Ab Initio Valence Bond Method Research Articles

The roles of charge transfer and polarization in non-covalent interactions: a perspective from ab initio valence bond methods.

Noncovalent interactions are ubiquitous and have been well recognized in chemistry, biology and material science. Yet, there are still recurring controversies over their natures, due to the wide range of noncovalent interaction terms. In this Essay, we employed the Valence Bond (VB) methods to address two types of interactions which recently have drawn intensive attention, i.e., the halogen bonding and the CH‧‧‧HC dihydrogen bonding. The VB methods have the advantage of interpreting molecular structures and properties in the term of electron-localized Lewis (resonance) states (structures), which thereby shed specific light on the alteration of the bonding patterns. Due to the electron localization nature of Lewis states, it is possible to define individually and measure both polarization and charge transfer effects which have different physical origins. We demonstrated that both the ab initio VB method and the block-localized wavefunction (BLW) method can provide consistent pictures for halogen bonding systems, where strong Lewis bases NH3, H2O and NMe3 partake as the halogen bond acceptors, and the halogen bond donors include dihalogen molecules and XNO2 (X = Cl, Br, I). Based on the structural, spectral, and energetic changes, we confirm the remarkable roles of charge transfer in these halogen bonding complexes. Although the weak C-H∙∙∙H-C interactions in alkane dimers and graphene sheets are thought to involve dispersion only, we show that this term embeds delicate yet important charge transfer, bond reorganization and polarization interactions.

Anti-Electrostatic Main Group Metal–Metal Bonds That Activate CO2

There has been growing interest in the CO2 capture and reduction by transition-metal-free catalysts. Here we performed a proof-of-concept study using an ab initio valence bond method called the block-localized wave function (BLW) method. The integrated BLW and density function theory (DFT) computations demonstrated that heterobimetallic Ae+/Al(I) (Ae represents alkaline earth metals Mg and Ca) Lewis acid/base combinations without transition metals can facilely capture and activate CO2. There are two remarkable findings in this study. The first concerns the ionic nature of the metal-metal bonds. The experimentally synthesized low valent aluminum compound with a bidentate β-diketiminate (BDI) ligand, or (BDI)Al(I) in brief, is a Lewis base due to the lone pair on the aluminum cation though overall Al(I) is positively charged. Al(I) can form ionic metal-metal bonds with the alkaline earth metals of the positively charged Lewis acids (BDI)Ae+. This type of ionic metal-metal bonds is counterintuitive and antielectrostatic as both metals carry positive charges. The second finding is the CO2 activation mechanism. (BDI)Al(I) can effectively bind and activate CO2 by transferring one electron to CO2, and the resulting complex can be best expressed as [(BDI)Al(I)]+[CO2]-. The participation of (BDI)Ae+ further enhances the capture and activation of CO2 by (BDI)Al(I).

Resonance-Assisted but Antielectrostatic Intramolecular Au···H-O Hydrogen Bonding in Gold(I) Complexes: A Computational Verification.

The peculiar Au···H hydrogen bonding has garnered significant interests, but its existence and nature remain an open question in gold chemistry. In this paper, we established and authenticated the first intramolecular Au···H-O hydrogen bonding in gold(I) complexes. Our computational results based on an ab initio valence bond (VB) method, namely the block-localized wave function (BLW) method, clarified that this Au···H-O hydrogen bonding is a new type of resonance-assisted hydrogen bond (RAHB). In this RAHB, π conjugation in the hydrogen bond donor has the capability to modulate the Au···H-O hydrogen bonding. In contrast to conventional RAHBs, however, the Au···H-O hydrogen bonding is antielectrostatic and is dominated by the charge transfer interaction including cooperative σ electron donation from the d orbital of the metal center to the antibonding orbital of the hydroxyl group and π conjugation from the hydroxyl group to adjacent π deficient or strong π electron withdrawing groups. This novel theoretical perspective not only confirms the existence and reveals the nature of intramolecular Au···H hydrogen bonding but also provides a promising strategy to rationally design strong gold hydrogen bonds.

A Unified Theory for the Blue- and Red-Shifting Phenomena in Hydrogen and Halogen Bonds.

