Unitary group approach to the many-electron problem. I. Matrix element evaluation and shift operators

This is the first paper in a series of three directed toward the evaluation of spin-dependent Hamiltonians directly in the spin-orbit basis. In this paper we present a new and complete derivation of the matrix elements of the U(n) generators in the electronic Gel'fand basis. The approach employed differs from previous treatments in that the matrix elements of nonelementary generators are obtained directly. A general matrix element formula is derived which explicitly demonstrates the segment level formalism obtained previously by Shavitt using different methods. A simple relationship between the matrix elements of raising and lowering generators is determined which indicates that in CI calculations, only the matrix elements of raising generators need be calculated. Some results on the matrix elements of products of two generators are also presented.     

Autoionization of CO after C 1s→ Zπ* excitation: a comparison with photoemission and auger decay

We have calculated the entire autoionization spectrum of CO following core-to-bound, i.e. C 1s→2π excitation, within a Green's function formalism. Approximate autoionization transition intensities can be related to the Hamiltonian matrix elements. Initialstate screening is important for obtaining realistic autoionization probabilities. For the low-lying ion states there is a one-to-one correspondence between the photoelectron and the autoionization spectrum. The connection between autoionization and Auger decay is discussed.     

An empirical relation between oscillator strengths calculated from the dipole length and dipole velocity formalisms in the optical absorption of conjugated molecules

It is found that a ratio between the oscillator strengths of the optical absorption calculated from the dipole length formalism and those calculated from the dipole velocity formalism is almost constant for many conjugated molecules if the calculation is made using the theoretically obtained transition energy. The value of the ratio becomes very sensitive to the molecular geometry if the calculation is made using the experimentally obtained transition energy. The origin of the constancy of the ratio is discussed.     

Theoretical rate constants of super-exchange hole transfer and thermally induced hopping in DNA

Recently, the electronic properties of DNA have been extensively studied, because its conductivity is important not only to the study of fundamental biological problems, but also in the development of molecular-sized electronics and biosensors. We have studied theoretically the reorganization energies, the activation energies, the electronic coupling matrix elements, and the rate constants of hole transfer in B-form double-helix DNA in water. To accommodate the effects of DNA nuclear motions, a subset of reaction coordinates for hole transfer was extracted from classical molecular dynamics (MD) trajectories of DNA in water and then used for ab initio quantum chemical calculations of electron coupling constants based on the generalized Mulliken-Hush model. A molecular mechanics (MM) method was used to determine the nuclear Franck-Condon factor. The rate constants for two types of mechanisms of hole transfer-the thermally induced hopping (TIH) and the super-exchange mechanisms-were determined based on Marcus theory. We found that the calculated matrix elements are strongly dependent on the conformations of the nucleobase pairs of hole-transferable DNA and extend over a wide range of values for the "rise" base-step parameter but cluster around a particular value for the "twist" parameter. The calculated activation energies are in good agreement with experimental results. Whereas the rate constant for the TIH mechanism is not dependent on the number of A-T nucleobase pairs that act as a bridge, the rate constant for the super-exchange process rapidly decreases when the length of the bridge increases. These characteristic trends in the calculated rate constants effectively reproduce those in the experimental data of Giese et al. [Nature 2001, 412, 318]. The calculated rate constants were also compared with the experimental results of Lewis et al. [Nature 2000, 406, 51].     

Determination of alignment parameters for symmetric top molecules using nonresonant two-photon absorption

The polarization dependence of the two-photon absorption signal is described directly in terms of the matrix elements of the irreducible representation of the two-photon absorption tensor operator for an ensemble with cylindrical symmetry probed with identical photons of linear polarization. Non vanishing matrix elements are easily determined from the known tensor patterns of the specific two-photon transition. The formalism is applicable to the extraction of alignment parameters for symmetric top molecules as well as diatomics produced in collisions of unpolarized particles or in the photodissociation with a single photon of linear polarization.     

