Valence Bond Approach Research Articles

Polarizable Solute in Polarizable and Flexible Solvents: Simulation Study of Electron Transfer Reaction Systems

A polarizable solute model, based on the empirical valence bond approach, is developed and applied to electron transfer (ET) reactions in polarizable and flexible water solvents. The polarization effect is investigated in comparison with a nonpolarizable solute and solvent model. With free energy curves constructed by a molecular dynamics simulation, the activation energy barrier and the reorganization energy related to ET processes are investigated. The present simulation results show that the activation energy barrier becomes larger in the polarizable model than in the nonpolarizable model and that this makes the ET rate slower than that with the nonpolarizable model. It is shown that the effect of the electronic energy difference of solute molecule on free energy profiles is remarkable and that, corresponding to this effect, the reorganization energy is significantly modified. These results indicate that the process of solvent polarization by the polarized solute to enhance the solute-solvent interaction is a key factor and that treating the polarization of both solute and solvent at the same time is essential. Also, the polarization effect on the diffusive motion of the solute molecule in the polarization solvent is studied. The polarized solute molecule shows slower diffusive motion compared with that in the nonpolarizable model.

Nucleophilic Substitution Reactions at Liquid/Liquid Interfaces: Molecular Dynamics Simulation of a Model SN1 Dissociation Reaction at the Water/Carbon Tetrachloride Interface

The ionic dissociation step of the nucleophilic substitution reaction t-BuCl --> t-Bu(+) + Cl(-) is studied at the water/carbon tetrachloride interface using molecular dynamics computer simulations. The empirical valence bond approach is used to couple two diabatic states, covalent and ionic, in the electronically adiabatic limit. The umbrella sampling technique is used to calculate the potential of mean force along the reaction coordinate (defined as the t-Bu to Cl distance) at several interface regions of varying distances from the Gibbs dividing surface. We find a significant increase of the ionic dissociation barrier height and of the reaction free energy at the interface relative to bulk water. This is shown to be due to the reduced polarity of the interface which causes a destabilization of the pure ionic state. However, deformation to the neat interface structure in the form of water protrusions into the organic phase may provide partial stabilization of the ionic species. The importance of these structural effects is examined by repeating the calculations with an artificially smooth interface. The destabilization of the ionic state at the interface also manifests itself with a rapid (picosecond time scale) recombination dynamics of the ions to form the parent molecule followed by a slow vibrational relaxation.

A molecular-dynamics study of a model SN1 dissociation reaction at the water liquid/vapor interface

The thermodynamics and dynamics of a model S(N)1 reaction: t-BuCl --> t-Bu+ + Cl- is studied at the water liquid/vapor interface using molecular-dynamics computer simulations. The empirical valence bond approach is used to couple two diabatic states, covalent and ionic, in the electronically adiabatic limit. Umbrella sampling calculations are used to calculate the potential of mean force along the reaction coordinate (defined as the t-Bu to Cl distance) in bulk water and in several locations at the interface. We find a significant increase of the dissociation barrier height and of the reaction free energy at the interface relative to the bulk. This is shown to be due to the reduced polarity of the interface. Reactive flux correlation function calculations show significant deviation of the rate constant from the transition-state theory: The transmission coefficients range from 0.49 in the bulk to 0.05 above the Gibbs surface. The low transmission coefficient at the interface despite the lower friction is shown to be due to slow vibrational relaxation.

Correlated geminal wave function for molecules: an efficient resonating valence bond approach.

We show that a simple correlated wave function, obtained by applying a Jastrow correlation term to an antisymmetrized geminal power, based upon singlet pairs between electrons, is particularly suited for describing the electronic structure of molecules, yielding a large amount of the correlation energy. The remarkable feature of this approach is that, in principle, several resonating valence bonds can be dealt simultaneously with a single determinant, at a computational cost growing with the number of electrons similar to more conventional methods, such as Hartree-Fock or density functional theory. Moreover we describe an extension of the stochastic reconfiguration method, which was recently introduced for the energy minimization of simple atomic wave functions. Within this extension the atomic positions can be considered as further variational parameters, which can be optimized together with the remaining ones. The method is applied to several molecules from Li(2) to benzene by obtaining total energies, bond lengths and binding energies comparable with much more demanding multiconfiguration schemes.

