# Improving the Efficiency and Accuracy of Molecular Modeling Through the use of Natural Orbitals

## Faculty Sponsor

Gergely Gidofalvi, Gonzaga University

## Research Project Abstract

The governing principles of quantum chemistry are contained in the Schrodinger equation, and its solution, the wave function, allows the computation of all physical and chemical properties of molecules. The computational cost for solving the Schrodinger equation scales *at least * as n^{4}, where n corresponds to the number of orbitals. Thus, *doubling* the number of orbitals increases the time to solution at least *sixteen-fold*. Previous research in our group has explored the possibility of reducing the computational cost by eliminating orbitals that are deemed insignificant according to some selection criteria. Our results indicate that such truncation schemes work best with natural orbitals (instead of regular molecular orbitals) for which the importance is governed by the average number of electrons in the orbital (instead of the orbital energy), known as the occupation number. Thus, natural orbitals with low occupation numbers are expected to contribute less to the electronic structure of the molecule and may be eliminated from the computation. Although these truncated calculations require a significantly shorter time to solution, discarding some orbitals results in an energy increase called the truncation error. In this work we present our latest efforts to account for the truncation error. In particular, we discuss and compare the relative merits of using methods based on extrapolation and composite approaches.

## Session Number

PS2

## Location

Graves Gym

## Abstract Number

PS2-g

Improving the Efficiency and Accuracy of Molecular Modeling Through the use of Natural Orbitals

Graves Gym

The governing principles of quantum chemistry are contained in the Schrodinger equation, and its solution, the wave function, allows the computation of all physical and chemical properties of molecules. The computational cost for solving the Schrodinger equation scales *at least * as n^{4}, where n corresponds to the number of orbitals. Thus, *doubling* the number of orbitals increases the time to solution at least *sixteen-fold*. Previous research in our group has explored the possibility of reducing the computational cost by eliminating orbitals that are deemed insignificant according to some selection criteria. Our results indicate that such truncation schemes work best with natural orbitals (instead of regular molecular orbitals) for which the importance is governed by the average number of electrons in the orbital (instead of the orbital energy), known as the occupation number. Thus, natural orbitals with low occupation numbers are expected to contribute less to the electronic structure of the molecule and may be eliminated from the computation. Although these truncated calculations require a significantly shorter time to solution, discarding some orbitals results in an energy increase called the truncation error. In this work we present our latest efforts to account for the truncation error. In particular, we discuss and compare the relative merits of using methods based on extrapolation and composite approaches.