enduring persistence of this myth It is true that a naïve application of hybridization and perfect pairing approach simple Lewis pairing without consideration of the important effect of fourelectron Pauli repulsion in such a structure would predict a doubly bonded and closedshall O2 which is in fact related to the 1g excited state of O2 As the two present authors showed 2257 pp 9497 O2 avoids the Pauli repulsion and assumes a triplet ground state which is highly stabilized by resonance in its two threeelectron bonds Similar descriptions were given recently by us 91 and by Borden et al 92 It remains therefore a mystery how this wrong picture could propagate through decades despite the many VB treatments which showed that the ground state is a triplet state 72 The Myth of the Photoelectron Spectroscopies PES of CH4 and H2O With the emergence of e2e spectroscopy 93 an oldnew myth is being propagated with an attempt to rule out the legitimacy of localized orbitals This experimental technique of ionizing molecules by collision with an electron beam as well as the related photoelectron spectroscopy which uses photons for the ionization led to the claim that these experimental results provide a proof of the initial occupation of electrons in canonical MOs which is something that defies the fundamentals of quantum mechanics CH4 is a classical molecule which once in a while is pulled out as a proof that electrons reside only in delocalized canonical MOs CMOs The argument starts from the description of methane as having four localized bond orbitals LBOs or LMOs and it goes on as follows Since methane has four equivalent LBOs ergo the molecule should exhibit only a single ionization peak in PES However since the PES of methane exhibits two different ionization peaks corresponding to 2A1 and 2T2 states of the cation or to the orbitals of the neutral ergo VB theory fails to predict the ionization spectrum This argument is false for two reasons firstly as has been known since the 1930s the LBOs for methane or any molecule can be obtained by a unitary transformation of the delocalized MOs 7394 Thus both MO and VB descriptions of methane can be cast in terms of LMOsLBOs Secondly in VBT like in any quantum theory the wave function of the CH4 cation must be represented by a symmetryadapted wave function As such if one starts from the LBOLMO description of methane and ionizes the molecule the electron can come out of any one of the LBOs which are identical by symmetry 22 pp 104106 Hence a physically correct representation of the CH4 cationic state in VBT is a linear combination of the four cationic configurations which arise due to electron ejection from each of the four bonds One can achieve the correct physical description either by combining the LBOs back to canonical MOs 74 or by taking symmetryadapted linear combinations of the four VB configurations that correspond to one bond ionization 22 pp 104106 thereby producing the 2A1 and 2T2 states of the cation 2T2 being a triply degenerate VB state of the Molecules 2021 26 1624 15 of 24 cation Thus the two ionization peaks in PES of CH4 are accountable by use of the LMO or VB frameworks as well as in the CMO starting wave function The two experimental ionization peaks of H2O have also often been invoked as an argument against VB theory and the hybridization concept which is used in the classical representation of water with its lone electron pairs located in two equivalent hybrid orbitals the socalled rabbitears 709596 This latter picture is popular among chemists as it readily explains for example the anomeric effect or the structure of ice with each water molecule being the site of four hydrogen bonds from neighboring molecules arranged along tetrahedral directions with respect to the oxygen atoms etc As in the CH4 case the rebuttal of this argument is straightforward the correct VB representation of ionized H2O is a combination of two VB structures which couple the two rabbit ear hybrids in either a positive or negative fashion leading to two states 2A1 and 2B2 giving rise to two distinct ionization potentials 22 p 79 Thus here are two myths that have been dispelled and refuted many a time but survive in modern teaching textbooks and in papers It seems that some chemists are unable to get used to these two seemingly different but otherwise identical pictures 8 Modern VB Theory The Renaissance of VB theory is marked by a twopronged surge of activity i Devel opment of new methods and program packages that enable applications to moderatesized molecules These have been recently reviewed in a paper by Chen and Wu 97 ii Creation of general qualitative models based on VB theory Some of these developments are discussed below without pretenses of rendering an exhaustive coverage We of course apologize for omissions Modern Quantitative VBT Approaches Sometime in the 1970s a stream of nonempirical VB methods which were attended by many applications of rather accurate calculations began to appear All these programs divide the orbitals in a molecule into inactive and active subspaces treating the former as a closed shell and the latter by some VB formalism The programs optimize the orbitals and the coefficients of the VB structures but they differ in the manners by which the VB orbitals are defined Goddard and coworkers developed the generalized VB GVB method 4144 that uses semilocalized atomic orbitals having small delocalization tails employed originally by Coulson and Fischer for the H2 molecule cf Figure 