Valence Bond Mixing and Curve Crossing Diagrams in Chemical Reactivity and Bonding

Extended Mulliken-Hush Method with Applications to the Theoretical Study of Electron Transfer

A novel adiabatic-to-diabatic (ATD) transformation strategy, namely, the extended Mulliken-Hush (XMH) method, is proposed to evaluate diabatic properties including electronic couplings, potential energy surfaces, and their crossings. The XMH method is developed by adopting our recently proposed ATD transformation formula of a general vectorial physical observable, in which a useful ATD transformation is further determined by using an auxiliary dipole between localized frontier orbitals as a simple approximation of the diabatic transition dipole. The XMH method is simple and practical that provides a flexible way to construct diabatic states. To some extent, it can be regarded as an extension of the generalized Mulliken-Hush (GMH) method since the latter takes a stronger approximation, in which the diabatic transition dipole is assumed to be vanishing. Test calculations on the HeH₂⁺ system show that the electronic couplings predicted by the XMH method are closer to the ones calculated by the valence bond block-diagonalization approach than the GMH ones since the XMH method takes into account both the magnitude and direction of the diabatic transition dipole, which is consistent with the properties of this molecule. In the study of electron transfer in the two kinds of donor-bridge-acceptor systems, the XMH method maintains the simplicity of the GMH method and gives reasonable results even when the latter fails, wherein the diabatic transition dipole is nearly perpendicular to the difference of the initial and final adiabatic dipoles. More importantly, the XMH method can be easily combined with high-level electronic structure methods, in which the properties of the ground and excited states may be more accurately calculated, and hence, one may expect that further development of the XMH method would result in a general computational model for studying electron transfer reactions.

Ab initio valence bond theory: A brief history, recent developments, and near future

This Perspective presents a survey of several issues in ab initio valence bond (VB) theory with a primary focus on recent advances made by the Xiamen VB group, including a brief review of the earlier history of the ab initio VB methods, in-depth discussion of algorithms for nonorthogonal orbital optimization in the VB self-consistent field method and VB methods incorporating dynamic electron correlation, along with a concise overview of VB methods for complex systems and VB models for chemical bonding and reactivity, and an outlook of opportunities and challenges for the near future of the VB theory.

A tutorial for understanding chemical reactivity through the valence bond approach

This is a tutorial on the usage of valence bond (VB) diagrams for understanding chemical reactivity in general, and hydrogen atom transfer (HAT) reactivity in particular. The tutorial instructs the reader how to construct the VB diagrams and how to estimate HAT barriers from raw data, starting with the simplest reaction H + H2 and going all the way to HAT in the enzyme cytochrome P450. Other reactions are treated as well, and some unifying principles are outlined. The tutorial projects the unity of reactivity treatments, following Coulson's dictum "give me insight, not numbers", albeit with its modern twist: giving numbers and insight.

Solvent effects and potential of mean force: a multilayered-representation quantum mechanical/molecular mechanics study of the CH3Br + CN− reaction in aqueous solution

The potential of mean force for the CH₃Br + CN⁻ reaction was obtained at the CCSD(T)/MM level of theory using a multilayered-representation quantum mechanical/molecular mechanics approach, as well as the reactant, transition state and product complexes along the reaction pathway in aqueous solution.

Type-I dyotropic reactions: understanding trends in barriers

To understand the factors that control the activation barrier of type-I 1,2-dyotropic reactions (X-EH(2)-CH(2)-X*→X*-EH(2)-CH(2)-X, with E=C and Si, X=H, CH(3), SiH(3), F to I) and trends therein as a function of the migrating groups X, we have explored ten archetypal model reactions of this class using relativistic density functional theory (DFT) at ZORA-OLYP/TZ2P. The main trends in reactivity are rationalized using the activation strain model of chemical reactivity, which had to be extended from bimolecular to unimolecular reactions. Thus, the above type-I dyotropic reactions can be conceived as a relative rotation of the CH(2)CH(2) and [X···X] fragments in X-CH(2)-CH(2)-X. The picture that emerges from these analyses is that reduced C-X bonding in the transition state is the origin of the reaction barrier. Also the trends in reactivity on variation of X can be understood in terms of how sensitive the C-X interaction is towards adopting the transition-state geometry. A valence bond analysis complements the analyses and confirms the picture emerging from the activation strain model.

