Semiempirical Valence Bond Research Articles

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.

Importance of Polarization in Quantum Mechanics/Molecular Mechanics Descriptions of Electronic Excited States: NaI(H2O)n Photodissociation Dynamics as a Case Study

Sodium iodide has long been a paradigm for ionic and covalent curve crossing and ultrafast nonadiabatic dynamics, and our interest lies in the influence of solvation on this process. The NaI(H2O)n photodissociation dynamics are simulated with the molecular dynamics with quantum transitions method. A quantum mechanics/molecular mechanics (QM/MM) description is adopted for the NaI(H2O)n electronic states, in which a semiempirical valence bond approach is used to describe the NaI electronic structure, and a polarizable optimized potential for cluster simulations model is used to describe solute-solvent and solvent-solvent interactions. In contrast to previous work with a nonpolarizable MM model [Koch et al., J. Phys. Chem. A, 2006, 110, 1438], this approach predicts that the NaI ionic ground- to covalent first-excited-state Franck-Condon energy gaps reach a plateau by cluster size 16, in relatively good agreement with experiment and electronic structure calculations; this allows us to safely extend our previous simulations to larger cluster sizes, i.e., n > 4. The simulations suggest that the disappearance of the two-photon ionization probe signals observed in femtosecond pump-probe experiments of NaI(H2O)n, n >/= 4, is due to the shift of the NaI curve-crossing region toward larger NaI internuclear separations because of solvent stabilization of the NaI ionic state. Further, the latter causes the adiabatic ground and excited states to acquire pure ionic and covalent character, respectively, by cluster 8, resulting in NaI ionic ground-state recombination or dissociation. To make a connection with electron transfer in solution, free energy curves have been generated as a function of a solvent coordinate similar to that of solution theory. Inspection of the free energy curves together with the results of excited-state simulations reveal that the electron-transfer process in clusters is not governed by the collective motion of the solvent molecules, as in solution, but that it rather proceeds along the NaI internuclear separation coordinate, as in the gas phase. In fact, solvation in small clusters mainly influences the nonadiabatic dynamics by modulating the NaI internuclear separation at which the ionic and covalent curve-crossing region occurs. Furthermore, the simulations show that electron transfer does not occur in the inverted regime, as predicted by the free energy curves, because of the extreme nonequilibrium nature of the NaI(H2O)n photodissociation process, and the rate of electron transfer increases with cluster size and increasing solvation. Overall, this work demonstrates the importance of including polarization in realistic excited-state simulations of NaI(H2O)n relaxation.

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.

Electronic structures of intermolecular charge-transfer states in fast electron transfers with tetrathiafulvalene donor. Thermal and photoactivation of [2 + 4] cycloaddition to o-chloranil acceptor

Tetrathiafulvalene (TTF) spontaneously forms a series of unusual charge-transfer complexes with various quinonoid acceptors such as o-chloranil (CA) that show pronounced near-IR absorption (lambda(CT) = 1100 nm). The successful isolation of the corresponding [1 : 1] donor-acceptor complex from solution and X-ray crystallographic analysis at low temperatures reveal the polarized charge-transfer state: [TTF(q+),CA(q-)] with high degree of charge-transfer (q = 0.6), which is spectrally and crystallographically distinguished from the separate redox (ion-pair) state: [TTF(+*) + CA(-*) ]. The unique interconversion of charge-transfer and electron-transfer states is theoretically well-accommodated by Mulliken theory using semi-empirical valence-bond and molecular-orbital methodologies. Mechanistic implications are discussed of both the thermally activated and the photochemically promoted processes via fast (intracomplex) electron transfer followed by collapse of the adiabatic and the non-adiabatic (vibrationally-excited) ion-pairs, respectively, to the [2 + 4] cycloadduct of tetrathiafulvalene and o-chloranil.

Combined valence bond-molecular mechanics potential-energy surface and direct dynamics study of rate constants and kinetic isotope effects for the H+C2H6 reaction