3 40 The GVB method is incorporated in GAUSSIAN and in most other MObased packages Sometime later Gerratt Raimondi and Cooper developed a related VB method called the spin coupled SC theory now called SCGVB which also uses atomic orbitals AOs with delocalization tails This is followed up by configuration interaction using the SCVB method 98100 These methods are now incorporated in the MOLPRO software GVB and SCGVB theories do not employ covalent and ionic structures explicitly Nevertheless the delocalization tails of these AOs effectively incorporate all the ionic structures 22 pp 4041 and thereby enable one to express the electronic structures in compact forms based on formally covalent pairing schemes BalintKurti and Karplus 101 developed a multistructure VB method that may utilize explicitly covalent and ionic structures with local atomic orbitals In a later development by van Lenthe and BalintKurti 102103 and by Verbeek and van Lenthe 104105 the multistructure method is referred to as a VB selfconsistent field VBSCF method In a subsequent development van Lenthe Verbeek and coworkers generated the multipurpose VB program called TURTLE 106107 which has been incorporated into the MObased package of programs GAMESSUK Matsen 108109 McWeeny 110 and Zhang and coworkers 111112 developed spinfree VB approaches based on symmetric group methods Subsequently Wu et al extended the spinfree approach and produced a generalpurpose VB program initially Molecules 2021 26 1624 16 of 24 called the XIAMEN99 package and more recently named XMVB 113114 XMVB is becoming faster and more efficient every year and its VBSCF routine can include up to 26 orbitals26 electrons in the VB space 97115 and can also handle molecules with two transition metals and as many as 10 ligands like CO 116 The new XMVB versions also have DFVB methods which combine DFT and VBT 117 Soon after the XIAMEN99 package Li and McWeeny announced their VB2000 soft ware which is also a generalpurpose program including a variety of methods 118 Another software of multiconfigurational VB MCVB called CRUNCH and based on the symmetric group methods of Young was written by Gallup and coworkers 119120 During the early 1990s Hiberty and coworkers developed the breathing orbital VB BOVB method which also utilizes covalent and ionic structures but in addition allows them to have their own unique set of orbitals 121125 In this manner BOVB introduces dynamic correlation to bonding and improves the quantitative results vis à vis VBSCF The method is now incorporated into the TURTLE and XMVB packages XMVB is versatile Thus Wu et al 126 developed a VBCI method which is akin to BOVB but can be applied to larger systems since the method starts from VBSCF and improves the orbitals by excitation to virtual orbitals without changing the number of VB structures In a more recent work the same authors coupled VB theory with the solvent model PCM and produced the VBPCM program that enables one to study reactions in solution 127 More recent developments involve coupling simple VBSCF calculations which are fast with Monte Carlo Simulations to retrieve missing correlation effects 128 These VBMonte Carlo methods project a fruitful future direction for VBT Finally Truhlar and coworkers 129 developed the VBbased multiconfiguration molecular mechanics method MCMM to treat dynamic aspects of chemical reactions while Landis and coworkers 130 introduced the VALBOND method that is capable of predicting structures of transition metal complexes using Paulings ideas of orbital hybridization A recent monograph by Landis and Weinhold makes use of VALBOND as well as of natural resonance theory to discuss a variety of problems in inorganic and organometallic chemistry 131 Our monograph on VBT 22 includes a chapter that mentions the main program packages and methods and outlines their features The generation of so many different VB methods has advantages as well as some less productive byproducts Thus the advent of a number of good VB programs has caused a surge of applications of VB theory to problems ranging from bonding in main group elements to transition metals 116 conjugated systems aromatic and antiaromatic species all the way to excited states and full pathways of chemical reactions with moderate to very good accuracies For example a recent calculation of the barrier for the identity hydrogen exchange reaction H HH HH H by Song et al 132 shows that it is possible to calculate the reaction barrier accurately with just eight classical VB structures Furthermore just recently the BOVB and stateaveraged BOVB methods were applied to some notoriously challenging excited states like the ionic V state of ethylene 133 and the 11B2 and 21A2 states of ozone and sulfur dioxide 134 In all cases the BOVB calculated transition energies from the ground state with less than ten VB structures were found to be as accurate as standard MOCI calculations involving tens of millions of configurations Thus in many respects VB theory is coming of age with the development of faster and more accurate ab initio VB methods 125 The less attractive byproduct of the developments of many alternative VB methods is that this multiplicity does not converge to a unified VB community but rather creates segmented cults eg preferring localized AOs or AOs with delocalization tails or still orthogonal AOs These cults often criticize or simply ignore one another and claim uniqueness and truth for one of the choices rather than finding the common ground that