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.     

Solvation dynamics of formamide and N,N-dimethylformamide in aerosol OT reverse micelles

The solvation dynamics of formamide and N,N-dimethylformamide in Aerosol OT reverse micelles has been investigated in this work. The solvation dynamics of formamide and N,N-dimethylformamide in the reverse micelles is more than 100 times slower than that of the pure solvents. The solvation dynamics of formamide in the reverse micelle solution depends strongly on the molar ratio between formamide and Aerosol OT (w = [polar solvent]/[Aerosol OT]), but that of N,N-dimethylformamide in the reverse micelle solution shows a tiny w dependence. We have estimated the interaction energies of the geometry-optimized clusters of a simple model of the Aerosol OT polar headgroup (CH3SO3-) and formamide or N,N-dimethylformamide by ab initio calculations (the second-order M?ller-Plesset perturbation theory) to find their interactions. The interaction energies of the mimic clusters estimated by the ab initio calculations and the features of the slow solvation dynamics and w dependence in formamide and N,N-dimethylformamide reverse micelles are discussed.     

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.     

On the peculiarities of the diabatic framework: new insight

In this article we consider the electronic diabatic presentation of a two-state system with the aim of earning insight regarding the distribution of conical intersections in a given region. In this process we revealed explicit relationship between the diabatic potentials and the locations of conical intersections. The study is accompanied with numerical examples as worked out for a model and ab initio potential energy surfaces of the Na+H2 system.     

Quantum versus classical electron transfer energy as reaction coordinate for the aqueous Ru2+/Ru3+ redox reaction

Applying density functional theory (DFT)-based molecular dynamics simulation methods we investigate the effect of explicit treatment of electronic structure on the solvation free energy of aqueous Ru²⁺ and Ru³⁺.Our approach is based on the Marcus theory of redox half reactions, focussing on the vertical energy gap for reduction or oxidation of a single aqua ion. We compare the fluctuations of the quantum and classical energy gap along the same equilibrium ab initio molecular dynamics trajectory for each oxidation state. The classical gap is evaluated using a standard point charge model for the charge distribution of the solvent molecules (water). The quantum gap is computed from the full DFT electronic ground state energies of reduced and oxidized species, thereby accounting for the delocalization of the electron in the donor orbital and reorganization of the electron cloud after electron transfer (ET). The fluctuations of the quantum ET energy are well approximated by gaussian statistics giving rise to parabolic free energy profiles. The curvature is found to be independent of the oxidation state in agreement with the linear response assumption underlying Marcus theory. By contrast, the diabatic free energy curves evaluated using the classical gap as order parameter, while also quadratic, are asymmetric reflecting the difference in oxidation state. The response of these two order parameters is further analysed by a comparison of the spectral density of the fluctuations and the corresponding reorganization free energies.     

Theoretical prediction of the electronic excited states and resonance Raman intensities in formamide from coupled cluster calculations

Electronic excitations and the resonance Raman spectrum of formamide were obtained from ab initio electron correlation calculations using the equation of motion coupled cluster (EOM-CCSD) method. Interpretation of the UV spectrum on the basis of calculated vertical excitation energies and oscillator strengths accounts for all experimental bands previously assigned. Our assignment, however, suggests an additional Rydberg band at about 7.4 eV which may be hidden under the main absorption. We also show that the Rydberg states appear pairwise, corresponding to n and π hole states, respectively. Using analytic derivative techniques, derivatives of the excited state energies with respect to normal coordinates of the ground state were calculated. Approximate resonance Raman intensities have been determined.     

Charge transfer in the electron donor-acceptor complex BH3NH3

As a simple yet strongly binding electron donor-acceptor (EDA) complex, BH(3)NH(3) serves as a good example to study the electron pair donor-acceptor complexes. We employed both the ab initio valence bond (VB) and block-localized wave function (BLW) methods to explore the electron transfer from NH(3) to BH(3). Conventionally, EDA complexes have been described by two diabatic states: one neutral state and one ionic charge-transferred state. Ab initio VB self-consistent field (VBSCF) computations generate the energy profiles of the two diabatic states together with the adiabatic (ground) state. Our calculations evidently demonstrated that the electron transfer between NH(3) and BH(3) falls in the abnormal regime where the reorganization energy is less than the exoergicity of the reaction. The nature of the NH(3)-BH(3) interaction is probed by an energy decomposition scheme based on the BLW method. We found that the variation of the charge-transfer energy with the donor-acceptor distance is insensitive to the computation levels and basis sets, but the estimation of the amount of electron transferred heavily depends on the population analysis procedures. The recent resurgence of interest in the nature of the rotation barrier in ethane prompted us to analyze the conformational change of BH(3)NH(3), which is an isoelectronic system with ethane. We found that the preference of the staggered structure over the eclipsed structure of BH(3)NH(3) is dominated by the Pauli exchange repulsion.     

