Grid-based density functional calculations of many-electron systems (original) (raw)
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Grid-based density functional calculation of many-electron systems
2010
Exploratory variational pseudopotential density functional calculations are performed for the electronic properties of many-electron systems in the 3D cartesian coordinate grid (CCG). The atom-centered localized gaussian basis set, electronic density and the two-body potentials are set up in the 3D cubic box. The classical Hartree potential is calculated accurately and efficiently through a Fourier convolution technique. As a first step, simple local density functionals of homogeneous electron gas are used for the exchange-correlation potential, while Hay-Wadt-type effective core potentials are employed to eliminate the core electrons. No auxiliary basis set is invoked. Preliminary illustrative calculations on total energies, individual energy components, eigenvalues, potential energy curves, ionization energies, atomization energies of a set of 12 molecules show excellent agreement with the corresponding reference values of atom-centered grid as well as the grid-free calculation. Results for 3 atoms are also given. Combination of CCG and the convolution procedure used for classical Coulomb potential can provide reasonably accurate and reliable results for many-electron systems.
A new density functional method for electronic structure calculation of atoms and molecules
arXiv: Chemical Physics, 2019
This chapter concerns with the recent development of a new DFT methodology for accurate, reliable prediction of many-electron systems. Background, need for such a scheme, major difficulties encountered, as well as their potential remedies are discussed at some length. Within the realm of non relativistic Hohenberg-Kohn-Sham (HKS) DFT and making use of the familiar LCAO-MO principle, relevant KS eigenvalue problem is solved numerically. Unlike the commonly used atom-centered grid (ACG), here we employ a 3D cartesian coordinate grid (CCG) to build atom-centered localized basis set, electron density, as well as all the two-body potentials directly on grid. The Hartree potential is computed through a Fourier convolution technique via a decomposition in terms of short- and long-range interactions. Feasibility and viability of our proposed scheme is demonstrated for a series of chemical systems; first with homogeneous, local-density-approximated XC functionals followed by non-local, gradi...
Pseudopotential density functional treament of atoms and molecules in cartesian coordinate grid
2010
This is a follow-up of our recently proposed work on pseudopotential calculation (Ref. [21]) of atoms and molecules within DFT framework, using cartesian coordinate grid. Detailed results are presented to demonstrate the usefulness, applicability of the same for a larger set of species (5 atoms; 53 molecules) and exchange-correlation functionals (local, nonlocal). A thorough comparison on total, component, ionization, atomization energies, eigenvalues, potential energy curves with available literature data shows excellent agreement. Additionally, HOMO energies for a series of molecules show significant improvements by using the Leeuwen-Baerends exchange potential, compared to other functionals considered. Comparison with experiments has been made, wherever possible.
Exchange-Correlation Functional Comparison of Electronic Energies in Atoms Using a Grid Basis
Journal of Applied Mathematics and Physics
Calculation of total energies of the electronic ground states of atoms forms the basis for the frozen-core pseudopotentials used in atomistic calculations of much larger scale. Reference values for these energies provide a benchmark for the validation of new software to calculate such potentials. In addition, basic atomic-scale electronic properties such as the (first) ionization energy provide a simple check on the approximation used in the calculation method. We present a comparison of the total energies and ionization energies of atoms Z = 1-92 calculated in density functional theory with several levels of exchange-correlation functional and the Hartree-Fock method, comparing ionization energies to experiment. We also investigate the role of relativistic treatment on these energies.
Asian journal of chemical sciences, 2017
A new energy functional is proposed for basis free Density Functional Theory (DFT) calculation. Electronic density is calculated using atomic radii considering the atom as spherical. Groundstate electronic energies and ionization energies of atoms with Z = 1 − 120 are presented. Energy functional is partitioned numerically. Thus, this method may be termed as partitioned classical density functional theory (PCDFT). It is demonstrated that one can define an energy functional solely on the classical grounds which reduce the computational cost of storage and time. Calculated electronic energies and ionization energies are in reasonably good agreement with the quantum mechanical results of Relativistic Hartree Fock (RHF) method in the large basis set. Total energies and ionization energies show mean absolute percent deviations as 0.887 and 8.73 respectively. Given the fact that it is a simple, basis-set free, easy to implementable, one-step method, it could be useful for larger systems.
The Journal of Chemical Physics
We present a purely numerical approach in Cartesian grid, for efficient computation of Hartree-Fock (HF) exchange contribution in the HF and density functional theory models. This takes inspiration from a recently developed algorithm [Liu et al., J. Chem. Theor. Comput. 13, 2571 (2017)]. A key component is the accurate evaluation of electrostatic potential integral, which is the rate-determining step. This introduces the Fourier convolution theorem in conjunction with a range-separated Coulomb interaction kernel. The latter is efficiently mapped into real grid through a simple optimization procedure, giving rise to a constraint in the range-separated parameter. The overall process offers logarithmic scaling with respect to molecular size. It is then extended towards global hybrid functionals such as B3LYP, PBE0 and BHLYP within pseudopotential Kohn-Sham theory, through an LCAO-MO ansatz in Cartesian grid, developed earlier in our laboratory. For sake of comparison, a parallel semi-numerical approach has also been worked out that exploits the familiar Obara-Saika recursion algorithm. An excellent agreement between these two routes is demonstrated through total energy and orbital energy in a series of atoms and molecules (including 10 πelectron molecules), employing an LANL2DZ-type basis function. A critical analysis of these two algorithms reveals that the proposed numerical scheme could lead to very attractive and competitive scaling. The success of our approach also enables us for further development of optimally tuned range-separated hybrid and hyper functionals.
Density functional electric response properties of molecules in Cartesian grid
International Journal of Quantum Chemistry, 2018
Within the finite-field Kohn-Sham framework, static electric response properties of diatomic molecules are presented. The electronic energy, dipole moment (µ), static dipole polarizability (α) and first-hyperpolarizability (β) are calculated through a pseudopotential-DFT implementation in Cartesian coordinate grid, developed in our laboratory earlier. We engage the Labello-Ferreira-Kurtz (LFK) basis set; while four local and non-local exchange-correlation (LDA, BLYP, PBE and LBVWN) functionals have been adopted. A detailed analysis of grid convergence and its impact on obtained results, is presented. In each case the electric field optimization was carefully monitored through a recently prescribed technique. For all three molecules (HCl, HBr, HI) considered, the agreement of all these quantities with widely successful and popular atom-centered-grid procedure, is excellent. To assess the efficacy and feasibility, companion calculations are performed for these on a representative molecule (HCl) at distorted geometries, far from equilibrium. Wherever possible, relevant comparison is made with available all-electron data and experimental results. This demonstrates that Cartesian grid provides accurate, reliable results for such properties of many-electron systems within pseudopotential representation.