On the Origins of the Linear Free Energy Relationships: Exploring the Nature of the Off-Diagonal Coupling Elements in S(N)2 Reactions

Understanding the relationship between the adiabatic free energy profiles of chemical reactions and the underlining diabatic states is central to the description of chemical reactivity. The diabatic states form the theoretical basis of Linear Free Energy Relationships (LFERs) and thus play a major role in physical organic chemistry and related fields. However, the theoretical justification for some of the implicit LFER assumptions has not been fully established by quantum mechanical studies. This study follows our earlier works(1,2) and uses the ab initio frozen density functional theory (FDFT) method(3) to evaluate both the diabatic and adiabatic free energy surfaces and to determine the corresponding off-diagonal coupling matrix elements for a series of S(N)2 reactions. It is found that the off-diagonal coupling matrix elements are almost the same regardless of the nucleophile and the leaving group but change upon changing the central group. Furthermore, it is also found that the off diagonal elements are basically the same in gas phase and in solution, even when the solvent is explicitly included in the ab initio calculations. Furthermore, our study establishes that the FDFT diabatic profiles are parabolic to a good approximation thus providing a first principle support to the origin of LFER. These findings further support the basic approximation of the EVB treatment.

Application of the valence bond mixing configuration diagrams to hypervalency in trihalide anions: a challenge to the Rundle-Pimentel model

The X(3)(-) hypercoordinated anions (H, F, Cl, Br, I) are studied by means of the breathing-orbital valence bond ab initio method. The valence bond wave functions describe the different X(3)(-) complexes in terms of only six valence bond structures and yield energies relative to the two exit channels, X(2) + X(-) and X(2)(-) + X(*), in very good agreement with reference CCSD(T) calculations. Although H(3)(-) is unstable and dissociates to H(2) + H(-), all the trihalogen anions are stable intermediates, Br(3)(-) and I(3)(-) being more stable than F(3)(-) and Cl(3)(-). As a challenge to the traditional Rundle-Pimentel model, the different energies of the hypercoordinated species relative to the normal-valent dissociation products X(2) + X(-) are interpreted in terms of valence bond configuration mixing diagrams and found to correlate with a single parameter of the X(2) molecule, its singlet-triplet energy gap. Examination of the six-structure wave functions show that H(3)(-), Cl(3)(-), Br(3)(-), and I(3)(-) share the same bonding picture and can be mainly described in terms of the interplay of two Lewis structures. On the other hand, F(3)(-) is bonded in a different way and possesses a significant three-electron bonding character that is responsible for the dissociation of this complex to F(2)(-) + F(*), instead of the more stable products F(2) + F(-). This counterintuitive preference for the thermodynamically disfavored exit channel is found to be an experimental manifestation of the large charge-shift resonance energy that generally characterizes fluorine-containing bonds.

The rates of S(N)2 reactions and their relation to molecular and solvent properties

The energy barriers of symmetrical methyl exchanges in the gas phase have been calculated with the reaction path of the intersecting/interacting-state model (ISM). Reactive bond lengths increase down a column of the Periodic Table and compensate for the decrease in the force constants, which explains the near constancy of the intrinsic barriers in the following series of nucleophiles: F(-) approximately Cl(-) approximately Br(-) approximately I(-). This compensation is absent along the rows of the Periodic Table and the trend in the reactivity is dominated by the increase in the electrophilicity index of the nucleophile in the series C<N<O<F. Solvent effects have been quantitatively incorporated into the ISM model through a correlation between electrophilicity and the solvent acceptor number. This correlation is transferable between nucleophiles and solvents and allows the methyl transfer rate constants in solution to be calculated with remarkable simplicity and accuracy. The relationship between the S(N)2 and electron-transfer mechanisms is clarified and it is shown that smaller solvent static effects should be expected for electron transfer in the absence of a thermodynamic driving force.