Typical hydrogen and halogen bonds exhibit red-shifts of their vibrational frequencies upon the formation of hydrogen and halogen bonding complexes (denoted as D···Y-A, Y = H and X). The finding of blue-shifts in certain complexes is of significant interest, which has led to numerous studies of the origins of the phenomenon. Because charge transfer mixing (i.e., hyperconjugation in bonding systems) has been regarded as one of the key forces, it would be illuminating to compare the structures and vibrational frequencies in bonding complexes with the charge transfer effect "turned on" and "turned off". Turning off the charge transfer mixing can be achieved by employing the block-localized wave function (BLW) method, which is an ab initio valence bond (VB) method. Further, with the BLW method, the overall stability gained in the formation of a complex can be analyzed in terms of a few physically meaningful terms. Thus, the BLW method provides a unified and physically lucid way to explore the nature of red- and blue-shifting phenomena in both hydrogen and halogen bonding complexes. In this study, a direct correlation between the total stability and the variation of the Y-A bond length is established based on our BLW computations, and the consistent roles of all energy components are clarified. The n(D) → σ*(Y-A) electron transfer stretches the Y-A bond, while the polarization due to the approach of interacting moieties reduces the HOMO-LUMO gap and results in a stronger orbital mixing within the YA monomer. As a consequence, both the charge transfer and polarization stabilize bonding systems with the Y-A bond stretched and red-shift the vibrational frequency of the Y-A bond. Notably, the energy of the frozen wave function is the only energy component which prefers the shrinking of the Y-A bond and thus is responsible for the associated blue-shifting. The total variations of the Y-A bond length and the corresponding stretching vibrational frequency are thus determined by the competition between the frozen-energy term and the sum of polarization and charge transfer energy terms. Because the frozen energy is composed of electrostatic and Pauli exchange interactions and frequency shifting is a long-range phenomenon, we conclude that long-range electrostatic interaction is the driving force behind the frozen energy term.

Nonorthogonal orbital based N-body reduced density matrices and their applications to valence bond theory. I. Hamiltonian matrix elements between internally contracted excited valence bond wave functions

In this series, the n-body reduced density matrix (n-RDM) approach for nonorthogonal orbitals and their applications to ab initio valence bond (VB) methods are presented. As the first paper of this series, Hamiltonian matrix elements between internally contracted VB wave functions are explicitly provided by means of nonorthogonal orbital based RDM approach. To this end, a more generalized Wick's theorem, called enhanced Wick's theorem, is presented both in arithmetical and in graphical forms, by which the deduction of expressions for the matrix elements between internally contracted VB wave functions is dramatically simplified, and the matrix elements are finally expressed in terms of tensor contractions of electronic integrals and n-RDMs of the reference VB self-consistent field wave function. A string-based algorithm is developed for the purpose of evaluating n-RDMs in an efficient way. Using the techniques presented in this paper, one is able to develop new methods and efficient algorithms for nonorthogonal orbital based many-electron theory much easier than by use of the first quantized formulism.

DFVB: A Density-Functional-Based Valence Bond Method.

A new ab initio valence bond method with density-functional-based correlation correction, so-called DFVB, is presented. In the DFVB method, the dynamic correlation energy is taken into account by use of density correlation functional(s), while the static correlation energy is covered by the VBSCF wave function. Owing to incorporation of DFT methods, DFVB provides an economic route to improving the accuracy of ab initio VB theory. Various tests of the method are presented, including the spectroscopic parameters of a series of diatomic molecules, the dipole moments of the NF molecule for different electronic states, and the singlet-triplet gaps of the diradical species, chemical reactions barriers, and total charge-shift resonance energies. These tests show that DFVB is capable of providing high accuracy with relatively low computational cost by comparison to the currently existing post-VBSCF methods.

