Master Course for Theoretical Chemistry and Computational Modelling (TCCM) Using Valence Bond Theory to Model (Bio)Chemical Reactivity Fernanda Duarte Department of Chemistry, Oxford September 7th 2016 1 General Outline of Lecture • Motivation & History of VB • Basic Concepts • ab initio VB theory • Multiscale VB simulations • Empirical VB theory Motivation Concepts and heuristic models Quantitative theory (Localised view ) (Delocalised view) H = E H X C Y H H Lewis model Curly-Arrows VSEPR Hybridisation ... Delocalised particles Localised electron pairs indistinguishable and interacting Chemical bond concept 3 (no chemical bond) Historical Timeline ROOTS OF VB THEORY 3 Valence bond theory in Pauling’s view is6 a Aquantum BRIEF STORY chemical OF VALENCE version BOND THEORY of Lewis’s theory of valence Pauling-Wheland's resonating picture HL- Wave function Covalent-ionic superpositionHuckel's delocalized π-MO picturePauling's three-electron in a bond, A–B bond Interaction Between Neutral Atoms and Homopolar Binding K1 K2 AB AB AB • HH HH O •• O ••• a b Rumer’s A B O D1 D2 D3 Heitler & London canonical structures 2 1 2 Ψ = 3c1(K1 + K2) + c2(D1 + D2 + D3) c1 > c2 σu 5 6 Scheme 1.2 σg 1916 1927 1929 antiaromaticity,1931 and its articulation1933 by organic chemists1950 in the 1950s 1970s À G.N. Lewis Slater 4 will constitute a major cause for the acceptance of MO theory and the rejection of VB theory (4). Determinant The description of benzene in terms of a superposition (resonance) of two The Atom and The Molecule Scheme 1.1 Pauling (1939) Kekule´ structures appeared for the first time in the work of Slater, as a case belonging to a class of species in which each atomWheland possesses (1955) more neighbors than electrons it can share, much like in metals (21).VB TwoTextbooks years later, Pauling and Wheland (37) applied HLVB theory to benzene. They developed a less As demonstrated by Heisenberg, the mixing of [wn(1)wm(2)] and [wn(2)wm(1)] led cumbersome computational approach, compared with Hu¨ ckel’s previous to a new energy term that caused aHLVB splitting treatment, betweenL. using Pauling the the five two canonical wave structures functions in 6, and approximated the matrix elements between the structures by retaining only close neighbor CA and CB. He called this term ‘‘resonance’’The Nature using of the a Chemical classical Bond analogy of two resonance interactions. Their approach allowed them to extend the treatment oscillators that, by virtue of possessingto naphthalene the same and frequency, to a great variety form of aother resonating species. Thus, in the HLVB A Chemist’ssituation Guide with to Valence characteristic Bond Theory, by Sason exchange Shaikapproach, and energy. Philippe benzene C. Hiberty is described as a ‘‘resonance hybrid’’ of the two4 Kekule´ structures and the three Dewar structures; the latter had already appeared In modern terms, the bonding inbefore H2 incan Ingold’s be idea accounted of mesomerism, for which by itself the is rooted wave in Lewis’s concept function drawn in 1, in Scheme 1.1.of This electronic wave tautomerism function (6). In is his a book, superposition published for the of first time in 1944, Wheland explains the resonance hybrid with the biological analogy of two covalent situations in which, in themule first = donkey form + ( horsea) one (38). electron The pictorial has a representation spin-up of the wave (a spin), while the other has spin-downfunction, (b spin), the link and to Kekul vicee´’s versa oscillation in the hypothesis, second and to Ingold’s mesomerism, which were known to chemists, made the HLVB representation form (b). Thus, the bonding in H2veryarises popular due among to practicing the quantum chemists. mechanical ‘‘resonance’’ interaction between the twoWith patterns these two of seemingly spin arrangement different treatments that of benzene, are the chemical required in order to form a singletcommunity electron was pair. faced with This two ‘‘resonance alternative descriptions energy’’ of one of its molecular icons, and this began the VB MO rivalry that seems to accompany chemistry accounted for 75% of the totalto bonding the Twenty-first of Century the molecule,À (5). This rivalry and involved thereby most of the prominent projected that the wave function in chemists1, which of various is referred periods (e.g., to henceforth Mulliken, Hu¨ ckel, as J. the Mayer, Robinson, Lapworth, Ingold, Sidgwick, Lucas, Bartlett, Dewar, Longuet-Higgins, HL-wave function, can describe the chemicalCoulson, Roberts, bonding Winstein, in a Brown). satisfactory A detailed manner. and interesting account of This ‘‘resonance origin’’ of the bondingthe nature was of this a rivalry