镧系元素f-f跃迁光谱计算

运用不可约张量算符方法,建立了f-f超灵敏跃迁光谱的计算模型,编制了计算f离子^2s+1L~J能级、约化矩阵元、晶体场Stark能级、晶体场态-态跃迁振子强度及模拟吸收光谱的计算机程序.其中,自由f离子能级计算采用包括双电子与叁电子组态相互作用的二三参数模型,晶体场Stark分裂计算采用单电子轨道近似,用Newman角叠加模型计算晶体场参数.f-f跃迁振子强度计算包括静电诱导偶极跃、配体极化偶极跃、振动诱导电偶极跃迁及磁偶极跃迁的贡献.     

Toward accurate thermochemical models for transition metals: G3Large basis sets for atoms Sc-Zn

An augmented valence triple-zeta basis set, referred to as G3Large, is reported for the first-row transition metal elements Sc through Zn. The basis set is constructed in a manner similar to the G3Large basis set developed previously for other elements (H-Ar, K, Ca, Ga-Kr) and used as a key component in Gaussian-3 theory. It is based on a contraction of a set of 15s13p5d Gaussian primitives to 8s7p3d, and also includes sets of f and g polarization functions, diffuse spd functions, and core df polarization functions. The basis set is evaluated with triples-augmented coupled cluster [CCSD(T)] and Brueckner orbital [BD(T)] methods for a small test set involving energies of atoms, atomic ions, and diatomic hydrides. It performs well for the low-lying s-->d excitation energies of atoms, atomic ionization energies, and the dissociation energies of the diatomic hydrides. The Brueckner orbital-based BD(T) method performs substantially better than Hartree-Fock-based CCSD(T) for molecules such as NiH, where the starting unrestricted Hartree-Fock wavefunction suffers from a high degree of spin contamination. Comparison with available data for geometries of transition metal hydrides also shows good agreement. A smaller basis set without core polarization functions, G3MP2Large, is also defined.     

Evaluation of electronic matrix elements of long-range electron transfer in proteins by the recursive residue generation method

An efficient method for calculating electronic matrix elements for electron-transfer reactions in biological systems is proposed. We use the tight-binding model to describe the motion of one-electron in an array representing the system: donor (D), acceptor (A), and all other atoms that compose the protein. The matrix elements |T_DA|;² is evaluated at the estimated electron energy. The essential part of the method lies in the evaluation of the off-diagonal Green function 〈I|G|F〉 between the site I neighboring with the donor and the site F with the acceptor. The recursive residue generation method is used to evaluate 〈I|G|F|〉. As an application, these matrix elements in metal-labeled myoglobin are calculated and the results are compared with those evaluated with the renormalized-perturbation-expansion approach. © 1994 John Wiley & Sons, Inc.     

Core–Valence correlations and relativistic effects in heavy atoms for molecular applications

Theoretical core effective potential methods are widely used in valence-only electron molecular calculations. These methods, which imply the frozen-core approximation, work well for the elements of the righthand side of the periodic table but are often unrealistic for metallic elements with highly polarizable cores. For these atoms one has to consider the polarization of the cores under the influence of the electric field created by the valence electrons. Moreover, relativistic corrections must be added for heavy atoms. Various theoretical approaches of core–valence interactions (polarization and core–valence correlations) will be reviewed, with a special emphasis on practical methods of calculation. The problem of handling the relativistic effects will mainly be discussed within the two-component Pauli formalism. It will be shown that the Foldy–Wouthuysen transformation is not the unique way for deriving relativistic corrections and that the second-order Dirac equation also provides a good starting point for obtaining relativistic corrections. Analytical exact results are given for the hydrogen atom. The accuracy of this approach is tested on many-electron atoms and molecules. It is finally shown that the problem of the core-valence separation is relevant to the general methodology of effective Hamiltonians that seems to provide the best promising way for filling the gap between the semiempirical and purely theoretical ab initio methods.     

