Analysis Tools for Linear Scaling Quantum Chemistry Calculations

Per‐Åke Malmqvist

Moritz P. Haag, Markus Reiher

Significant progress in the development of efficient and fast algorithms for quantum chemical calculations has been made in the past two decades. The main focus has al-ways been the desire to be able to treat ever larger molecules or molecular assemblies— especially linear and sub-linear scaling techniques are devoted to the accomplishment of this goal. However, as many chemical reactions are rather local, they usually involve only a limited number of atoms so that models of about two hundred (or even less) atoms embedded in a suitable environment are sufficient to study their mechanisms. Thus, the system size does not need to be enlarged, but remains constant for reactions of this type that can be described by less than two hundred atoms. The question then arises how fast one can obtain the quantum chemical results. This question is not directly answered by linear-scaling techniques. In fact, ideas such as haptic quantum chemistry or interactive quantum chemistry require an immediate provision of quan-tum chemical information which demands the calculation of data in “real time”. In this perspective, we aim at a definition of real-time quantum chemistry, explore its realm and eventually discuss applications in the field of haptic quantum chemistry. For the latter we elaborate whether a direct approach is possible by virtue of real-time quantum chemistry. Submitted for publication as a perspective article in Int. J. Quantum Chem.

Moritz P. Haag, Markus Reiher

Abstract Significant progress in the development of efficient and fast algorithms for quantum chemical calculations has been made in the past two decades. The main focus has always been the desire to be able to treat ever larger molecules or molecular assemblies—especially linear and sublinear scaling techniques are devoted to the accomplishment of this goal. However, as many chemical reactions are rather local, they usually involve only a limited number of atoms so that models of about 200 (or even less) atoms embedded in a suitable environment are sufficient to study their mechanisms. Thus, the system size does not need to be enlarged, but remains constant for reactions of this type that can be described by less than 200 atoms. The question then arises how fast one can obtain the quantum chemical results. This question is not directly answered by linear‐scaling techniques. In fact, ideas such as haptic quantum chemistry (HQC) or interactive quantum chemistry require an immediate provision of quantum chemical information which demands the calculation of data in “real time.” In this perspective, we aim at a definition of real‐time quantum chemistry, explore its realm and eventually discuss applications in the field of HQC. For the latter, we elaborate whether a direct approach is possible by virtue of real‐time quantum chemistry. © 2012 Wiley Periodicals, Inc.

Kazuya Ishimura, Masato Kobayashi

Xin Xing, Lin Lin

Coupled cluster theory is one of the most popular post-Hartree-Fock methods for molecular quantum chemistry. The finite-size error of the correlation energy in periodic coupled cluster calculations for three-dimensional insulating systems has been observed to satisfy the inverse volume scaling, even in the absence of any correction schemes. This is surprising, as simpler theories that utilize only a subset of the coupled cluster diagrams exhibit much slower decay of the finite-size error, which scales inversely with the length of the system. In this study, we review the current understanding of finite-size error in quantum chemistry methods for periodic systems. We introduce new tools that elucidate the mechanisms behind this phenomenon in the context of coupled cluster doubles calculations. This reconciles some seemingly paradoxical statements related to finite-size scaling. Our findings also show that singularity subtraction can be a powerful method to effectively reduce finite-size errors in practical quantum chemistry calculations for periodic systems. Published by the American Physical Society 2024

和也 石村, カズヤ イシムラ, Kazuya Ishimura