全相对论多组态原子结构及物理量的精密计算——构建准完备基以及组态相互作用

从第一原理出发计算原子结构有多种理论方法,它们都是基于变分原理的,其关键是构建一组最适合描述真实物理体系的且适用于变分原理的准完备基.本文阐明了如何利用全相对论计算程序GRASPVU,通过单组态Dirac-Fock计算以及多组态Dirac-Fock自洽场计算建立准完备基.然后利用该准完备基进行组态相互作用计算以充分考虑关联作用;在此基础上,进一步考虑电磁相互作用的延迟效应和量子电动力学等修正.该准完备基对原子结构和电磁跃迁等物理量可进行精密的理论计算.最简单的He体系的能级和跃迁速率等物理量的计算值与目前最准确的理论计算值以及精密的实验测量值符合很好,验证了本文提出的方案的适用性.本文计算是全相对论的,可推广到相对论效应很重要的高Z类He体系,以面向重离子储存环相关实验测量.同时该方案也适用于其他任何多电子原子体系;对Mg进行了精密理论计算,阐明了其33D,43D精细结构次序变化的机理.     

Density functional theory calculations of nuclear quadrupole coupling constants with calibrated 14N quadrupole moments

Density functional calculations of the electric field gradient tensor at the nitrogen nucleus in 13 test molecules, containing 14 nitrogen sites, have been performed using the linear combination of Gaussian-type orbital Kohn-Sham density functional theory (LCGTO-KSDFT) approach. Local and gradient corrected functionals were used for all-electron calculations. All the molecular structures were optimized at their respective levels of theory with extended basis sets. Calibrated ¹⁴N nuclear quadrupole moments were obtained through a fitting procedure between calculated electric field gradients and experimental nuclear quadrupole coupling constants of the test set of molecules for each basis set and functional considered. With these calibrated ¹⁴N nuclear quadrupole moments, the nuclear quadrupole coupling constants of the following selected systems were determined: fluoromethylisonitrile, pyridine, pyrrole, imadazole, pyrazole, 1,8-bis(dimethyl-amino)naphthalene, cyclotetramethylenetetranitramine, cocaine and heroin.     

Application of the method of asymptotic projection to the calculation of vertical ionization potentials

An alternative method is proposed for the calculation of ionized states corresponding to the excitation of both valence and core electrons. Unlike the well-known approaches, in which such states are constructed by removing an electron from the corresponding spin orbital, the method proposed employs the requirement that all the spin orbitals of the ionized system are orthogonal to the spin orbitals of the neutral system. The proper spin symmetry and the orthogonality of the wave functions of these states to the wave function of the neutral molecule are ensured by a simple-to-use method of taking into account the orthogonality that was proposed by us earlier. The adequacy of the proposed scheme is demonstrated by the calculation of 15 ionization potentials of diatomic and triatomic molecules at different levels of the theory. The results of the calculations, performed in optimized basis sets including three to five Gaussian s functions per electron, are in good agreement with experimental data and state-of-the-art results obtained by other methods in extended basis sets.     

Experimental and theoretical investigations into the electronic structure of CF2Br2 by electron momentum spectroscopy

The binding energy spectra and electron momentum density distributions for the valence orbitals of CF₂Br₂ have been obtained by using electron momentum spectroscopy (EMS) at an impact energy of 1200 eV plus binding energy. The measured electron momentum profiles are compared with Hartree–Fock (HF) and density functional theory (DFT) calculations with different-sized basis sets. In general, the DFT-B3LYP calculation using the large basis sets of 6-311++G** and aug-cc-pVTZ fairly describe the experimental results. Moreover, the controversial orderings of the outer valence orbitals have been reassigned. The pole strength of the main ionization transition from the inner valence orbital of 1b₂ is determined.     