A two-step method of calculation of the electronic structure of molecules with heavy atoms: Theoretical aspect

An approach for a space-separated calculation of the wave function in the valence and core regions of a molecule is proposed. As the first step, the calculation of the orbitals (or two-component spinors in the relativistic case) in the valence region by the effective core potential (ECP ) method is performed. Then, it is followed by a restoration of orbitals (four-component spinors) expanded on spherical harmonics in the core regions of heavy atoms. Theoretical questions of the variational calculation of the molecular orbitals are considered in some core region limited by a sphere. Inclusion from the electronic cloud outside this region is reduced by the necessity of taking into account the orthonormality and boundary conditions together with an effective external field in respect to the selected core region. This method may be used for calculation of matrix elements of operators that are singular near nuclei (P, T-odd interactions, hyperfine structure, etc.). A substantial computational saving can be reached because the method enables, by the most optimal way, to combine the advantages of two well-developed approaches: molecular ECP calculations in the Gaussian basis set and one-center numerical atomic calculations with an external field. It is especially important when the relativistic effects are taken into account. © 1996 John Wiley & Sons, Inc.     

Effect of through-space electron transfer on infrared spectrum of amorphous selenium

In this paper we present theoretical analyses on an infrared (IR) spectrum of amorphous selenium. The system is described by a 216-atom-chain model, and a set of molecular-dynamics simulations is performed to generate vitreous structures and vibrational modes. To describe an electronic structure of the system we employ a complete neglect of differential overlap model parametrized by ab initio cluster calculations. An IR intensity is evaluated with the Berry-phase formula for an electronic polarization. The effect of the through-space electron transfer on the IR spectrum is studied by artificially changing the magnitude of matrix elements associated with the electron transfer between nonbonded atoms in the chain. We find that the through-space electron transfer leads to (i) the enhancement of the bending IR peak at 135 cm(-1) and (ii) the appearance of a new low-frequency peak around 50 cm(-1), thus resulting in a good agreement with the experiment. The mechanism is discussed by a simple dipole model.     

对含重元素体系的接合二分量-标量相对论密度泛函计算方法

在相对论密度泛函ZORA方法的基础上,提出一种用于含重元素体系的接合二分量-标量相对论密度泛函计算方法.对于只含少数几个重元素的较大体系,仅对其中旋轨耦合作用强的重元素作二分量相对论计算,而对体系的其余部分则作标量相对论计算,通过对动能矩阵元的近似处理实现两种计算的接合.对一系列含6p区重元素分子进行计算的结果表明,当非重元素是第三周期以前的元素时,此方法与二分量ZO-RA方法的计算结果吻合得很好.当非重元素为第四周期元素时,计算结果有一定偏差,表明在后一种情况下旋轨耦合作用已比较显著,但误差仍在目前近似密度泛函计算的精度范围内.此方法可以有效地节省计算量,而且避免了Dyall方法的缺点.     

Extension of SINDO1 to transition metal compounds

The semiempirical MO method SINDO1, originally suitable for first- and second-row atoms, is extended to transition metals from scandium to zinc. The core Hamiltonian elements in a symmetrically orthogonalized atomic orbital (OAO) basis set are modified and the parameters are optimized to reproduce the experimental geometries, heats of formation, and ionization potentials. An application of the method to a selected number of molecules, as well as a comparison between calculated and experimental data is reported.     

Complete basis set, Gaussian, and hybrid density functional theory evaluation of the proton affinities of water and ammonia

An ab inito computation of reorganization energy for the electron transfer (ET) reactions between metal–benzene and metal ion–benzene complexes is presented. The geometry optimization of the metal–benzene complexes was performed. The metal atoms (or metal ions)– benzene molecule separation distances computed using an ab initio method were found to agree with earlier reported results. Values of reorganization energies using George-Griffith Marcus (GGM) method (the contribution from only diagonal elements of force constant matrix) and Hessian matrix method (including the contribution from both diagonal and off-diagonal elements) were computed. Results of reorganization energy show that the GGM method gives much lower values compared to those obtained using the Hessian method, suggesting that the coupling interactions between different vibrational modes are important to the inner-sphere reorganization energy for the ET reactions in gaseous phase.     

