Takahito Nakajima

The higher-order Douglas–Kroll transformation

The higher-order Douglas–Kroll (DK) Hamiltonians in an external potential are explicitly derived. Application of an exponential-type unitary operator with the 2n+1 rule significantly simplifies the formulations of the high-order DK Hamiltonians. The third-order DK method has been implemented practically. Numerical results for one- and many-electron systems show that good accuracy can be obtained even with the DK Hamiltonian correct to third order in the external potential.

Accurate relativistic Gaussian basis sets for H through Lr determined by atomic self-consistent field calculations with the third-order Douglas–Kroll approximation

Highly accurate relativistic Gaussian basis sets are developed for the 103 elements from H(Z=1) to Lr (Z=103). Orbital exponents are optimized by minimizing the atomic self-consistent field (SCF) energy with the scalar relativistic third-order Douglas–Kroll approximation. The basis sets are designed to have equal quality and to be appropriate for the incorporation of relativistic effects. The basis set performance is tested by calculations on prototypical molecules, hydrides, and dimers of copper, silver, and gold using SCF, Moller–Plesset theory, and the singles and doubles coupled-cluster methods with and without perturbative triples [CCSD, CCSD(T)]. Spectroscopic constants and dissociation energies are reported for the ground state of each species. The effects of relativity, electron correlation, and the basis set superposition error (BSSE) are investigated. At the BSSE corrected CCSD(T) level, the mean absolute error relative to experiment in De for three dimers (hydrides) is 0.13 (0.09) eV; for Re th...

A new relativistic theory: a relativistic scheme by eliminating small components (RESC)

Abstract A new relativistic theory has been proposed by the elimination of small components of the Dirac equation. It is variationally stable and can easily be incorporated into any electronic structure theory. The present formalism is tested in standard problems of Ag and Au atoms and their hydrides at various levels of theory including single- and multi-reference-based methods. Numerical results show that good accuracy can be obtained.

A density functional study on the adsorption of methanethiolate on the (111) surfaces of noble metals

The adsorption energies and structures of methanethiolate, SCH3, on the (111) surfaces of Au, Ag, and Cu have been studied using a density functional theory. The results obtained for the Au surface are in good agreement with experiments and previous calculations. The strength of the adsorption energies is found to be Cu>Ag>Au, and the nature of the chemisorption bond is discussed. The strong interaction between the SCH3 and Cu surface can be explained in a similar way to that as for the binding energy of SCH3 with metal atoms. Scalar-relativistic effects in the adsorption energies and adsorption structures, which dominate the differences observed between the Ag and Au surfaces, are studied using quasirelativistic and nonrelativistic pseudopotentials. The relativistic effects decrease the adsorption energy of SCH3 on the Au(111) surface, although the binding energy of the AuSCH3 complex is increased by relativity. The unexpected relativistic effects are also discussed.

Extended Douglas–Kroll transformations applied to the relativistic many-electron Hamiltonian

A new generalized Douglas–Kroll (DK) approach is proposed for the relativistic many-electron Hamiltonian including the electron–electron interaction. In order to consider the higher-order DK transformation to the two-electron interaction, the present approach adopts the effective one-electron potential in the Dirac–Hartree–Fock/Dirac–Kohn–Sham operator as an expansion parameter in the DK transformation. Its numerical performance is tested for the atomic Hg and molecular HAt and At2 systems. The third-order DK transformation to both one-electron and two-electron Hamiltonians, which is the highest level of theory treated in this study, gives excellent agreement with the four-component relativistic approach. The first-order DK correction to the two-electron interaction is shown to be satisfactory for both atomic and molecular systems.

Accurate relativistic Gaussian basis sets determined by the third-order Douglas–Kroll approximation with a finite-nucleus model

Highly accurate relativistic Gaussian basis sets with a finite-nucleus model are developed for the 103 elements from H (Z=1) to Lr (Z=103). The present GTO sets augment the relativistic basis sets with a point-charge model proposed in the first paper of this series. The relativistic third-order Douglas–Kroll approach is adopted in optimizing the orbital exponents of a basis set by minimizing the atomic self-consistent field (SCF) energy. The basis sets are designed to have equal quality and to be appropriate for the incorporation of relativistic effects. The performance of the present basis sets is tested by calculations on a prototypical molecule, gold dimer using SCF and the singles and doubles coupled-cluster model with perturbative triples [CCSD(T)]. Several spectroscopic constants are calculated for the ground state of Au2. At the basis set superposition error (BSSE) corrected CCSD(T) level, the deviation from experiment is ΔRe=0.018 A, Δωe=−3 cm−1, and ΔDe=−0.17 eV. The finite-size nucleus effect ma...

