Variational approach for the electronic structure calculation on the second-order reduced density matrices and the $N$-representability problem

TL;DR

This paper reviews the variational reduced-density-matrix method for electronic structure calculations, highlighting its potential as a simpler alternative to traditional quantum chemistry methods, with results comparable to CCSD(T).

Contribution

It provides an overview of the theory, methods, history, and new computational results for the reduced-density-matrix approach in quantum chemistry.

Findings

Results are comparable to CCSD(T) in accuracy.

The method offers a constant number of variables regardless of system size.

The approach simplifies electronic structure calculations.

Abstract

The reduced-density-matrix method is an promising candidate for the next generation electronic structure calculation method; it is equivalent to solve the Schr\"odinger equation for the ground state. The number of variables is the same as a four electron system and constant regardless of the electrons in the system. Thus many researchers have been dreaming of a much simpler method for quantum mechanics. In this chapter, we give a overview of the reduced-density matrix method; details of the theories, methods, history, and some new computational results. Typically, the results are comparable to the CCSD(T) which is a sophisticated traditional approach in quantum chemistry.