Intrinsic relationships between broken symmetry energies

TL;DR

This paper explores intrinsic relationships between broken symmetry energies to estimate Heisenberg exchange coupling constants, using mathematical and computational methods to identify optimal parameters in molecular models.

Contribution

It introduces a method leveraging overdetermined systems and SVD to determine exchange parameters, revealing only two possible sets consistent with the data.

Findings

Only two sets of exchange coupling parameters are possible.

SVD effectively identifies best-fit parameters within computational accuracy.

The approach links broken symmetry energies to intrinsic molecular properties.

Abstract

The present paper deals with the use of the so-called broken symmetry method for the estimation of the Heisemberg exchange coupling constants. Tetra-nuclear model (square-H4) and chemical (Bis(di-mu-ethoxo-bis(3,5-di-tert-butylsemiquinonato)dicopper(II))) molecules are considered for the analysis. The overdetermination of the problem at hand was exploited to lead to intrinsic relationships between BS energies (independent of spin or exchange couplings). It is demonstrated that only 2 sets of exchange coupling parameters can be obtained from the calculations. The singular values decomposition (SVD) is proposed for the collection of the best parameters that satisfy all linear equations, within modern computers accuracy. Numerical applications as well as the composition of broken symmetry determinants as function of real spin states are discussed.