Can Aromaticity Coexist with Diradical Character? An Ab Initio Valence Bond Study of S2N2 and Related 6π‐Electron Four‐Membered Rings E2N2 and E42+ (E=S, Se, Te)

A series of 6π-electron 4-center species, E(2)N(2) and E(4)(2+) (E=S, Se, Te) is studied by means of ab initio valence bond methods with the aims of settling some controversies on 1) the diradical character of these molecules and 2) the radical sites, E or N, of the preferred diradical structure. It was found that for all molecules, the cumulated weights of the two possible diradical structures are always important and close to 50 %, making these molecules comparable to ozone in terms of diradical character. While the two diradical structures are degenerate in the E(4)(2+) dications, they have on the contrary strongly unequal weights in the E(2)N(2) neutral molecules. In these three molecules, the electronic structure is dominated by one diradical structure, in which the radical sites are the two nitrogen atoms, while the other diradical structure is much less important. The ordering of the various VB structures in terms of their calculated weights is confirmed by the relative energies of individual VB structures. In all cases, the major diradical structure (or both diradical structures when they are degenerate) is (are) the lowest one(s), while the covalent VB structures lie higher in energy. The vertical resonance energies are considerable in S(2)N(2) and S(4)(2+), about 80 % of the estimated value for benzene, and diminish as one goes down the periodic table (S→Se→Te). This confirms the aromatic character of these species, as already demonstrated for S(2)N(2) on the basis of magnetic criteria. This and the high weights and stabilities of one or both diradical structures in all systems indicates that aromaticity and diradical character do not exclude each other, contrary to what is usually claimed. Furthermore, it is shown that the diradical structures find their place in a collective electron flow responsible for the ring currents in the π system of these species.

VB/MM Protein Landscapes: A Study of the SN2 Reaction in Haloalkane Dehalogenase

QM/MM methods are widely used for studies of reaction mechanisms in water and protein environments. Recently, we have developed the VB/MM method in which the QM part is implemented by the ab initio valence bond (VB) method. Here, we report on further improvement of the VB/MM method which makes it possible to use the method for reactivity studies in systems where the QM and MM parts are connected by covalent bonds followed by first ab initio VB study of reactivity in proteins. We implemented a simple link atom scheme to treat the boundary interactions. We tested the performance of the link atom treatment in combination with the VB/MM method on an S(N)2 reaction and found it to be sufficiently accurate. We then used the VB/MM method to study the S(N)2 reaction in haloalkane dehalogenase (DhlA). We show that the predicted reaction barrier heights are in good agreement with estimated experimental values, thereby validating the method. Finally, we analyze the reaction energetics in terms of contributions of the VB configurations and conclude that such analysis is instrumental in pinpointing the essential features of the catalytic mechanism.

The Physical Origin of Saytzeff’s Rule

Hyperconjugation, hybridization, or what? The hyperconjugative effects in primary, secondary, and tertiary alkenes were estimated using ab initio valence bond methods to trace the origin of the empirical Saytzeff rule, which states that the formation of the more substituted alkene is preferred. Hyperconjugation between the π bond and the π-donating substituents governs Saytzeff's rule, whereas all other factors support an anti-Saytzeff pathway.

New problems for ab-initio valence bond theory

The ab-initio valence bond method previously developed in our laboratory proved to be particularly useful in the description of electronic structure of molecules and the evaluation of ionization potentials. More recently, the photoelectron spectrum of pyridine has been described by the same method allowing for the assignment of the n+ and π+ bands. From these studies a variational valence bond method of calculating intermolecular forces stemmed, that was applied to the He-He and He-Li systems. Its main feature is the use of a nonorthogonal basis set in order to avoid over-extension basis error. Another application is the theoretical study of the formation of acetylene from two CH fragments which revealed a sudden change in spin coupling in the approach of the two fragments. A more elaborate procedure to obtain a basis set to be used in the description of excited states has been developed and successfully applied to the LiH molecule.

Topology of Electron Charge Density for Chemical Bonds from Valence Bond Theory: A Probe of Bonding Types

To characterize the nature of bonding we derive the topological properties of the electron charge density of a variety of bonds based on ab initio valence bond methods. The electron density and its associated Laplacian are partitioned into covalent, ionic, and resonance components in the valence bond spirit. The analysis provides a density-based signature of bonding types and reveals, along with the classical covalent and ionic bonds, the existence of two-electron bonds in which most of the bonding arises from the covalent-ionic resonance energy, so-called charge-shift bonds. As expected, the covalent component of the Laplacian at the bond critical point is found to be largely negative for classical covalent bonds. In contrast, for charge-shift bonds, the covalent part of the Laplacian is small or positive, in agreement with the weakly attractive or repulsive character of the covalent interaction in these bonds. On the other hand, the resonance component of the Laplacian is always negative or nearly zero, and it increases in absolute value with the charge-shift character of the bond, in agreement with the decrease of kinetic energy associated with covalent-ionic mixing. A new interpretation of the topology of the total density at the bond critical point is proposed to characterize covalent, ionic, and charge-shift bonding from the density point of view.

