高精度相对论密度泛函计算方法

对适用于含重元素体系的高精度相对论密度泛函计算方法作简要的评述.结合本实验室的研究工作,重点介绍严格处理相对论效应的四分量相对论密度泛函计算方法和近似处理相对论效应的两分量和标量相对论密度泛函计算方法,包括零级规则展开近似(ZORA)方法及其改进和排除奇点的近似展开(SEAX)方法,以及适合处理局部包含重元素大体系的接合两分量-标量相对论(或非相对论)计算方法.     

水溶液中碳酸铀酰化合物的电子结构

应用相对论密度泛函理论系统研究了水溶液中非水合化和水合化碳酸铀酰化合物Cn/m(其中n和m分别为结构中碳酸配体和水配体的个数)的结构.溶剂效应采用类导体屏蔽模型(COSMO),并采用零级规整近似(ZORA)方法考虑标量相对论效应和旋-轨耦合相对论效应.电子跃迁采用包含旋-轨耦合相对论效应的含时密度泛函理论并在相关交换势中采用轨道势能统计平均(SAOP)做近似计算.结果表明碳酸配体对配合物结构和电子跃迁有很大的影响.C3/0配合物的稳定性可归于5f轨道参与了高占据轨道的成键作用.增加碳酸盐配体导致最大波长的蓝移,并在近可见光区域出现高强度的吸收.     

高精度的非相对论与完全相对论密度泛函理论计算方法和程序

介绍非相对论与完全相对论密度泛函理论计算方法和相应的计算程序（ＮＲ／Ｒ－ＤＦＴ）的结构和功能。本程序是目前用密度泛函理论方法计算完全相对论总能量能达到最高精度的程序。利用本程序可以高精度地计算含重元素体系的总能量、分子轨道能级、原子化能、键合能、偶极矩，分析化学键性质等。     

含重元素大体系的分区密度泛函计算

将分区计算方法推广应用于含过渡金属或重主族金属元素大体系的非相对论、标量相对论和二分量相对论密度泛函计算. 将大体系划分为若干分区, 每个分区视为相对独立的量子力学子体系. 计及各子体系之间势场的作用和Pauli排斥, 对各子体系分别求解Kohn-Sham方程: (F^K+F^K_P)C^K=S^KC^Kε^K K = A, B, C, … 式中F^K, C^K, S^K, ε^K分别为子体系K的Fock矩阵、轨道系数矩阵、基组重叠矩阵和本征值矩阵, F^K_p反映不同子体系的电子之间的Pauli排斥作用. F^K可以是非相对论、标量相对论或者二分量相对论的Fock矩阵, 由计算中采用的密度泛函理论方法决定, 其他矩阵与矩阵F^K相匹配. 汇总各子体系的计算结果给出整个体系的电子结构信息. 对几个含过渡金属镍和重主族金属元素铊和铋的化合物进行了整体和分区计算, 比较两种计算的结果, 考察分区计算方法的可行性. 结果表明, 只要子体系计算的基组足够大, 分区与整体计算结果的精度实际上是相同的. 采用适当的比较小的子体系计算基组, 分区算法结果的精度就可以达到现有近似能量密度泛函实际具有的精度. 因此, 分区算法可用于含重元素大体系的高精度非相对论、标量相对论和二分量相对论的密度泛函计算.     

元素电负性和硬度的密度泛函理论研究

应用密度泛函理论的DFT LDA、DFT LDA/NL和改进的Slater过渡态方法,把元素的电离能和电子亲合能的计算扩展到周期表的103种元素.并用有限差分方法计算了这103种元素的电负性和硬度.计算中考虑了相对论效应.计算结果比以前Robles等用密度泛函理论的XGL和Xα近似的交换相关泛函的计算结果有所改进,更接近实验值.     

