An eigenvalue problem with limitations in a finite movable basis

An asymptotic method for taking into account the constraints of the orthogonality type when solving eigenvalue problems is developed. The features of the variational determination of eigenvalues are considered, with various finite-dimensional Hilbert subspaces being used to calculate different eigenvalues. A hydrogen molecular ion is used as an example to study the influence of the finite-dimensional approximation and basis optimization on the accuracy of determining the states of identical symmetry. Calculations have shown that the method proposed makes it possible to construct a flexible, consistent scheme for determining the energies of the ground and excited states. The total energy values obtained in a basis of 29 primitive Gaussian functions differ from exact values by 0.228 μH for the ground 1σ_g state and 0.413 μH (microhartree) for the excited 2σ_g state.     

Partially restricted Hartree-Fock method for singlet excited states

A version of the partially spin-restricted Hartree-Fock method is proposed to construct a reference Slater determinant in calculations of singlet excited states having the same symmetry as the ground one. On the one hand, this approach can be used for a rather simple, in comparison with the fully unrestricted determinant, construction of a pure spin state. On the other hand, it is suitable, in contrast to the Roothaan theory for open shells, for the development of the perturbation scheme for taking into account correlation effects in an excited state, which retains the calculation advantages of the Moller-Plesset perturbation theory with single annihilation for the ground state. The efficiency of the method is demonstrated by calculations of electronic excitation energies for BH and CH⁺ molecules.     

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.     

Extension of the Local Approach to excited states of molecules

The Local Approach for the calculation of electronic correlation energies in molecules is generalized to excited states. Within the Local Approach correlated states are obtained by applying a local projection operator on the Hartree-Fock ground state or simple reference states, which are used as zeroth order approximations for the excited states, respectively. In the case of excited states one has in addition to require the correlated states to be orthogonal on the states lower in energy. This is done by using Schmidt's orthogonalization. The method is applied to a simple model of the H₆-ring for which an exact solution is available. The results obtained are of comparable quality as for the ground state.     

Parameterized Effective Potential for Excited States and Its Application to the Calculation of Transition Dipole Moments

Optics and Spectroscopy - A parameterized effective potential method that was proposed earlier for the ground state has been developed for excited states with symmetry of the ground state. Various...     

On the computation of electronic excitations in solids

An approximation scheme is proposed for calculating electronic excitations in solids. It is described within a projection operator formalism of the Mori-Zwanzig type. The approximation consists in successively limiting the space of dynamical variables which are treated. The selection of the variables is done by making use of the local character of the correlation hole which is surrounding an electron. The method is distinct from a perturbation expansion and can be related to a variational ansatz via the Sauermann functional. The computation of the spectral density of the Green's function is reduced to the diagonalization of matrices. Their dimension depends on the required degree of accuracy of the calculations. The present method can be considered as an extension to excited states of a previously developed. Local Approach for ground state calculations.Dedicated to Prof. S. Methfessel on the occasion of his 60th birthday     

Parameterized effective potential for excited electronic states

The method of the parameterized effective potential (PEP) is developed for constructing the potential curves of excited electronic states of the same symmetry. Unlike the traditional methods of the density functional theory, the PEP is constructed as the direct mapping of an external potential. The PEP generates the one-particle orbitals such that the corresponding single-determinant Kohn-Sham function constructed on their basis is orthogonal to the determinant functions of lower-lying states. A comparison of the potential curves constructed for the HeH and H₂ molecules by the PEP method with the precision data obtained based on the time-consuming configuration interaction methods shows that the PEP method can provide good accuracy for the geometry of an equilibrium configuration and the vertical excitation energies.     

Brueckner-type reference determinants in applications of coupled cluster methods to excited states

Model studies have been undertaken of the efficiency of single-reference state coupled cluster (SR-CC) methods defined in terms of several Brueckner type orbitals in applications to excited states of a predominately closed shell structure. The H4 model was used, which offers an easy way of representing any set of symmetry adapted orbitals together with the possibility of varying the degree of quasi-degeneracy of the states considered. Standard Brueckner orbitals (BOs) and orbitals generated in the projective and variational Brueckner CC (BCC) methods have been obtained and compared for the first time for excited states. Some attention has been paid to the stability of the BOs. Results of applying Brueckner-type and RHF orbitals in CCD, CCSD, and CCSDT calculations for excited states of rather strong degrees of quasi-degeneracy are presented. It is shown that in most cases proceeding from RHF orbitals to Brueckner-type orbitals results in an improvement in the accuracy of the SR-CC energies. Differences and similarities in the characteristics of Brueckner-type orbitals and SR-CC results for excited states and the ground state are identified and 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：     

Electron–hole transition energy for a spherical quantum dot confined in a nano-cylindrical wire

A single-band constant confining potential is applied to InAs spherical quantum dot confined in a GaAs cylindrical nano-wire to determine the electronic structure. The energy eigenvalues and transition energies are numerically calculated as a function of the dot radius. The calculations were performed within the effective mass approximation, using the finite element method. The effect of both spherical and cylindrical confinement, the size dependence of the ground and first excited state energies for electron and heavy hole and transition energies are reported and compared with experimental and theoretical results in relevant conditions.     

