CRYSTAL23: A Program for Computational Solid State Physics and Chemistry

Abstract

The Crystal program for quantum-mechanical simulations of materials has been bridging the realm of molecular quantum chemistry to the realm of solid state physics for many years, since its first public version released back in 1988. This peculiarity stems from the use of atom-centered basis functions within a linear combination of atomic orbitals (LCAO) approach and from the corresponding efficiency in the evaluation of the exact Fock exchange series. In particular, this has led to the implementation of a rich variety of hybrid density functional approximations since 1998. Nowadays, it is acknowledged by a broad community of solid state chemists and physicists that the inclusion of a fraction of Fock exchange in the exchange-correlation potential of the density functional theory is key to a better description of many properties of materials (electronic, magnetic, mechanical, spintronic, lattice-dynamical, etc.). Here, the main developments made to the program in the last five years (i.e., since the previous release, Crystal17) are presented and some of their most noteworthy applications reviewed.

Elastic Properties of Binary d-Metal Oxides Studied by Hybrid Density Functional Methods

“…These calculations were carried out with CRYSTAL23. 31 Full technical details for all elastic property calculations are openly available as CRYSTAL output files at a Github repository. 32 Nonstochiometric rutile-type oxide TaO 2 not previously reported in ref 22 was also included, the calculations being performed with a k-mesh of 8 × 8 × 12.…”

Anharmonic Terms of the Potential Energy Surface: A Group Theoretical Approach

“…30−40 A numerically robust and computationally efficient finite difference scheme (namely, EGH), based on a Taylor's expansion of the PES in the basis of the normal modes, has been proposed in 2008 for molecular systems by Lin et al, which requires a minimal set of nuclear configurations to be explored in the definition of a 2M4T or 3M4T representation of the PES. 16 Such a scheme (based on the analysis of the relative importance of different types of cubic and quartic terms) has recently been extended to solids by some of the present authors 41 and implemented in the CRYSTAL program, 42,43 along with the vibrational self-consistent field (VSCF) and vibrational configuration interaction (VCI) methods for computation of anharmonic vibrational states. 44−46 In this work, we illustrate how group theoretical arguments can be used to drastically reduce the number of configurations N conf needed to achieve a quartic representation of the PES on both molecules and materials belonging to high point symmetry groups.…”

Perturbation Theory Treatment of Spin–Orbit Coupling. III: Coupled Perturbed Method for Solids

“…In modern electronic structure programs, relativistic effects are typically accounted for through self-consistent field (SCF) treatments, either in a two- or four-component spinor basis (2c-SCF or 4c-SCF), − or by perturbation methods. − Within these approaches, a particularly convenient representation of the Dirac equation from a computational perspective is provided through the relativistic effective core potential (RECP), including both scalar-relativistic and spin–orbit coupling (SOC), or nonscalar, effects. , In Part II of this series, we developed a molecular pure-state coupled perturbed Kohn–Sham (CPKS) density functional theory (DFT) treatment for including SOC effects, which was implemented within the Crystal program. ,, This approach has the potential for over an order of magnitude savings in computation times w.r.t. 2c-SCF and, moreover, provides a convenient starting point for improvements to treat strongly correlated, multireference systems, where an ensemble treatment would be necessary. ,,− …”

“…28,29 In Part II of this series, we developed a molecular pure-state coupled perturbed Kohn−Sham (CPKS) density functional theory (DFT) treatment for including SOC effects, which was implemented within the CRYSTAL program. 27,30,31 This approach has the potential for over an order of magnitude savings in computation times w.r.t. 2c-SCF and, moreover, provides a convenient starting point for improvements to treat strongly correlated, multireference systems, where an ensemble treatment would be necessary.…”

“…38−47 In this paper, we generalize the molecular CPKS treatment to periodic systems. After developing the formalism, our perturbation theory (PT) treatment is implemented in a developmental version of the CRYSTAL23 program, 31 and validated on a family of 2D tungsten dichalcogenide layered compounds, where excellent agreement with reference 2c-SCF calculations is demonstrated, not only for the total energy, but also for band structures and SCDFT density variables.…”