Covalent Excited States of Polyenes C2nH2n+2 (n = 2-8) and Polyenyl Radicals C2n-1H2n+1 (n = 2-8): An Ab Initio Valence Bond Study.

The ab initio valence bond (VB) methods, VBSCF and VBCI, are applied to the ground states and the covalent excited states of polyenes C2nH2n+2 (n = 2-8) and polyenyl radicals C2n-1H2n+1 (n = 2-8). The excitation energy gap was computed at the ab initio VB level, which is in good agreement with the semiempirical VB method, VBDFT(s), and the experimental values as well as with the molecular orbital theory based methods, CASPT3 and MRCI. The ab initio VB wave functions of systems are also in very good agreement with those of the VBDFT(s) method, even though the former is based on the ab initio VB scheme while the latter is a semiempirical Hückel type method, in which no orbital optimization procedure is performed. The computational results show that the ab initio VB method is capable now of providing numerical accuracy not only for bond forming and breaking processes, as shown in the past, but also for excitation energies, as shown here. In addition, the computational results validate the efficiency of the VBDFT(s) method, which is a simple VB model with less computational effort but which provides intuitive insights into the excited states of conjugated molecules.

Block-Localized Wavefunction (BLW) Method at the Density Functional Theory (DFT) Level

The block-localized wavefunction (BLW) approach is an ab initio valence bond (VB) method incorporating the efficiency of molecular orbital (MO) theory. It can generate the wavefunction for a resonance structure or diabatic state self-consistently by partitioning the overall electrons and primitive orbitals into several subgroups and expanding each block-localized molecular orbital in only one subspace. Although block-localized molecular orbitals in the same subspace are constrained to be orthogonal (a feature of MO theory), orbitals between different subspaces are generally nonorthogonal (a feature of VB theory). The BLW method is particularly useful in the quantification of the electron delocalization (resonance) effect within a molecule and the charge-transfer effect between molecules. In this paper, we extend the BLW method to the density functional theory (DFT) level and implement the BLW-DFT method to the quantum mechanical software GAMESS. Test applications to the pi conjugation in the planar allyl radical and ions with the basis sets of 6-31G(d), 6-31+G(d), 6-311+G(d,p), and cc-pVTZ show that the basis set dependency is insignificant. In addition, the BLW-DFT method can also be used to elucidate the nature of intermolecular interactions. Examples of pi-cation interactions and solute-solvent interactions will be presented and discussed. By expressing each diabatic state with one BLW, the BLW method can be further used to study chemical reactions and electron-transfer processes whose potential energy surfaces are typically described by two or more diabatic states.

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).

Classical and Distonic Radical Cations: A Valence Bond Approach

The conventional radical cations arising from the ionization of CH(3)CH(2)X (X=F, OH, NH(2), Cl, SH, PH(2)), and their distonic isomers, CH(2)CH(2)XH(.+), were studied by means of standard Møller-Plesset and G2 methods, and by an ab initio valence bond method. Among the conventional structures, two distinct states are considered. In the so-called c' states, the unpaired electron is in an orbital that lies in the plane of the heavy atoms, while the c'' states have their unpaired electron in an orbital lying out of the plane. It is shown that c' states are, as a rule, more stable than the c'' states, by up to approximately 20 kJ mol(-1) depending on the nature of X, owing to a stabilizing interplay of resonating structures. While the geometries of the c'' states are rather similar to those of the neutral molecules, some of the c' states display very different geometries, characterized by elongated C--C bonds, particularly when X=F or, to a lesser extent, when X=OH or Cl. These peculiar geometric features are rationalized by the valence bond analysis, which reveals that the C--C bond in these species is better viewed as a two-center, one-electron bond. The distonic radical cations are generally more stable than the conventional ones (by 20-100 kJ mol(-1)), except for the less electronegative X groups of the series, namely X=SH and PH(2). In these two cases, together with X=NH(2), the radical cation displays a classical distonic structure, as regards the geometry and electronic state. On the other hand, considerable C--X elongation is found for X=F or Cl. In these last cases, the valence bond analysis shows that the radical cation is better viewed as an ion-molecule complex between an ionized ethylene and a neutral HX molecule. The electronic structure of the distonic radical cation with X=OH lies between the two previous limiting descriptions.

