## Completely broken-symmetry solutions as a basis for non-orthogonal configuration interaction

Eric Jon Sundstrom and Martin Head-Gordon

Department of Chemistry, University of California, Berkeley, California, USA.

Mardi 18 Juin 2013, 11^{h}00

bibliothèque LCT, tour 12 - 13, 4e étage

Since the early days of quantum chemistry, there has been a great deal of discussion regarding symmetry-breaking of Hartree-Fock (HF) wavefunctions, including a full group-theoretical classification of these solutions[1]. Despite the considerable discourse, many of these broken-symmetry methods (other than simple unrestriction) never gained popularity within the quantum chemistry community, largely due to computational concerns. Completely broken-symmetry wavefunctions have recently come back into vogue and there are many groups working with methods related to these wavefunctions[2].

Here we present the use of these broken-symmetry wavefunctions within a non-orthogonal configuration interaction (NOCI) framework. Unlike traditional CI approaches, the basis of Hatree-Fock solutions are not eigenfunctions of the same Fock operator and thus are non-orthogonal, but by utilizing Löwdin's pairing theorem this basis may be made biorthogonal and therefore tractable[3]. For many systems, the high scaling of other multi-configurational approaches may be prohibitive, but the low scaling of NOCI, *O*(max(*n*_{e}^{3},*N*^{2})) where *n*_{e} is the number of electrons and *N* is the size of atomic orbital basis, makes it applicable to large systems. Broken-symmetry solutions may provide a more compact representation of the true ground-state wavefunction as each Slater determinant is made from a linear combination of the standard CI's orthogonal determinants, typically with energies lower than those of the orthogonal ones. For the different broken-symmetry solutions we compute spin operators in order to ascertain their equivalence, which may be useful in determining their importance in the expansion.

[1] H. Fukutome, Int. J. Quantum Chem. **20** 955 (1981)

[2] C. A. Jiménez-Hoyos, T. M. Henderson, T. Tsuchimochi, and G. E. Scuseria, J. Chem. Phys. **136** 164109 (2012)

[3] A. J. W. Thom and M. Head-Gordon, J. Chem. Phys. **131** 124113 (2009)