Hydrated hydride anion clusters

On the basis of density functional theory (DFT) and high level ab initio theory, we report the structures, binding energies, thermodynamic quantities, IR spectra, and electronic properties of the hydride anion hydrated by up to six water molecules. Ground state DFT molecular dynamics simulations (based on the Born-Oppenheimer potential surface) show that as the temperature increases, the surface-bound hydride anion changes to the internally bound structure. Car-Parrinello molecular dynamics simulations are also carried out for the spectral analysis of the monohydrated hydride. Excited-state ab initio molecular dynamics simulations show that the photoinduced charge-transfer-to-solvent phenomena are accompanied by the formation of the excess electron-water clusters and the detachment of the H radical from the clusters. The dynamics of the detachment process of a hydrogen radical upon the excitation is discussed.     

Hybrid ab initio VB/MM method--a valence bond ride through classical landscapes

The development of a new hybrid (QM/MM) method, where the QM part is treated by ab initio valence bond (VB) theory is presented. This VB/MM method has the advantages of empirical VB (EVB) methodology but does not rely on empirical parameterization for the quantum part. The method implements embedding of the quantum region of each diabatic state separately, by treating the electrostatic interactions between QM and MM regions classically. Additionally, it assumes that changes of the off diagonal matrix element due to different environments are such that the overall resonance integral does not change. These assumptions are discussed in detail and the validity of the method is shown to be successful in three different bond dissociation processes, where bond dissociation as well as solvation energies compare very well with the experimental data.     

Flexible H2O2 in water: electronic structure from photoelectron spectroscopy and ab initio calculations

The effect of hydration on the electronic structure of H(2)O(2) is investigated by liquid-jet photoelectron spectroscopy measurements and ab initio calculations. Experimental valence electron binding energies of the H(2)O(2) orbitals in water are, on average, 1.9 eV red-shifted with respect to the gas-phase molecule. A smaller width of the first peak was observed in the photoelectron spectrum from the solution. Our experiment is complemented by simulated photoelectron spectra, calculated at the ab initio level of theory (with EOM-IP-CCSD and DFT methods), and using path-integral sampling of the ground-state density. The observed shift in ionization energy upon solvation is attributed to a combination of nonspecific electrostatic effects (long-range polarization) and of the specific interactions between H(2)O(2) and H(2)O molecules in the first solvation shell. Changes in peak widths are found to result from merging of the two lowest ionized states of H(2)O(2) in water due to conformational changes upon solvation. Hydration effects on H(2)O(2) are stronger than on the H(2)O molecule. In addition to valence spectra, we report oxygen 1s core-level photoelectron spectra from H(2)O(2)(aq), and observed energies and spectral intensities are discussed qualitatively.     

Bond length alternation and energy gap in (CH)x. Application of the intermediate exciton formalism

Previous ab initio LCAO Hartree-Fock (HF) self-consistent field (SCF) band structure calculations predicted the alternating all trans (CH)_x (polyacetylene or polyene) to be energetically more stable than the equidistant metallic chain, however, the gap of those calculations was too large (≈7 eV). The present discussion based on semi-empirical PPP hamiltonian explains how electronic correlation neglected in the HF theory reduces this gap to ≈4 eV, while the excitation energy for the creation of excitons is estimated to be below 2 eV. The formalism for this estimation is an intermediate-binding exciton theory with explicit use of numerical Wannier functions. It is concluded that the gap is not due to a spin-density-wave state of the equidistant chain, as expected by Ovchinnikov .     

Theoretical results for the excited states of ozone

On the basis of ab initio calculations (configuration interaction and generalized valence bond), we find eight excited states of ozone with vertical excitation energies less than 7 eV. Using these results the various experimental transitions are assigned. One state has an equilateral triangle as the minimum energy geometry (1.5 eV above the ground state).     