密度泛函理论及其数值方法新进展

综述了密度泛函理论及其数值方法的最新进展.密度泛函理论的发展以寻找合适 的交换相关近似为主线,从最初的局域密度近似、广义梯度近似到现在的非局域泛函、自相 互作用修正,多种泛函形式的相继出现使得密度泛函理论可以提供越来越精确的计算结果. 除了交换相关近似的发展,近年来密度泛函理论向含时理论、相对论等方面的扩展也很活跃 .另外,在密度泛函理论体系发展的同时,相应的数值计算方法的发展也非常迅速.从古老 的有限差分、有限元到新兴的小波分析都被用来实现密度泛函理论的数值计算.与此同时, 线性标度的密度泛函理论算法日趋成熟,使得通过密度泛函理论研究诸如生物大分子之类的 体系成为可能.随着密度泛函理论本身及其数值方法的发展,它的应用也越来越广泛,一些新的应用领域和研究方向不断涌现.     

等电子三原子铀化物OUO2+、NUN和NUO+的结构和谐振频率的CCSD(T)计算研究

用小核相对论有效势和CCSD(T)方法计算了三原子铀化物OUO²⁺, NUN和NUO⁺的平衡键长和谐振频率. 计算结果显示U原子内层5s5p5d 电子相关能对这些化合物性质的影响非常小. 除NUN的弯曲振动频率,旋轨耦合效应对这些化合物的结构和频率的影响并不明显. 本文的计算结果与其他研究组的计算结果以及已有的实验值相比符合较好, 这表明作为单参考态方法, CCSD(T)能够对这些体系的键长和频率给出较精确的计算结果. 与此前密度泛函理论(DFT)的计算结果相比, CCSD(T)方法与PBE0泛函的结果吻合最好. 本文的工作有助于在用密度泛函方法研究这些体系时选择合适的交换相关泛函, 也为今后的实验研究提供了新的理论数据.     

Yb、YbO电子激发态的相对论含时密度泛函理论研究

本文用基于精确二分量哈密顿（exact two—component Hamiltonian）的相对论含时密度泛函理论（time-dependent relativistic density functional theory）计算了Yb和YbO的电子激发态,并利用对称性、自然原子轨道对激发态性质和归属进行了详细分析,所得结果支持实验对YbO基态与激发态的指认．     

含旋轨耦合的运动方程耦合簇理论计算闭壳层原子激发能

本文采用X2C(exact two-component)哈密顿量,结合我们最近发展的含旋轨耦合的运动方程耦合簇方法,在EOM-CCSD级别上,用接近完备的基函数计算了一系列闭壳层原子体系的最低单重和三重激发能以及激发态的旋轨耦合分裂能.结果显示,对于IIA族原子、IIB族原子、IIIA族阳离子以及稀有气体原子,本文计算得到的激发能与实验值差别通常在0.1 e V以内.对于IB族正离子,由于CCSD方法对其基态存在较大误差,因此激发能被显著高估.对于激发态的旋轨耦合分裂能,前五周期IIA族原子、IIB族原子、IIIA族阳离子计算结果与实验结果吻合非常好,差别通常在1%以内.对于第六周期体系,这个方法得到的激发态旋轨耦合分裂能与实验比有一定误差,这可能是由于求解Hartree-Fock方程时忽略了旋轨耦合所导致.对惰性气体原子,即使是较轻元素,这个方法给出的旋轨耦合分裂能与实验值也有一定差别.     

镱硫属化合物的密度泛函理论研究

用密度泛函理论(DFT)研究镱硫属化合物的电子结构和性质,通过与实验比较考察了现有的几种近似密度泛函公式对镧系元素化合物的适用程度和相对论效应的影响.结果表明,用DFT计算的YbO键长对实验值的偏差约为0.002nm;但得到的键能即使在考虑梯度校正和相对论效应之后,仍比实验值高,在定域密度近似基础上引入交换梯度校正使键能计算值减小,其中PW86x使键能计算值减小稍多些,结果更接近实验值;相关梯度校正使键能计算值升高.相对论效应使键长缩短0.004～0.006nm,键能减小约0.5eV.计算结果的分析表明,Yb的5d轨道和配体的np轨道间形成σ键和π键.在所研究的分子体系中,配体原子从O到Te、Yb原子的5d轨道布后数依次减少,同键能减弱的顺序一致.相对论效应使键能减小的主要原因是在成键过程中发生了Yb的6s电子向5d轨道的转移,而相对论效应使该过程能量增加.偶极矩和电荷分布的计算表明,Yb-L键以共价性为主,相对论效应使共价性成份增加.     

