Highly accurate excited-state energies from direct computation of the 2-electron reduced density matrix by the anti-Hermitian contracted Schrödinger equation

ABSTRACT

Directly solving for the 2-electron reduced density matrix (2-RDM) via the anti-Hermitian contracted Schrödinger equation (ACSE) enables computations for excited states energies without the N-electron wave function. Of particular interest are excitations and dissociation curves that exhibit strong multi-reference correlation effects. The ground and excited states of the molecules HF, H₂O, and N₂ are examined at both equilibrium and non-equilibrium geometries to compare the ability of the ACSE and widely used ab initio techniques to treat strong multi-reference electron correlation. Calculations are performed with double-ζ basis sets for calibration with full configuration interaction (FCI). Multi-reference second-order perturbation theory (MRPT2) and the ACSE both provide qualitative precision with respect to FCI data, although the ACSE's capability to include higher order correlation effects permits near-FCI accuracy for ground and excited states and excitation energies.

KEYWORDS:

• Reduced density matrices
• electron correlation
• excited states

Acknowledgements

Erica J. Sturm would like to thank Charles Heaps and Dr Gergely Gidofalvi for their enlightening discussions and assistance. David A. Mazziotti gratefully acknowledges the NSF CHE-1152425 and the Army Research Office (ARO) STTR Grant W911NF-14-P-0048 for their support.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

David A. Mazziotti is supported by the NSF grant [grant number CHE-1152425] and the Army Research Office (ARO) STTR grant [grant number W911NF-14-P-0048].