Formulation and Implementation of Density Functional Embedding Theory Using Products of Basis Functions

Within a basis set of one-electron functions that form linearly independent products (LIPs), it is always possible to construct a unique local (multiplicative) real-space potential that is precisely equivalent to an arbitrary given operator. Although standard basis sets of quantum chemistry rarely form LIPs in a numerical sense, occupied and low-lying virtual canonical Kohn–Sham orbitals often do so, at least for small atoms and molecules. Using these principles, we construct atomic and molecular exchange–correlation potentials from their matrix representations in LIP basis sets of occupied canonical Kohn–Sham orbitals. The reconstructions are found to imitate the original potentials in a consistent but exaggerated way. Since the original and reconstructed potentials produce the same ground-state electron density and energy within the associated LIP basis set, the procedure may be regarded as a rigorous solution to the Kohn–Sham inversion problem within the subspace spanned by the occupied Kohn–Sham orbitals.

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Reconstruction of Exchange–Correlation Potentials from Their Matrix Representations

Oueis

Staroverov

2022

“…However, in practice, HK is hampered by the lack of accurate approximations for the kinetic energy functional. , The KG functional combines the two formalisms by exploiting the partitioning in subsystems. The total electronic density ρ tot is computed as the sum over the subsystems densities ρ A , which are constructed by restricting the expansion to the basis set functions {ϕ α, A ( r )} belonging to the subsystem itself The total energy is then obtained as In principle, one can also use the full-system basis to expand the subsystem densities as is done in the density functional embedding context . The advantage of the current scheme, restricting the subsystem density expansion to the subsystem basis, is that, thanks to the partitioning, P is by construction block-diagonal, as well as the KS matrix, since only terms of the type P α A β A are considered.…”

Section: Corrected Subsystem Dftmentioning

confidence: 99%

Subsystem Density Functional Theory Augmented by a Delta Learning Approach to Achieve Kohn–Sham Accuracy

Pauletti

Rybkin

Iannuzzi

2021

Self Cite

Simulations based on electronic structure theory naturally include polarization and have no transferability problems. In particular, Kohn−Sham density functional theory (KS-DFT) has become the method of reference for ab initio molecular dynamics simulations of condensed matter systems. However, the high computational cost often poses strict limits on the affordable system size as well as on the extension of sampling (number of configurations). In this work, we propose an improvement to the subsystem density functional theory approach, known as the Kim− Gordon (KG) scheme, thus enabling the sampling of configurations for condensed molecular systems keeping the KS-DFT level accuracy at a fraction of computer time. Our scheme compensates the known KG shortcomings of the electronic kinetic energy term by adding a simple correction and can match KS-DFT accuracy in energies and forces. The computationally cheap correction is determined by means of a machine learning procedure. The proposed KG scheme is applied within a linear scaling self-consistent field formalism and is assessed by a series of molecular dynamics simulations of liquid water under different conditions. Although system-dependent, the correction is transferable between system sizes and temperatures.

“…Carter and co-workers have been the pioneers of molecule (WFT)-in-periodic(DFT) embedding; however, their implementations have usually relied on a plane-wave DFT calculation for the periodic system and localized basis calculation for the molecular subsystem. ,,, Therefore, to construct the embedding potential for the molecular subsystem, a transformation from the plane-wave to localized basis is necessary which is not trivial. Recently, an implementation based on mixed Gaussian plane-wave basis has been reported using products of atomic orbital BFs . Chulhai and Goodpaster’s QSoME embedding software based on PySCF is a recent example of an implementation utilizing Gaussian basis for the periodic subsystem; however, PySCF calculates potential matrices in reciprocal space which leads to efficiency issues especially for the Coulomb term.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, an implementation based on mixed Gaussian plane-wave basis has been reported using products of atomic orbital BFs. 22 Chulhai and Goodpaster’s QSoME embedding software 19 based on PySCF 19 is a recent example of an implementation utilizing Gaussian basis for the periodic subsystem; however, PySCF calculates potential matrices in reciprocal space which leads to efficiency issues especially for the Coulomb term. Notable implementations supporting periodic systems are also found in KOALA 23 (Gaussian basis) and Quantum ESPRESSO 24 , 25 (plane-wave basis) programs.…”

Section: Introductionmentioning

confidence: 99%

Efficient Implementation of Density Functional Theory Based Embedding for Molecular and Periodic Systems Using Gaussian Basis Functions

Sharma

Sierka

2022

A practical and effective implementation of density functional theory based embedding is reported, which allows us to treat both periodic and aperiodic systems on an equal footing. Its essence is the expansion of orbitals and electron density of the periodic system using Gaussian basis functions, rather than planewaves, which provides a unique all-electron direct-space representation, thus avoiding the need for pseudopotentials. This makes the construction of embedding potential for a molecular active subsystem due to a periodic environment quite convenient, as transformation between representations is far from trivial. The three flavors of embedding, molecule-in-molecule, molecule-inperiodic, and periodic-in-periodic embedding, are implemented using embedding potentials based on non-additive kinetic energy density functionals (approximate) and level-shift projection operator (exact). The embedding scheme is coupled with a variety of correlated wave function theory (WFT) methods, thereby providing an efficient way to study the ground and excited state properties of low-dimensional systems using high-level methods for the region of interest. Finally, an implementation of real time−timedependent density functional embedding theory (RT-TDDFET) is presented that uses a projection operator-based embedding potential and provides accurate results compared to full RT-TDDFT for systems with uncoupled excitations. The embedding potential is calculated efficiently using a combination of density fitting and continuous fast multipole method for the Coulomb term. The applicability of (i) WFT-in-DFT embedding, in predicting the adsorption and excitation energies, and (ii) RT-TDDFET, in predicting the absorption spectra, is explored for various test systems.