Ab Initio Valence Bond Theory Research Articles

Planar Four-Membered Diboron Actinide Compound with Double Möbius Aromaticity.

The Möbius rule predicts that a planar four-membered metallacycle can be aromatic with four mobile electrons, but such a simple ring has escaped recognition because it usually favors Hückel anti-aromaticity. Here, we report that a quasi-square four-membered actinide compound (Pa2B2) is doubly Möbius aromatic. Chemical bonding analyses reveal that this diboron protactinium molecule has four delocalized π electrons in addition to four delocalized σ electrons, satisfying the 4n Möbius rule for both σ and π components. Energetically, the block-localized wavefunction method, which is the simplest variant of ab initio valence bond theory, shows that the delocalization energy for the π and σ electrons reaches up to 65.0 and 72.3 kcal/mol, respectively, while the extra cyclic resonance energy (ECRE) amounts to 45 kcal/mol. The large positive ECRE values strongly confirm the unprecedented double Möbius aromaticity in Pa2B2. We anticipate that this new type of aromatic molecule can enrich the concept of Möbius aromaticity and open a new avenue for actinide compounds.

Metal-Ligand Bonds in Rare Earth Metal-Biphenyl Complexes.

A series of theoretical methods, including density functional theory, multiconfiguration molecular orbital theory, and ab initio valence bond theory, are devoted to understanding the metal-ligand bonds in M-BP (BP = biphenyl; M = Sc, Y, or La) complexes. Different from most transition metal-BP complexes, the most stable metal-biphenyl conformers are not half-sandwich but clamshell. Energy decomposition analysis results reveal that the M-BP bonds in the clamshell conformers possess extra-large orbital relaxation. According to the wave function analysis, 2-fold donations and 2-fold back-donations exist in the clamshell M-BP bonds. The back-donations from M to BP are quite strong, while donations from BP to M are quite weak. Our work improves our understanding of the metal-ligand bonds, which can be considered as the "reversed" Dewar-Chatt-Duncanson model.

The strength and selectivity of perfluorinated nano-hoops and buckybowls for anion binding and the nature of anion-π interactions.

Perfluorinated cycloparaphenylenes (F-[n]CPP, n= 5-8), boron nitride nanohoop (F-[5]BNNH), and buckybowls (F-BBs) were proposed as anion receptors via anion-π interactions with halide anions (Cl- , Br- and I- ), and remarkable binding strengths up to -294.8kJ/mol were computationally verified. The energy decomposition approach based on the block-localized wavefunction method, which combines the computational efficiency of molecular orbital theory and the chemical intuition of ab initio valence bond theory, was applied to the above anion-π complexes, in order to elucidate the nature and selectivity of these interactions. The overall attraction is mainly governed by the frozen energy component, in which the electrostatic interaction is included. Remarkable binding strengths with F-[n]CPPs can be attributed to the accumulated anion-π interactions between the anion and each conjugated ring on the hoop, while for F-BBs, additional stability results from the curved frameworks, which distribute electron densities unequally on π-faces. Interestingly, the strongest host was proved to be the F-[5]BNNH, which exhibits the most significant anisotropy of the electrostatic potential surface due to the difference in the electronegativities of nitrogen and boron. The selectivity of each host for anions was explored and the importance of the often-overlooked Pauli exchange repulsion was illustrated. Chloride anion turns out to be the most favorable anion for all receptors, due to the smallest ionic radius and the weakest destabilizing Pauli exchange repulsion.

Explicit construction of diabatic state and its application to the direct evaluation of electronic coupling.

A valence bond (VB) block-diagonalization approach, named VBBDA, is proposed to construct the charge-localized diabatic state explicitly within the framework of ab initio VB theory. Since the VB structure built upon the localized orbitals represents the charge localized character of the diabatic state faithfully, we are able to obtain accurate electronic coupling between diabatic states by using a very compact VB wave function. Moreover, the potential energy curves of the diabatic states and hence the crossing points of them can be accurately evaluated. The pilot applications showed that the electronic couplings computed by the VB method are consistent with the complete active space self-consistent field method and may even be close to the results of other high-level ab initio methods such as full configuration interaction and multireference configuration interaction. In addition, the computed electronic couplings show the expected exponential attenuation for the donor-acceptor systems as the distance increases. Moreover, VBBDA has the capability for handling complicated systems based on either two-state or multi-state treatment. Finally, because of the outstanding performance of the Xiamen Valence Bond software package, which is an ab initio VB program, VBBDA is capable for systems consisting more than 1000 basis functions.

