Direct minimization methods in quantum chemistry

Janani Chandrasekhar

Lori A. Burns, C. David Sherrill, Benjamin P. Pritchard

While the many-body expansion (MBE) and counterpoise treatments are commonly used to mitigate the high scaling of accurate ab initio methods, researchers may need to piece together tools and scripts if their primary chosen software does not support targeted features. To further modular software in quantum chemistry, the arbitrary-order, multiple-model-chemistry, counterpoise-enabled MBE implementation from Psi4 has been extracted into an independent, lightweight, and open-source Python module, QCManyBody, with new schema underpinning, application programming interface, and software integrations. The package caters to direct users by facilitating single-point and geometry optimization MBE calculations backed by popular quantum chemistry codes through the QCEngine runner and by defining a schema for requesting and reporting many-body computations. It also serves developers and integrators by providing minimal, composable, and extensible interfaces. The design and flexibility of QCManyBody are demonstrated via integrations with geomeTRIC, OptKing, Psi4, QCEngine, and the QCArchive project.

Poul Joergensen

Heinz‐Jürgen Flad, Thorsten Rohwedder, Reinhold Schneider

Abstract In this article, we summarize the results of our numerical analysis for various adaptive schemes in electronic structure calculations. Starting from a general form of iterative schemes used in quantum chemistry, we discuss miscellaneous features which are of importance when passing to an adaptive version of an algorithm in order to provide rigorous estimates. The key features are maintainance of convergence under small perturbations while keeping control of the computational complexity.As a prototype for correlation methods, we consider the configuration interaction (CI) method and discuss a quasi-optimal algorithm for computation of the ground state energy. Our analysis of the coupled cluster method shows that various properties of the CI method can be transferred hereunto as well. First numerical examples demonstrate the potential of the coupled cluster residual, measured in a norm on the dual space, as an error estimator. These studies are supplemented by our result for the best N-term approximation of electron-pair correlations by wavelets.For Hartree-Fock and Kohn-Sham methods, we discuss our results of the convergence analysis for a direct minimization scheme, the best N-term approximation of orbitals and s *-compressibility of the Fock operator which altogether may serve as a basis for an adaptive version of these methods.

L. Veis, Jan Brandejs, J. (Jiří) Pittner

This paper is an introduction to a density matrix renormalization group method (DMRG) and its use in quantum chemistry. Firstly we define the term of strongly correlated systems and explain why the standard methods of quantum chemistry are not suitable for use with such systems. Then, motivated by the principle of locality, we introduce the wave function approximation in the form of matrix product state (MPS), its graphical representation and calculation of expectation values of operators. In the next section, we present the canonical form of MPS expansion and show its relationship to the algorithm of the DMRG method as a form of optimization of matrices in MPS in the sense of variational minimization of energy. Then, a brief overview is given to the properties of DMRG method, with its computational complexity and the resulting limitations, followed by a list of methods for inclusion of the remaining dynamical correlation. Finally, we provide example calculations on realistic, chemically interesting molecules.