Distributed Gaussian orbitals for the description of electrons in an external potential (original) (raw)
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Distributed Gaussian orbitals for molecular calculations: application to simple systems
Molecular Physics
In this article, the possible use of sets of basis functions alternative with respect to the usual atom-centred orbitals sets is considered. The orbitals describing the inner part of the wavefunction (i.e. the region close to each nucleus) are still atomic Gaussian functions: tight Gaussian orbitals having different angular momenta and large exponential coefficients, centred on each nucleus. On the other hand, the outer part of the wavefunction is described through a set of s-type distributed Gaussian orbitals: s-type Gaussians having a unique fixed exponent, and whose fixed centres are placed on a uniform mesh of points evenly distributed in the region surrounding all the atoms of the molecule. The resulting basis sets are applied to various oneelectron systems in order to assess the capability to describe different types of oneelectron wavefunctions. Moreover, the hydrogen atom and the dihydrogen cation, for which accurate solutions exist, are also considered for comparison, to assess the effectiveness of the proposed approach. Preliminary results concerning the treatment of electron correlation, necessary for a quantitatively correct description of manyelectron atoms and molecules, are also presented.
Solving One-Electron Systems in a Novel Gaussian-Sinc Mixed Basis Set
A novel Gaussian-Sinc mixed basis set for the calculation of the one-electron electronic structure within a uniform magnetic field in three dimensions is presented. The one-electron system is used to demonstrate the utility of this new methodology and is a first step in laying the foundation for further development of many-electron atomic and molecular methodology. It is shown in this manuscript how to effectively calculate all basis set integrals, which includes the mixed Gaussian-Sinc integrals, with a fast and accurate method. The Sinc basis is invariant to the choice of the position of the Coulomb potential, as opposed to traditional grid based methods. This invariance guarantees that the choice of the grids origin has no effect on the electronic structure calculation. This is because the Coulomb potential is treated properly in this methodology, as opposed to DVR methodologies. The off-diagonal terms are sparse but very important around the Coulomb singularity. In general, five to six significant digits of accuracy on all converged results without the linear dependency problems of the Gaussian methodologies are achievable. This methodology is applied to calculate the ground state energy of H atom, H+2 ion and H2+3 ion in magnetic fields up to a magnetic field strength of 2.35x1013 G (10,000 au). From these calculations it is shown that H2+3 ion is unstable without relativistic considerations.
A detailed derivation of Gaussian orbital-based matrix elements in electron structure calculations
European Journal of Physics, 2010
A detailed derivation of the analytic solutions is presented for overlap, kinetic, nuclear attraction and electron repulsion integrals involving Cartesian Gaussian type orbitals. It is demonstrated how s-type orbitals can be used to evaluate integrals with higher angular momentum via the properties of Hermite polynomials and differentiation with respect to non-integration variables.
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.
Grid-based density functional calculations of many-electron systems
International Journal of Quantum Chemistry, 2008
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.
Smeared Coulomb potential orbitals: I—asymptotic expansion
Journal of Mathematical Chemistry
We consider an 1-electron model Hamiltonian, whose potential energy corresponds to the Coulomb potential of an infinite wire with charge Z distributed according to a Gaussian function. The time independent Schrödinger equation for this Hamiltonian is solved perturbationally in the asymptotic limit of small amplitude vibration (Gaussian function width close to zero). We propose to use the naturally polarized functions soobtained, as orbital basis sets for quantum chemical calculations. In particular, they should be well suited to perform electron-nucleus mean field configuration interaction calculations. Since the free-parameters of the model have the remarkable property to factorize the perturbative corrections to the eigenfunctions, these corrective part in factor can be simply added as additional functions to standard basis sets, leaving it to the molecular orbital calculation to optimize the free parameters within molecular orbital coefficients.
Physical Review A, 1991
The self-consistent-field treatment of the frequency-independent Breit interaction is reviewed with applications to many-electron atoms. The implementation of the matrix Dirac-Fock-Breit self-consistent-field procedure is presented for Gaussian-type basis sets that show no near-linear dependency problem. The matrix Dirac-Fock-Breit procedure has the advantage over the finitediference approach that it does not complicate the self-consistent-field procedure in basis-set expansion calculations. Basis sets of evenand well-tempered Gaussian functions were used to expand the large and small components of Dirac four-spinors. Expressions are derived for evaluating the matrix elements of the Dirac-Fock-Breit equations. Calculations done on rare-gas atoms He, Ne, Ar, Kr, and Xe and alkaline-earth metals Be, Mg, Ca, and Sr are presented.