Brønsted acidity of protic ionic liquids: a modern ab initio valence bond theory perspective.

Room temperature ionic liquids (ILs), especially protic ionic liquids (PILs), are used in many areas of the chemical sciences. Ionicity, the extent of proton transfer, is a key parameter which determines many physicochemical properties and in turn the suitability of PILs for various applications. The spectrum of computational chemistry techniques applied to investigate ionic liquids includes classical molecular dynamics, Monte Carlo simulations, ab initio molecular dynamics, Density Functional Theory (DFT), CCSD(t) etc. At the other end of the spectrum is another computational approach: modern ab initio Valence Bond Theory (VBT). VBT differs from molecular orbital theory based methods in the expression of the molecular wave function. The molecular wave function in the valence bond ansatz is expressed as a linear combination of valence bond structures. These structures include covalent and ionic structures explicitly. Modern ab initio valence bond theory calculations of representative primary and tertiary ammonium protic ionic liquids indicate that modern ab initio valence bond theory can be employed to assess the acidity and ionicity of protic ionic liquids a priori.

Modern ab initio valence bond theory calculations reveal charge shift bonding in protic ionic liquids.

The nature of bonding interactions between the cation and the anion of an ionic liquid is at the heart of understanding ionic liquid properties. A particularly interesting case is a special class of ionic liquids known as protic ionic liquids. The extent of proton transfer in protic ionic liquids has been observed to vary according to the interacting species. Back proton transfer renders protic ionic liquids volatile and to be considered as inferior ionic liquids. We try to address this issue by employing modern ab initio valence bond theory calculations. The results indicate that the bonding in the cation and the anion of a prototypical ionic liquid, ethylammonium nitrate, is fundamentally different. It is neither characteristic of covalent/polar covalent bonding nor ionic bonding but rather charge shift bonding as a resonance hybrid of two competing ionic molecular electronic structure configurations. An investigation of other analogous protic ionic liquids reveals that this charge shift bonding seems to be a typical characteristic of protic ionic liquids while the ionic solid analogue compound ammonium nitrate has less charge shift bonding character as compared to protic ionic liquids. Further the extent of charge shift bonding character has been found to be congruent with the trends in many physicochemical properties such as melting point, conductivity, viscosity, and ionicity of the studied ionic liquids indicating that percentage charge shift character may serve as a key descriptor for large scale computational screening of ionic liquids with desired properties.

The essential role of charge-shift bonding in hypervalent prototype XeF2

Hypervalency in XeF₂ and isoelectronic complexes is generally understood in terms of the Rundle-Pimentel model (which invokes a three-centre/four-electron molecular system) or its valence bond version as proposed by Coulson, which replaced the old expanded octet model of Pauling. However, the Rundle-Pimentel model is not always successful in describing such complexes and has been shown to be oversimplified. Here using ab initio valence bond theory coupled to quantum Monte Carlo methods, we show that the Rundle-Pimentel model is insufficient by itself in accounting for the great stability of XeF₂, and that charge-shift bonding, wherein the large covalent-ionic interaction energy has the dominant role, is a major stabilizing factor. The energetic contribution of the old expanded octet model is also quantified and shown to be marginal. Generalizing to isoelectronic systems such as ClF₃, SF₄, PCl₅ and others, it is suggested that charge-shift bonding is necessary, in association with the Rundle-Pimentel model, for hypervalent analogues of XeF₂ to be strongly bonded.