A simplified relativistic time-dependent density-functional theory formalism for the calculations of excitation energies including spin-orbit coupling effect

In the present work we have proposed an approximate time-dependent density-functional theory (TDDFT) formalism to deal with the influence of spin-orbit coupling effect on the excitation energies for closed-shell systems. In this formalism scalar relativistic TDDFT calculations are first performed to determine the lowest single-group excited states and the spin-orbit coupling operator is applied to these single-group excited states to obtain the excitation energies with spin-orbit coupling effects included. The computational effort of the present method is much smaller than that of the two-component TDDFT formalism and this method can be applied to medium-size systems containing heavy elements. The compositions of the double-group excited states in terms of single-group singlet and triplet excited states are obtained automatically from the calculations. The calculated excitation energies based on the present formalism show that this formalism affords reasonable excitation energies for transitions not involving 5p and 6p orbitals. For transitions involving 5p orbitals, one can still obtain acceptable results for excitations with a small truncation error, while the formalism will fail for transitions involving 6p orbitals, especially 6p1/2 spinors.     

Stochastic path-integral method for chemical reaction dynamics: Application to the full 3D H3 system

A stochastic path-integral (SPI) technique for chemical reaction dynamics is explored. It is shown that this technique enables the direct computation of the transition amplitude with a finite space-time range, by generating a set of classical paths subject to simultaneous stochastic differential equations. The numerical values of the Boltzmann matrix elements for a harmonic potential are in good agreement with the analytical ones. Within the quantum transition state theory, the flux-flux autocorrelation function is also evaluated at 630 K for the H + H₂ exchange reaction and is found to give a satisfactory agreement with the previous studies. To appraise the influence of the dimensionality, both one-dimensional Eckart potential and a full three-dimensional (3D) Liu-Siegbahn-Truhlar-Horowitz (LSTH) potential calculations have been performed. The calculated values of the Boltzmann matrix elements for the colinear and the full 3D cases are found to deviate slightly from each other in the lower temperature range. The 3D thermal rate constant is in very good agreement with the previous one. © 1996 John Wiley & Sons, Inc.     

金属原子（离子）-苯配合物的电子转移反应

用密度泛函理论（ＤＦＴ／ＢＬＹＰ）在６－３１Ｇ基组水平上研究了金属原子－苯与离子－苯配合物的气相电子转移过程,得到了Ｍ（Ｌｉ,Ｎａ,Ｍｇ）－Ｃ６Ｈ６和Ｍ＾＋－Ｃ６Ｈ６络合物以及它们之间电子转移过程的先驱络合物的最优几何构型和电子结构。同时,利用线性坐标确定了过滤态的结构,结果表明：ＤＦＴ方法计算得到的单体,即原子（离子）－苯的构型,同ＭＰ２结果较为一致。先驱络合物具有Ｃ６ν对称性,给体与受体间距离     

Non-condon scheme of radiationless transitions for the morse oscillator model

The non-adiabatic coupling matrix elements responsible for radiationless deactivation of an electronically excited molecule are calculated without invoking the Condon approximation. Assuming the Morse potential surfaces for vibrational motion along the local and totally symmetric normal coordinates, the vibronic part of the radiationless rate constant is calculated. It is shown that the rate constant in the non-Condon scheme exceeds that obtained in the Condon approximation by about two orders of magnitude. The calculated dependence of the radiationless rate constant on the energy gap is in good agreement with the experimentally observed energy gap law for intersystem crossing T₁ → S₀ rate constants in aromatic hydrocarbons.     

