Embedded mean-field theory: Toward a large-scale ab-initio molecular dynamics

Abstract

Mitigating a trade-off between accuracy and computational costs is at the heart of quantum chem. A natural approach to this problem is a quantum embedding method which treats a small subset of a whole system at a high-level of theory while treating the rest at a low-level of theory. Although many attempts have been made in developing quantum embedding theories (esp. in the context of embedding a correlated wavefunction method into a mean-field method), there is no approach specialized for embedding mean-field theories without a priori user-level input for the no. of electrons in each subsystem. We introduce embedded meanfield theory (EMFT), an approach that allows for embedding of one mean-field theory in another without the need to specify or fix the no. of particles in each subsystem. Its gradient theory is notably simple as it merely inherits the gradient theory of the parent mean-field theories. We report extensive benchmark calcns. of EMFT for the case where the subsystems are treated using different levels of Kohn-Sham theory. In most cases, the performance is at least as good as that of ONIOM, a widely used embedding method, but the advantages of EMFT are highlighted by examples that involve partitions across multiple bonds or through arom. systems and by examples that involve more complicated electronic structure. Furthermore, another variant of EMFT, embedding of Kohn-Sham theory in D. Functional Tight-Binding (DFTB), is formulated. As DFTB avoids the evaluation of electron repulsion integrals which is a fundamental bottleneck in Kohn-Sham theory, this variant will reduce computational costs more substantially and hence is very appealing in multi-scale electronic structure theory.