The generalized block-localized wavefunction method: A case study on the conformational preference and C–O rotational barrier of formic acid

A Lewis structure corresponding to the most stable electron-localized state is often used as a reference for the measure of electron delocalization effect in the valence bond (VB) theory. As the simplest variant of ab initio VB theory, the generalized block-localized wavefunction (BLW) method defines the wavefunction for an electron-localized state with block-localized orbitals without the orthogonalization constraint on different blocks. The validity of the method can be critically examined with experimental evidences. Here the BLW method has been applied to the investigation of the roles of both the π conjugation and σ hyperconjugation effects in the conformational preference of formic acid for the trans (Z) conformer over the cis (E) conformer. On one hand, our computations showed that the deactivation of the π conjugation or σ hyperconjugation has little impact on the Z-E energy gap, thus neither is decisive and instead the local dipole-dipole electrostatic interaction between the carbonyl and hydroxyl groups is the key factor determining the Z-E energy gap. On the other hand, the present study supported the conventional view that π conjugation is largely responsible for the C-O rotation barrier in formic acid, though the existence of hyperconjugative interactions in the perpendicular structure lowers the barrier considerably.

ChemInform Abstract: Rotational Barriers in Alkanes

AbstractReview: 56 refs.

Rotational barriers in alkanes

AbstractRotational barriers in alkanes play a fundamental role in the stereochemistry and dynamics of alkanes and others such as proteins. Yet, the proper understanding of their origin which is central to chemical theory remains controversial. Currently, there are two major competing models to interpret the barriers, one is the steric repulsion model and the other is hyperconjugation model. No consensus has been reached. It is thus important to critically examine the quantum mechanical approaches producing conflicting data which lead to these models, as various approximations must be introduced to derive either the steric or hyperconjugative interaction energies in these approaches. The hyperconjugation model is largely based on the popular natural bond orbital (NBO) analysis which can estimate individual interactions between occupied bond orbitals and vicinal unoccupied antibond orbitals. But the concern is that these localized bond orbitals are projected out from a delocalized wavefunction and thus nonoptimal. Alternatively, recent studies with other methods notably the ab initio valence bond theory where localized orbitals are self‐consistently optimized reinstate the conventional steric repulsion model, although the NBO method correctly predicts that there is stronger hyperconjugative interaction in staggered structures than in eclipsed structures. After all, it is the steric effect rather than the hyperconjugation effect that plays a dominating role in rotational barriers in alkanes. © 2011 John Wiley & Sons, Ltd. WIREs Comput Mol Sci 2011 1 164‐171 DOI: 10.1002/wcms.22This article is categorized under: Structure and Mechanism > Computational Materials Science

How to properly compute the resonance energy within the ab initio valence bond theory: a response to the ZHJVL paper

Valence bond (VB) theory describes a conjugated system by a set of electron-localized Lewis resonance structures. VB assumes that the magnitude of the intramolecular electron delocalization can be measured in terms of a resonance energy (RE), taken to be the energy difference between the real conjugated system (delocalized) and the corresponding most stable virtual resonance structure (localized). Proper RE estimates within VB theory require both delocalized and localized states to be defined at the same theoretical level, and the definition of the localized state to closely correspond to the intuitive picture of the corresponding VB structure. In contrast, the VB-delocal and VB-local computational approaches adopted by Zielinski, et al. [preceding paper in this issue] used definitions for either the delocalized or the localized states which, in our view, depart from the intuitive chemical picture. Consequently, their RE estimates are much lower than seemingly appropriate experimental evaluations with which they strongly disagree. Very large basis sets approaching completeness blur the boundaries among resonance structures and result in “basis set artifact” problems within any variant of VB theory. However, block-localized wavefunction (BLW) computations with mid-size basis sets not only exhibit insignificant variations with theoretical levels, but the resulting RE estimates also are justified by comparisons with those employing experimental data and MO computations. We stress that RE differs from the aromatic stabilization energy (ASE). The RE measures the total stabilization of an aromatic system, whereas ASE measures only the part of the RE that exceeds that of appropriate conjugated (but non-aromatic) reference molecules.

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.