remarkable and the major feat players of can the be found new in the treatment of Brush (3,4). Interestingly, back in the 1930s, Slater (22) and van Vleck and quantum theory, since until then it was not obvious how two neutral species could be at all bonded. In the winter of 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 (10,12). In both treatments (9,12) the authors considered ionic structures for homopolar bonds, but discarded their mixing as being too small. In London’s paper, there is also a consideration of ionic (so-called polar) bonding. In essence, the HL theory was a quantum mechanical version of Lewis’s electron-pair theory. Thus, even though Heitler and London did their work independently and perhaps unaware of the Lewis model, the HL-wave function still precisely described the shared-pair bond of Lewis. In fact, in his letter to Lewis (8), and in his landmark paper (13), Pauling points out that the HL and London treatments are ‘entirely equivalent to G.N. Lewis’s successful theory of shared electron pair ...’’. Thus, although the final formulation of the 6 A BRIEF STORY OF VALENCE BOND THEORY Huckel'sHistorical delocalized π-MO picture TimelinePauling-Wheland's resonating picture 6 A BRIEF STORY OFROOTS VALENCE OF BOND VB THEORY THEORY 3 K1 K2 Pauling-Wheland's resonating picture Covalent-ionic superpositionHuckel's delocalized π-MO picture HL- Wave functionLennard-Jones MO Theory Pauling's three-electron in a bond, A–B D1 D2 Dbond3 O2 MullikenΨ = c1(K 1& + K Hund2) + c2(D1 + D2 + D3) c1 > c2 K1 K2 AB AB5 AB 6 • HH HH Huckel Model O •• O Scheme 1.2 ••• a b Benzene Rumer’s antiaromaticity, and A its articulationB by organic chemists in the 1950s O1970s2D1 D2 D3 Heitler & London will constitute a major cause for thecanonical acceptance of structures MO theory and the rejectionÀ 1 2 Ψ = 3c1(K1 + K2) + c2(D1 + D2 + D3) of VB theory (4). c > c The description of benzene in terms of a superposition (resonance) of two 1 2 Kekule´ structuresσu appeared for the first time5 in the work of Slater, as a case 6 belonging to a class of species in which each atom possesses more neighbors Scheme 1.2 than electronsσ itg can share, much like in metals (21). Two years later, Pauling and Wheland (37) applied HLVB theory to benzene. They developed a less 1916 1927 1929 antiaromaticity,1931 and its articulation1933 by organic chemists1950 in the 1950s 1970s cumbersome computational approach, compared with Hu¨ ckel’s previous À G.N. Lewis SlaterHLVB 4 treatment, usingwill the constitute five canonical a major structures cause for in 6 the, and acceptance approximated of MO theory and the rejection the matrix elementsof between VB theory the structures (4). by retaining only close neighbor Determinant resonance interactions.Scheme TheirThe 1.1 description approach allowed of benzene them to in extend terms the of treatment a superpositionPauling (resonance)(1939) of two to naphthalene andKekul to a greate´ structures variety of appeared other species. for Thus, the first in the time HLVB in the work of Slater, as a case approach, benzene isbelonging described as to a a ‘‘resonance class of species hybrid’’ in of which the two each Kekul atomWhelande´ possesses (1955) more neighbors structures and the three Dewar structures; the latter had already appeared than electrons it can share, much like in metals (21). Two years later, Pauling before in Ingold’s idea of mesomerism, which itself is rooted in Lewis’s conceptVB Textbooks and Wheland (37) applied HLVB theory to benzene. They developed a less As demonstrated by Heisenberg,of electronic tautomerism the mixing (6). In ofhis book, [wn(1) publishedwm(2)] for the and first time [wn in(2) 1944,wm(1)] led Wheland explains thecumbersome resonance hybrid computational with the biological approach, analogy compared of with Hu¨ ckel’s previous to a new energy term thatmule caused = donkey + a horseHLVB splitting (38). treatment, The between pictorialL. using Pauling representation the the five two canonical of wave the structures wave functions in 6, and approximated function, the linkthe to Kekul matrixe´’s elements oscillation between hypothesis, the structures and to Ingold’s by retaining only close neighbor CA and CB. He called this term ‘‘resonance’’The Nature using of the a Chemical classical Bond analogy of two mesomerism, which wereresonance known interactions. to chemists, made Their the approach HLVB representation allowed them to extend the treatment oscillators that, by virtuevery of popular possessing amongto practicing naphthalene the chemists. same and frequency, to a great variety form of aother resonating species. Thus, in the HLVB With these two seemingly different treatments of