stitches all these choices to a single cultural fabric What the late John Pople did for MO theory was to assemble many MO methods and later also DFT methods under one roof The MOT front is united because of the leadership Molecules 2021 26 1624 17 of 24 of a methodologist with a great vision VBT is yearning to reach such a situation with the community of VB proponents focusing on seeing and understanding the others method Nevertheless it is a fact that computational VB theory is coming of age producing faster and more accurate ab initio VB methods 9 Modern Conceptual Approaches in VBT A few general qualitative models based on VB theory started to appear in the late 1970s and early 1980s Among these models we also count semiempirical approaches based eg on the Heisenberg and Hubbard Hamiltonians 135140 as well as Hückeloid VB methods 141144 which can handle with clarity ground and excited states of molecules Methods that map MObased wave functions to VB wave functions offer a good deal of interpretative insight Among these mapping procedures we note the halfdeterminant method of Hiberty and Leforestier 62 and the method by Karafiloglou 145 Following Linnets reformulation of threeelectron bonding in the 1960s 146 Harcourt 89147 developed a VB model that describes electronrich bonding in terms of increased valence structures and showed its occurrence in bonds of main elements and transition metals A general model for the origins of barriers in chemical reactions was proposed in 1981 by one of the present authors SS in a manner that incorporates the role of orbital sym metry 22 ch 6 141148149 Subsequently in collaboration with Pross 150151 and Hiberty 22 ch 6 152 the model has been generalized for a variety of reaction mecha nisms 149 and used to shed new light on the problems of aromaticity and antiaromaticity in isoelectronic series 153 The present authors have shown the existence of chargeshift bonding CSB in electron pair bonds 32 as well as in oddelectron bonds 91 In addition Shaik and Hiberty and coworkers have demonstrated that CSBs form a unique family of bonding with special properties and experimental manifestations One of these manifestations in chemical reactivity leads to quantification of the covalentionic resonance energy RECS of electron pair bonds 32 VBT also led to the formulation of the theory of nopair ferromagnetic NPFM bond ing 154 which involve tripletpair bonds TPB that can delocalize and give rise to large clusters of monovalent metals with maximum spin n1Mn The bonding in such clus ters can reach as much as 20 kcal mol1 per single atom These magnetic clusters are experimentally observable 155156 VB ideas have also contributed to the revival of theories for photochemical reactivity Early VB calculations by Oosterhoff et al 157158 revealed a potentially general mech anism for the course of photochemical reactions Michl 159 articulated this VBbased mechanism and highlighted the importance of funnels as the potential energy features that mediate the excited state species back into the ground state Subsequently Robb et al 160 showed that these funnels are conical intersections that can be computed at a high level of sophistication As we SS and PCH showed recently 22 pp 157163 the structure of the conical intersection can be predicted by simple VB arguments from VB diagrams Similar applications of VB theory to deduce the structure of conical intersections in photoreactions were performed by Shaik and Reddy 161 VB theory enables a very straightforward account of environmental effects such as those imparted by solvents andor protein pockets A major contribution to the field was made by Warshel who has created his empirical VB EVB method and by incorporating van der Waals and London interactions by the molecular mechanical MM method created the QM VBMM method for the study of enzymatic reaction mechanisms 162164 His pioneering work ushered the now emerging QMMM methodologies for studying enzymatic processes 165 Hynes et al have shown how to couple solvent models into VB and create a simple and powerful model for understanding and predicting chemical processes in solution 166 Molecules 2021 26 1624 18 of 24 One of us has shown how a solvent effect can be incorporated in an effective manner to the reactivity factors that are based on VB diagrams 167168 More recently the VB diagram model was applied to reactions in the presence of external electric fields 169171 Another area where VBT is making promising strides is the description of excited states with a minimal number of VB structures 133134143172173 All in all VBT is seen to offer a widely applicable framework for thinking and pre dicting chemical trends Some of these qualitative models and their predictions have been discussed in a monograph on VBT 22 and in review papers 149152 Quantitatively VBT is improving very fast and is starting to inspire other methods Thus a recent benchmark of modern VB methods by Shurki et al 174 showed that methods like VBCI BOVB and VBPT2 exhibit mean unsigned errors as low as 4513 kcalmol very close to highlevel MObased treatments All this activity makes the LewisPauling legacy alive and well 10 VBMotivated Approaches As mentioned above 5 London extended the HL method to full potential energy surfaces and has created a VBmotivated method for MD in chemical reactions His method was modified throughout the years and is now called LEPS after London Eyring Polanyi and Saito It is still very useful for studying the full potential energy