Vibrationally resolved charge transfer ofO3+with molecular hydrogen

Charge transfer due to collisions of ground state ${\mathrm{O}}^{3+}(2{s}^{2}2p{\phantom{\rule{0.2em}{0ex}}}^{2}{P}^{o})$ ions with molecular hydrogen are investigated using the quantum-mechanical molecular-orbital (QMO) coupled-channel method. The QMO calculations utilize $ab$ initio adiabatic potentials and nonadiabatic radial coupling matrix elements obtained with the spin-coupled valence-bond approach for a representative range of orientation angles and diatom internuclear separations. Vibrationally resolved cross sections for nondissociative single electron capture are obtained for energies between 0.1 eV∕u and 10 keV∕u for ${\mathrm{H}}_{2}$ in its ground vibrational level using the infinite order sudden approximation (IOSA). Two further approximations are considered in which the electronic radial couplings are assumed to be independent of the diatom stretching. In the first case, vibrational motion is taken into account by multiplying the electronic radial couplings by Franck-Condon (FC) ionization factors while in the second, vibrational motion is completely neglected. We refer to these two approaches as the vibrational sudden approximation (VSA) and the electronic approximation (EA), respectively. In the latter, the resulting cross sections for electronic transitions are multiplied by FC factors to obtain relative vibrationally resolved cross sections which are independent of the collision energy (the centroid approximation). Comparison with existing experimental data for total and electronic state-selective cross sections shows best agreement with IOSA and VSA, but discrepancies for EA. The triplet-singlet electronic cross section ratio reveals a departure at low collision energies from the statistical value.

Use of an electron equivalent relationship between bond length and bond order to study chemical bonding. Part II. A study of bond orders, bond lengths and aromaticity in polycyclic aromatic hydrocarbons

Using the recently introduced concept of electron equivalent bond order, the characteristic bond orders of benzenoid hydrocarbons were studied based on experimental data. Fragmentation schemes can be used successfully to interpret the results and provide a very simple, consistent and useful valence bond approach for benzenoid hydrocarbons. The characteristic bond orders determined from experimental bond lengths can only assume eight discrete values in a relatively narrow range between 1 2 3 and 1 1 4 and primarily depend on the number of adjacent carbon–carbon bonds in the structure. The bond orders can also be used to define a quantitative scale of aromaticity for bonds, rings or entire molecules. A method, based on the optimization of quantified tendency toward maximum aromaticity and minimum octet-rule violation simultaneously, is also presented for the prediction of bond orders (and therefore bond lengths) of benzenoid hydrocarbons without any previous experimental information.

Scattering, Trapping, and Ionization of HCl at the Surface of Liquid Glycerol

A model for the interactions between HCl and liquid glycerol, based on the Empirical Valence Bond (EVB) approach, is developed and used to investigate by molecular dynamics computer simulations the early events following the collision of an HCl molecule with the glycerol surface. The calculated trapping probability at 2.4 and 22 kcal/mol collision energies and the fractional energy loss of scattered HCl molecules agree well with experiments. The potential of mean force for HCl in the bulk and at the glycerol surface exhibits a low barrier to the formation of the contact ion pair, suggesting the possibility of proton transfer at the interface. Trapped HCl molecules undergo rapid relaxation and solvation and begin to form contact ion pairs on the picosecond time scale, which is consistent with the low barrier to the formation of the ion pair derived from the equilibrium potential of mean force calculations.

Converting conformational changes to electrostatic energy in molecular motors: The energetics of ATP synthase.

F1-ATPase is the catalytic component of the ATP synthase molecular machine responsible for most of the uphill synthesis of ATP in living systems. The enormous advances in biochemical and structural studies of this machine provide an opportunity for detailed understanding of the nature of its rotary mechanism. However, further quantitative progress in this direction requires development of reliable ways of translating the observed structural changes to the corresponding energies. This requirement is particularly challenging because we are dealing with a large system that couples major structural changes with a chemical process. The present work provides such a structure-function correlation by using the linear response approximation to describe the rotary mechanism. This approach allows one to evaluate the energy of transitions between different conformational states by considering only the changes in the corresponding electrostatic energies of the ligands. The relevant energetics are also obtained by calculating the linear response approximation-based free energies of transferring the ligands from water to the different sites of F1-ATPase in their different conformational states. We also use the empirical valence bond approach to evaluate the actual free-energy profile for the ATP synthesis in the different conformational states of the system. Integrating the information from the different approaches provides a semiquantitative structure-function correlation for F1-ATPase. It is found that the conformational changes are converted to changes in the electrostatic interaction between the protein and its ligands, which drives the ATP synthesis.

Valence-bond spin-liquid state in two-dimensional frustrated spin-1/2 Heisenberg antiferromagnets.

