Frozen Density Embedding with External Orthogonality in Delocalized Covalent Systems

Abstract

Frozen density embedding (FDE) has become a popular subsystem density functional theory (DFT) method for systems with weakly overlapping charge densities. The failure of this method for strongly interacting and covalent systems is due to the approximate kinetic energy density functional (KEDF), although the need for approximate KEDFs may be eliminated if each subsystem's Kohn-Sham (KS) orbitals are orthogonal to the other, termed external orthogonality (EO). We present an implementation of EO into the FDE framework within the Amsterdam density functional program package, using the level-shift projection operator method. We generalize this method to remove the need for orbital localization schemes and to include multiple subsystems, and we show that the exact KS-DFT energies and densities may be reproduced through iterative freeze-and-thaw cycles for a number of systems, including a charge delocalized benzene molecule starting from atomic subsystems. Finally, we examine the possibility of a truncated basis for systems with and without charge delocalization, and found that subsystems require a basis that allows them to correctly describe the supermolecular delocalized orbitals.

eQE: An open‐source density functional embedding theory code for the condensed phase

“…[31][32][33] In addition, Turbomole [34] has its own implementation by the Della Sala group. [35][36][37][38][39] We also mention here that other embedding methods, which can be categorized as exact density embedding, exact orbital embedding, or electrostatic embedding, are now found in ADF, [40] MOLPRO, [41][42][43][44][45] Q-Chem, [46,47] CP2K, [48] NWChem, [49] and GAMESS. [50] In this work, we present a novel implementation of the FDE approach that aims at filling the following gap that has persisted over the years, namely, the absence of a code that: (1) has a proven strong parallel efficiency that consistently outperforms semilocal KS-DFT, (2) has the ability to Figure 1 [12] The k-point grids and simulation cells (basis sets) are subsystem-specific, achieving the best performance.…”

“…In addition, Turbomole has its own implementation by the Della Sala group . We also mention here that other embedding methods, which can be categorized as exact density embedding, exact orbital embedding, or electrostatic embedding, are now found in ADF, MOLPRO, Q‐Chem, CP2K, NWChem, and GAMESS…”

iOI: an Iterative Orbital Interaction Approach for Solving the Self-Consistent Field Problem

“…As a matter of fact, the best answer to this was already provided by chemists in the early days of chemistry: as the basic building units, functional groups or fragments in general reflect best the locality of chemical systems. As such, various fragment-based quantum chemical methods have been developed in the last decades, including mixed quantum mechanics/molecular mechanics (QM/MM), [4][5][6][7] multilayer QM/QM, [8][9][10][11] divide-and-conquer (DC), [12][13][14][15] embedding, [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31] and orbital- [32][33][34][35][36][37][38][39][40][41] and energy-based [42][43][44][45][46][47][48][49][50][51][52]…”

Serenity: A subsystem quantum chemistry program

“…In particular, approximations for the non‐additive kinetic energy and/or the corresponding potential are needed (see, e.g., the reviews in Refs. ), the approximation for needed for the embedding potential may be replaced by a reconstructed potential, the approximation for can be completely avoided if mutual orthogonality of orbitals of different subsystems is ensured, either through projection or through additional Lagrangian multipliers, the choice for the non‐additive XC functional may be different from the XC approximation used within the subsystems. In fact, this is a practical necessity if orbital‐dependent functionals, including hybrids, shall be applied .…”