Two-state model based on the block-localized wave function method

The block-localized wave function (BLW) method is a variant of ab initio valence bond method but retains the efficiency of molecular orbital methods. It can derive the wave function for a diabatic (resonance) state self-consistently and is available at the Hartree-Fock (HF) and density functional theory (DFT) levels. In this work we present a two-state model based on the BLW method. Although numerous empirical and semiempirical two-state models, such as the Marcus-Hush two-state model, have been proposed to describe a chemical reaction process, the advantage of this BLW-based two-state model is that no empirical parameter is required. Important quantities such as the electronic coupling energy, structural weights of two diabatic states, and excitation energy can be uniquely derived from the energies of two diabatic states and the adiabatic state at the same HF or DFT level. Two simple examples of formamide and thioformamide in the gas phase and aqueous solution were presented and discussed. The solvation of formamide and thioformamide was studied with the combined ab initio quantum mechanical and molecular mechanical Monte Carlo simulations, together with the BLW-DFT calculations and analyses. Due to the favorable solute-solvent electrostatic interaction, the contribution of the ionic resonance structure to the ground state of formamide and thioformamide significantly increases, and for thioformamide the ionic form is even more stable than the covalent form. Thus, thioformamide in aqueous solution is essentially ionic rather than covalent. Although our two-state model in general underestimates the electronic excitation energies, it can predict relative solvatochromic shifts well. For instance, the intense pi-->pi* transition for formamide upon solvation undergoes a redshift of 0.3 eV, compared with the experimental data (0.40-0.5 eV).

Identity SN2 Reactions X−+CH3X→XCH3+X− (X=F, Cl, Br, and I) in Vacuum and in Aqueous Solution: A Valence Bond Study

The recently developed (L. Song, W. Wu, Q. Zhang, S. Shaik, J. Phys. Chem. A 2004, 108, 6017) valence bond method coupled with a polarized continuum model (VBPCM) has been applied to the identity SN2 reaction of halides in the gas phase and in aqueous solution. The barriers computed at the level of the breathing orbital VB method (P. C. Hiberty, J. P. Flament, E. Noizet, Chem. Phys. Lett. 1992, 189, 259), BOVB and VBPCM//BOVB, are comparable to CCSD(T) and CCSD(T)//PCM results and to experimentally derived barriers in solution (W. J. Albery, M. M. Kreevoy, Adv. Phys. Org. Chem. 1978, 16, 85). The reactivity parameters needed to apply the valence bond state correlation diagram (VBSCD) method (S. Shaik, J. Am. Chem. Soc. 1984, 106, 1227), were also determined by VB calculations. It has been shown that the reactivity parameters along with their semiempirical derivations provide a satisfactory qualitative and quantitative account of the barriers.

Valence bond theory for chemical dynamics

This essay provides a perspective on several issues in valence bond theory: the physical significance of semilocal bonding orbitals, the capability of valence bond concepts to explain systems with multireferences character, the use of valence bond theory to provide analytical representations of potential energy surfaces for chemical dynamics by the method of semiempirical valence bond potential energy surfaces (an early example of specific reaction parameters), by multiconfiguration molecular mechanics, by the combined valence bond-molecular mechanics method, and by the use of valence bond states as coupled diabatic states for describing electronically nonadiabatic processes (photochemistry). The essay includes both ab initio and semiempirical approaches.

A G2(+) level investigation of the gas-phase non-identity SN2 reactions of halides with halodimethylamine

The gas-phase non-identity S(N)2 reactions on nitrogen Y(-) + NMe(2)X --> NMe(2)Y + X(-) (Y, X = F, Cl, Br, and I) were evaluated at the G2(+) level. The reactions are exothermic only when the nucleophile is the lighter halide. The complexation enthalpies for complexes Y(-) em leader Me(2)NX are found to correlate with electronegativity of X. Both central and overall barriers can be interpreted with the aid of Marcus equation. Kinetic and thermodynamic investigations predict that the nucleophilicity of X(-) decreases in the order: F(-) > Cl(-) > Br(-) > I(-) and the leaving-group ability increases in the order: F < Cl < Br < I.

Isomerization around a CN double bond and a CC double bond with a nitrogen atom attached: thermal and photochemical routes

The Longuet-Higgins phase change theorem is used to show that, in certain photochemical reactions, a single product is formed via a conical intersection. The cis-trans isomerization around the double bond in the formaldiminium cation and vinylamine are shown to be possible examples. This situation is expected to hold when the reactant can be converted to the product via two distinct elementary ground-state reactions that differ in their phase characteristics. In one, the total electronic wavefunction preserves its phase in the reaction; in the other, the phase is inverted. Under these conditions, a conical intersection necessarily connects the first electronic excited state to the ground state, leading to rapid photochemical isomerization following optical excitation. Detailed quantum chemical calculations support the proposed model. The possibility that a similar mechanism is operative in other systems, among them the rapid photo-induced cis-trans isomerization of longer protonated Schiff bases (the parent chromophores of rhodopsins), is discussed.