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

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 plane-waves, 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-in-periodic, 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–time-dependent 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.