Spin-orbit relativistic long-range corrected time-dependent density functional theory for investigating spin-forbidden transitions in photochemical reactions

A long-range corrected (LC) time-dependent density functional theory (TDDFT) incorporating relativistic effects with spin-orbit couplings is presented. The relativistic effects are based on the two-component zeroth-order regular approximation Hamiltonian. Before calculating the electronic excitations, we calculated the ionization potentials (IPs) of alkaline metal, alkaline-earth metal, group 12 transition metal, and rare gas atoms as the minus orbital (spinor) energies on the basis of Koopmans' theorem. We found that both long-range exchange and spin-orbit coupling effects are required to obtain Koopmans' IPs, i.e., the orbital (spinor) energies, quantitatively in DFT calculations even for first-row transition metals and systems containing large short-range exchange effects. We then calculated the valence excitations of group 12 transition metal atoms and the Rydberg excitations of rare gas atoms using spin-orbit relativistic LC-TDDFT. We found that the long-range exchange and spin-orbit coupling effects significantly contribute to the electronic spectra of even light atoms if the atoms have low-lying excitations between orbital spinors of quite different electron distributions.     

Gradients for two-component quasirelativistic methods. Application to dihalogenides of element 116

The authors report the implementation of geometry gradients for quasirelativistic two-component Hartree-Fock and density functional methods using either the zero-order regular approximation Hamiltonian or spin-dependent effective core potentials. The computational effort of the resulting program is comparable to that of corresponding nonrelativistic calculations, as it is dominated by the evaluation of derivative two-electron integrals, which is the same for both types of calculations. Besides the implementation of derivatives of matrix elements of the one-particle Hamiltonian with respect to nuclear displacements, the calculation of the derivative exchange-correlation energy for the open shell case involves complicated expressions because of the noncollinear approach chosen to define the spin density. A pilot application to dihalogenides of element 116 shows how spin-orbit coupling strongly affects the chemistry of the superheavy p-block elements. While these molecules are bent at a scalar-relativistic level, spin-orbit coupling is so strong that only the 7p3/2 atomic orbitals of element 116 are involved in bonding, which favors linear molecular geometries for dihalogenides with heavy terminal halogen atoms.     

Calculation of indirect nuclear spin-spin coupling constants within the regular approximation for relativistic effects

A new method for calculating the indirect nuclear spin-spin coupling constant within the regular approximation to the exact relativistic Hamiltonian is presented. The method is completely analytic in the sense that it does not employ numeric integration for the evaluation of relativistic corrections to the molecular Hamiltonian. It can be applied at the level of conventional wave function theory or density functional theory. In the latter case, both pure and hybrid density functionals can be used for the calculation of the quasirelativistic spin-spin coupling constants. The new method is used in connection with the infinite-order regular approximation with modified metric (IORAmm) to calculate the spin-spin coupling constants for molecules containing heavy elements. The importance of including exact exchange into the density functional calculations is demonstrated.     

A singularity excluded approximate expansion scheme in relativistic density functional theory

 A singularity excluded approximate expansion (SEAX) scheme, which can be considered as one between Breit-Pauli expansion and RA expansion schemes, is proposed to expand the total energy of 4-component relativistic density functional theory. The one-electron equation can be derived variationally from the approximate total energy expression. The Hamiltonian of the one-electron equation is bounded from below and can be dealt with variationally, and the gauge dependency error in the ZORA method is essentially eliminated. It is easier to solve the SEAX equation than the IORA equation. The results related to the valence orbitals by solving the scalar SEAX equation agree very well with those by the scalar ZORA ESA method, and the results related to the inner-shell electrons of heavy elements by the two component SEAX calculations agree quite well with those by the 4-component relativistic density functional calculations. Received: 20 February 2002 / Accepted: 29 April 2002 / Published online: 8 July 2002     

Relativistic density functional calculations using two-spinor minimax finite-element method and linear combination of atomic orbitals for ZnO, CdO, HgO, UubO and Cu2, Ag2, Au2, Rg2

