Equilibrium Bond Lengths from Orbital-Free Density Functional Theory

Abstract

This work presents an investigation to model chemical bonding in various dimers based on the atomic fragment approach. The atomic fragment approach is an ab-initio, parameter-free implementation of orbital-free density functional theory which is based on the bifunctional formalism, i.e., it uses both the density and the Pauli potential as two separate variables. While providing the exact Kohn-Sham Pauli kinetic energy when the orbital-based Kohn-Sham data are used, the bifunctional formalism allows for approximations of the functional derivative which are orbital-free. In its first implementation, the atomic fragment approach uses atoms in their ground state to model the Pauli potential. Here, it is tested how artificial closed-shell fragments with non-integer electron occupation perform regarding the prediction of bond lengths of diatomics. Such fragments can sometimes mimic the electronic structure of a molecule better than groundstate fragments. It is found that bond lengths may indeed be considerably improved in some of the tested diatomics, in accord with predictions based on the electronic structure.

Detailed analysis of deformation potentials with application in orbital-free density functional theory

“…The first test case with c = 0 and d = 0 is the bare atomic fragment approach itself, in which case the equilibrium bond distances directly follow the size of the core shells, which decrease from Li to Ne and thus, yield a very short bond length in the case of Ne 2 [for a detailed explanation see Finzel (2021)]. The construction of a deformation potential with c = 2 and d = 0 means that one electron pair interacts constructively, while there are no destructive terms at all.…”

Deformation Potentials: Towards a Systematic Way beyond the Atomic Fragment Approach in Orbital-Free Density Functional Theory

“…Similar to previously published methods [ 53 , 54 ], energy minimization has been performed by optimization of the respective exponents for the valence region of the participating atoms, where the electron density is represented by atom-centered, squared, real-type nodeless Slater functions of 1S and 2S-type only Those nodeless spherical Slater functions are given by [ 70 , 71 ] with …”

“…In the applied formalism, the choice of atomic fragments markedly influences the ability of the method to properly model chemical bonding curves. It has been shown that artificially constructed closed-shell atoms better mimic the corresponding atomic fragments within the molecule, and thus yield better equilibrium bond lengths compared to experimental data [ 54 ] than the ordinary ground-state atoms. In the recently introduced OF-DFT methods, the total kinetic energy was given by employing the fragment Pauli kinetic energy given in terms of a bifunctional where the molecular Pauli potential is approximated by its atomic fragment variant and is the KS Pauli potential for atom A .…”

“… Equilibrium bond length for second-row homonuclear dimers. Black squares: Experimental values [ 67 , 68 ], green circles: Kohn–Sham calculations from ADF/LDA/QZ4P level, blue diamonds: OF-DFT using the bare atomic fragment approach (some of the data previously published here [ 54 ]), red triangles: OF-DFT using the deformation potential and electron counts from MO theory. …”

“…The aim of the present work is to provide a further contribution in this conceptual direction. It has recently been shown that chemical bonding of increasing accuracy can be obtained from non-parameterized, ab initio, orbital-free methods [ 52 , 53 , 54 ] via the bifunctional approach [ 52 , 53 , 54 , 55 , 56 , 57 ] (exploiting the homogenous scaling behavior of the functionals [ 58 ]), and the introduced atomic fragment approximation [ 52 , 53 , 54 , 56 , 57 ]. The target of the present study is to shed some light on potential systematic pathways beyond the atomic fragment approximation.…”