Efficient iterative method for solving the Dirac-Kohn-Sham density functional theory

We present for the first time an efficient iterative method to directly solve the four-component Dirac-Kohn-Sham (DKS) density functional theory. Due to the existence of the negative energy continuum in the DKS operator, the existing iterative techniques for solving the Kohn-Sham systems cannot be efficiently applied to solve the DKS systems. The key component of our method is a novel filtering step (F) which acts as a preconditioner in the framework of the locally optimal block preconditioned conjugate gradient (LOBPCG) method. The resulting method, dubbed the LOBPCG-F method, is able to compute the desired eigenvalues and eigenvectors in the positive energy band without computing any state in the negative energy band. The LOBPCG-F method introduces mild extra cost compared to the standard LOBPCG method and can be easily implemented. We demonstrate our method in the pseudopotential framework with a planewave basis set which naturally satisfies the kinetic balance prescription. Numerical results for Pt$_{2}$, Au$_{2}$, TlF, and Bi$_{2}$Se$_{3}$ indicate that the LOBPCG-F method is a robust and efficient method for investigating the relativistic effect in systems containing heavy elements.Comment: 31 pages, 5 figure

The Chronus Quantum software package

The Chronus Quantum (ChronusQ) software package is an open source (under the GNU General Public License v2) software infrastructure which targets the solution of challenging problems that arise in ab initio electronic structure theory. Special emphasis is placed on the consistent treatment of time dependence and spin in the electronic wave function, as well as the inclusion of relativistic effects in said treatments. In addition, ChronusQ provides support for the inclusion of uniform finite magnetic fields as external perturbations through the use of gauge-including atomic orbitals. ChronusQ is a parallel electronic structure code written in modern C++ which utilizes both message passing implementation and shared memory (OpenMP) parallelism. In addition to the examination of the current state of code base itself, a discussion regarding ongoing developments and developer contributions will also be provided. This article is categorized under: Software > Quantum Chemistry Electronic Structure Theory > Ab Initio Electronic Structure Methods Electronic Structure Theory > Density Functional Theory

Kramers-restricted self-consistent 2-spinor fields for heavy-element chemistry

The relativistic pseudopotential (PP) method is one of the most common and successful approximations in computational quantum chemistry. If suitably parameterized -- e.g., fitted to atomic valence total energies from highly accurate relativistic reference calculations --, atomic PPs provide effective (spin�orbit) 1-electron operators mimicking the chemically inert atomic core subsystem, which thus is excluded from explicit considerations. This work deals with the development of a Kramers-restricted, 2-component PP Hartree�Fock SCF program based on the spin-restricted, 1-component HF SCF modules of the "Quantum Objects Library" of C++ program modules at the Dolg and Hanrath groups at Cologne University. Kramers' restriction, i.e. time reversal symmetry, is addressed at the lowest hierarchical level of the (formally complexified) matrix algebra modules. PP matrix elements are computed using PP integral subroutines of the ARGOS program, which are interfaced to the existing structure. On this basis, a set of spin-restricted, 1-component (all-electron and) spin-free PP, and Kramers-restricted, 2-component spin--orbit PP HF SCF programs is implemented. "Optimal damping" and initial guess density matrices constructed from atomic densities are shown to improve SCF convergence significantly. As first steps towards correlated 2-component calculation schemes, a modular structure for matrix--matrix multiplication-driven 4-index integral transformations to the Fockian eigenbasis is developed, and preliminary 2-component MP2 calculations are presented

Exact decoupling of the relativistic Fock operator

It is generally acknowledged that the inclusion of relativistic effects is crucial for the theoretical description of heavy-element-containing molecules. Four-component Dirac-operator-based methods serve as the relativistic reference for molecules and highly accurate results can be obtained—provided that a suitable approximation for the electronic wave function is employed. However, four-component methods applied in a straightforward manner suffer from high computational cost and the presence of pathologic negative-energy solutions. To remove these drawbacks, a relativistic electron-only theory is desirable for which the relativistic Fock operator needs to be exactly decoupled. Recent developments in the field of relativistic two-component methods demonstrated that exact decoupling can be achieved following different strategies. The theoretical formalism of these exact-decoupling approaches is reviewed in this paper followed by a comparison of efficiency and result

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

An up-to-date overview of the CFOUR program system is given. After providing a brief outline of the evolution of the program since its inception in 1989, a comprehensive presentation is given of its well-known capabilities for high-level coupled-cluster theory and its application to molecular properties. Subsequent to this generally well-known background information, much of the remaining content focuses on lesser-known capabilities of CFOUR, most of which have become available to the public only recently or will become available in the near future. Each of these new features is illustrated by a representative example, with additional discussion targeted to educating users as to classes of applications that are now enabled by these capabilities. Finally, some speculation about future directions is given, and the mode of distribution and support for CFOUR are outlined