Self-consistent field theory of collisions: Orbital equations with asymptotic sources and self-averaged potentials

The self-consistent field theory of collisions is formulated, incorporating the unique dynamics generated by the self-averaged potentials. The bound state Hartree–Fock approach is extended for the first time to scattering states, by properly resolving the principal difficulties of non-integrable continuum orbitals and imposing complex asymptotic conditions. The recently developed asymptotic source theory provides the natural theoretical basis, as the asymptotic conditions are completely transferred to the source terms and the new scattering function is made fullyintegrable. The scattering solutions can then be directly expressed in terms of bound state HF configurations, establishing the relationship between the bound and scattering state solutions. Alternatively, the integrable spin orbitals are generated by constructing the individual orbital equations that contain asymptotic sources and self-averaged potentials. However, the orbital energies are not determined by the equations, and a special channel energy fixing procedure is developed to secure the solutions. It is also shown that the variational construction of the orbital equations has intrinsic ambiguities that are generally associated with the self-consistent approach. On the other hand, when a small subset of open channels is included in the source term, the solutions are only partiallyintegrable, but the individual open channels can then be treated more simply by properly selecting the orbital energies. The configuration mixing and channel coupling are then necessary to complete the solution. The new theory improves the earlier continuum HF model.     

SiN自由基X2∑+, A2Π和B2∑+ 电子态的光谱常数研究

采用内收缩多参考组态相互作用(MRCI)方法, 结合价态范围内的最大相关一致基aug-cc-pV6Z, 计算了SiN自由基X²∑⁺, A²Π 和B²∑⁺电子态的势能曲线. 采用Davidson修正来避免由于MRCI方法本身的大小一致性缺陷产生的误差. 为了提高计算精度, 进一步考虑了相对论修正和核价相关修正对势能曲线的影响. 本文的相对论修正是利用二阶Douglas-Kroll 哈密顿近似在cc-pV5Z基组水平进行的; 同时核价相关修正是在cc-pCV5Z基组水平进行的. 对这些势能曲线进行拟合, 得到各种水平下三个电子态的光谱常数(T_e, R_e, ω_e, ω_ex_e, α_e和B_e), 并详细分析了Davidson修正、相对论修正和核价相关修正对光谱常数的影响. 与其他理论结果和实验数据进行比较, 可知本文的结果更精确、更完整.     

Non-orthogonal tight-binding approach to surface states of covalent semiconductors

A non-orthogonal tight-binding approach to the surface electronic structure of covalent semiconductors is formulated. Using a non-orthogonal basis of bonding, antibonding and dangling-bond orbital surface states, in particular empty surface resonances in the conduction band are computed. Calculations are performed for Si (111) ideal and relaxed surfaces, leading to results in good agreement with self-consistent calculations. The advantage of using a non-orthogonal basis which effectively results in improved orbital localization is demonstrated.     

Fast calculation technique for scattering in T-matrix method

In scattering calculations using the T-matrix method, the calculation of the T-matrix involves multiplication and inversion of matrices. These two types of matrix operations are time-consuming, especially for the matrices with large size. Petrov et al. [D. Petrov, Y. Shkuratov, G. Videen, Opt. Lett. 32 (2007) 1168] proposed an optimized matrix inversion technique, which suggests the inversion of two matrices, each of which contains half the number of rows. This technique reduces time-consumption significantly. On the basis of this approach, we propose another fast calculation technique for scattering in the T-matrix method, which obtains the scattered fields through carrying out only the operations between matrices and the incident field coefficient. Numerical results show that this technique can decrease time-consumption by more than half that of the optimized matrix inversion technique by Petrov et al.     

Addendum

A continuum model potential taking into account a spatially varying dielectric constant is employed to make a fully self-consistent calculation of the enhancement of the donor polarizability as a function of donor concentration N_D as N_D approaches N_c, the critical concentration for metallic behavior. The results yield a new self-consistent Clausius-Mossotti criterion for the polarization catastrophe at N_c. Using the dilute concentration value of the donor polarizability N_c is uniquely determined. The results are compared with earlier experimental results for N-type silicon and with other theoretical calculations.     

Electronic structure and magnetism of FeGe2

The electronic band structure of FeGe₂ has been calculated using the self-consistent full potential non-orthogonal local orbital minimum basis scheme based on the density functional theory. In the band structure of FeSn₂, Fe 3d and Sn 5p states play important roles near the Fermi level. Our calculations show that large enhancement of the static susceptibility over its non-interacting value is found due to a peak in the density of states at the Fermi level.     