A survey of recent developments in ab initio valence bond theory

Starting from the 1980s and onwards, Valence Bond theory has been enjoying renaissance that is characterized by the development of a growing number of ab initio methods, and by many applications to chemical reactivity and to the central paradigms of chemistry. Owing the increase of computational power of modern computers and to significant advances in the methodology, valence bond theory begins to offer a sound and attractive alternative to Molecular Orbital theory. This review aims at summarizing the most important developments of ab initio valence bond methods during the last two or three decades, and is primarily devoted to a description of what the various methods can actually achieve within their specific scopes and limitations. Key available softwares are surveyed.

Origins of Rotational Barriers in Hydrogen Peroxide and Hydrazine.

Compared with their isoelectronic system ethane, both hydrogen peroxide and hydrazine exhibit a double well torsional energy curve where skew conformers are favored over trans conformers and cis conformers are energy-maximum states. Clearly, the involvement of the lone oxygen and nitrogen pairs, or more specifically, the enhanced stabilizing n→σ* negative hyperconjugation effect and destabilizing repulsion among lone pairs, complicates the conformational analysis. In this work, the modern ab initio valence bond (VB) method is employed to quantitatively investigate the torsional energy curves of hydrogen peroxide and hydrazine in terms of hyperconjugative stabilization, steric repulsion, and structural and electronic relaxations. It is found that if the hyperconjugation effect is completely quenched, the trans conformers will be favored, while the cis conformers are the only transition state pertaining to the torsional motion in the potential energy surfaces of H2O2 and N2H4. Although usually the steric effect includes the contributions from the electronic and geometric changes, our energy decomposition analysis shows that even the steric effect favors the skew conformers, while the electronic and geometric changes stabilize the trans conformers. Thus, we conclude that both the hyperconjugative and steric interactions lower the energy of skew conformers and eventually form low barriers from skew to trans conformers and high barriers from skew to cis conformers in both H2O2 and N2H4. Comparison between the VB and the natural bond orbital (NBO) results show similarities and discrepancies between the two methods.

Valence bond calculations of hydrogen transfer reactions: a general predictive pattern derived from theory.

Hydrogen abstraction reactions of the type X(*) + H-H' --> X-H + H'(*) (X = F, Cl, Br, I) are studied by ab initio valence bond methods and the VB state correlation diagram (VBSCD) model. The reaction barriers and VB parameters of the VBSCD are computed by using the breathing orbital valence bond and valence bond configuration interaction methods. The combination of the VBSCD model and semiempirical VB theory leads to analytical expressions for the barriers and other VB quantities that match the ab initio VB calculations fairly well. The barriers are influenced by the endo- or exothermicity of the reaction, but the fundamental factor of the barrier is the average singlet-triplet gap of the bonds that are broken or formed in the reactions. Some further approximations lead to a simple formula that expresses the barrier for nonidentity and identity hydrogen abstraction reactions as a function of the bond strengths of reactants and products. The semiempirical expressions are shown to be useful not only for the model reactions that are studied in this work, but also for other nonidentity and identity hydrogen abstraction reactions that have been studied in previous articles.

Charge Transfer in the Electron Donor—Acceptor Complex BH3NH3

AbstractFor Abstract see ChemInform Abstract in Full Text.

The magnitude of hyperconjugation in ethane: a perspective from ab initio valence bond theory.

Steric effect dominates: Ab initio valence bond and block-localized wavefunction methods are used to estimate the contributions of hyperconjugation and steric effects to the ethane rotation barrier. The results show that hyperconjugation stabilizes the staggered conformer by about 4 kJ mol−1 relative to the eclipsed form (see picture) and steric hindrance is the major driving force behind the favoring of the staggered conformation in ethane.