Vibrational distributions of the N2 first positive system produced in a flowing helium afterglow

Series of wavefunctions for the ground state of BeH₂ have been compared in the frameworks of the valence bond and the molecular orbital theories for Be-H distances between 1·5 a.u. and 6·0 a.u. using minimum basis sets of Slater-type orbitals with exponents optimized at each internuclear distance. It is confirmed that the model based on the resonance valence state can be useful, particularly when ionic configurations are incorporated with it, although the model emphasizing perfect pairing and including an additional parameter to determine ionic character provides significantly the lowest energies for cases where there is a single degree of freedom in the mixing of valence bond structures. Both molecular orbital and valence bond calculations indicate it is a very good approximation to consider BeH₂ as involving localized electron-pair bonds.     

Calculation of ground and excited states for atoms with an open <Emphasis Type="Italic">f</Emphasis>-shell in the Hartree-Fock-Roothaan approximation

Application of the Roothaan-Bagus method (Hartree-Fock atomic theory) for atoms with one open fⁿ-shell is considered. Energy values for lanthanide atoms in the ground and excited states are calculated by minimization methods of the first and second orders within the limits of Roothaan-Hartree-Fock atomic theory using orbital exponents of Slater-type atomic orbitals. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 75, No. 6, pp. 776–781, November–December, 2008.     

Hartree-fock equations for atoms with two open shells

We have formulated the Hartree-Fock equations for multielectron systems with two open shells (the Huzinaga method) in terms of the density matrix in the LCAO approximation. In order to solve the Hartree-Fock equations, in the algebraic approximation we have obtained expressions for the derivatives of the energy with respect to the density matrix elements and the nonlinear atomic orbital parameters (the orbital exponents). We discuss the question of calculating the open shell parameters (the vector coupling coefficients) in the configurations s¹p^N and s¹d^N within the Huzinaga method. We have calculated the energy for a series of atoms with two open shells in these configurations. Using rather narrow basis sets of Slater-type atomic orbitals), we have obtained energy values close to the results of a numerical solution of the Hartree-Fock equations with sufficiently high accuracy of the virial ratio. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 74, No. 2, pp. 145–152, March–April, 2007     

Visualization of deficiencies in approximate molecular wave functions: the local orbital energy function for the matrix Hartree—Fock model

The local orbital energy function is used to assess the quality of approximate Hartree-Fock orbitals obtained by invoking the algebraic approximation and using a finite basis set expansion. Systematic sequences of distributed universal even-tempered basis sets of spherical-harmonic Gaussian-type functions are used to generate orbitals for which the corresponding total Hartree-Fock energy approaches the 1 μE_h level of accuracy. A pilot study of the behaviour of the local energy function is made for the hydrogenic atom described by a sequence of even-tempered Gaussian basis sets. The results of prototype calculations for the Hartree-Fock ground state of the BF molecule at its equilibrium geometry are presented. Sequences of calculations which use atom-centred basis sets are investigated as well as sequences which also include bond centred functions. The effects of the bond centred functions on the local orbital energy function are analysed. The local orbital energy function is seen as a measure of the quality of calculations carried out within the matrix Hartree-Fock approximation which can be employed in cases where the corresponding finite difference Hartree-Fock results are not available.     

铜(Ⅱ)四配位卤素络离子的电子结构与吸收光谱

本文给出了在络离子CuX₄^--(X=Cl,Br)中的配位体与中心离子的晶场能级。在考虑晶场效应之后,利用改进了的Wolfsberg-Helmholz分子轨道法,计算了该络离子的基态与一些激发态的能量。计算结果与所观察到的配位场跃迁带及电子迁移带的一些特性基本相符。     

A comparison of finite basis set and finite difference Hartree-Fock calculations for the open- shell (X2Σ+) molecules BeF,MgF, CaF and SrF

A comparison is made of the accuracy with which the total electronic energy can be calculated by using either the finite basis set approach (the algebraic approximation) or finite difference methods in calculations employing the restricted Hartree-Fock model for the open-shell ground (X²Σ+) states of the Group Ha fluorides BeF, MgF, CaF and SrF. The convergence of the calculations carried out within the algebraic approximation is monitored by employing systematically constructed basis sets of increasing size. By using two different grids, the accuracy of the finite difference calculations has been estimated to be of the order of 10^?2 μE _h. The average difference between the finite basis set and finite difference total Hartree-Fock energies is 2.75 μE_h. Dipole moments determined within the algebraic approximation are also compared with the corresponding finite difference expectation values.     

