Extension and acceleration of relativistic density functional theory based on transformed density operator.

We report an extension of relativistic density functional theory (RDFT) within one-component or two-component expressions that relies on a unitary-transformed density operator as well as a unitary-transformed Hamiltonian [Oyama et al., Chem. Phys. Lett. 680, 37 (2017)]. The transformed density operator is introduced to avoid the picture-change effect in the electron density, density gradient, kinetic energy density, and exchange-correlation potential. We confirmed that the implementation based on the spin-free infinite-order Douglas-Kroll-Hess method gives total, orbital, and excitation energies close to the reference values given by four-component RDFT calculations. To reduce the computational cost due to the transformed density operator, the local unitary transformation was also implemented. Numerical assessments revealed that the present scheme enabled the RDFT calculation of polyatomic systems with negligibly small picture-change effect.

RAQET: Large-scale two-component relativistic quantum chemistry program package.

The Relativistic And Quantum Electronic Theory (RAQET) program is a new software package, which is designed for large-scale two-component relativistic quantum chemical (QC) calculations. The package includes several efficient schemes and algorithms for calculations involving large molecules which contain heavy elements in accurate relativistic formalisms. These calculations can be carried out in terms of the two-component relativistic Hamiltonian, wavefunction theory, density functional theory, core potential scheme, and evaluation of electron repulsion integrals. Furthermore, several techniques, which have frequently been used in non-relativistic QC calculations, have been customized for relativistic calculations. This article introduces the brief theories and capabilities of RAQET with several calculation examples. © 2018 Wiley Periodicals, Inc.

Gauge-origin independent formalism of two-component relativistic framework based on unitary transformation in nuclear magnetic shielding constant.

This article proposes a gauge-origin independent formalism of the nuclear magnetic shielding constant in the two-component relativistic framework based on the unitary transformation. The proposed scheme introduces the gauge factor and the unitary transformation into the atomic orbitals. The two-component relativistic equation is formulated by block-diagonalizing the Dirac Hamiltonian together with gauge factors. This formulation is available for arbitrary relativistic unitary transformations. Then, the infinite-order Douglas-Kroll-Hess (IODKH) transformation is applied to the present formulation. Next, the analytical derivatives of the IODKH Hamiltonian for the evaluation of the nuclear magnetic shielding constant are derived. Results obtained from the numerical assessments demonstrate that the present formulation removes the gauge-origin dependence completely. Furthermore, the formulation with the IODKH transformation gives results that are close to those in four-component and other two-component relativistic schemes.

Accompanying coordinate expansion and recurrence relation method using a transfer relation scheme for electron repulsion integrals with high angular momenta and long contractions.

An efficient algorithm for the rapid evaluation of electron repulsion integrals is proposed. The present method, denoted by accompanying coordinate expansion and transferred recurrence relation (ACE-TRR), is constructed using a transfer relation scheme based on the accompanying coordinate expansion and recurrence relation method. Furthermore, the ACE-TRR algorithm is extended for the general-contraction basis sets. Numerical assessments clarify the efficiency of the ACE-TRR method for the systems including heavy elements, whose orbitals have long contractions and high angular momenta, such as f- and g-orbitals.

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.