Accurate ab Initio Spin Densities

Katharina Boguslawski, Konrad H. Marti, Örs Legeza and Markus Reiher Journal of Chemical Theory and Computation 2012, 8, 1970 (Paywall)

The spin density problem
Obtaining accurate spin density distributions and predicting the correct ground state from a number of close lying states of different spin is a challenging problem in quantum chemistry, particularly when transition metal systems are considered. This paper highlights how density-matrix renomarlization group¹ (DMRG) based methods can be used to calculate spin density distributions for molecules that are too large to be treated by complete-active-space self-consistent-field (CASSCF) methods. What I found particularly exciting is the prospect of using DMRG results in the benchmarking and development of new density functionals.

Benchmarking DMRG
The electronic structure of a simple model system of iron nitrosyl is manipulated by surrounding it with point-charges (simulating ligands), adjusting the position of these charges means the system becomes either single- or multi-reference. The results convincingly show how DMRG can converge to a CASSCF(7,7) reference spin density by controlling the number of reference active-system states in the DMRG. The DMRG calculations were carried out using the Reiher group's Qc-Dmrg-ETH code.

Spin densities for large active spaces and comparison to DFT
A problem arrises in CASSCF when the number of active electrons and orbitals required to correctly describe the system becomes too large (this article suggests 18 electrons in 18 orbitals as a practical limit). The paper goes on to show that much larger active spaces are possible with DMRG and, more importantly, that the spin density converges very quickly both with respect to active space and the number of active-system states. The resulting spin densities are then compared to a number of common density functionals, none of which accurately reproduces the DMRG result. Whilst DMRG calculations are not yet commonplace in the computational chemistry community, this paper convinces me that they will have an important role to play in solving the spin density problem.

References
(1) For an introduction to DMRG see: Chan, G. K.-L.; Dorando, J. J.; Ghosh, D.; Hachmann. J.; Neuscamman, E.; Wang, H.;Yanai, T. An Introduction to the Density Matrix Renormalization Group Ansatz in Quantum Chemistry. In Frontiers in Quantum Systems in Chemistry and Physics, 1st ed.; Wilson, S., Grout, P. J.; Maruani, J., Delgado-Barrio, G., Piecuch, P., Eds.; Springer: Dordrecht, The Netherlands, 2008; Vol. 18, pp 49-65. arXiv:0711.1398v1.