In previous work the authors have presented a highly accurate two-spinor fully relativistic solution of the two-center Coulomb problem utilizing the finite-element method (FEM) and furthermore developed a relativistic minimax two-spinor linear combination of atomic orbitals (LCAO). In the present paper the authors present Dirac-Fock-Slater (DFS-) density functional calculations for two-atomic molecules up to super heavy systems using the fully nonlinear minimax FEM and the minimax LCAO in its linearized approximation (linear approximation to relativistic minimax). The FEM gives highly accurate benchmark results for the DFS functional. Especially considering molecules with up to super heavy atoms such as UubO and Rg2, the authors found that LCAO fails to give the correct systematic trends. The accurate FEM results shed a new light on the quality of the DFS-density functional.     

Relativistic effects on the Fukui function

The extent of relativistic effects on the Fukui function, which describes local reactivity trends within conceptual density functional theory (DFT), and frontier orbital densities has been analysed on the basis of three benchmark molecules containing the heavy elements: Au, Pb, and Bi. Various approximate relativistic approaches have been tested and compared with the four-component fully relativistic reference. Scalar relativistic effects, as described by the scalar zeroth-order regular approximation methodology and effective core potential calculations, already provide a large part of the relativistic corrections. Inclusion of spin–orbit coupling effects improves the results, especially for the heavy p-block compounds. We thus expect that future conceptual DFT-based reactivity studies on heavy-element molecules can rely on one of the approximate relativistic methodologies.     

Time-dependent four-component relativistic density functional theory for excitation energies

Time-dependent four-component relativistic density functional theory within the linear response regime is developed for calculating excitation energies of heavy element containing systems. Since spin is no longer a good quantum number in this context, we resort to time-reversal adapted Kramers basis when deriving the coupled Dirac-Kohn-Sham equation. The particular implementation of the formalism into the Beijing density functional program package utilizes the multipolar expansion of the induced density to facilitate the construction of the induced Coulomb potential. As the first application, pilot calculations on the valence excitation energies and fine structures of the rare gas (Ne to Rn) and Group 12 (Zn to Hg) atoms are reported. To the best of our knowledge, it is the first time to be able to account for spin-orbit coupling within time-dependent density functional theory for excitation energies.     

Spin-orbit configuration interaction study of the electronic structure of the 5f (2) manifold of U(4+) and the 5f manifold of U(5+)

The energy levels of the 5f configuration of U(5+) and 5f(2) configuration of U(4+) have been calculated in a dressed effective Hamiltonian relativistic spin-orbit configuration interaction framework. Electron correlation is treated in the scalar relativistic scheme with either the multistate multireference second-order multiconfigurational perturbation theory (MS-CASPT2) or with the multireference single and double configuration interaction (MRCI) and its size-extensive Davidson corrected variant. The CASPT2 method yields relative energies which are lower than those obtained with the MRCI method, the differences being the largest for the highest state (1)S(0) of the 5f(2) manifold. Both valence correlation effects and spin-orbit polarization of the outer-core orbitals are shown to be important. The satisfactory agreement of the results with experiments and four-component correlated calculations illustrates the relevance of dressed spin-orbit configuration interaction methods for spectroscopy studies of heavy elements.     

Solvent effects on heavy atom nuclear spin-spin coupling constants: a theoretical study of Hg-C and Pt-P couplings.

The computation of indirect nuclear spin-spin coupling constants, based on the relativistic two-component zeroth order regular approximate Hamiltonian, has been recently implemented by us into the Amsterdam Density Functional program. Applications of the code for the calculation of one-bond metal-ligand couplings of coordinatively unsaturated compounds containing (195)Pt and (199)Hg, including spin-orbit coupling or coordination effects by solvent molecules, show that relativistic density functional calculations are able to reproduce the experimental findings with good accuracy for the systems under investigation. Spin-orbit effects are rather small for these cases, while coordination of the heavy atoms by solvent molecules has a great impact on the calculated couplings. Experimental trends for different solvents are reproduced. An orbital-based analysis of the solvent effect is presented. The scalar relativistic increase of the coupling constants is of the same order of magnitude as the nonrelativistically obtained values, making a relativistic treatment essential for obtaining quantitatively correct results. Solvent effects can be of similar importance.