This article presents a multifaceted study of the reaction H+C(2)H(6)-->H(2)+C(2)H(5) and three of its deuterium-substituted isotopologs. First we present high-level electronic structure calculations by the W1, G3SX, MCG3-MPWB, CBS-APNO, and MC-QCISD/3 methods that lead to a best estimate of the barrier height of 11.8+/-0.5 kcal/mol. Then we obtain a specific reaction parameter for the MPW density functional in order that it reproduces the best estimate of the barrier height; this yields the MPW54 functional. The MPW54 functional, as well as the MPW60 functional that was previously parametrized for the H+CH(4) reaction, is used with canonical variational theory with small-curvature tunneling to calculate the rate constants for all four ethane reactions from 200 to 2000 K. The final MPW54 calculations are based on curvilinear-coordinate generalized-normal-mode analysis along the reaction path, and they include scaled frequencies and an anharmonic C-C bond torsion. They agree with experiment within 31% for 467-826 K except for a 38% deviation at 748 K; the results for the isotopologs are predictions since these rate constants have never been measured. The kinetic isotope effects (KIEs) are analyzed to reveal the contributions from subsets of vibrational partition functions and from tunneling, which conspire to yield a nonmonotonic temperature dependence for one of the KIEs. The stationary points and reaction-path potential of the MPW54 potential-energy surface are then used to parametrize a new kind of analytical potential-energy surface that combines a semiempirical valence bond formalism for the reactive part of the molecule with a standard molecular mechanics force field for the rest; this may be considered to be either an extension of molecular mechanics to treat a reactive potential-energy surface or a new kind of combined quantum-mechanical/molecular mechanical (QM/MM) method in which the QM part is semiempirical valence bond theory; that is, the new potential-energy surface is a combined valence bond molecular mechanics (CVBMM) surface. Rate constants calculated with the CVBMM surface agree with the MPW54 rate constants within 12% for 534-2000 K and within 23% for 200-491 K. The full CVBMM potential-energy surface is now available for use in variety of dynamics calculations, and it provides a prototype for developing CVBMM potential-energy surfaces for other reactions.

Nonadiabatic Trajectory Studies of NaI(H2O)n Photodissociation Dynamics

We have investigated the photodissociation dynamics of NaI(H(2)O)(n) [n = 1-4] clusters using the molecular dynamics with quantum transitions method and a quantum mechanics/molecular mechanics description of NaI(H(2)O)(n), which involves a semiempirical valence-bond approach to describe the NaI electronic structure and classical solvent-solvent and solute-solvent interaction potentials. Our simulation results show that the NaI(H(2)O)(n) excited-state population decay upon reaching the NaI curve-crossing region increases with cluster size due to the stabilization of the ionic branch of the NaI excited state by the surrounding water molecules, and the resulting increase in nonadiabatic transition probability. After reaching the curve-crossing region for the first time, however, the excited-state population decay resembles that of bare NaI because of rapid evaporation of 99% and 95% of the water molecules for NaI(H(2)O) and NaI(H(2)O)(n) [n = 2-4], respectively. This extensive evaporation is due to the reversed NaI polarity in the Franck-Condon region of the NaI first excited state, which causes strong repulsive NaI-H(2)O forces and induces rapid nonstatistical water evaporation, where product water molecules are formed more rotationally than translationally hot. A few water molecules (5% or less) remain transiently or permanently bound to NaI, forming long-lived clusters, when NaI remains predominantly ionic, i.e., remains in the excited state, after reaching the curve-crossing region. To connect simulation results with experiment, we have simulated femtosecond probe signals resulting from two-photon and one-photon excitation to the X and I NaI(+) probe states. In agreement with experimental findings, the probe signals resulting from the two-photon probe scheme, where excitation occurs from the covalent branch of the excited state, decay exponentially over the NaI first excited-state vibrational period, with very little evidence of long-time dynamics. The one-photon probe scheme (not used for experimental cluster studies) is shown to be less sensitive to solvation, in that excitation energies will remain similar over a range of cluster sizes, as the ionic branch of the excited state and the NaI(+) probe states are stabilized to the same extent by the presence of water molecules. The resulting probe signals are also more revealing of the NaI(H(2)O)(n) photodissociation dynamics than the two-photon probe signals, as they may allow monitoring of solvation effects on the NaI nonadiabatic dynamics and of successive evaporation of water molecules. Time-resolved photoelectron spectra provide limited additional information regarding the NaI(H(2)O)(n) photodissociation dynamics. A key consequence of the rapid water evaporation demonstrated here is that experimentally observed signals may arise from the photodissociation of much larger NaI(H(2)O)(n) parent clusters.

The ground and excited states of polyenyl radicals C2n-1H2n + 1 (n = 2-13): a valence bond study.

The semiempirical valence bond (VB) method, VBDFT(s), is applied to the ground states and the covalent excited states of polyenyl radicals C2n - 1H2n + 1 (n = 2-13). The method uses a single scalable parameter with a value that carries over from the study of the covalent excited states of polyenes (W. Wu, D. Danovich, A. Shurki, S. Shaik, J. Phys. Chem. A, 2000, 104, 8744). Whenever comparison is possible, the VB excitation energies are found to be in good accord with sophisticated molecular orbital (MO)-based methods like CASPT2. The symmetry-adapted Rumer structures are used to discuss the state-symmetry and VB constitution of the ground and excited states, and the expansion to VB determinants is used to gain insight on spin density patterns. The theory helps to understand in a coherent and lucid manner the properties of polyenyl radicals, such as the makeup of the various states, their geometries and energies, and the distribution of the unpaired electrons (the neutral solitons).