HEH(EHP)萃取稀土元素时萃取动力学行为的递变规律

采用恒界面池法研究了2-乙基己基2-乙基己基膦酸[HEH(EHP),P~5~0~7]在盐酸介质中萃取稀土元素时萃取动力学行为的递变规律,讨论了稀土元素分配比(D)和分离因数(β)随时间变化的规律,并测算出正向萃取速率常数(k~f)和逆向萃取速率常数(k~b).发现了萃取动力学中萃取速率常数的"四分组效应","斜W效应"和"钆断"现象,提出利用动态萃取体系分离稀土元素     

Equilibrium/nonequilibrium initial configurations in forward/reverse electron transfer within mixed-metal hemoglobin hybrids

In a protein-protein electron transfer (ET) photocycle, the "forward" ET reaction is initiated with the excited complex, [3DA], in an equilibrium ensemble of configurations, the majority of which exhibit less than the maximal ET matrix element. In contrast, the charge-separated intermediate complex is formed in a nonequilibrium set of configurations with maximal ET matrix elements and would be expected to return to the ground state with the largest rate constant possible unless conformational interconversion first "breaks the connection" and the complex converts to less-reactive substates. According to this analysis, the forward and back ET reactions should show a differential response to viscosity, and the latter could even show an increased rate constant under conditions which suppress departure from the reactive configuration(s). We now report that the viscosity dependences of forward and back ET rate constants for the photocycle within the [alpha2(Zn),beta2(Fe3+N3-)] mixed-metal hemoglobin hybrid at pH 7 show the anticipated behavior: kf decreases as viscosity increases, but, in sharp contrast, kb increases strongly.     

Electron tunneling dynamics in anharmonic bath

Tunneling transition probability for a particle interacting with an anharmonic bath is found in a time-dependent Hartree approximation. The general expression is presented in terms of medium Keldysh functions that are assumed to be known. Furthermore, the transition probability is calculated in the noninteracting-blip approximation where the rate constant does not exhibit an activation dependence at high temperatures. The reorganization energy E(r) and the renormalized reaction heat epsilon are expressed in terms of the correlation matrix for a solvent and internal modes in both quantum and classical regimes. It is shown that E(r) and epsilon are temperature dependent.     

A comparison between interfacial electron-transfer rate constants at metallic and graphite electrodes

The Fermi golden rule formalism has been used to derive the rate constant for interfacial electron transfer from a semimetallic electrode, such as highly ordered pyrolytic graphite (HOPG), to a redox couple in solution. A simple expression is presented that semiquantitatively relates the electron-transfer rate constant at a semimetallic electrode to that at a metallic electrode. The approach allows for the estimation of the value of the rate constant for interfacial charge transfer to nonadsorbing outer-sphere redox species at semimetallic electrodes. Rate constants for interfacial electron transfer for a variety of one-electron redox couples at semimetallic electrodes have been calculated relative to the rate constant of the ferrocenium/ferrocene redox couple at a gold electrode. Good agreement is found, in general, between the calculated and observed rate constants.     

A novel formalism to characterize the degree of unsaturation of organic molecules

The existing formalism to calculate the degree of unsaturation from the molecular formula of organic molecules cannot be applied to charged and/or disconnected species. Moreover, the calculated value depends on the assumed formal valence of each of the elements. In this work, we introduce a new formalism that eliminates these problems. The suggested property, degree of unsaturation, can be calculated from the molecular formula as well as from any structural representation of a molecule corresponding to that molecular formula.     

Introduction

The formalism for a configuration interaction approach is presented, in which explicit introduction of interelectronic coordinates into individual configurations is accomplished through the use of spherical Gaussian correlation factors. Formulas for all required matrix elements over these configurations are derived, and a computationally convenient algorithm to evaluate the matrix elements is presented. In addition, analysis of the form of the correlation factor shows that both angular and radial correlation can be obtained using spherical Gaussian correlation factors.     