Fermionic valence-bond approach in terms of SU(4) representation is proposed to describe the J1-J2 frustrated Heisenberg antiferromagnetic (AF) model on a bipartite square lattice. A uniform mean field solution without breaking the translational and rotational symmetries describes a valence-bond spin-liquid state, interpolating the two different AF ordered states in the large J1 and large J2 limits, respectively. This novel spin-liquid state is gapless with the vanishing density of states at the Fermi nodal points. Moreover, a sharp resonance peak in the dynamic structure factor is predicted for momenta q=(0,0) and (pi,pi) in the strongly frustrated limit J(2)/J(1) approximately 1/2, which can be checked by neutron scattering experiments.

A Generalized Unpaired Electron Spin Density Equation and Organic Hyperconjugation Mechanism

A large class of stereochemcial and related interactions in organic chemistry are repulsive and others are attractive, but the relative orientation of two methyl groups and the amount of energy required to twist one relative to the other (the hindered rotation energy barriers), or the alignment of such a group with respect to a conjugated ring to which it is attached (widely attributed to a mechanism called “hyperconjugation”) are estimated to be small in compared with the total energy of the molecule. We used theories of both isotropic and anisotropic proton hyperfine interactions in the π-electron systems developed in the early sixties. They are approximated by the magnetic dipole nteractions between each proton and an electron spin magnetization that is distributed in 2s and 2p Slater atomic orbitals center on carbon atoms. We have extended these theories to the non-planar olefinic cation radicals, which are very important in biochemistry as well as in petroleum catalysis. A three dimensional electron spin density equation has been developed in this paper to handle some Jahn-Teller vibronic molecules. The new electron spin density equation related the observed proton hyperfine splittings to the non-planar structures of the open-chain alkene cation radicals generated by radiolysis and various chemical oxidation methods. The spin densities and the conformational calculations based on valence bond theory and symmetry principles are compared with some more elaborated molecular orbital calculations in the literature. The localized valence bond approaches are better in accord with our experimental results. The anomalous line-width effect of the four methyl groups observed in the 2,3-dimethyl-2-butene cation radicals also confirmed the positive sign of the electron-proton hyperfine constant of hyper-conjugation mechanism. A methyl substituent attached to a conjugated molecule often behaves as if it formed part of the region of conjugation; the charge appears to flow from the methyl group into the π electron system and it may also give rise to an appreciable dipole moment. Methylation also gives rise to an appreciable dipole moment, and the resultant red shift of electronic absorption bands is of some importance in the design of dye molecules.

Ab initiostudy of charge transfer inB2+low-energy collisions with atomic hydrogen

Charge transfer processes due to collisions of ground state B{sup 2+}(2s {sup 2}S) ions with atomic hydrogen are investigated using the quantum-mechanical molecular-orbital close-coupling (MOCC) method. The MOCC calculations utilize ab initio adiabatic potentials and nonadiabatic radial and rotational coupling matrix elements obtained with the spin-coupled valence-bond approach. Total and state-selective cross sections and rate coefficients are presented. Comparison with the existing experiments shows our results to be in good agreement. When E 400 eV/u, inclusion of rotational coupling increases the total cross section by 50%-80%, improving the agreement between the current calculations and experiments. For state-selective cross sections, rotational coupling induces mixing between different symmetries; however, its effect, especially at low collision energies, is not as important as had been suggested in previous work.

Autonomy, explanation, and theoretical values: physicists and chemists on molecular quantum mechanics.

The emergence of quantum chemistry in the early twentieth century was an international as well as an interdisciplinary affair, involving dialogue between physicists and chemists in Germany, the United States, and Britain. Historians of science have recently documented both the causes and effects of this internationalism and interdisciplinarity. Chemists and physicists involved in the development of quantum chemistry in its first few decades tended to argue for opposing views on acceptable standards of explanation in their field, although the debate did not divide along disciplinary lines. The purpose of this paper is to investigate these different positions, through the methodological reflections of John Clarke Slater, Linus Pauling, and Charles Coulson. Slater tended to argue for quantum-mechanical rigor and the application of fundamental principles as the values guiding models of molecular bonding. Although they were on different sides of the debate between the valence-bond and molecular-orbital approaches, Pauling and Coulson both emphasized the recovery of traditional chemical explanations and systematic explanatory power within chemistry.