Quantum state of muon and proton in crystalline silicon

Quantum state and dynamics of muon and proton in crystalline silicon have been studied by solving one‐particle Schrödinger equations for the impurities. The ground state wavefunctions and energies are determined as a function of local distortion of the host Si lattice, where the Si–H interaction we used is that parameterized by Ramírez and Herrero following the results of earlier pseudopotential‐density‐functional calculation. It is shown that quantum zero‐point motion of muon induces an effective potential barrier between the tetrahedral‐symmetry (T) site and the bond‐center (BC) site, which ensures bistability of muonium states observed in experiments. It is also shown that, if we fully consider the quantum effect with the present model potential, the BC site becomes less stable than the T site on the contrary to the experiments and former theoretical calculations.     

Calculation of Binding Energies of the Ground and Excited States of a Donor in Quantum Wells: A Functional Variational Approach

The calculations of the ground and a few low-lying excited states of impurity in the quantum wells (QW's) are presented by making use of a functional variational approach. A new trial wave function is proposed. It is taken by the product of the exact subband state in the Q W and the state of two-dimensional (2D) hydrogenic-like donor with an effective charge distribution along the z-direction (perpendicular to the well interfaces). The variation of binding energies of the donor states in the QW with the well-width is calculated. The calculated result is compared with that obtained by the earlier variational method. The functional variational approach proposed here has some benefits such as, to bring a great flexibility and to apply to a relatively large species of trial wave functions.     

外场下丙烯酸甲酯的激发特性研究

采用密度泛函B3LYP方法在6-311+ +G* *基组上优化了不同外电场作用下丙烯酸甲酯分子的基态几何结构、电偶极矩和分子的总能量,并且分析了分子的HOMO-3到LUMO+3轨道的能量变化,然后利用杂化CIS-DFT方法(CIS-B3LYP)在相同基组下探讨了无电场时丙烯酸甲酯分子前9个激发态的激发能、波长和振子强度和外电场对丙烯酸甲酯分子激发态的影响规律.结果表明,分子的几何构型与外电场大小有着较强的依赖关系.随着外电场的增大,分子总能量先增大后减小,电偶极矩μ先减小后增大,激发能随电场 关键词： 丙烯酸甲酯 外电场 振子强度 激发能     

Squeezed magnetobipolarons in two-dimensional quantum dot

In this Letter, a different method was given for calculating the energies of the magnetobipolarons confined in a parabolic QD (quantum dot). We introduced single-mode squeezed states transformation, which are based on the Lee-Low-Pines and Huybrechts (LLP-H) canonical transformations. This method can provide results not only for the ground state energy but also for the excited states energies. Moreover, it can be applied to the entire range of the electron-phonon coupling strength. Comparing with the results of the LLP-H transformations, we have obtained more accurate results for the ground state energy, excited states energies and binding energy of the bipolarons. It shows that the magnetic field and the quantum dot can facilitate the formation of the bipolarons when η is smaller than some value.     

Vibronic spectra, ab initio calculations, and structures of conformationally non-rigid molecules of oxalyl halides in the ground and lowest excited electronic states. Part II: Theoretical investigation of oxalyl chloride

The structures of the oxalyl chloride molecule (COCl)₂ in the ground and the four lowest (two singlet and two triplet) excited electronic states were investigated by means of the CASPT2(8-6)/cc-pVTZ technique. The equilibrium geometric parameters, harmonic vibrational frequencies, and adiabatic energies of the electronic transitions were determined for all states under investigation. The calculations predicted the existence of the trans- and gauche- conformers in the ground state and the trans- and cis-conformers in all excited states. For the ground electronic state, the conformer energy difference and the barriers to conformational transitions were estimated using extrapolation to the complete basis set within a Valence Focal-Point Analysis procedure. The internal rotation in the excited electronic states was found to be strongly coupled with the non-planar symmetric CCOCl wagging. Two-dimensional potential energy surface sections along internal rotation and non-planar coordinates were constructed, and the corresponding anharmonic vibrational problems for the trans-conformer were solved.     