Symmetry forbidden vibronic spectra and internal conversion in benzene

The spectra of symmetry-forbidden transitions and internal conversion were investigated in the present work. Temperature dependence was taken into account for the spectra simulation. The vibronic coupling, essential in the two processes, was calculated based on the Herzberg-Teller theory within the Born-Oppenheimer approximation. The approach was employed for the symmetry-forbidden absorption/fluorescence, and internal conversion between 1(1)A(1g) and 1(1)B(2u) states in benzene. Vibrational frequencies, normal coordinates, electronic transition dipole moments, and non-adiabatic coupling matrix elements were obtained by ab initio quantum chemical methods. The main peaks, along with the weak peaks, were in good agreement with the observed ones. The rate constant of the 1(1)A(1g)← 1(1)B(2u) internal conversion was estimated within the order of 10(3) s(-1). This could be regarded as the lower limit (about 4.8 × 10(3) s(-1)) of the internal conversion. It is stressed that the distortion effect was taken into account both in the symmetry-forbidden absorption/fluorescence, and the rate constants of internal conversion in the present work. The distortion effects complicate the spectra and increase the rate constants of internal conversion.     

Interactions between frenkel excitons. I. Formalism and preliminary results

For the tightest-bound Frenkel excitons a many-particle hamiltonian is adopted which includes terms representing interactions between the excitons. The parameters of the model are the excitation energy of an isolated localized excitation, the excitation-transfer matrix elements, and the interaction energies. Several special cases, involving particular relations between the latter two sets of parameters, are treated qualitatively. Equations are translated into the language of spin-$\text{1}\text{2}$ lattices, so that use may be made of the results of that theory. Favorable conditions for observation of polyexcitons and of phase transition to a liquid of excitons are discussed. A standard formalism for the determination of absorption and emission spectra and of their moments is adapted to the present problem. Possible generalizations of the model are briefly discussed.     

The calculation of excitation energies based on the relativistic two-component zeroth-order regular approximation and time-dependent density-functional with full use of symmetry

In the present work, we propose a relativistic time-dependent density-functional theory (TDDFT) based on the two-component zeroth-order regular approximation and a noncollinear exchange-correlation (XC) functional. This two-component TDDFT formalism has the correct nonrelativistic limit and affords the correct threefold degeneracy of triplet excitations. The relativistic TDDFT formalism is implemented into the AMSTERDAM DENSITY FUNCTIONAL program package for closed-shell systems with full use of double-group symmetry to reduce the computational effort and facilitate the assignments. The performance of the formalism is tested on some closed-shell atoms, ions, and a few diatomic molecules containing heavy elements. The results show that the fine structure of the excited states for most atoms and ions studied here can be accurately accounted for with a proper XC potential. For the excitation energies of the molecules studied here, the present formalism shows promise and the error encountered is comparable to that of nonrelativistic TDDFT calculations on light elements.     

Matrix elements of N-particle explicitly correlated Gaussian basis functions with complex exponential parameters

In this work we present analytical expressions for Hamiltonian matrix elements with spherically symmetric, explicitly correlated Gaussian basis functions with complex exponential parameters for an arbitrary number of particles. The expressions are derived using the formalism of matrix differential calculus. In addition, we present expressions for the energy gradient that includes derivatives of the Hamiltonian integrals with respect to the exponential parameters. The gradient is used in the variational optimization of the parameters. All the expressions are presented in the matrix form suitable for both numerical implementation and theoretical analysis. The energy and gradient formulas have been programmed and used to calculate ground and excited states of the He atom using an approach that does not involve the Born-Oppenheimer approximation.     

Canonical statistical adiabatic channel model calculations of the H + CH3 → CH4 recombination reaction on an ab initio potential energy surface. The role of the transitional modes

The canonical formalism of the statistical adiabatic channel model is used to calculate limiting high pressure rate constants for the H + CH₃ → CH₄ recombination reaction on a recently reported analytic potential energy surface based on ab initio calculations. An effective adiabatic channel potential which incorporates the G_?? matrix element of the twofold degenerate H₃C? H transitional bending mode, quartic anharmonicity, and state selected mode coupling effects is implemented. The rate constants calculated over the temperature range 200–1000 K are in very good agreement with recent canonical variational transition state theory calculations performed on the same surface. The comparison with experimental results is also discussed.