Model Valence-Bond Studies of Aspects of Electron Conduction along a Linear Chain of Lithium Atoms

Two valence bond mechanisms for electron conduction along a linear chain of six or eight lithium atoms are studied using an ab initio valence bond approach. The initial step is of the type (−)(LiALiB)(LiCLiD)(LiELiF)...(+) → (−)(LiALiB)+(LiCLiD)-(LiELiF)...(+), in which the transferred electron occupies either the 2pσC atomic orbital (Pauling mechanism) or the antibonding σ*CD molecular orbital. An external potential is modeled by use of negative and positive charges located to the left and to the right of the chain of atoms. It is calculated that (−)(LiLi)+(LiLi)-(LiLi)...(+) → (−)(LiLi)(LiLi)+(LiLi)-...(+), which involves electron and positive hole transfer, as well as (−)(LiLi)+(LiLi)-(LiLi)...(+) → (−)(LiLi)+(LiLi)(LiLi)-...(+), with electron transfer only, contribute to the second electron transfer process. Resonance between the valence bond structures associated with the second step helps lower the energy of the second step of either mechanism. The antibonding molecular orbital mechanism is calculat...

Charge transfer ofO3+ions with atomic hydrogen

Charge transfer processes due to collisions of ground state ${\mathrm{O}}^{3+}{(2s}^{2}2p{}^{2}P)$ ions with atomic hydrogen are investigated using the quantum-mechanical molecular-orbital close-coupling (MOCC) method. The MOCC calculations utilize ab initio adiabatic potentials and nonadiabatic radial and rotational coupling matrix elements obtained with the spin-coupled valence-bond approach. Total and state-selective cross sections and rate coefficients are presented. Comparison with existing experimental and theoretical data shows our results to be in better agreement with the measurements than the previous calculations, although problems with some of the state-selective measurements are noted. Our calculations demonstrate that rotational coupling is not important for the total cross section, but for state-selective cross sections, its relevance increases with energy. For the ratios of triplet to singlet cross sections, significant departures from a statistical value are found, generally in harmony with experiment.

A theoretical study of cis–trans isomerization in HONO using an empirical valence bond potential

The empirical valence bond (EVB) approach proposed by Chang and Miller [J. Phys. Chem. 94, 5884 (1990)] for constructing global potential energy surfaces has the potential for treating large molecular systems. In this work, we slightly modify the expression of Chang and Miller by adding a damping function along the reaction coordinate to ensure the proper asymptotic behavior of the potential. We apply the EVB method to describe the cis–trans isomerization in HONO, and compute the isomerization rates in the low-energy tunneling regime by employing the semiclassical method that treats tunneling within classical trajectory calculations.

Three-dimensional reactive surfaces for the LiH2+ system: an analysis of accurate ab initio results

Abstract Calculations for the reactive potential energy surfaces, which are relevant for examining the low-energy channels connected with the LiH 2 + three atom ionic system, are carried out using a multireference valence bond (MRVB) approach. More than 11.000 points have been computed over the grid of the three relevant coordinates (two bond distances and the enclosed angle) and the lowest three electronic states have been followed over the spatial configuration of the above coordinates. Several aspects of the reactive behavior could be gleaned from an analysis of the computed surfaces and various features of the reactive outcomes are extracted from that analysis.

Ab Initio QM/MM Simulation with Proper Sampling: “First Principle” Calculations of the Free Energy of the Autodissociation of Water in Aqueous Solution

Quantum mechanical calculations of activation free energies of chemical reactions in condensed phases present a major challenge for computational chemistry. On one hand, it is important to use high-level ab initio methods to obtain reliable results. On the other hand, it is essential to perform sufficient configurational sampling to obtain meaningful free energies. Although the advance of quantum mechanical/molecular mechanics (QM/MM) approaches has made this problem tractable, it still requires an enormous amount of computer time. The present work advances several strategies that allow one to perform practical ab initio QM/MM calculations of free energy profiles in solutions and proteins. The basic idea is the use of a simple reference potential for the ab initio calculations (e.g., Bentzien; et al. J. Phys. Chem. B 1998, 102, 2293). One version of this approach evaluates the free energy of transfer from the reference potential to the ab initio potential by a single step free energy perturbation (FEP) approach. A new version evaluates this free energy by the linear response approximation (LRA), which involves running trajectories on both the reference and the ab initio potentials. The performance of both approaches is examined by calculating the potential of mean force for the autodissociation reaction of water in solution. It is found that the LRA approach allows one to obtain reasonable results even in cases where the ab initio and reference potentials are significantly different. The present work also explores options for increasing the size of the quantum mechanical region. Here it is shown that the constrained DFT (CDFT) method provides a promising strategy. Finally, the general issue of modeling the autodissociation reaction by quantum mechanical approaches is briefly considered. It is pointed out that the use of the empirical valence bond (EVB) approach in the sampling process should provide a way for evaluating the elusive nonequilibrium solvation effect.