surfaces of atom transfer reactions 175176 eg for purposes of dynamics and tunneling studies VBmotivated methods also infiltrate DFT in terms of pairdensity function approaches Thus the recently developed method by Truhlar and Gagliardi of separatepair and separate pair density functional theory is akin to SCGVB It is more compact than analogous CASSCF wave functions and is also highly accuratemore accurate than GVBPP 177179 This is a useful import of VB ideas into multiconfigurational density functional theory which undergoes continuing development Very fruitful VBmotivated methods are those which analyze the probability density of the molecule and extract thereby information on Lewis bonds lone pairs and even covalent and ionic structures 180182 11 Conclusions Scientific wars leave behind bitterness and lack of understanding for the other views In the present case the MOVB wars created several myths about VB failures O2 anti aromaticity etc and about its inefficient capability to compute bonding structure and reactivity We hope that this essay straightens out these impressions and shows the richness and beauty of VB theory Having parallel universes for understanding chemistry and predicting new trends is a boon Author Contributions Conceptualization SS and PCH methodology all authors software all authors validation all authors formal analysis SS and PCH investigation DD resources all authors data curation all authors writingoriginal draft preparation SS writingreview and editing PCH and DD supervision all authors project administration SS All authors have read and agreed to the published version of the manuscript Funding This research in Jerusalem was funded by the ISF grant number ISF 52018 and the APC was funded by DL Cooper Institutional Review Board Statement Not applicable Informed Consent Statement Not applicable Data Availability Statement Not applicable Acknowledgments The authors are thankful to colleagues postdocs and students who collaborated with them through the years DL Copper is thanked for the funding Conflicts of Interest The authors declare no conflict of interest Molecules 2021 26 1624 19 of 24 References 1 Lewis GN The Atom and the Molecule J Am Chem Soc 1916 38 762785 CrossRef 2 Shaik S The Lewis Legacy The Chemical BondA Territory and Heartland of Chemistry J Comput Chem 2007 28 5161 CrossRef 3 Heitler W London F Wechselwirkung neutraler Atome un homöopolare Bindung nach der Quantenmechanik Z Phys 1927 44 455472 CrossRef 4 London F On The Quantum Theory of Homopolar Valence Numbers Z Phys 1928 46 455477 CrossRef 5 London F Quntenmechanische Deutung Des Vorgangs Der Aktivierung Z Elektrochem Angew Phys Chem 1929 35 552555 6 Hager T Force of Nature The Life of Linus Pauling Simon and Schuster New York NY USA 1995 p 63 7 Pauling L The Nature of the Chemical Bond 3rd ed Cornell University Press Ithaca NY USA 1939 pp 127 73100 8 Hund F Zur Frage der Chemischen Bindung Z Phys 1931 73 130 CrossRef 9 Hund F Zur Deutung der Molekelspektren IV Z Phys 1928 51 759795 CrossRef 10 Mullliken RS The Assignment of Quantum Numbers for Electrons in Molecules I Phys Rev 1928 32 186222 CrossRef 11 Mullliken RS The Assignment of Quantum Numbers for Electrons in Molecules II Correlation of Atomic and Molecular Electron States Phys Rev 1928 32 761772 CrossRef 12 Mullliken RS The Assignment of Quantum Numbers for Electrons in Molecules III Diatomic Hydrides Phys Rev 1929 33 730747 CrossRef 13 Mullliken RS Electronic Structures of Polyatomic Molecules and Valence II General Considerations Phys Rev 1932 41 4971 CrossRef 14 LennardJones JE The Electronic Structure of Some Diatomic Molecules Trans Faraday Soc 1929 25 668687 CrossRef 15 Hückel E Zur Quantentheorie der Doppelbindung Z Phys 1930 60 423456 CrossRef 16 Hückel E Quantentheoretische Beitrag zum Benzolproblem I Dies Elektronenkonfiguration des Benzols und verwandter Verbindungen Z Phys 1931 70 204286 CrossRef 17 Hückel E Quantentheoretische Beitrag zum Problem der aromatischen ungesättigten Verbindungen III Z Phys 1932 76 628648 CrossRef 18 Coulson CA Valence Oxford University Press London UK 1952 19 Dewar MJS Electronic Theory of Organic Chemistry Clarendon Press Oxford UK 1949 20 Lewis GN Valence and Tautomerism J Am Chem Soc 1913 35 14481455 CrossRef 21 Shaik S Chemistry as a Game of Molecular Construction Wiley Sons Inc Hobboken NJ USA 2016 pp 179180 22 Shaik S Hiberty PC A Chemists Guide to Valence Bond Theory WileyInterscience Hobboken NJ USA 2008 Chapters 1 and 6 pp 125 4041 79 9497 104106 157163 23 Lewis DE 18601861 Magic Years in the Development of the Structural Theory of Organic Chemistry Bull Hist Chem 2019 44 7791 24 Lewis GN Valence and the Structure of Atoms and Molecules The Catalog Company Inc New York NY USA 1923 pp 29 91 25 Langmuir I The arrangement of electrons in atoms and molecules J Am Chem Soc 1919 41 868934 CrossRef 26 Jensen WB Abegg Lewis Langmuir and the Octet Rule J Chem Educ 1984 61 191200 CrossRef 27 Ingold CK Mesomerism and Tautomerism Nature 1934 133 946947 CrossRef 28 Nye MJ From Chemical Philosophy to Theoretical Chemistry University of California Press Los Angeles CA USA 1993 pp 158 191 194 199 202207 216220 29 Servos JW Physical Chemistry from Ostwald to Pauling Princeton University Press Princeton NJ USA 1990 p 135 30 Kohler RE Jr Irving Langmuir and the Octet Theory of Valence Histor Stud Phys Sci 1974 4 3987 CrossRef 31 Heisenberg W Mehrkörperproblem und Resonanz in der Quantenmechanik Z Phys 1926 38 411426 CrossRef 32 Shaik S Danovich D