Calculation of the ground state energy of neutral atoms (Z ≤ 54) by the algebraic variant of the Hartree-Fock method

High-precision calculations of the ground-state energy of atoms He through Xe are performed in the algebraic approximation of the Hartree-Fock method. The orbital exponents of Slater-type basis functions are optimized using the second-order minimization methods, which allows the virial theorem to be fulfilled to within 10^?15–10^?17 for the first time. The energies of atoms calculated with rather limited basis sets are, in terms of accuracy, as good as the results obtained by using the numerical procedure for solving the Hartree-Fock equations.     

Valence-bond studies on BH3

Valence-bond calculations using a minimal Slater basis set are reported for the ground state of BH₃. The energy obtained with various configurations is compared. A small build-up study involving configurations of natural atomic orbitals is described. The most important configuration is 1s²2sp _x p _y h ₁ h ₂ h ₃. Calculations using hybrid orbitals are described. The perfect pairing, resonance valence-state and molecular orbital approximations are compared with the valence-bond results. The perfect-pairing approximation involving neutral B gives a lower energy than the molecular orbital approximation.     

以一组统一的高斯函数为基函数的双原子分子的Hartree-Fock-Roothaan波函数(Ⅱ)——H2和第一列元素的同核双原子体系A2,A2~±和A2

采用文献的一组统一的doublezeta收缩高斯型函数为基函数,从头计算H₂和第一列元素的同核双原子体系的电子波函数和轨道能量、总能量等物理量。电子态包括同核体系的基态A₂,一些低激发态A₂~*和正负离子态A₂~±,A表示周期表中Li到F的各种元素。计算限于闭壳层电子组态或只带一个未填满的开壳层电子组态。作为例子,报道了H₂和几种基态A₂的电子波函数表。 关键词：     

Application of combined Hartree-Fock-Roothaan theory to atoms with an arbitrary number of closed and open shells of any symmetry

The applicability of a combined open-shell Hartree-Fock theory of atomic-molecular and nuclear systems to the states of a single configuration which has the arbitrary symmetry of open shells is explicitly demonstrated by calculations based on the combined Hartree-Fock-Roothaan equations for atoms. As examples of an application of the combined theory using single-zeta Slater-type basis sets, the calculations have been performed for the lowest states of the lowest and excited electronic configurations of carbon and nitrogen atoms containing one-, two- and three-open shells. For the case of single-open shells for carbon and nitrogen atoms, the double-zeta basis-set calculations are also presented. The results of computer calculations for the orbitals, kinetic and total energies, linear combination coefficients and virial ratios are given.     

The single-determinant approximation with a local potential for excited states

The specific features of the calculations of the electronic structure in the approximation of a local exchange potential that is identical for all the electrons involved are considered. An optimized effective potential method is proposed for calculating the energies of excited electronic states of the same symmetry. A single-particle Schrö dinger equation is derived for an excited state whose orbitals are described by a single-determinant wave function orthogonal to the ground state. The equations determining the local potential for excited states are obtained within the variational approach. The solution to these equations is analyzed in the framework of the parameterized representation of the effective potential. The efficiency of the proposed method is demonstrated by calculating the energies of three excited states of the same symmetry for a HeH molecule. The difference between the results obtained by the Hartree-Fock method and the method proposed in this paper is equal, on average, to 0.05%. A comparison with the results obtained from precise calculations based on the configuration interaction method shows that the accuracy in determining the energy of the excited states by the optimized effective potential method is comparable to the accuracy in calculating the energy of the ground state.     