A new computational scheme for the Dirac–Hartree–Fock method employing an efficient integral algorithm

A highly efficient computational scheme for four-component relativistic ab initio molecular orbital (MO) calculations over generally contracted spherical harmonic Gaussian-type spinors (GTSs) is presented. Benchmark calculations for the ground states of the group IB hydrides, MH, and dimers, M2 (M=Cu, Ag, and Au), by the Dirac–Hartree–Fock (DHF) method were performed with a new four-component relativistic ab initio MO program package oriented toward contracted GTSs. The relativistic electron repulsion integrals (ERIs), the major bottleneck in routine DHF calculations, are calculated efficiently employing the fast ERI routine SPHERICA, exploiting the general contraction scheme, and the accompanying coordinate expansion method developed by Ishida. Illustrative calculations clearly show the efficiency of our computational scheme.

Third-order Douglas-Kroll relativistic coupled-cluster theory through connected single, double, triple, and quadruple substitutions: Applications to diatomic and triatomic hydrides

Coupled-cluster methods including through and up to the connected single, double, triple, and quadruple substitutions have been derived and implemented automatically for sequential and parallel executions by an algebraic and symbolic manipulation program TCE (TENSOR CONTRACTION ENGINE) for use in conjunction with a one-component third-order Douglas-Kroll approximation for relativistic corrections. A combination of the converging electron-correlation methods, the accurate relativistic reference wave functions, and the use of systematic basis sets tailored to the relativistic approximation has been shown to predict the experimental singlet-triplet separations within 0.02 eV (0.5 kcal/mol) for five triatomic hydrides (CH2, NH2+, SiH2, PH2+, and AsH2+), the experimental bond lengths (re or r0) within 0.002 angstroms, rotational constants (Be or B0) within 0.02 cm(-1), vibration-rotation constants (alphae) within 0.01 cm(-1), centrifugal distortion constants (De) within 2%, harmonic vibration frequencies (omegae) within 8 cm(-1) (0.4%), anharmonic vibrational constants (xomegae) within 2 cm(-1), and dissociation energies (D0(0)) within 0.02 eV (0.4 kcal/mol) for twenty diatomic hydrides (BH, CH, NH, OH, FH, AlH, SiH, PH, SH, ClH, GaH, GeH, AsH, SeH, BrH, InH, SnH, SbH, TeH, and IH) containing main-group elements across the second through fifth rows of the periodic table. In these calculations, spin-orbit effects on dissociation energies, which were assumed to be additive, were estimated from the measured spin-orbit coupling constants of atoms and diatomic molecules, and an electronic energy in the complete-basis-set, complete-electron-correlation limit has been extrapolated in two ways to verify the robustness of the results: One assuming Gaussian-exponential dependence of total energies on double through quadruple zeta basis sets and the other assuming n(-3) dependence of correlation energies on double through quintuple zeta basis sets.

A new implementation of four-component relativistic density functional method for heavy-atom polyatomic systems

A new four-component Dirac–Kohn–Sham (DKS) method is presented. The method provides a computationally efficient way to perform fully relativistic and correlated ground state calculations on heavy-atom molecular systems with reliable accuracy. The DKS routine has been implemented in the four-component Dirac–Hartree–Fock program system REL4D. Two-component generally contracted, kinetically balanced Gaussian-type spinors (GTSs) are used as basis spinors. The one-electron and Coulomb integrals are computed analytically, and exchange-correlation potentials are calculated with a numerical grid-quadrature routine. An approximation scheme is presented to reduce the evaluation time of the two-electron repulsion integrals over full sets of small-component GTSs, (SS|SS). Benchmark calculations for the ground states of the group IB hydrides, MH, and dimers, M2 (M=Cu, Ag, and Au), by the DKS method are presented.

Theoretical study of the electronic ground state of iron(II) porphine. II

Ten low-lying electronic states of Fe(II) porphine, 5A1g, 5Eg, 5B2g, 3A2g, 3B2g, 3Eg(A), 3Eg(B), 1A1g, 1B2g, and 1Eg states, are studied with multiconfigurational second-order perturbation (CASPT2) calculations with complete active space self-consistent field (CASSCF) reference functions with larger active space and basis sets. The enlargement of active space and basis sets has no influence on the conclusion of a previous multireference Moller–Plesset perturbation (MRMP) study. The present CASPT2 calculation concludes that the 5A1g state is the ground state. A relativistic correction has been performed by the relativistic scheme of eliminating small components (RESC). For energetics, no significant contribution from the relativistic correction was found. The relative energies and orbital energies are not changed appreciably by the introduction of a relativistic correction. The present result does not agree with all the spectroscopic observations, but is consistent with a magnetic moment study.