Ab initio quantum mechanical/molecular mechanical simulation of electron transfer process: fractional electron approach

Electron transfer (ET) reactions are one of the most important processes in chemistry and biology. Because of the quantum nature of the processes and the complicated roles of the solvent, theoretical study of ET processes is challenging. To simulate ET processes at the electronic level, we have developed an efficient density functional theory (DFT) quantum mechanical (QM)/molecular mechanical (MM) approach that uses the fractional number of electrons as the order parameter to calculate the redox free energy of ET reactions in solution. We applied this method to study the ET reactions of the aqueous metal complexes Fe(H(2)O)(6)(2+/3+) and Ru(H(2)O)(6)(2+/3+). The calculated oxidation potentials, 5.82 eV for Fe(II/III) and 5.14 eV for Ru(II/III), agree well with the experimental data, 5.50 and 4.96 eV, for iron and ruthenium, respectively. Furthermore, we have constructed the diabatic free energy surfaces from histogram analysis based on the molecular dynamics trajectories. The resulting reorganization energy and the diabatic activation energy also show good agreement with experimental data. Our calculations show that using the fractional number of electrons (FNE) as the order parameter in the thermodynamic integration process leads to efficient sampling and validate the ab initio QM/MM approach in the calculation of redox free energies.     

Calculation of electron affinities of polycyclic aromatic hydrocarbons and solvation energies of their radical anion

Electron affinities (EAs) and free energies for electron attachment (DeltaGo(a,298K)) have been directly calculated for 45 polynuclear aromatic hydrocarbons (PAHs) and related molecules by a variety of theoretical methods, with standard regression errors of about 0.07 eV (mean unsigned error = 0.05 eV) at the B3LYP/6-31 + G(d,p) level and larger errors with HF or MP2 methods or using Koopmans' Theorem. Comparison of gas-phase free energies with solution-phase reduction potentials provides a measure of solvation energy differences between the radical anion and neutral PAH. A simple Born-charging model approximates the solvation effects on the radical anions, leading to a good correlation with experimental solvation energy differences. This is used to estimate unknown or questionable EAs from reduction potentials. Two independent methods are used to predict DeltaGo(a,298K) values: (1) based upon DFT methods, or (2) based upon reduction potentials and the Born model. They suggest reassignments or a resolution of conflicting experimental EAs for nearly one-half (17 of 38) of the PAH molecules for which experimental EAs have been reported. For the antiaromatic molecules, 1,3,5-tri-tert-butylpentalene and the dithia-substituted cyclobutadiene 1, the reduction potentials lead to estimated EAs close to those expected from DFT calculations and provide a basis for the prediction of the EAs and reduction potentials of pentalene and cyclobutadiene. The Born model has been used to relate the electrostatic solvation energies of PAH and hydrocarbon radical anions, and spherical halide anions, alkali metal cations, and ammonium ions to effective ionic radii from DFT electron-density envelopes. The Born model used for PAHs has been successfully extended here to quantitatively explain the solvation energy of the C60 radical anion.     

The Hartree-Fock-Heitler-London method, III: Correlated diatomic hydrides

In a recently proposed model, called Hartree-Fock-Heitler-London (HF-HL) (Corongiu, G. J. Phys. Chem. A 2006, 110, 11584), the molecular wave function was variationally obtained by merging two traditional models, Hartree-Fock (HF) and Heitler-London (HL). In the new method, the non-dynamical correlation energy-which includes state avoided crossing-is explicitly calculated with a few configurations. In this work the dynamical correlation energy for diatomic hydrides of the first and second period is computed both ab initio, via short MC-HF and MC-HL expansions-including ionic and excited covalent structures-and semiempirically, using the Coulomb hole algorithm, a density functional proposed by Clementi in the early 1960s. The Coulomb Hole correction is applied to HF and HF-HL functions, and, departing from tradition, also to HL functions. Few ab initio HF-HL configurations with inclusion of ionic structures yield reasonable binding energies not only for the hydrides considered but also for the van der Waals HeH molecule. The computed binding energies (in kcal/mol) from HF-HL functions corrected with the Coulomb hole functional are as follows: 109.48 (109.48) for H2[1Sigma+g]; 0.01 (0.01) for HeH [2Sigma+]; 59.22 (58.00) for LiH [1Sigma+], 49.55 (49.83) for BeH [2Sigma+], 86.77 (84.1) for BH [1Sigma+], 82.65 (83.9) for CH [2Pi], 81.57 (80.5) for NH [3Sigma-], 107.18 (106.6) for OH [2Pi], and 140.91 (141.5) for HF [1Sigma+]; experimental values are given in parentheses. The computed total energies are in good agreement with exact nonrelativistic values. The combined availability of the correlation and binding energies from HF, HL, and HF-HL models allows a novel analyses on the hydrides chemical bond, in agreement with accepted physical chemistry concept derived from MO and VB theories.     