Galraith JM Braida B Wu W Hiberty PC ChargeShift Bonding A New and Unique Form of Bonding Angew Chem Int Ed 2020 59 9841001 CrossRef 33 Slater JC The Theory of Complex Spectra Phys Rev 1929 34 12931322 CrossRef 34 Slater JC Molecular Energy Levels and Valence Bonds Phys Rev 1931 38 11091144 CrossRef 35 Rumer G Zum Theorie der Spinvalenz Gottinger Nachr 1932 3 337498 36 Gallup GA A Short History of VB Theory In Valence Bond Theory Cooper DL Ed Elsevier Amsterdam The Netherlands 2002 pp 140 37 Wang SC The Problem of the Normal Hydrogen Molecule in the New Quantum Mechanics Phys Rev 1928 31 579586 CrossRef 38 Rosen N The Normal State of the Hydrogen Molecule Phys Rev 1931 38 20992114 CrossRef 39 Weinbaum S The Normal State of the Hydrogen Molecule J Chem Phys 1933 1 593596 CrossRef 40 Coulson CA Fischer I Notes on the Molecular Orbital Treatment of the Hydrogen Molecule Phil Mag 1949 40 386393 CrossRef 41 Goddard WA III Dunning TH Jr Hunt WJ Hay PJ Generalized Valence Bond Description of Bonding in LowLying States of Molecules Acc Chem Res 1973 6 368376 CrossRef 42 Goddard WA III Improved Quantum Theory of ManyElectron Systems II The Basic Method Phys Rev 1967 157 8193 CrossRef Molecules 2021 26 1624 20 of 24 43 Goddard WA III Harding LB The Description of Chemical Bonding from AbInitio Calculations Annu Rev Phys Chem 1978 29 363396 CrossRef 44 Goddard WA III The Symmetric Group and the Spin Generalized SCF Method Int J Quant Chem 1970 4 593600 CrossRef 45 Pauling L The SharedElectron Chemical Bond Proc Natl Acad Sci USA 1928 14 359362 CrossRef 46 Slater JC Directed Valence in Polyatomic Molecules Phys Rev 1931 37 481489 CrossRef 47 Slater JC Note on Molecular Structure Phys Rev 1932 41 255257 CrossRef 48 Pauling L The Nature of the Chemical Bond Application of Results Obtained from the Quantum Mechanics and from a Theory of Magnetic Susceptibility to the Structure of Molecules J Am Chem Soc 1931 53 13671400 CrossRef 49 Pauling L The Nature of the Chemical Bond II The OneElectron Bond and the ThreeElectron Bond J Am Chem Soc 1931 53 32253237 CrossRef 50 Galbraith JM Blank E Shaik S Hiberty PC π Bonding in second and Third Row Molecules Testing the Strength of Linuss Blanket Chem Eur J 2000 6 24252434 CrossRef 51 Shaik S Danovich D Braida B Wu W Hiberty PC New Landscape of ElectronPair Bonding Covalent Ionic and ChargeShift Bonds Struct Bonding Chem Bond II 2016 170 169212 52 Pauling L Wheland GW The Nature of the Chemical Bond V The QuantumMechanical Calculation of the Resonance Energy of Benzene and Naphthalene and the Hydrocarbon Free Radicals J Chem Phys 1933 1 362374 CrossRef 53 Rice RE A Reverie Kekulé and His First Dream An Interview Bull Hist Chem 2015 40 114119 54 Wheland GW Resonance in Organic Chemistry Wiley New York NY USA 1955 pp 4 39 148 55 Brush SG Dynamics of Theory Change in Chemistry Part 1 The Benzene Problem 18651945 Stud Hist Phil Sci 1999 30 2181 CrossRef 56 Brush SG Dynamics of Theory Change in Chemistry Part 2 Benzene and Molecular Orbitals 19451980 Stud Hist Phil Sci 1999 30 263282 CrossRef 57 Shaik S Hiberty PC Valence Bond Theory Its History Fundamentals and ApplicationsA Primer Rev Comput Chem 2004 20 1 58 Berson JA Chemical Creativity Ideas from the Work of Woodward Hückel Meerwein and Others WileyVCH NewYork NY USA 1999 59 Hoffmann R Shaik S Hiberty PC Conversation on VB vs MO Theory A Never Ending Rivalry Acc Chem Res 2003 36 750756 CrossRef 60 Van Vleck JH Sherman A The Quantum Theory of Valence Rev Mod Phys 1935 7 167228 CrossRef 61 Hiberty PC Ohanessian G The Valence Bond Description of Conjugated Molecules II A Very Simple Method to Approximate the Structural Weights of a Fully Correlated Valence Bond Wave Function Int J Quant Chem 1985 27 259272 CrossRef 62 Hiberty PC Leforestier C Expansion of Molecular Orbital Wave Functions into Valence Bond Wave Functions A Simplified Procedure J Am Chem Soc 1978 100 20122017 CrossRef 63 Tantardini GF Simonetta M Ab Initio ValenceBond Calculations 5 Benzene J Am Chem Soc 1977 99 29132918 CrossRef 64 Hoffmann R An Extended Huckel Theory I Hydrocarbons J Chem Phys 1963 39 13971412 CrossRef 65 Pople JA Beveridge DL Approximate Molecular Orbital Theory McGrawHill New York NY USA 1970 66 Hehre WJ Radom L Schleyer PvR Pople JA Ab Initio Molecular Orbital Theory John Wiley New York NY USA 1986 67 Woodward RB Hoffmann R The Conservation of Orbital Symmetry Verlag Chemie Academic Press Weinheim Germany 1971 68 Kohn W Sham LJ SelfConsistent Equations Including Exchange and Correlation Effects Phys Rev 1965 140 A1133A1138 CrossRef 69 Te Velde G Bickelhaupt FM Baerends EJ Fonseca Guerra C Van Gisbergen SJA Snijders JG Ziegler T Chemistry with ADF J Comput Chem 2001 22 931967 CrossRef 70 Grushow A Is it time to retire the hybrid atomic orbital J Chem Ed 2011 88 860862 CrossRef 71 Brion CE Wolfe S Zheng S Cooper G Zheng Y An investigation of hybridization and the orbital models of molecular electronic structure for CH4 NH3 and H2O Can J Chem 2017 95 13141322 CrossRef 72 Boys SF Construction of Some Molecular Orbitals to Be Approximately Invariant for Changes from One Molecule to Another Rev Mod Phys 1960 32 296299 CrossRef 73 Edmiston C Ruedenberg K Localized Atomic and Molecular Orbitals Rev Mod Phys 1963 35 457465 CrossRef 74 Honegger E Heilbronner E The Equivalent Orbital Model and the Interpretation of PE Spectra In Theoretical Models of Chemical Bonding Maksic ZB Ed Springer Verlag BerlinHeidelberg Germany 1991 Volume 3 pp 100151 75 Gillespie RJ The electronpair repulsion