A simulation study of vibrational relaxation of I− 3 in liquids

The temperature dependence of the vibrational relaxation of a flexible model of triiodide in a Lennard-Jones solvent (xenon) has been studied using equilibrium molecular dynamics simulations. The internal dynamics of the ion is calculated from a previously published semi-empirical valence bond model with a limited number of basis states. Vibrational decorrelation rates of the symmetric and antisymmetric stretching modes were found from the time correlation functions of the normal coordinate velocities and the vibrational energy relaxation rates from the time correlation functions of the kinetic energy in each mode. The vibrational dephasing rates and the energy relaxation rates decrease slowly as the temperature is lowered and do not show a discontinuity when the fluid solidifies, although the reorientational diffusion rates change rapidly at low temperatures. In order to interpret the results, perturbation theory expressions for the relaxation rates were evaluated for simulations of a rigid model of the ion and found to agree well with the direct observations. These showed that, unusually, both the solvent force and its derivative, the solvent potential curvature, contribute to the dephasing of the symmetric mode. The relevant fluctuation correlation times are very short, which may explain the insensitivity of the vibrational relaxation to the state of the solvent.

Semiempirical valence‐bond resonance energies for alternant conjugated hydrocarbons containing four‐membered rings

AbstractResonance energies of alternant conjugated hydrocarbons containing six‐membered and four‐membered rings are discussed via the semiempirical valence bond (VB) theory. After generating the higher‐order effective VB model according to cluster‐expansion theory, the aromaticity or antiaromaticity of the above compounds is quantified in a correct manner. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003

VBDFT(s)—a semi-empirical valence bond method: Application to linear polyenes containing oxygen and nitrogen heteroatoms

A semi-empirical valence bond (VB) method, VBDFT(s), is applied to the series of linear polyenes with heteroatoms CM−1HMO, CM−2HM−2O2, CM−1HM + 1N, and CM−2HMN2 (M = 4–26). The computational results show that the VBDFT(s) method, which was first applied to linear polyenes, is also suitable for treatment of linear polyenes with polar bonds. Properties such as the wavefunction, extent of delocalization, the resonance energy, and the energy additivity are discussed.

Semi-empirical valence bond models of conjugated alkenes with donor and acceptor substituents

The Heisenberg model is used to describe low-lying states of conjugated alkene ‘bridges’ with donor and/or acceptor substituents. Using a compact set of transferable exchange parameters, each fitted to the ground state ab initio energy of just one molecule, useful semi-empirical energies can be generated for different donor/acceptor combinations and for different chain lengths. A new Hamiltonian is introduced which augments the covalent description with additional parameters for ionic configurations, and for the mixing between covalent and ionic spaces. This leads to useful energies also for higher states. The general approach should be applicable to a wide range of different donor/acceptor/bridge combinations.

Computational study on small water clusters using a semiempirical valence bond approach

Small clusters of water (H2O)n, n = 3-8, are studied using a semiempirical valence bond approach to investigate the bonding energy contribution and hydrogen-bonding structure in the most stable conformation. The energy contribution was decomposed into electron pair-pair interactions and valence-bond energy for each water monomer. Our study shows that there is significant bonding difference between small clusters (n [Formula: see text] 5) of water and larger clusters (n > 5). In the larger clusters, there are structures containing tetravalent oxygen centers, which is impossible in the small clusters. The contribution to the binding energy from each H-bond varies from -4.7 kcal/mol to -7.3 kcal/mol in the water clusters considered here. The contribution of -5.9 kcal/mol per H-bond in the cubic octamer is comparable to the experimental value (-6.7 kcal/mol) of the binding energy in ice.Keywords: semi-empirical, valence bond, hydrogen bonding, water clusters.

Computational study on small water clusters using a semiempirical valence bond approach

Small clusters of water (H2O)n, n = 3-8, are studied using a semiempirical valence bond approach to investigate the bonding energy contribution and hydrogen-bonding structure in the most stable conformation. The energy contribution was decomposed into electron pair-pair interactions and valence-bond energy for each water monomer. Our study shows that there is significant bonding difference between small clusters (n 5) of water and larger clusters (n > 5). In the larger clusters, there are structures containing tetravalent oxygen centers, which is impossible in the small clusters. The contribution to the binding energy from each H-bond varies from -4.7 kcal/mol to -7.3 kcal/mol in the water clusters considered here. The contribution of -5.9 kcal/mol per H-bond in the cubic octamer is comparable to the experimental value (-6.7 kcal/mol) of the binding energy in ice.Keywords: semi-empirical, valence bond, hydrogen bonding, water clusters.