CASPT2 and CCSD(T) calculations of dipole moments and polarizabilities of acetone in excited states

The acetone molecule is investigated in its ground state and valence ^1,3n-π*, ^1,3π-π*, and ^1,3σ-π* excited states and Rydberg ^1,3n-3s, ^1,3π-3?, ^1,3n-3p_y and ^1,3π-3p_y states using the CASSCF, CASPT2, and CCSD(T) methods. Equilibrium geometries of excited states are obtained and their changes with respect to the ground state are discussed. For most excited states the C_2v symmetry of the ground state is lowered to the C_s symmetry. A series of valence vertical and adiabatic excitation energies is presented along with excitation energies for Rydberg states. The main body of the paper contains Finite-Field Perturbation Theory (FFPT) calculations of electric properties of the vertically as well as geometry relaxed excited states. Dipole moments of valence excited states decrease significantly upon excitation, being about one half of the ground state dipole moment. Polarizabilities usually change upon excitation much less (increase by about 30%) but hyperpolarizabilities are enhanced up to one or two orders of magnitude. The orientation of the dipole moment is reversed in some vertically excited Rydberg states. Properties of the ground and excited states are discussed considering alterations of the electronic structure and shifts in the geometry.     

Ab initio study of the ground and excited states of hydrogen sulphide using SCF and CI calculations

Results from ab initio SCF and CI calculations on the ground state and low-lying valence and Rydberg states of H₂S are reported. A double ξ basis of contracted gaussian functions augmented by polarization and diffuse 3d, 4s and 4p functions is used for the calculations. The geometries of various excited states are studied by means of SCF calculations. The first observed band in the absorption spectrum is predicted to arise from the overlapping of transitions from the 2b₁ orbital to a Rydberg 4s and strongly bent valence upper state. The calculations support the assignment of other spectral features to transitions from the 2b₁ to components of the Rydberg 3d and 4p orbitals.     

Ab initio SCF and limited CI calculations of the d-d transitions in cobalt oxide

Ab initio calculations using an extended set of gaussian-type orbitals have been performed for the CoO₆ ^10- cluster in the Hartree-Fock approximation and with a limited configuration interaction. The results have been compared with those of crystal-field theory. CoO is found to be a very ionic system with localized d-electrons. The excited d-states may be described using a simple configuration interaction scheme, which is found to be almost equivalent to a crystal-field parameterized configuration interaction built on Hartree-Fock results. Localization and delocalization phenomena in openshell systems have been discussed.     

以一组统一的高斯函数为基函数的双原子分子的Hartree-Fock-Roothaan波函数(Ⅰ)——第一,二列元素的双原子氢化物AH,AH±和AH*

我们采用一组统一的基函数,从头计算第一、二列元素的双原子氢化物以及第一列元素的同核和异核双原子体系的波函数。本文是三篇一组文章的第一篇,得到了双原子氢化物的电子波函数以及轨道能量和总能量等物理量,原子核间距取实验值和(或)理论值。这些波函数是狭义Hartree-Fock方程的以Double Zeta收缩高斯型函数为基函数的展开式。这些态包括体系的基态AH、一些低激发态AH^*和正负离子态AH^±,A表示周期表中Li到F和Na到Cl的各种元素。计算限于闭壳层电子组态或只带一个没有填满的开壳层电子组态。作为例子,三种基态AH的电子波函数表报道于文中。 关键词：     

First principles analysis of the MgAl2O4:Ni absorption spectrum

Analysis of the energy-level scheme and absorption spectrum of the Ni²⁺ ion in MgAl₂O₄ was performed. The recently developed first-principles approach to the analysis of the absorption spectra of impurity ions in crystals based on the discrete variational multi-electron (DV-ME) method [K. Ogasawara, et al., Phys. Rev. B 64 (2001) 115413) was used in the calculations. The method is based on the numerical solution of the Dirac equation; no phenomenological parameters are used in the calculations. As a result, complete energy-level scheme of Ni²⁺ and its absorption spectra were calculated, assigned and compared with experimental data on the ground and excited state absorption spectra. Numerical contributions of all possible electron configurations into the calculated energy states were determined. By performing analysis of the molecular orbitals population, numerical contributions of the oxygen 2p- and 2s-orbitals into the 3d molecular orbitals were determined.     

