Embedded Mean-Field Theory

Abstract

We introduce embedded mean-field theory (EMFT), an approach that flexibly allows for the embedding of one mean-field theory in another without the need to specify or fix the number of particles in each subsystem. EMFT is simple, is well-defined without recourse to parameters, and inherits the simple gradient theory of the parent mean-field theories. In this paper, we report extensive benchmarking of EMFT for the case where the subsystems are treated using different levels of Kohn-Sham theory, using PBE or B3LYP/6-31G* in the high-level subsystem and LDA/STO-3G in the low-level subsystem; we also investigate different levels of density fitting in the two subsystems. Over a wide range of chemical problems, we find EMFT to perform accurately and stably, smoothly converging to the high-level of theory as the active subsystem becomes larger. In most cases, the performance is at least as good as that of ONIOM, but the advantages of EMFT are highlighted by examples that involve partitions across multiple bonds or through aromatic systems and by examples that involve more complicated electronic structure. EMFT is simple and parameter free, and based on the tests provided here, it offers an appealing new approach to a multiscale electronic structure.

Linear-Response Time-Dependent Embedded Mean-Field Theory

“…For example, methods based on localized molecular orbitals lead to complicated implementations for analytical gradients and properties, while many embedding methods place constraints on the subsystem particle numbers, spin state, and spatial extent of the excitation, or they neglect particle-number fluctuations between subsystems, or the environmental response to the excitation. Removing such constraints has motivated the recent development of embedding strategies that are formally exact in the description of subsystem interactions [25][26][27][28][29][30][31][32][33][34][35][36][37] and allow for particle-number fluctuations between subsystems via their description as open quantum systems. [35][36][37] Here, we introduce time-dependent embedded mean-field theory (TD-EMFT), a linear-response approach to describe excited electronic states using the EMFT framework.…”

“…Removing such constraints has motivated the recent development of embedding strategies that are formally exact in the description of subsystem interactions [25][26][27][28][29][30][31][32][33][34][35][36][37] and allow for particle-number fluctuations between subsystems via their description as open quantum systems. [35][36][37] Here, we introduce time-dependent embedded mean-field theory (TD-EMFT), a linear-response approach to describe excited electronic states using the EMFT framework. 37,38 TD-EMFT provides subsystem embedding at different levels of mean-field theory, avoiding the need to specify or fix the particle number or spin state for each subsystem.…”

“…[35][36][37] Here, we introduce time-dependent embedded mean-field theory (TD-EMFT), a linear-response approach to describe excited electronic states using the EMFT framework. 37,38 TD-EMFT provides subsystem embedding at different levels of mean-field theory, avoiding the need to specify or fix the particle number or spin state for each subsystem. It is simple to implement, and because EMFT is itself a mean-field theory, calculation of analytical nuclear gradients and response properties remains straightforward.…”

Communication: Density functional theory embedding with the orthogonality constrained basis set expansion procedure

“…10 and 12, with geometries obtained from Ref. 10, except for the bond length of OH , which is 0.978 Å as given in Ref. 12.…”

“…If no carbon atoms are in the active subsystem, the reaction energy error is the difference between the reaction energies computed at the high and low levels of theory. 10 The first test case is a simple substitution reaction in which chlorodecane reacts with a hydroxide anion to form decanol and a chloride anion [ Fig. 1(a)].…”