Design and optimization of 2D photonic crystal waveguides based on silicon

The existence and properties of photonic band gaps was investigated for a square lattice of dielectric cylinders in air. Band structure calculations were performed using the transfer matrix method as function of the dielectric constant of the cylinders and the cylinder radius-to-pitch ratio r/a. It was found that band gaps exist only for transverse magnetic polarization for a dielectric contrast larger then 3.8 (index contrast >1.95). The optimum r/a ratio is 0.25 for the smallest index contrast. For silicon cylinders (n = 3.45) the widest gap is observed for r/a = 0.18. Band structure calculations as function of r/a show that up to four gaps open for the silicon structure. The effective index was obtained from the band structure calculations and compared with Maxwell–Garnett effective medium theory. Using the band structure calculations we obtained design parameters for silicon based photonic crystal waveguides. The possibility and limitations of amorphous silicon, silicon germanium and silicon-on-insulator structures to achieve index guiding in the third dimension is discussed.     

Semiempirical studies of core electron binding energy shifts: Part 5. SCC—MO investigation of keto—enol tautomerism in some 1,3-diketones and related anhydrides

The keto—enol tautomerism in malonaldehyde and some related 1,3-diketones is thoroughly discussed by the calculation of inner-core binding energies. The semiempirical wave-functions were obtained by the self-consistent charge (SCC—MO) molecular orbital procedure. The calculated O(1s) binding energies are generally in good agreement with available experimental data. The discrepancy found for the alcohol-type oxygen in acetylacetone is so large that it strongly indicates an error in experimental assignment. The calculations also provide conclusive evidence that enol-forms possess asymmetric hydrogen-bonded protons.     

The calculation of dynamic polarizabilities and of the dipole-dipole and dipole-quadrupole contributions to the dispersion energy

By using a single Slater-type 2p orbital with a frequency-dependent exponent in the basis set for the variation solution of the first-order time-dependent perturbation equation, good results are obtained for the dipole dynamic polarizability of the hydrogen atom. The accuracy attained has been reproduced only by variation calculations with larger basis sets. The same happens with the quadrupole dynamic polarizability: a single 3d Slater-type orbital with a similarly optimized exponent in the basis of states for the variation calculation is enough to yield results which are very close to the exact values for all frequencies. Using the frequency-dependent dipole and quadrupole polarizabilities thus obtained we have calculated the dipole and quadrupole contributions to the dispersion energy of two hydrogen atoms and found results which are within 1 per cent of the exact values.

Considering the simplicity of our wavefunction as compared with the four-term wavefunction used by Chan and Dalgarno [5] to construct the basis for their variation calculation and the excellent agreement we obtain, it is important to emphasize the value of using optimized frequency-dependent exponents in the basis of states used for the variation calculation.     

Microscopic theory of surface dielectric response in a local representation

We give a formulation of surface dielectric response in a local LCAO or Wannier representation. It is shown that this representation allows for a practical solution of the response integral equation and thus makes possible an explicit and self-consistent calculation of the nonlocal RPA response function ?^-1. The formulation takes into account lattice potential effects and is therefore particularly suited for investigations of surface dielectric response and screening in transition metals, semiconductors and insulators. We present model calculations of charge densities induced in a metal thin film by localized perturbations in the surface region. It is demonstrated that “surface effects”, resulting from differences in the effective atomic potential for different layers, must be included in calculations of surface response in systems with tightly bound electrons.     

Optimum basis sets of spherical Gaussian functions and their structure for high-precision calculations of the energies of molecules in the Hartree-Fock approximation

Specific features of the construction of variationally optimized basis sets providing a high accuracy in calculations of molecular energies in the Hartree-Fock approximation are described. Equations for the optimization of basis sets are obtained for systems with closed and open electronic shells and the structure of an energy hypersurface in the space of nonlinear parameters is considered. The structure of optimum basis sets is studied to develop simple models for generation of orbital exponents and centers of atomic functions. It is shown that, for different molecules, there exist characteristic features of optimum basis sets that are retained with increasing size of a set. Possible strategies for generation of the parameters of basis sets are proposed and preliminary results of their application to the calculation of the ground-state energies of simple diatomic molecules are discussed.     

