arXiv subjects

Tomasz A. Wesolowski

Publications and source records attributed to Tomasz A. Wesolowski.

3 recordsLinked to original sources

arXiv2022

Nuclear cusps and singularities in the non-additive kinetic potential bi-functional from analytical inversion

The non-additive kinetic potential $v^{\text{NAD}}$ is a key quantity in density-functional theory (DFT) embedding methods, such as frozen density embedding theory and partition DFT. $v^{\text{NAD}}$ is a bi-functional of electron densities $ρ_{\rm B}$ and $ρ_{\rm tot} = ρ_{\rm A} + ρ_{\rm B}$. It can be evaluated using approximate kinetic-energy functionals, but accurate approximations are challenging. The behavior of $v^{\text{NAD}}$ in the vicinity of the nuclei has long been questioned, and singularities were seen in some approximate calculations. In this article, the existence of singularities in $v^{\text{NAD}}$ is analyzed analytically for various choices of $ρ_{\rm B}$ and $ρ_{\rm tot}$, using the nuclear cusp conditions for the density and Kohn-Sham potential. It is shown that no singularities arise from smoothly partitioned ground-state Kohn-Sham densities. We confirm this result by numerical calculations on diatomic test systems HeHe, HeLi$^+$, and H$_2$, using analytical inversion to obtain a numerically exact $v^{\rm NAD}$ for the local density approximation. We examine features of $v^{\rm NAD}$ which can be used for development and testing of approximations to $v^{\rm NAD}[ρ_{\rm B},ρ_{\rm tot}]$ and kinetic-energy functionals.

physics.chem-ph↗

arXiv2020

Frozen-Density Embedding Theory based simulations with experimental electron densities

The basic idea of Frozen-Density Embedding Theory (FDET) is the constrained minimisation of the Hohenberg-Kohn density functional $E^{HK}[ρ]$ performed using the auxiliary functional $E_{v_{AB}}^{FDET}[Ψ_A,ρ_B]$, where $Ψ_A$ is the embedded $N_A$-electron wave-function and $ρ_B(\vec{\mathrm{r}})$ a non-negative function in real space integrating to a given number of electrons $N_B$. This choice of independent variables in the total energy functional $E_{v_{AB}}^{FDET}[Ψ_A,ρ_B]$ makes it possible to treat the corresponding two components of the total density using different methods in multi-level simulations. We demonstrate, for the first time, the applications of FDET using $ρ_B(\vec{\mathrm{r}})$ reconstructed from X-ray diffraction data on a molecular crystal. For eight hydrogen-bonded clusters involving a chromophore (represented with $Ψ_A$) and the glycylglycine molecule (represented as $ρ_B(\vec{\mathrm{r}})$), FDET is used to derive excitation energies. It is shown that experimental densities are suitable to be used as $ρ_B(\vec{\mathrm{r}})$ in FDET based simulations.

physics.chem-ph↗

arXiv2008

Orbital-free effective embedding potential at nuclear cusp

A new approach to approximate the kinetic-energy-functional dependent component ($v_t[ρ_A,ρ_B](\vec{r})$) of the effective potential in one-electron equations for orbitals embedded in a frozen density environment (Eqs. 20-21 in [Wesolowski and Warshel, {\it J. Phys. Chem.} {\bf 97}, (1993) 8050]) is proposed. The exact limit for $v_t$ at $ρ_A\longrightarrow 0$ and $\int ρ_B d\vec{r}=2$ is enforced. The significance of this limit is analysed formally and numerically for model systems including a numerically solvable model and real cases where $\int ρ_B d\vec{r}=2$. A simple approximation to $v_t[ρ_A,ρ_B](\vec{r})$ is constructed which enforces the considered limit near nuclei in the environment. Numerical examples are provided to illustrate the numerical significance of the considered limit for real systems - intermolecular complexes comprising, non-polar, polar, charged constituents. Imposing the limit improves significantly the quality of the approximation to $v_t[ρ_A,ρ_B](\vec{r})$ for systems comprising charged components. For complexes comprising neutral molecules or atoms the improvement occurs as well but it is numerically insignificant.

physics.chem-ph↗