Computational study of structures and proton transfer in hydrogen-bonded ammonia complexes using semiempirical valence-bond approach

Computational study of structures and proton transfer in hydrogen-bonded ammonia complexes using semiempirical valence-bond approach

VBDFT(s): a Hückel-type semi-empirical valence bond method scaled to density functional energies. Application to linear polyenes

A semi-empirical valence bond (VB) method, called VBDFT(s), is described and applied to C n H n+2 conjugated hydrocarbons. The method is a Hückel-type VB scheme with energies scaled to density functional theory energies based on a single parameter; the matrix element λ due to spin transposition between bonded atoms. Total energies, excitation energies, resonance and π-bond energies are presented for the various species. The insight that can be derived from the corresponding wavefunctions is discussed.

Can the Low-Lying Electronic States of Benzenoid Hydrocarbons Be Described by the Semiempirical Valence Bond Approach?

The low-lying excited states of benzenoid hydrocarbons with up to 22 π-electrons have been obtained from exact semiempirical valence bond (VB) calculations. The effective valence bond (EVB) model, which implements nonadjacent and cyclic six-body interactions on the basis of the classical valence bond (CVB) model, is shown to give satisfactory predictions of the low-lying excited spectra of small benzenoids with no more than 14 π-electrons. For larger benzenoid systems, the CVB model can account well for their lowest excited spectra, being in good agreement with the available experimental data and semiempirical PPP molecular orbital results. In addition, a good quadratic relationship between the energy difference between the ground and first excited states and the number of Kekulé valence structures is revealed among the isomeric benzenoid systems.

Topological dependence of ferromagnetic coupling strength in some π-conjugated radicals

The Lanczos method has been employed to solve the semi-empirical valence bond model exactly for a series of organic di- and poly-radicals of benzenoid type of up to 18 π electrons. The calculated energy gaps between the high-spin ground and first excited states have been applied to gain some insight into the topological dependence of the strength of ferromagnetic spin coupling in these molecules.

An analysis of semi-empirical valence bond models for MX 2 potential energy surfaces: a case study of LiF 2

An analysis of three semi-empirical valence-bond (VB) models of alkali-dihalide systems MX 2 is presented for the prototype molecule LiF 2. Starting with a “minimum basis” diatomics-in-molecules (DIM) Hamiltonian matrix (24 basis functions), we examine the approximations which are necessary to arrive at the simple models of Zeiri and Shapiro and Goldfield et al. and we confirm their validity within the context of the larger DIM model. The simple models owe their success to the fact that, except in some collinear configurations F:Li:F, the directional behaviour of the atomic states is of marginal importance. Also, for configurations relevant to chemical reaction, the basis functions involving the coupling of the atoms to triplet states may be safely omitted. The sensitivity of the shapes of the potential surfaces to variation of the input data for these models is also investigated.

Resonance theoretical description of magnetic zero field splitting energies of benzenoid hydrocarbons. Structural dependance of the parameterD

The zero field splitting (ZFS) parameters D of the triplet ground states of benzene, naphthalene, anthracene, and phenanthrene are calculated within the framework of a semiempirical valence bond (VB) theory. The VB theoretical results are utilized to develop a much simpler resonance theoretical model which stresses the relationship between molecular structure, aromaticity, and magnitude of the ZFS parameter. The resonance theoretical approximation of the electronic wavefunction is anlysed in terms of triplet benzene subunits which describe a benzene-type resonance of the “triplet electrons” on a particular hexagon of the molecular structure. The ZFS parameter can be approximated by contributions from all triplet benzene subunits of the molecule. The resonance theoretical model can be applied successfully to larger hydrocarbons where a VB theoretical description becomes too complicated. Moreover, the model allows for a simple qualitative understanding of the dependence of the ZFS parameter D on the molecul...

Mutual neutralization and chemiionization in collisions of alkali metal and halogen atoms

A semiempirical valence bond method is used to obtain realistic potential curves for the three lowest 1∑+ curves of NaF, KF, LiCl, NaCl, KCl, Lil, and Nal. They are used together with a model functional form for the diabiatic coupling to compute quantal chemiionization and mutual neutralization cross sections. The accuracy of one-electron estimates of the interaction energies in the crossing regions is explored. The Landau–Zener method is found to be very reliable except for collisions involving iodine, for which modifications are necessary.