Comparison between analytical and numerical methods as applied to calculations of excited atomic states

This article presents a comparison between two approaches for implementing a variational method when calculating excited states of atoms, namely a numerical approach in which the equations arising from the requirement of an extremum of the variational functional (the Hartree—Fock equations) are solved, and an analytical approach in which the energy functional expressed in terms of analytical test functions is minimized. Both approaches are analyzed from the point of view of the approximations used to ensure that the conditions are satisfied for the complete wave function of the excited state being sought to be orthogonal to all wave functions of lower-lying energy states having the same symmetry. The well-known ATOM package is used for numerically solving the Hartree—Fock equations and the MINMAX package is used for the analytical variational calculations. It is shown that the analytical approach based on the minimax method possesses greater possibilities for taking account of relaxation effects. A comparison is made between single-electron wave functions, the matrix elements, and the energies of dipole transitions for a number of excited states of the Ne atom, as calculated using both approaches. State Pedagogical University, Tomsk. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 120–128, July, 1998.     

Lipkin模型下最陡下降法的理论计算

书由Cioslowski提出和被文根旺推广了的最陡下降法用于Lipkin可解模型,计算结果表明,用该方法对基态的近似计算可以达到任意精度,在相互作用较强的情况下,随着激发态能量的升高,所得激发态结果的精度将逐渐降低。该方法原则上不受相互作用强度的限制,在微扰论不适用的强相互作用下亦可得到满意的结果。该方法确实可望成为一种实用的量子力学计算方案。     

7LiH分子基态及若干激发态的平衡几何及垂直激发能的从头算

使用“对称性匹配簇-组态相互作用方法”(SAC/SAC-CI),在多种基组下计算了7LiH分子X1Σ 、A1Σ 、B1Π及b3Π态的平衡几何,并将由“几何优化”得到的相应各态的平衡几何与“单点能扫描”得到的结果进行了比较。比较的结果表明,由“几何优化”得到的相应各态的平衡几何,与“单点能扫描”得到的结果存在着差异。分析的结果表明,在完全活性空间中,由“SAC/SAC-CI”方法进行“单点能扫描”得到的结果,比“几何优化”得到的结果更加合理。首次报告了使用6-311G(3df,3pd)基组进行“单点等扫描”得到的相应各态的平衡几何。其值分别是:基态(X1Σ )为0.1588 nm、单重态的第一激发态(A1Σ )为0.2487 nm、单重态的第二激发态(B1Π)为0.2434 nm、三重态的第二激发态(b3Π)为0.1958 nm。这一计算结果与实验值非常接近。还研究了从基态到上述相应各态的垂直激发能,在基态的平衡位置处,其值分别为(A1Σ ←X1Σ )3.613 eV(、B1Π←X1Σ )4.612 eV和(b3Π←X1Σ )4.233 eV。与其它理论计算结果进行比较后得出,本文的计算结果非常接近于使用很复杂的计算方法获得的结果。     

基态和单态第一激发态的联氨单分子分解反应的密度泛函研究

本文运用密度泛函B3LYP/6-311+G(3df,2p)方法研究了联氨分子的电子结构和能量,并系统分析了联氨分子的分解反应,计算绘制了单分子联氨在基态和单态第一激发态下沿N-N分解反应的势能曲线。本文计算发现联氨分子在这两种电子态下的离解能分别是：基态58.8 kcal/mol,单态第一激发态495.5 kcal/mol。基态分子分解反应是吸热反应,而单态第一激发态分解反应是放热反应。计算发现单态第一激发态的激发能是554.2 kcal/mol。结合这两种电子态下联氨分子的红外振动频率分析,本文认为,在非强制断键的情况下,联氨分子沿N-N键均裂而生成两个NH2自由基的可能性很小。     

Selected aspects of the quantum dynamics and electronic structure of atoms in magnetic microtraps

We analyze the quantum properties of atoms in a magnetic quadrupole field. The quantum dynamics of ground state atoms in this field configuration is studied firstly. We formulate the Hamiltonian and perform a symmetry analysis. Due to the particular shape of the quadrupole field in general there exist no stable states. We provide resonance energies, lifetimes and calculate the density of states and investigate under what conditions quasi-bound states occur that possess long lifetimes. An effective scalar Schrödinger equation describing such states is derived. As a next step we explore the influence of a high gradient quadrupole field on the electronic structure of excited atoms. An effective one-body approach together with the fixed nucleus approximation is employed in order to derive the electronic Hamiltonian. We present the energy spectrum and discuss peculiar features such as non-trivial spin densities and magnetic field induced electric dipole moments.