The Resonance Energy of Benzene: A Revisit

Zielinski and van Lenthe recently extended the block-localized wave function (BLW) method by introducing the resonating BLW (RBLW) method and performed test calculations on hexagonal H(6) and benzene [J. Phys. Chem. A 2008, 112, 13197]. However, the Pauling's resonance energies from their RBLW and ab initio valence bond (VB) calculations were greatly underestimated largely due to the imperfect use of either one-electron orbitals (method = delocal) or resonance structures (method = local). Whereas it has been well recognized that electronic resonance within a molecular system plays a stabilizing role, there are many indirect experimental evidences available to evaluate the resonance energy and, thus, to justify computational results. Here we used the BLW method, which can be regarded as the simplest variant of modern ab initio VB theory, to re-evaluate the resonance energy of benzene at the B3LYP level, following the original definition by Pauling and Wheland, who obtained the resonance energy "by subtracting the actual energy of the molecule in question from that of the most stable contributing structure". The computed vertical resonance energy (or quantum mechanical resonance energy) in benzene is 88.8, 92.2, or 87.9 kcal/mol with the basis sets of 6-31G(d), 6-311+G(d,p), or cc-pVTZ, respectively, while the adiabatic resonance energy (or theoretical resonance energy) is 61.4, 63.2, or 62.4 kcal/mol, exhibiting insignificant basis set dependency for moderate basis sets. In line with predictions, the geometry optimization of the elusive cyclohexatriene (i.e., the Kekule structure) with the BLW method also resulted in carbon-carbon bond lengths (e.g., 1.322 and 1.523 A with the cc-pVTZ basis set) comparable to those in ethylene or ethane.

On the construction of diabatic and adiabatic potential energy surfaces based on ab initio valence bond theory.

A theoretical model is presented for deriving effective diabatic states based on ab initio valence bond self-consistent field (VBSCF) theory by reducing the multiconfigurational VB Hamiltonian into an effective two-state model. We describe two computational approaches for the optimization of the effective diabatic configurations, resulting in two ways of interpreting such effective diabatic states. In the variational diabatic configuration (VDC) method, the energies of the diabatic states are variationally minimized. In the consistent diabatic configuration (CDC) method, both the configuration coefficients and orbital coefficients are simultaneously optimized to minimize the adiabatic ground-state energy in VBSCF calculations. In addition, we describe a mixed molecular orbital and valence bond (MOVB) approach to construct the CDC diabatic and adiabatic states for a chemical reaction. Note that the VDC-MOVB method has been described previously. Employing the symmetric S(N)2 reaction between NH(3) and CH(3)NH(3)(+) as a test system, we found that the results from ab initio VBSCF and from ab initio MOVB calculations using the same basis set are in good agreement, suggesting that the computationally efficient MOVB method is a reasonable model for VB simulations of condensed phase reactions. The results indicate that CDC and VDC diabatic states converge, respectively, to covalent and ionic states as the molecular geometries are distorted from the minimum of the respective diabatic state along the reaction coordinate. Furthermore, the resonance energy that stabilizes the energy of crossing between the two diabatic states, resulting in the transition state of the adiabatic ground-state reaction, has a strong dependence on the overlap integral between the two diabatic states and is a function of both the exchange integral and the total diabatic ground-state energy.

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.

Steric Strain versus Hyperconjugative Stabilization in Ethane Congeners

Rotation barriers in the group IVB ethane congeners H(3)X-YH(3) (X, Y = C, Si, Ge, Sn, Pb) have been systematically studied and deciphered using the ab initio valence bond theory in terms of the steric strain and hyperconjugation effect. Our results show that in all cases the rotation barriers are dominated by the steric repulsion whereas the hyperconjugative interaction between the X-H bond orbitals and the vicinal Y-H antibond orbitals (and vice versa) plays a secondary role, although indeed the hyperconjugation effect favors staggered structures. By the independent estimations of the hyperconjugative and steric interactions in the process of rotations, we found that the structural effect which mainly refers to the central X-Y bond relaxation makes a small contribution to the rotational barriers. Therefore, we conclude that both the rigid and fully relaxed rotations in the group IVB ethane congeners H(3)X-YH(3) observe the same mechanism which is governed by the conventional steric repulsion.

II conjugation in the butadiene

AbstractThe π electronic delocalization in trans‐C4H6 and cis‐C4H6 has been investigated in the frame of ab initio valence bond theory with 6–31G basis set. The result shows that the Csp2‐Csp2 single bond length (1.506 Å) is only about 0.024 Å shorter than the Csp3‐Csp3 bond, thus the central bond length shortening would be mainly due to π conjugation. The theoretical resonance energies of the trans‐C4H6 and cis‐C4H6 are 8.48 and 7.44 kcal/mol, respectively.