Analytic energy derivatives in relativistic quantum chemistry

Abstract

In this review, we discuss the current status of analytic derivative theory in relativistic quantum chemistry. A brief overview of the basic theory for the available relativistic quantum chemical methods as well as the state-of-the-art development of their analytic energy derivatives is given. Among the various relativistic quantum chemical methods, cost-effective approaches based on spin separation and/or on the matrix representation of two-component theory have been proven particularly promising for the accurate and efficient treatment of relativistic effects in electron correlation calculations. We highlight analytic derivative techniques for these cost-effective relativistic quantum chemical approaches including direct perturbation theory, the spin-free Dirac-Coulomb approach, and the exact two-component theory in its one-electron variant. An outlook is given on future developments of analytic energy derivative techniques for relativistic quantum chemical methods, again with an emphasis on cost-effective schemes.

Libcint: An efficient general integral library for Gaussian basis functions

“…The magnetically balanced basis naturally introduces the diamagnetic contributions to the relativistic NMR theory, which is comparable to the diamagnetic terms in the nonrelativistic calculations. Since the theory of the relativistic analytic gradients and magnetic properties is out of the scope of present paper, we refer the readers to the literatures [26,32,[49][50][51][52] for more theoretical details. Table 2 documents all the 49 types of integrals which are required in these calculations.…”

“…One source of the new integrals is the calculation of molecular properties: Response theory requires the integral derivatives; Gauge including atomic orbitals (GIAO) needs high order integrals. Relativistic effect is another source that brings new integrals:: Breit‐Pauli Hamiltonian introduces many one‐electron and two‐electron operators in terms of the products of p and r operators; The kinetic (magnetic) balance conditions in 4‐component (4C) relativistic theory result in many one‐electron and two‐electron j ‐adapted (spinor) integrals. Besides properties and relativistic effects, explicitly correlated methods also complicates the integral computation.…”

Coupled-cluster techniques for computational chemistry: The CFOUR program package

“…Following the work of the original team, and beginning their careers in the groups of the main authors, many more young scientists actively contributed to CFOUR. The primary authors of CFOUR now include Lan Cheng, who has contributed extensively with relativistic quantum chemical methods 56,[58][59][60] for both energy and property calculations; Devin A. Matthews, who has This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.…”

Perturbative treatment of spin-orbit coupling within spin-free exact two-component theory

“…A further advantage of the X2C scheme is that its simple block-diagonalization technique greatly facilitates the construction of analytic derivatives of the X2C Hamiltonian matrix elements. [39][40][41][42][43][44] As the exact block diagonalization of the four-component Hamiltonian matrix requires information about the four-component wave function, the construction of the X2C Hamiltonian matrix elements is as expensive as the solution of the corresponding four-component equation. Therefore, the practical computational efficiency of the X2C approach originates from using the X2C Hamiltonian matrix constructed at a lower level of theory in higher-level quantum-chemical calculations, since the computational cost is usually dominated by the level of theory used for treating the electron-electron interactions.…”