Matrix elements in configuration interaction calculations

A method is proposed for the calculation of matrix elements among various states of atoms. A set of tensor operators is the only entity in the formalism, and all formulas involve merely the vacuum expectation values of these tensor operators and the recoupling transformation coefficients. Some numerical examples are given for the Coulomb interaction matrix elements.     

Potentials of an alternative scheme for ab initio polymer band structure calculations. Illustration on the chain of hydrogen atoms

An alternative scheme for ab initio polymer band structure calculations based on a Filon-type quadrature is proposed. This scheme avoids the explicit calculation and the storage of the “troublesome” Fourier transforms of the LCAO density matrix elements and is a first step towards a better control of the convergence of the different lattice sums appearing in the configuration space LCAO-SCF-CO method. The potential of the proposed technique is illustrated by a minimal basis set calculations on an infinite chain of H atoms.     

Calculation of adiabatic polarization of atomic photofragments under the influence of long range quadrupole-quadrupole interactions

General equations for diagonalization of the quadrupole-quadrupole interaction matrix for diatomic molecules are presented. Eigenvalue and eigenvector solutions are tabulated for atoms with levels J < or = 2. The use of the eigenvector solutions for determination of adiabatic molecule-frame photofragment polarization is illustrated, and polarization parameters a and a are tabulated. Even if knowledge of the photofragment scattering matrix is limited, we illustrate how coherent polarization parameters a0(1) and a0(2) can be calculated from the tabulated adiabatic expansion coefficients, for example, by making use of available experimental data.     

Theory of depolarization of fluorescence in molecular pairs

Depolarization of fluorescence as a result of energy transfer is studied phenomenologically for a model pair of electronically coupled molecules. The usual rate equations are replaced by the Stochastic Liouville Equations and new radiative terms are included. An expression for the fluorescence polarization for all strengths of electronic coupling between the molecules is obtained. The inclusion of off-diagonal density matrix elements is essential for resolving a paradox arising in the Förster theory of depolarization. The calculation points the way toward using a previously untapped source of information on coherence in complex systems.     

Consistent modifications of SINDO1: I. Approximations and parameters

A consistent modification, MSINDO, of the semiempirical MO method SINDO1 is presented. Different basis sets are used for one- and two-center interactions. The treatment of the core matrix elements in the nonorthogonal basis is retained with changes only for hydrogen and 3d orbitals. Orthogonalization corrections are now restricted to nonvanishing core matrix elements in the INDO approximation. The set of atomic parameters is increased, but bond parameters are no longer used. An automatic nonlinear least-squares algorithm with a restricted step constraint is used for the optimization of parameters. Heats of formation are adjusted with inclusion of zero-point energies obtained by a scaling procedure of the force constant matrix. The present version MSINDO provides significant improvements over previous versions. A brief comparison for ground-state properties of the elements H, C, N, O, F, and Na to Cl is given. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 563–571, 1999     

Measurement of atomic fine structure collision transfer cross sections in laser produced vapours

An experimental method is presented which allows the measurement of collision transfer cross sections of atoms almost independent of the volatility of the elements. Laser ablation from solids into a gas atmosphere and laser induced fluorescence in the laser produced vapour cloud is used. The method is demonstrated by the laser atomization of a low alloy steel matrix and by the measurement of fine structure collision transfer cross sections by argon in silicon and chromium which are trace elements in iron.     