Convergence acceleration for the multilevel Hartree–Fock model

In the previously introduced multilevel Hartree–Fock (HF) model, the electronic density is optimised in a given region of the molecular system. The approach is based on generating an active occupied and active virtual space by decomposing a start guess density for the entire system. In this work, a diagonalisation based implementation for Roothaan–Hall (RH) with direct inversion in iterative subspace (DIIS) and a quasi-Newton minimisation procedure using the augmented RH (ARH) approach are described for accelerating convergence for the multilevel HF model. The equations are derived to be consistent with convergence acceleration for traditional atomic orbital based HF calculations. The main idea is to formulate all quantities in the molecular orbital basis to exploit that the active molecular orbital basis is significantly smaller than the atomic orbital basis, and thus enable the application of wave function approaches that are well-studied for small molecular systems to large molecular systems. Thus, all equations are formulated such that no atomic orbital density or Fock matrices are needed for the DIIS and ARH algorithms. Results show that the acceleration schemes yield efficient optimisation of the multilevel HF wave function.     

CASPT2 study on low-lying states of HBS+ and HSB+ cations

Some low-lying states of the nine-valence-electron systems HBS⁺ and HSB⁺ cations have been studied by large-scale theoretical calculations using three methods CASSCF, CASPT2, and DFT B3LYP with the contracted atomic natural orbital and cc-pVTZ basis sets. The geometries of all stationary points along the potential energy surfaces were optimized and the energies were calculated. The potential energy curves of isomerization reactions between HBS⁺ and HSB⁺ were calculated as a function of HBS bond angle. The calculated results indicated that the ground-state HBS⁺ is linear, while the ground-state HSB⁺ is bent, which is in contradiction to Walsh's rules predicting linear structures for the HXY systems containing 10 or less valency electrons.     

Role of point defects on conductivity, magnetism and optical properties in In2O3

In order to assess the effects of point defects including transition metal doping on its electronic structure, the self-consistent band structure of the transparent oxide In₂O₃ (in the Ia₃ structure) has been calculated with oxygen vacancies, oxygen and indium interstitial atoms and several transition metal dopants using density functional theory based first principles calculations. An oxygen vacancy alone does not act as a strong native donor but when combined with interstitial indium and (substitutional) transition metal doping, shallow donor levels close to the conduction band are formed. Spin polarized calculations show measurable magnetism in some of the transition metal doped systems while the dielectric functions indicate whether such systems remain transparent among other things.     

The accuracy of local MP2 methods for conformational energies

The relative energies of 95 conformers of four peptide models are studied using MP2 and LMP2 methods and correlation consistent basis sets ranging from double-zeta to augmented quintuple-zeta quality. It is found that both methods yield quite similar results, and the differences between MP2 and LMP2 decrease systematically with increasing basis set. Due to reduced intramolecular basis set superposition effects (BSSE), the LMP2 results converge more slowly to the basis set limit for most of these rather small systems. However, for larger peptides, the BSSE has a very large effect on the energy difference between extended and helical structures, leading to a very strong basis set dependence of the canonical MP2 results. It is demonstrated for alanine octapeptides that the basis set error exceeds 30 and 20kJ mol^?1, respectively, if augmented double-zeta and triple-zeta basis sets are used. On the other hand, the LMP2 results are only slightly affected by the basis set size, and, even with augmented double-zeta basis sets, reasonably accurate results are obtained. Furthermore, for the larger systems, the computation times for the LMP2 calculations are shown to be up to one order or magnitude shorter than for canonical MP2 calculations with the same basis set.     

Raman optical activity spectra: basis set and electron correlation effects

Raman and vibrational Raman optical activity (ROA) spectra have been calculated for three molecules: H₂O₂, CHDTF and CHDTOH. The effects of electron correlation on the ROA parameters of these relatively small systems have been investigated by means of the multiconfigurational self-consistent field (SCF) approach. A range of correlation-consistent basis sets has been used in the calculations. The basis set convergence of the calculated ROA parameters is fairly well achieved when sets of at least d-aug-cc-pVTZ quality are used. On the other hand, the aug-cc-pVDZ set seems to be sufficient for a qualitative analysis. Diffuse functions, possibly a double set, are essential to ensure a good quality of the calculated ROA spectrum. In most cases the sign and approximate magnitude of the ROA are correctly predicted at the SCF level, and the corresponding ROA spectra should be considered qualitatively accurate.