Searching for distinct classes of atomic and molecular states using convergence and separability criteria

Author(s)

Lopez-Castillo, Alejandro ^[1]

Affiliation

^[1] Univ Fed Sao Carlos, Dept Chem, BR-13565905 Sao Carlos, SP - Brazil

• Document type: Journal article
• Source: THEORETICAL CHEMISTRY ACCOUNTS; v. 139, n. 9 AUG 16 2020.
• Web of Science Citations: 0

Abstract

We demonstrated that the solution psi to the Schrodinger equation (SE)\& x124;psi = epsilon psi converges logarithmically in the classically forbidden region, i.e., as epsilon ` approaches to the correct eigenvalue epsilon, the approximate solution psi ` logarithmically converges to psi. Knowing that this approximate eigenvalue procedure generates a straightforward but inefficient method to solve a general problem ofn-bodies, we thereby discuss the main characteristic of the usual methods to obtain a better convergence for atoms and molecules. Such usual methods consider that the solution of SE can be approached through a linear combination of solutions of systems with analytical solutions. Hydrogen-like atom solutions are used to describe atoms and molecules. This solution avoids the convergence problem of psi ` even for approximate eigenvalues epsilon ` since all the terms of the linear combination decay asymptotically to zero. We argue that this type of solution works very well for a large class of almost separable atomic and molecular states in which the separation of electronic (and nucleus) movements occurs. We also establish a comparison of this separability and other systems, like gravitational, in which separability is only possible in particular classes of restricted systems. Finally, we consider the existence of distinct atomic and molecular states that may not be described using usual methods that apply this type of solution, which implies the separability of restricted problems. Therefore, usual methods to describe atoms and molecules may be insufficient to reach solutions with different or more general electronic correlations, as discussed in the text. Strategies to achieve general or distinctive solutions, although approximated, should be further studied and developed. (AU)

• FAPESP's process: 19/12501-0 - Theoretical study of bidimensional systems
• Grantee: Alejandro López Castillo
• Support Opportunities: Regular Research Grants