model for molecular geometry J Chem Educ 1970 47 1823 CrossRef 76 Gerratt J Cooper DL Karadakov PB Raimondi M Modern Valence Bond Theory Chem Soc Rev 1997 26 87100 CrossRef 77 Penotti F Gerratt J Cooper DL Raimondi M The ab initio spincoupled description of methane J Mol Struc Theochem 1988 169 421436 CrossRef 78 Xu LT Dunning TH Jr Orbital Hybridization in Modern Valence Bond Wave Functions Methane Ethylene and Acetylene J Phys Chem A 2020 124 204214 CrossRef 79 Shaik S Danovich D Hiberty PC To hybridize or not to hybridize This is the dilemma Comput Theor Chem 2017 1116 242249 CrossRef Molecules 2021 26 1624 21 of 24 80 Shaik S Maitre P Sini G Hiberty PC The ChargeShift Bonding Concept ElectronPair Bonds with Very Large IonicCovalent Resonance Energies J Am Chem Soc 1992 114 78617866 CrossRef 81 Shaik S Danovich D Silvi B Lauvergant DL Hiberty PC ChargeShift BondingA Class of ElectronPair Bonds that Emerges from Valence Bond Theory and Is Supported by the Electron Localization Function Approach Chem Eur J 2005 11 63586371 CrossRef PubMed 82 Wheland GW The Electronic Structure of Some Polyenes and Aromatic Molecules VA Comparison of Molecular Orbital and Valence Bond Methods Proc R Soc Lond 1938 A159 397408 CrossRef 83 Wheland GW The Quantum Mechanics of Unsaturated and Aromatic Molecules A Comparison of Two Methods of Treatment J Chem Phys 1934 2 474481 CrossRef 84 Shurki A Hiberty PC Dijkstra F Shaik S Aromaticity and Antiaromaticity What Role do Ionic Configurations Play in Delocalization and Induction of Magnetic Properties J Phys Org Chem 2003 16 731745 CrossRef 85 Voter AF Goddard WA III The Generalized Resonating Valence Bond Description of Cyclobutadiene J Am Chem Soc 1986 108 28302837 CrossRef 86 Craig DP Cyclobutadiene and Some Other Pseudoaromatic Compounds J Chem Soc 1951 31753182 CrossRef 87 Craig DP Electronic Levels in Simple Conjugated Systems I Configuration Interaction in Cyclobutadiene Proc R Soc Lond 1950 A200 498506 88 Heitler W Pöschl G Ground State of C2 and O2 and the Theory of Valency Nature 1934 133 833834 CrossRef 89 Harcourt RD Qualitative ValenceBond Descriptions of ElectronRich Molecules Pauling 3Electron Bonds and Increased Valence Theory Lecture Notes Chem 1982 30 114135 90 Corry TA OMalley PJ Localized Bond Orbital Analysis of the Bonds of O2 J Phys Chem A 2020 124 97719776 CrossRef 91 Danovich D ForoutanNejad C Hiberty PC Shaik S Nature of the ThreeElectron Bond J Phys Chem A 2018 122 18731885 CrossRef 92 Borden WT Hoffmann R Stuyver T Chen B Dioxygen What Makes This Triplet Diradical Kinetically Persistent J Am Chem Soc 2017 139 90109018 CrossRef 93 Truhlar DG Hiberty PC Shaik S Gordon MS Danovich D Orbitals and Interpretation of Photoelectron Spectroscopy Experiments Angew Chem Int Ed 2019 58 1233212338 94 Van Vleck JH The Group Relation between the Mulliken and SlaterPauling Theories J Chem Phys 1935 3 803806 CrossRef 95 Clauss AD Nelsen SF Ayoub M Moore JW Landis CR Weinhold JW Rabbitears hybrids VSEPR sterics and other orbital anachronisms Chem Educ Res Pract 2014 15 417434 CrossRef 96 Hiberty PC Danovich D Shaik S Comment on Rabbitears hybrids VSEPR sterics and other orbital anachronisms Chem Educ Res Pract 2015 16 689693 CrossRef 97 Chen Z Wu W Ab initio valence bond theory A brief history recent developments and near future J Chem Phys 2020 153 090902090909 CrossRef 98 Cooper DL Gerratt J Raimondi M Application of SpinCoupled Valence Bond Theory Chem Rev 1991 91 929964 CrossRef 99 Cooper DL Gerratt JP Raimondi M Modern Valence Bond Theory Adv Chem Phys 1987 69 319397 100 Sironi M Raimondi M Martinazzo R Gianturco FA Recent Developments of the SCVB Method In Valence Bond Theory Cooper DL Ed Elsevier Amsterdam The Netherlands 2002 pp 261277 101 BalintKurti GG Karplus M Multistructure ValenceBond and AtomsinMolecules Calculations for LiF F2 and F2 J Chem Phys 1969 50 478488 CrossRef 102 Van Lenthe JH BalintKurti GG The ValenceBond SCF VB SCF Method Synopsis of Theory and Test Calculations of OH Potential Energy Curve Chem Phys Lett 1980 76 138142 CrossRef 103 Van Lenthe JH BalintKurti GG The ValenceBond SelfConsistent Field Method VBSCF Theory and Test Calculations J Chem Phys 1983 78 56995713 CrossRef 104 Verbeek J van Lenthe JH On the Evaluation of Nonorthogonal Matrix Elements J Mol Struc Theochem 1991 229 115137 CrossRef 105 Verbeek J van Lenthe JH The Generalized SlaterCondon Rules Int J Quant Chem 1991 40 201210 CrossRef 106 Verbeek J Langenberg JH Byrman CP Dijkstra F van Lenthe JH TURTLE An Ab Initio VBVBSCF Program Utrecht University Utrecht The Netherlands 2001 107 Van Lenthe JH Dijkstra F Havenith WA TURTLEA Gradient VBSCF Program Theory and Studies of Aromaticity In Valence Bond Theory Elsevier Amsterdam The Netherlands 2002 pp 79116 108 Matsen FA SpinFree Quantum Chemistry Adv Quant Chem 1964 1 59114 109 Matsen FA SpinFree Quantum Chemistry II ThreeElectron Systems J Phys Chem 1964 68 32823296 CrossRef 110 McWeeny R A Spin Free Form of Valence Bond Theory Int J Quant Chem 1988 34 2336 CrossRef 111 Qianer Z Xiangzhu L Bonded Tableau Method for Many Electron Systems J Mol Struct Theochem 1989 198 413425 CrossRef 112 Li X Zhang Q Bonded Tableau Unitary Group Approach to the manyElectron Correlation Problem Int J Quant Chem 1989 36 599632 CrossRef Molecules 2021 26 1624 22 of 24 113 Wu W Mo Y Cao Z Zhang Q A Spin Free Approach for Valence Bond Theory and Its Application In Valence Bond Theory Cooper DL Ed Elsevier Amsterdam The Netherlands 2002 pp 143186 114 Wu W Song L Mo Y