Electron capture in collisions of S4+ with helium

Charge transfer due to collisions of ground-stateS4+(3s2 1S) ions with helium is investigated for energiesbetween 0.1 meV u-1 and 10 MeV u-1. Total and state-selective singleelectron capture (SEC) cross sections and rate coefficients areobtained utilizing the quantum mechanical molecular-orbitalclose-coupling (MOCC), atomic-orbital close-coupling (AOCC),classical trajectory Monte Carlo (CTMC) and continuum distorted wavemethods. The MOCC calculations utilize ab initio adiabaticpotentials and nonadiabatic radial coupling matrix elements obtainedwith the spin-coupled valence-bond approach. Previous data arelimited to a calculation of the total SEC rate coefficient using theLandau-Zener model that is, in comparison to the results presentedhere, three orders of magnitude smaller. The MOCC SEC cross sectionsat low energy reveal a multichannel interference effect. True doublecapture is also investigated with the AOCC and CTMC approaches whileautoionizing double capture and transfer ionization (TI) is exploredwith CTMC. SEC is found to be the dominant process except forE>200 keV u-1 when TI becomes the primary capture channel.Astrophysical implications are briefly discussed.

Searching for the second oxidant in the catalytic cycle of cytochrome P450: a theoretical investigation of the iron(III)-hydroperoxo species and its epoxidation pathways.

Iron(III)-hydroperoxo, [Por(CysS)Fe(III)-OOH](-), a key species in the catalytic cycle of cytochrome P450, was recently identified by EPR/ENDOR spectroscopies (Davydov, R.; Makris, T. M.; Kofman, V.; Werst, D. E.; Sligar, S. G.; Hoffman, B. M. J. Am. Chem. Soc. 2001, 123, 1403-1415). It constitutes the last station of the preparative steps of the enzyme before oxidation of an organic compound and is implicated as the second oxidant capable of olefin epoxidation (Vaz, A. D. N.; McGinnity, D. F.; Coon, M. J. Proc. Natl. Acad. Sci. U.S.A. 1998, 95, 3555-3560), in addition to the penultimate active species, Compound I (Groves, J. T.; Han, Y.-Z. In Cytochrome P450: Structure, Mechanism and Biochemistry, 2nd ed.; Ortiz de Montellano, P. R., Ed.; Plenum Press: New York, 1995; pp 3-48). In response, we present a density functional study of a model species and its ethylene epoxidation pathways. The study characterizes a variety of properties of iron(III)-hydroperoxo, such as the O-O bonding, the Fe-S bonding, Fe-O and Fe-S stretching frequencies, its electron attachment, and ionization energies. Wherever possible these properties are compared with those of Compound I. The proton affinities for protonation on the proximal and distal oxygen atoms of iron(III)-hydroperoxo, and the effect of the thiolate ligand thereof, are determined. In accordance with previous results (Harris, D. L.; Loew, G. H. J. Am. Chem. Soc. 1998, 120, 8941-8948), iron(III)-hydroperoxo is a strong base (as compared with water), and its distal protonation leads to a barrier-free formation of Compound I. The origins of this barrier-free process are discussed using a valence bond approach. It is shown that the presence of the thiolate is essential for this process, in line with the "push effect" deduced by experimentalists (Sono, M.; Roach, M. P.; Coulter, E. D.; Dawson, J. H. Chem. Rev. 1996, 96, 2841-2887). Finally, four epoxidation pathways of iron(III)-hydroxperoxo are located, in which the species transfers oxygen to ethylene either from the proximal or from the distal sites, in both concerted and stepwise manners. The barriers for the four mechanisms are 37-53 kcal/mol, in comparison with 14 kcal/mol for epoxidation by Compound I. It is therefore concluded that iron(III)-hydroperoxo, as such, cannot be a second oxidant, in line with its significant basicity and poor electron-accepting capability. Possible versions of a second oxidant are discussed.

Reactive Behavior of the [LiH2]+ System I. Evaluation of the Lower-lying Electronic Potentials for the Collinear Geometries

The reactive behavior of the [LiH2]+ system is investigated by computing the potential energy surfaces (PES) for the collinear geometries. The three lowest-lying PESs have been obtained using a multireference valence bond approach and subsequently have been fitted with modified Laguerre functions. The results appear to exclude any significant nonadiabatic interaction between the first two electronic states and already suggest differences in the dynamical behavior of the title system when moving on each of these potential energy surfaces. Thus, at least within a collinear approach, a direct reactive dynamics should be expected for the ground-state reaction of LiH++H → Li++H2, while the formation of a temporary complex is suggested to occur for the partners interacting via the electronically excited PES pertaining to LiH+H+ → Li+H2+.