The content discusses the use of wavefunction models based on antisymmetric products of 2-electron functions (geminals) as a better starting point for strongly correlated chemical systems, compared to the dominant approach of using a single Slater determinant.
The authors first summarize the Lie algebras obtained by coupling electrons to singlets in groups of 2 spatial orbitals (so(5)), and in N levels (sp(N)). They then present the results necessary to employ a projected Schrödinger equation (pSE) approach for sp(N) geminals.
The key points are:
Closed-shell singlet geminals, the most common case, are restricted to the su(2) Lie algebra. The authors aim to explore the more general open-shell singlet structures using the sp(N) Lie algebra.
For closed-shell singlets, the expansion coefficients of the wavefunction in the Slater determinant basis can be expressed as matrix permanents, which are computationally challenging.
For the more general open-shell singlets, the expansion coefficients are expressed as sums over cosets of subgroups of the symmetric group, which provides a tractable computational approach.
The overlap matrix elements between the configuration state functions (CSFs) in the open-shell singlet basis are also derived, again using the coset structure of the symmetric group.
The authors conclude by stating that numerical results for small model systems clearly demonstrate the improvement of open-shell singlet geminals over closed-shell singlet pairs.
A otro idioma
del contenido fuente
arxiv.org
Consultas más profundas