Zhang Q XMVB A Program for Ab Initio Nonorthogonal Valence Bond Computations J Comput Chem 2005 26 514521 115 Chen Z Ying F Chen X Song J Su P Song L Mo Y Zhang Q Wu W XMVB 20 A New Version of Xiamen Valence Bond Program Int J Quant Chem 2015 115 731737 CrossRef 116 Joy J Danovich D Kaupp M Shaik S On the Covalent vs ChargeShift Nature of the MetalMetal Bond in Transition Metal Complexes J Am Chem Soc 2020 142 1227712287 CrossRef 117 Ying F Su P Chen Z Shaik S Wu W DFVB A DensityFunctionalBased Valence Bond Method J Chem Theory Comput 2012 8 16081615 CrossRef PubMed 118 Li J McWeeny R VB2000 An Ab Initio Valence Bond Program Based on Product Function Method and the Algebrant Algorithm SciNet Technologies San Diego CA USA 2000 119 Gallup GA Vance RL Collins JR Norbeck JM Practical Valence Bond Calculations Adv Quant Chem 1982 16 229292 120 Gallup GA The CRUNCH Suite of Atomic and Molecular Structure Programs University of NebraskaLincoln Lincoln NE USA 2001 121 Hiberty PC Flament JP Noizet E Compact and Accurate Valence Bond Functions with Different Orbitals for Different Configurations Application to the TwoConfiguration Description of F2 Chem Phys Lett 1982 189 259265 CrossRef 122 Hiberty PC The Breathing Orbital Valence Bond Method In Modern Electronic Structure Theory and Applications in Organic Chemistry Davidson ER Ed World Scientific River Edge NJ USA 1997 pp 289367 123 Hiberty PC Shaik S BreathingOrbital Valence BondA Valence Bond Method Incorporating Static and Dynamic Electron Correlation Effects In Valence Bond Theory Cooper DL Ed Elsevier Amsterdam The Netherlands 2002 pp 187226 124 Hiberty PC Shaik S BOVBA Modern Valence Bond Method That Includes Dynamic Correlation Theor Chem Acc 2002 108 255272 CrossRef 125 Wu W Su P Shaik S Hiberty PC Classical Valence Bond Approach by Modern Methods Chem Rev 2011 11 75577593 CrossRef 126 Wu W Song L Cao Z Zhang Q Shaik S A Practical Valence Bond Method Incorporating Dynamic Correlation J Phys Chem A 2002 106 27212726 CrossRef 127 Song L Wu W Zhang Q Shaik S VBPCM A Valence Bond Method that Incorporates a Polarizable Continuum Model J Phys Chem A 2004 108 60176024 CrossRef 128 Braida B Toulouse J Caffarel M Umrigar CJ Quantum Monte Carlo with Jastrowvalence bond wave functions J Chem Phys 2011 134 084108084111 CrossRef PubMed 129 Albu TV Corchado JC Truhlar DG Molecular Mechanics for Chemical reactions A Standard Strategy for Using Multiconfig uration Molecular Mechanics for Variational Transition State Theory with Optimized Multidimensional Tunneling J Phys Chem A 2001 105 84658487 CrossRef 130 Firman TK Landis CR Valence Bond Concepts Applied to Molecular Mechanics Description of Molecular Shapes 4 Transition Metals with πBonds J Am Chem Soc 2001 123 1172811742 CrossRef 131 Weinhold F Landis C Valency and Bonding A Natural Bond Orbital DonorAcceptor Perspective Cambridge University Press Cambridge UK 2005 132 Song L Wu W Hiberty PC Danovich D Shaik S An Accurate Barrier for the Hydrogen Exchange Reaction Is Valence Bond Theory Coming of Age Chem Eur J 2003 9 45404547 CrossRef 133 Wu W Zhang H Braïda B Shaik S Hiberty PC The V state of ethylene Valence bond theory takes up the challenge Theor Chem Acc 2014 133 1441 CrossRef 134 Braïda B Chen Z Wu W Hiberty PC Valence Bond Alternative Yielding Compact and Accurate Wave Functions for Challenging Excited States Application to Ozone and Sulfur Dioxide J Chem Theory Comput 2021 17 330343 CrossRef 135 Malrieu JP The Magnetic Description of Conjugated Hydrocarbons In Models of Theoretical Bonding Maksic ZB Ed Springer Berlin Germany 1990 pp 108136 136 Malrieu JP Maynau D A Valence Bond Effective Hamiltonian for Neutral States of πSystems 1 Methods J Am Chem Soc 1984 104 30213029 CrossRef 137 Matsen FA Correlation of Molecular Orbital and Valence Bond States in πSystems Acc Chem Res 1978 11 387392 CrossRef 138 Fox MA Matsen FA Electronic Structure in πSystems Part II The Unification of Hückel and Valence Bond Theories J Chem Educ 1985 62 477485 CrossRef 139 Fox MA Matsen FA Electronic Structure in πSystems Part III Application in Spectroscopy and Chemical Reactivity J Chem Educ 1985 62 551560 CrossRef 140 Ramasesha S Soos ZG Valence Bond Theory of Quantum Cell Models In Valence Bond Theory Cooper DL Ed Elsevier Amsterdam The Netherlands 2002 pp 635697 141 Shaik SS A Qualitative Valence Bond Model for Organic Reactions In New Theoretical Concepts for Understanding Organic Reactions Bertran J Csizmadia IG Eds NATO ASI Series C267 Kluwer Academic Publ Dordrecht The Netherlands 1989 pp 165217 Molecules 2021 26 1624 23 of 24 142 Wu W Zhong SJ Shaik S VBDFTs A HückelType Semiempirical Valence Bond Method Scaled to Density Functional Energies Applications to Linear Polyene Chem Phys Lett 1998 292 714 CrossRef 143 Wu W Danovich D Shurki A Shaik S Using Valence Bond Theory to Understand Electronic Excited States Applications to the Hidden Excited State 21Ag of C2nH2n2 n 214 Polyenes J Phys Chem A 2000 104 87448758 CrossRef 144 Wu W Luo Y Song L Shaik S VBDFTs A Semiempirical Valence Bond Method Application to Linear Polyenes Containing Oxygen and Nitrogen Heteroatoms Phys Chem Chem Phys 2001 3 54595465 CrossRef 145 Karafiloglou P A General πelectron Mullikenlike Population Analysis Chem Phys 1988 128 373381 CrossRef 146 Linnett JW The Electronic Structure of Molecules A New Approach Methuen Co Ltd London UK 1964 pp 1162 147 Harcourt RD Valence Bond Structures for Some Molecules with Four SinglyOccupied ActiveSpace Orbitals Electronic Structures