A theoretical investigation of charge transfer in several substituted acridinium ions

We present calculations for various properties of the ground and excited states of several arylamine-substituted acridinium ion systems that have been studied experimentally. Using ab initio and semiempirical quantum mechanical methods together with the generalized Mulliken-Hush (GMH) model, we examine the excitation energies, dipole moment shifts, and electronic coupling elements for the vertical charge shift (CSh) processes in these systems. We also examine solvent effects on these properties using a dielectric continuum reaction field model. The results are in generally good agreement with available experimental results and indicate that there is strong electronic coupling in these systems over a wide range of torsional angles. Nevetheless, the initial and final cationic states remain reasonably well-localized over this range, and thus TICT state formation is unlikely in these systems. Finally, a version of the GMH model based on Koopmans' Theorem is developed and found to yield coupling elements generally within a factor of 2 of the many-electron GMH for a sample acridinium system, but with overestimated adiabatic and diabatic dipole moment differences.     

Wavelength dependence of electronic relaxation in isolated adenine using UV femtosecond time-resolved photoelectron spectroscopy

Electronic relaxation pathways in photoexcited nucleobases have received much theoretical and experimental attention due to their underlying importance to the UV photostability of these biomolecules. Multiple mechanisms with different energetic onsets have been proposed by ab initio calculations yet the majority of experiments to date have only probed the photophysics at a few selected excitation energies. We present femtosecond time-resolved photoelectron spectra (TRPES) of the DNA base adenine in a molecular beam at multiple excitation energies between 4.7-6.2 eV. The two-dimensional TRPES data is fit globally to extract lifetimes and decay associated spectra for unambiguous identification of states participating in the relaxation. Furthermore, the corresponding amplitude ratios are indicative of the relative importance of competing pathways. We adopt the following mechanism for the electronic relaxation of isolated adenine; initially the S(2)(ππ*) state is populated by all excitation wavelengths and decays quickly within 100 fs. For excitation energies below ～5.2 eV, the S(2)(ππ*)→S(1)(nπ*)→S(0) pathway dominates the deactivation process. The S(1)(nπ*)→S(0) lifetime (1032-700 fs) displays a trend toward shorter time constants with increasing excitation energy. On the basis of relative amplitude ratios, an additional relaxation channel is identified at excitation energies above 5.2 eV.     

Density functional theory study on molecular structure and vibrational IR spectra of isocytosine

Density functional theory with the combined Becke3-LYP exchange-correlation energy functional [DFT(B3-LYP) method] using the 6-31G(d, p) basis set is applied to predict molecular parameters (geometries, rotational constants, dipole moments) and vibrational IR spectra (harmonic wavenumbers, absolute intensities) of six tautomers of the isocytosine molecule. The results are compared with the corresponding data calculated at the conventional ab initio Hartree-Fock (HF) level using the same basis set and with available experimental data. Calculations show that (a) three amino tautomers are slightly nonplanar species with, evidently, a distorted amino group, (b) the DFT (B3-LYP)/6-31G(d, p) method predicts better molecular parameters, than do the HF calculations, and (c) the DFT(B3-LYP)-calculated vibrational IR spectra of isocytosine agree well with the available recorded IR spectra, and they show marked improvement over the IR spectra predicted at the HF/6-31G(d, p) level. Tautomeric stabilities of isocytosine are discussed on the basis of computed electronic energies by the DFT(B3-LYP) and ab initio approaches [including the MP2 and MP4(SDQ) calculations of electronic energies] and predicted zero-point vibrational energies by DFT(B3-LYP) and HF methods. This relative energies at 0 K of the tautomeric forms of isocytosine predicted by both conventional ab initio and DFT(B3-LYP) methods correlate well with the experimental data, showing the predominance of the aminohydroxy tautomer of isocytosine for an isolated molecule. © 1997 John Wiley & Sons, Inc.