Simple molecular orbital theory interpretation of the photoelectron spectra of the azines ag

A modified Iterative Extended Hückel Method (MIEHM) is introduced and applied to the photoelectron spectra of benzene, pyridine, pyrazine, pyrimidine, pyridazine, s-triazine and s-tetrazine. Guided by comparison with available ab initio Hartree-Fock calculations, the molecular orbitals are divided into four categories. The correlation between calculated orbital energies and experimental ionization energies is then established separately for each group of orbitals, leading to a consistent interpretation of the first ten bands in the photoelectron spectra. The resulting assignment is in general agreement with the one proposed by Gleiter. Heilbronner and Hornung⁴ on the basis of empirical correlation procedures.     

Ab initio SCF CI study of the electronic spectrum of s-tetrazine

Configuration interaction (CI) studies of ground, n→ π* and π→ π* electronically excited states are reported for s-tetrazine. The first n→ π* singlet excited state (¹ B _3u ), which is responsible for the purple-red colour of the molecule, is calculated at 2·80 eV, compared to the experimental transition energy of 2·22–2·70 eV. The singlet-triplet split of the first n→ π* states (¹ B _3u and ³ B _3u states) is calculated to be 0·76 eV.

The interaction of nitrogen lone pair orbitals (n-orbitals) is studied in terms of the ordering of the n π* excited states and found that the SCF orbital ordering is qualitatively in accord with the ordering of the n π* excited states in the CI level.

The first π→ π* excited state (¹ B _2u ) is calculated at 5·99 eV, slightly above the observed range of absorption. Numerous other high-lying singlet states as well as the triplet states have been calculated and they are used to verify several proposals relating to the excited state dynamics in the photo-physical studies of s-tetrazine.     

Comparative electronic structure of a lanthanide and actinide diatomic oxide: Nd versus U

Using a modified version of the Alchemy electronic structure code and relativistic pseudopotentials, the electronic structure of the ground and low lying excited states of UO, NdO, and NdO⁺ have been calculated at the Hartree—Fock (HF) and multiconfiguration self-consistent field (MCSCF) levels of theory. Including results from an earlier study of UO⁺ this provides the information for a comparative analysis of a lanthanide and an actinide diatomic oxide. UO and NdO are both described formally as M⁺²O^?2 and the cations as M⁺³O^?2, but the HF and MCSCF calculations show that these systems are considerably less ionic due to large charge back-transfer in the π orbitals. The electronic states putatively arise from the ligand field (oxygen anion) perturbed f⁴, sf³, df³, sdf², or s²f² states of M⁺² and f³, sf² or df² states of M⁺³. Molecular orbital results show a substantial stabilization of the sf³ or s²f² configurations relative to the f⁴ or df³ configurations that are the even or odd parity ground states in the M⁺² free ion. The compact f and d orbitals are more destabilized by the anion field than the diffuse s orbital. The ground states of the neutral species are dominated by orbitals arising from the M⁺²sf³ term, and all the potential energy curves arising from this configuration are similar, which allows an estimate of the vibrational frequencies for UO and NdO of 862 cm^?1 and 836 cm^?1, respectively. For NdO⁺ and UO⁺ the excitation energies for the Ω states were calculated with a valence configuration interaction method using ab initio effective spin—orbit operators to couple the molecular orbital configurations. The results for NdO⁺ are very comparable with the results for UO⁺, and show the vibrational and electronic states to be interleaved.     

Ab initio calculation of the dipole moment of cyanamide

The He(I) photoelectron spectra of the isoelectronic series Fe(CO)₂(NO)₂, Co(CO)₃NO and Ni(CO)₄ are reported and interpreted by means of ab initio SCF-MO calculations. For the nitrosyl complexes it is found that ionization potentials calculated assuming Koopmans' theorem are seriously in error due to the considerably greater orbital relaxation accompanying ionization from metal than from NO valence orbitals. When such allowance is made for orbital relaxation by performing restricted Hartree-Fock (RHF) calculations on the ionic states, the experimental spectra are accurately reproduced and the observed similarity of the spectra of all three molecules is explained.