Relativistic correlating basis sets for the sixth-period d-block atoms from Lu to Hg

Implementation of Analytical Energy Gradient of Spin-Dependent General Hartree-Fock Method Based on the Infinite-Order Douglas-Kroll-Hess Relativistic Hamiltonian with Local Unitary Transformation

An analytical energy gradient for the spin-dependent general Hartree-Fock method based on the infinite-order Douglas-Kroll-Hess (IODKH) method was developed. To treat realistic systems, the local unitary transformation (LUT) scheme was employed both in energy and energy gradient calculations. The present energy gradient method was numerically assessed to investigate the accuracy in several diatomic molecules containing fifth- and sixth-period elements and to examine the efficiency in one-, two-, and three-dimensional silver clusters. To arrive at a practical calculation, we also determined the geometrical parameters of fac-tris(2-phenylpyridine)iridium and investigated the efficiency. The numerical results confirmed that the present method describes a highly accurate relativistic effect with high efficiency. The present method can be a powerful scheme for determining geometries of large molecules, including heavy-element atoms.

Extension of accompanying coordinate expansion and recurrence relation method for general-contraction basis sets

An algorithm of the accompanying coordinate expansion and recurrence relation (ACE-RR), which is used for the rapid evaluation of the electron repulsion integral (ERI), has been extended to the general-contraction (GC) scheme. The present algorithm, denoted by GC-ACE-RR, is designed for molecular calculations including heavy elements, whose orbitals consist of many primitive functions with and without higher angular momentum such as d- and f-orbitals. The performance of GC-ACE-RR was assessed for (ss|ss)-, (pp|pp)-, (dd|dd)-, and (ff|ff)-type ERIs in terms of contraction length and the number of GC orbitals. The present algorithm was found to reduce the central processing unit time compared with the ACE-RR algorithm, especially for higher angular momentum and highly contracted orbitals. Compared with HONDOPLUS and GAMESS program packages, GC-ACE-RR computations for ERIs of three-dimensional gold clusters Aun (n = 1, 2, …, 10, 15, 20, and 25) are more than 10 times faster.

Relativistic double-zeta, triple-zeta, and quadruple-zeta basis sets for the 4s, 5s, 6s, and 7s elements

Relativistic basis sets of double-zeta, triple-zeta, and quadruple-zeta quality have been optimized in Dirac-Hartree-Fock calculations for the 4s, 5s, 6s, and 7s elements: K, Ca, Rb, Sr, Cs, Ba, Fr, and Ra. The basis sets include SCF exponents for the occupied spinors and for the np shell, exponents of correlating and polarizing functions for the (n - 1) shell and correlating functions for the (n - 2) shell. For the group 2 elements, correlating functions are given for the ns and np shells, whereas for the group 1 elements, functions for polarization of the ns shell are provided. A finite nuclear size was used in all optimizations. Prescriptions are given for constructing contracted basis sets by addition of primitives to the SCF occupied functions.

Relativistic correlating basis sets for actinide atoms from90Th to103Lr

For 14 actinide atoms from (90)Th to (103)Lr, contracted Gaussian-type function sets are developed for the description of correlations of the 5f, 6d, and 7s electrons. Basis sets for the 6d orbitals are also prepared, since the orbitals are important in molecular environments despite their vacancy in the ground state of some actinides. A segmented contraction scheme is employed for the compactness and efficiency. Contraction coefficients and exponents are so determined as to minimize the deviation from accurate natural orbitals of the lowest term arising from the 5f(n-1)6d(1)7s(2) configuration. The spin-free relativistic effects are considered through the third-order Douglas-Kroll approximation. To test the present correlating sets, all-electron calculations are performed on the ground state of (90)ThO molecule. The calculated spectroscopic constants are in excellent agreement with experimental values.

Relativistic correlating basis sets for lanthanide atoms from Ce to Lu

Contracted Gaussian-type function (CGTF) sets for the description of the 4f subshell correlation and of the 6s and 5d subshell correlation are developed for lanthanide atoms from Ce to Yb. Also prepared are basis sets for the 5d orbitals, which are vacant in the ground states of most lanthanide atoms but are essential in molecular environments. In addition, correlating CGTF sets for the 4f subshell correlation are supplemented for the Lu atom. A segmented contraction scheme is employed for their compactness and efficiency. Contraction coefficients and exponents are determined by minimizing the deviation from accurate natural orbitals generated from configuration interaction calculations that include relativistic effects through the third-order Douglas-Kroll approximation. All-electron and model core potential calculations with the present correlating sets are performed on the ground state of the diatomic CeO molecule. The calculated spectroscopic constants are in good agreement with experimental values.

Theoretical study of Pt–Ng and Ng–Pt–Ng (Ng=Ar,Kr,Xe)

We have investigated the binding of noble-gas (Ng) atoms (Ng=Ar,Kr,Xe) with Pt atom by the ab initio coupled-cluster CCSD(T) method, taking into account the relativistic effects. It is shown that two Ng atoms can bind with Pt atom in linear geometry in the singlet lowest state where the second Ng atom attaches to Pt with the larger binding energy than the first Ng atom. The binding energy is evaluated as 8.2, 17.9, and 33.4 kcal/mol for Ar-Pt-Ar, Kr-Pt-Kr, and Xe-Pt-Xe, respectively, relative to the triplet ground state of the dissociation limit Pt ((3)D)+2Ng. The present results indicate that these Ng-Pt-Ng compounds are possible new gas-phase or matrix species.

Compact and efficient basis sets of s- and p-block elements for model core potential method

We propose compact and efficient valence-function sets for s- and p-block elements from Li to Rn to appropriately describe valence correlation in model core potential (MCP) calculations. The basis sets are generated by a combination of split MCP valence orbitals and correlating contracted Gaussian-type functions in a segmented form. We provide three types of basis sets. They are referred to as MCP-dzp, MCP-tzp, and MCP-qzp, since they have the quality comparable with all-electron correlation consistent basis sets, cc-pVDZ, cc-pVTZ, and cc-pVQZ, respectively, for lighter atoms. MCP calculations with the present basis sets give atomic correlation energies in good agreement with all-electron calculations. The present MCP basis sets systematically improve physical properties in atomic and molecular systems in a series of MCP-dzp, MCP-tzp, and MCP-qzp. Ionization potentials and electron affinities of halogen atoms as well as molecular spectroscopic constants calculated by the best MCP set are in good agreement with experimental values.