Matrix elements for operators for physical quantities in one-configuration functions of radicals

Some basis vectors are constructed for singly and doubly excited configurations of molecules and radicals for the method of configuration interaction in the second-quantization representation. The matrix elements of the Hamiltonian are derived for these. A method is given for calculating bond orders, transition moments, spin densities, and electron densities on atoms in the configuration-interaction method. An analog of Brillouin's theorem is obtained for radicals.Read at the II-nd Ukranian Republic Symposium on Quantum Chemistry. (Kiev, Dec. 1968).     

Spectroscopic properties of alkali atoms embedded in Ar matrix

We present a theoretical investigation of visible absorption and related luminescence of alkali atoms (Li, Na, and K) embedded in Ar matrix. We used a model based on core polarization pseudopotentials, which allows us to determine accurately the gas-to-matrix shifts of various trapping sites. The remarkable agreement between our calculated results and the experimental spectra recorded by several authors allows us to establish a clear assignment of the observed spectra, which are made of contributions from crystalline sites on the one hand, and of grain boundary sites on the other hand. Our study reveals remarkably large Stokes shifts, up to 9000 cm(-1), which could be observed experimentally to identify definitely the trapping sites.     

An INDO-CI method in π-approximation for the calculation of transition metal complexes with organic ligands—application to iron(II)-trisdiimine complexes

An INDO-CI method in π-approximation extended for transition metal complexes with organic ligands is presented. The σ-polarization in the complex is estimated using a two-dimensional EHT calculation and considered in the π-calculation by means of the diagonal Fock matrix elements. The method is tested for four trisdiimine iron(II) complexes. In agreement with the experimental absorption spectra the calculations show that diimine complexes with non-heterocyclicly bound nitrogen atoms exhibit a large red-shift of the characteristic charge-transfer transition increasing the number of aromatic rings. Contrarily, for diimine complexes with heterocyclicly bound nitrogen atoms no shift of the charge-transfer transition was obtained.     

Electronic structure of octavinyl- and octaphenylsilsesquioxane from XPS and DFT data

X-ray photoelectron spectroscopy (XPS) and density functional theory are employed to study the electronic structure of octasilsesquioxanes (RSiO_1.5)₈ with vinyl and phenyl terminal groups. Quantitative compositions determined from the XPS data are close to those estimated by empirical formulas. Narrow spectral lines corresponding to ionization from C1 _s core levels indicate similar chemical states of carbon atoms for both compounds. Experimental data are confirmed by close calculated values of effective charges on carbon atoms when polarization functions are included in the basis set and also by small energy ranges of core level electrons. The valence spectral region is interpreted based on the calculated energy values of electronic levels with regard to the density of states and ionization cross-sections.     

Core polarization and relativistic effects competition in the first ionization potentials for some systems in the Cu,Ag, and Au isoelectronic sequences

Single-configuration relativistic Hartree–Fock values of the first ionization potentials for Cu through Kr⁷⁺, Ag through I⁶⁺, and Au through Pb³⁺ are computed in “frozen” and “relaxed core” approximations with and without allowance for core polarization. Effects of polarization of the atomic core by the valence electron are included by introducing a polarization potential in the one-electron Hamiltonian of the valence electron. The core polarization potential depends on two parameters, the static dipole polarizability of the core α and the cut-off radius r₀, which are chosen independently of the ionization potential data. It is demonstrated that by including the core polarization potential with α and r₀ parameters, which are simply chosen instead of being empirically fitted, it is still possible to account, on the average, for at least 70% of the discrepancy between the single-configuration relativistic Hartree–Fock ionization potentials and the experiment, a discrepancy usually ascribed to the contribution of valence-core electron correlations, and to bring the theoretical ionization potentials to an average agreement with experiment of around 1%. It can be concluded from this study that for low and medium Z elements the core polarization dominates for neutral systems or systems in low ionization stages, whereas for highly ionized systems the relativistic effects prevail. For heavy elements, however, the core polarization influence is comparable to the relativistic one only for neutral systems, whereas for ions the relativistic effects are overwhelmingly predominant.