Is it possible to bring them together in a mutually beneficial manner?

1.

*How could quantum chemistry of finite molecules benefit from DMFT?*

This is considered in a PRL from Columbia.

An earlier post reviewed nice work that used LDA+DMFT to study myoglobin. [See also a recent PNAS].

Broadly, I think DMFT will be most appropriate and useful in molecular problems that look something like an Anderson impurity problem: a single metal atom with a fluctuating magnetic moment and/or valence that is coupled to a large number of approximately degenerate electronic states. Indeed myoglobin falls in this class.

2.

*How could DMFT treatments of solids benefit from quantum chemistry methods?*

*Three answers to are considered in a nice JCP by Dominika Zgid and Garnet Chan.*

A. It provides a way/framework to extend quantum chemical methods (approximations) to infinite crystals. This is most naturally done in the discrete bath formulation of DMFT.

B. Any DMFT treatment requires an “impurity solver” to treat the associated Anderson impurity-problem. In the discrete bath formulation this is solved by exact diagonalisation [called full configuration-interaction (CI) by chemists] and significantly limits the bath to less than a dozen states. However, the hierarchy of quantum chemistry approximations [HF, CCSD, CAS-SCF, ....] provide an alternative “lower cost” means to solve the bath problem and increase the number of bath states and possibly improve convergence.

C. It allows one to go beyond current ab initio DMFT studies that are based on Density Functional Theory (DFT) and its associated problems. Furthermore, such studies involve a certain amount of

“double counting” of correlations that are hard to correct for in a systematic manner.

Zgid and Chan treat the specific problem of cubic solid hydrogen for several different lattice spacings a. Qualitatively, this is analogous to the Hubbard model at half-filling with varying U/t. As the lattice constant increases there is a transition from a weakly correlated metal to a strongly correlated metal [3 peaks in the single particle spectral function] to a Mott insulator.

In a 2012 PRB, Zgid, Chan, and Emmanuel Gull study a 2 x 2 cluster DMFT treatment of the two-dimensional Hubbard model. They found that solving the associated impurity problem with a finite bath with quantum chemical approximations such as CCSD [coupled cluster singles and doubles] CAS(2,2) [complete active space with two electrons in two orbitals] produced reliable results at a fraction of the computational cost of exact diagonalisation.

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