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The differentiable manifolds of the electronic structure theory


The use of computational models in several fields of chemistry is constantly growing. Nowadays, a large portion of the research in chemistry requires the support of electronic structure calculations. Thus, more efficient methods that able to rigorously treat strongly correlated electronic systems, but of simple usage, are needed. The development of such methods is one of the big challenges of theoretical chemistry. In this project, we propose the study of the differentiable manifolds that appear in the electronic structure theory of atoms and molecules. The computational methods employed in theoretical chemistry are based on the solution of the Schrödinger equation restricted to a differentiable manifold of the Hilbert space associated to the system of many electrons. However, the geometrical and topological characteristics of these manifolds are seldom explored. We suggest that, with their study, the current methods of computational chemistry can be better understood. This study will boost the development of more robust algorithms for the well established computational methods and the development of new computational methods. In particular, we will give special attention to the multireference methods, that are of fundamental importance to the correct description of several chemical processes, but of difficult usage. (AU)

Scientific publications (4)
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
DE SOUZA, JHONATHAN ROSA; DE MORAES, MATHEUS MORATO F.; AOTO, YURI ALEXANDRE; HOMEM-DE-MELLO, PAULA. Can one use the electronic absorption spectra of metalloporphyrins to benchmark electronic structure methods? A case study on the cobalt porphyrin. Physical Chemistry Chemical Physics, v. 22, n. 41, p. 23886-23898, NOV 7 2020. Web of Science Citations: 0.
AOTO, YURI ALEXANDRE; DA SILVA, MARCIO FABIANO. Calculating the distance from an electronic wave function to the manifold of Slater determinants through the geometry of Grassmannians. Physical Review A, v. 102, n. 5 NOV 6 2020. Web of Science Citations: 0.
DE MORAES, MATHEUS MORATO F.; AOTO, YURI ALEXANDRE. Reference spaces for multireference coupled-cluster theory: the challenge of the CoH molecule. THEORETICAL CHEMISTRY ACCOUNTS, v. 139, n. 4 MAR 27 2020. Web of Science Citations: 0.
AOTO, YURI ALEXANDRE; BARGHOLZ, ARNE; KATS, DANIEL; WERNER, HANS-JOACHIM; KOEHN, ANDREAS. Perturbation Expansion of Internally Contracted Coupled-Cluster Theory up to Third Order. JOURNAL OF CHEMICAL THEORY AND COMPUTATION, v. 15, n. 4, p. 2291-2305, APR 2019. Web of Science Citations: 4.

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