Reaction Mechanisms Metallic Orbitals In Valence Bond Theory Cooper DL Ed Elsevier Amsterdam The Netherlands 2002 pp 349378 148 Shaik SS What Happens to Molecules As They React A Valence Bond Approach to Reactivity J Am Chem Soc 1981 103 36923701 CrossRef 149 Shaik S Shurki A Valence Bond Diagrams and Chemical Reactivity Angew Chem Int Ed 1999 38 586625 CrossRef 150 Pross A Shaik SS A Qualitative Valence Bond Approach to Chemical Reactivity Acc Chem Res 1983 16 363370 CrossRef 151 Pross A Theoretical and Physical Principles of Organic Reactivity John Wiley Sons New York NY USA 1995 pp 83124 235290 152 Shaik S Hiberty PC Curve Crossing Diagrams as General Models for Chemical Structure and Reactivity In Theoretical Models of Chemical Bonding Maksic ZB Ed Springer BerlinHeidelberg Germany 1991 Volume 4 pp 269322 153 Shaik S Shurki A Danovich D Hiberty PC A Different Story of πDelocalizationThe Distortivity of the πElectrons and Its Chemical Manifestations Chem Rev 2001 101 15011540 CrossRef 154 Danovich D Wu W Shaik S NoPair Bonding in the HighSpin 3Σu State of Li2 A Valence Bond Study of its Origins J Am Chem Soc 1999 121 31653174 CrossRef 155 Danovich D Shaik S Bonding with Parallel Spins HighSpin Clusters of Monovalent Metal Atoms Acc Chem Res 2014 47 417426 CrossRef 156 Danovich D Shaik S On the Nature of Bonding in Parallel Spins in Monovalent Metal Clusters Annu Rev Phys Chem 2016 67 419439 CrossRef 157 Van der Lugt WT Oosterhoff LJ Symmetry Control and Photoinduced Reactions J Am Chem Soc 1969 91 60426049 CrossRef 158 Mulder JJC Oosterhoff LJ Permutation Symmetry Control in Concerted Reactions Chem Commun 1970 305b307 CrossRef 159 Michl J Physical Basis of Qualitative MO Arguments in Organic Photochemistry Topics Curr Chem 1974 46 159 160 Robb MA Garavelli M Olivucci M Bernardi F A Computational Strategy for Organic Photochemistry Rev Comput Chem 2000 15 87146 161 Shaik S Reddy AC Transition States Avoided Crossing States and Valence Bond Mixing Fundamental Reactivity Paradigms J Chem Soc Faraday Trans 1994 90 16311642 CrossRef 162 Warshel A Weiss RM Empirical Valence Bond Approach for Comparing Reactions in Solutions and in Enzymes J Am Chem Soc 1980 102 62186226 CrossRef 163 Warshel A Russell ST Calculations of Electrostatic Interactions in Biological Systems and in Solutions Quart Rev Biophys 1984 17 283422 CrossRef 164 Warshel A Calculations of Chemical Processes in Solutions J Phys Chem 1979 83 16401652 CrossRef 165 BraunSand S Olsson MHM Warshel A Computer Modeling of Enzyme Catalysis and Its Relationship to Concepts in Physical Organic Chemistry Adv Phys Org Chem 2005 40 201245 166 Kim HJ Hynes JT A Theoretical Model for SN1 Ionic Dissociation in Solution 1 Activation Free Energies and TransitionState Structure J Am Chem Soc 1992 114 1050810528 CrossRef 167 Shaik S Solvent Effect on Reaction Barriers The SN2 Reactions 1 Application to the Identity Exchange J Am Chem Soc 1984 106 12271232 CrossRef 168 Shaik S Nucleophilic Reactivity and Vertical Ionization Potentials in CationAnion Recombinations J Org Chem 1987 52 15631568 CrossRef 169 Meir R Chen H Lai W Shaik S Oriented Electric Fields Accelerate the DielsAlder Reactions and Control the EndoExo Selectivity ChemPhysChem 2010 11 301310 CrossRef 170 Shaik S Mandal D Ramanan R Oriented Electric Fields as Future Smart Reagents in Chemistrty Nature Chem 2016 8 10911098 CrossRef PubMed 171 Shaik S Ramanan R Danovich D Mandal D Structure and ReactivitySelectivity Control by OrientedExternal Electric Fields Chem Soc Rev 2018 47 51255145 CrossRef PubMed 172 Luo Y Song L Wu W Danovich D Shaik S The Ground and Excited States of Polyenyl Radicals C2n1H2n1 n 213 A Valence Bond Study ChemPhysChem 2004 5 515528 CrossRef PubMed 173 Gu J Lin Y Ma B Wu W Shaik S Covalent Excited States of Polyenes C2nH2n2 n 28 and Polyenyl Radicals C2n1H2n1 n 28 An Ab Initio Valence Bond Study J Chem Theory Comput 2008 4 21012107 CrossRef 174 Karach I Botvinik A Truhlar DG Wu W Shurki A Assesing the Performance of Ab Inition Classical Valence Bond Methods Comput Theor Chem 2017 1116 234241 CrossRef Molecules 2021 26 1624 24 of 24 175 Parr CA Truhlar DG Potential energy Surfaces for Atom Transfer Reaction Involving Hydrogens and Halogens J Phys Chem 1971 75 18441860 176 Truhlar DG Steckler R Gordon MS Potential Energy Surfaces for Polyatomic Reaction Dynamics Chem Rev 1987 87 217236 CrossRef 177 Odoh SO Manni GL Carlson RK Truhlar DG Gagliardi L Separatepair Approximation and Separate Pair PairDensity Functional Theory Chem Sci 2016 7 23992413 CrossRef PubMed 178 Bao JL Odoh SO Gagliardi L Truhlar DG Predicting Bond Dissociation Energies of TrnsitionMetal Compounds by Multicinfiguration PairDensity Functional Theeory and SecondOrder Perturbation Theory Based on Correlated Participating Orbitals and Separate Pairs J Chem Theory Comput 2017 13 616626 CrossRef PubMed 179 Sarkash K Gagliardi L Truhlar DG Multiconfiguration PairDensity Functional Theory and Complete Active Space Second Order Perturbation Theory Bond Dissociation Energies of FeC NiC FeS NiS FeSe and NiSe J Phys Chem A 2017 121 93929400 CrossRef PubMed 180 Scemama A Caffarel M Savin A Maximum Probability domain from Quantum Monte Carlo Calculations J Comput Chem 2007 28 442454 CrossRef 181 Liu Y Frankcombe TJ Schmidt TW Chemical Bonding Motifs from a Tiling of the ManyElectron Wavefunction Phys ChemChem Phys 2016 18 1338513394 CrossRef 182 Heuer MA Reuter L Lüchow A Ab Initio Dot Structures Beyond the Lewis Picture Molecules 2021 26 911 CrossRef