Density Differences in Embedding Theory with External Orbital Orthogonality

Abstract

First results on electron densities and energies for a number of molecular complexes with different interaction strengths (ranging from ca. 0.3 to 40 kcal/mol), obtained using our recently introduced DFT-in-DFT embedding equations (i.e., Kohn-Sham equations with constrained electron density (KSCED) and external orbital orthogonality (ext orth), KSCED(x, ext orth), where x denotes the single particle support: monomer (m); supermolecular (s); or extended monomer (e)) are compared with densities from supermolecular Kohn-Sham (KS)-DFT calculations and traditional DFT-in-DFT results. Because our methodology does not rely on error-prone potentials that are not present in supermolecular KS-DFT calculations, it allows DFT-in-DFT calculations to achieve much higher accuracy than previous protocols of DFT-in-DFT that employed such potentials. It is shown that whereas conventional DFT-in-DFT embedding theory leads to errors in the electron density at the boundary between subsystems, the situation is remedied when orbital orthogonality between subsystems (i.e., external orthogonality) is enforced. Our approach reproduces KS-DFT total energies at least to the seventh decimal place (and exactly at most geometries) for the tested systems. Potential energy curves (PECs) of the separation of some of the tested systems into fragments are calculated. PECs, obtained with the new equations, using the usual Kohn-Sham equations with constrained electron density and supermolecular basis expansion [KSCED(s, ext orth, v(T) = 0), where v(T) is the nonadditive kinetic potential] were found to be virtually identical to those from conventional KS-DFT; equilibrium distances and interaction energies were reproduced to all reported digits for both local density approximation (LDA) and generalized gradient approximation (GGA) functionals. As an additional approximation, an alternative one-particle space (to the common monomer or supermolecular spaces) in which KS orbitals of a subsystem are expanded is introduced. This expansion, which we refer to as the extended monomer expansion [e.g., KSCED(e)], includes basis functions centered on atom(s) of the complementary subsystem in the interfacial region. Density differences and PECs obtained with the new equations and new one-particle space [i.e., KSCED(e, ext orth, v(T) = 0)] were closely related to those obtained from KSCED(s, ext orth, v(T) = 0). The new approach does not require any supermolecular calculations.

The Exploration of Chemical Reaction Networks

“…While this is feasible for single-referece methods such as explicitly correlated coupled cluster theories (105), which can typically be run as black boxes, this is not that straightforward for multi-configurational problems although significant progress has been made in this respect (106,107,108). Then, only feasibility consideration are an issue, but may be alleviated by embedding calculations (109,110,111,112,96). If an exploration protocol allows for such calculations on demand, then the determined error should be propagated through the network in order to reduce the uncertainties for the approximate exploration method.…”

Quantum Embedding Theories

“…Kohn-Sham projector formalisms to avoid the non-additive kinetic potential altogether. 35,36 However, we now consider the two common contexts in which DFT embedding is applied. The first is DFT in DFT embedding, 2 where both the subsystem A and environment B are treated with DFT.…”

No need for external orthogonality in subsystem density-functional theory

“…Hoffmann and co-workers have questioned that SDFT is formally exact. 21,22 Instead, they argue that an exact treatment of the nonadditive kinetic energy alone does not suffice to make SDFT equivalent to KS-DFT, but that it is mandatory to enforce the external orthogonality of the subsystem orbitals. Also Chulhai and Jensen have picked up the argument, based on the work by Hoffmann and co-workers, that non-additive kinetic-energy potentials as used in SDFT and FDE may lead to incorrect results even for the exact kinetic-energy functional.…”