Hartree-Fock Stability and Broken Symmetry Solutions of O2- and S2- Anions in External Confinement

2007 ◽  
Vol 72 (2) ◽  
pp. 197-222 ◽  
Author(s):  
Filip Holka ◽  
Pavel Neogrády ◽  
Miroslav Urban ◽  
Josef Paldus
Keyword(s):  
Model Systems ◽  
Basis Set ◽  
Broken Symmetry ◽  
Basis Sets ◽  
Gaussian Basis Sets ◽  
Hartree Fock ◽  
Harmonic Confinement ◽  
Electron Correlation Effects ◽  
Doubly Charged

We study the effect of a confining potential on systems that exhibit Hartree-Fock (HF) instabilities, and thus admit broken symmetry (BS) HF solutions, by relying on the O2- and S2- doubly-charged anions as model systems. We find that with the increasing strength of the external harmonic confinement potential, W(r) = 1/2(ωr)2 (with 0.0 ≤ ω < 0.2), the BS solutions are systematically eliminated. We use extended, diffuse, doubly-augmented Gaussian basis sets up to and including d-aug-cc-pV6Z, and find that the number and the character of BS solutions exhibit significant basis set effects. These basis sets were further extended by additional ghost basis functions, located away from the atomic center. The role of the electron correlation effects for the BS HF solutions was examined by the CCSD(T) method. In addition to modelling the confinement by the harmonic-like potential W(r), we also examined a more realistic "confinement", realized by a grid of point charges modelling the crystal structure of MgO. Again, we find that the HF instabilities and the implied BS solutions disappear with the increasing magnitude of the model charges simulating the crystal environment. At the same time, the O2- anion is energetically stabilized with respect to both the O- anion and the neutral oxygen atom.

scholarly journals Quantum Mechanical Study of YTiO3 to the Investigation of Piezoelectricity

2011 ◽  
Vol 2011 ◽  
pp. 1-5
Author(s):  
Raimundo Dirceu de Paula Ferreira ◽  
Marcos Antonio Barros dos Santos ◽  
Maycon da Silva Lobato ◽  
Jardel Pinto Barbosa ◽  
Marcio de Souza Farias ◽  
...  
Keyword(s):  
Total Energy ◽  
Piezoelectric Properties ◽  
Piezoelectric Effect ◽  
Basis Set ◽  
Basis Sets ◽  
Gaussian Basis Sets ◽  
Hartree Fock ◽  
Generator Coordinate ◽  
Mechanical Study ◽  
Quantum Mechanical Study

In previous articles we reported through theoretical studies the piezoelectric effect in BaTiO3, SmTiO3, and YFeO3. In this paper, we used the Douglas-Kroll-Hess (DKH) second-order scalar relativistic method to investigate the piezoelectricity in YTiO3. In the calculations we used the [6s4p] and [10s5p4d] Gaussian basis sets for the O (3P) and Ti (5S) atoms, respectively, from the literature in combination with the (30s21p16d)/[15s9p6d] basis set for the Y (3D) atom, obtained by generator coordinate Hartree-Fock (GCHF) method, and they had their quality evaluated using calculations of total energy and orbital energies (HOMO and HOMO-1) of the 2TiO+1 and 1YO+1 fragments. The dipole moment, the total energy, and the total atomic charges in YTiO3 in Cs space group were calculated. When we analyze those properties we verify that it is reasonable to believe that YTiO3 does not present piezoelectric properties.

Gaussian basis sets by generator coordinate Hartree–Fock method to ab initio calculations of electron affinities of enolates

2002 ◽  
Vol 587 (1-3) ◽  
pp. 9-17 ◽  
Author(s):  
R.M.L Savedra ◽  
J.C Pinheiro ◽  
O Treu Filho ◽  
R.T Kondo
Keyword(s):  
Ab Initio Calculations ◽  
Ab Initio ◽  
Basis Sets ◽  
Electron Affinities ◽  
Gaussian Basis Sets ◽  
Hartree Fock ◽  
Generator Coordinate

scholarly journals Role of Exchange and Correlation in High-Harmonic Generation Spectra of H2, N2 and CO2: Real-Time Time-Dependent Electronic-Structure Approaches

2020 ◽  
Author(s):  
Emanuele Coccia ◽  
Eleonora Luppi ◽  
Carlo Federico Pauletti
Keyword(s):  
Real Time ◽  
Harmonic Generation ◽  
Density Functional ◽  
High Harmonic ◽  
High Harmonic Generation ◽  
Time Dependent ◽  
Basis Sets ◽  
Gaussian Basis Sets ◽  
Hartree Fock ◽  
Exchange And Correlation

<p>This study arises from the attempt to answer the following question: how different descriptions of electronic exchange and correlation affect the high-harmonic generation (HHG) spectroscopy of H2, N2 and CO2 molecules? We compare HHG spectra for H2, N2 and CO2 with different ab initio electronic structures methods: real-time time-dependent configuration interaction (RT-TDCIS) and real-time time-dependent density functional theory (RT-TDDFT) using truncated basis sets composed of correlated wave functions expanded on Gaussian basis sets. In the framework of RT-TDDFT, we employ PBE and LC-ωPBE functionals. We study HHG spectroscopy by disentangling the effect of electronic exchange and correlation. We first analyse the electronic exchange alone and in the case of RT-TDDFT with LC-ωPBE, we use ω = 0.3 and ω = 0.4 to tune the percentage of long-range Hartree-Fock exchange and of short-range exchange PBE. Then, we added the correlation as described by PBE functional. All the methods give very similar HHG spectra and they seem not to be particularly sensitive to the different description of exchange and correlation or to the correct asymptotic behaviour of the Coulomb potential. Despite this general trend, some differences are found in the region connecting the cutoff and the background. Here, the harmonics can be resolved with different accuracy depending on the theoretical schemes used. We believe that the investigation of the molecular continuum and its coupling with strong fields merits further theoretical investigations in the next future. </p>

Gaussian basis sets for the atoms from K through Xe

2001 ◽  
Vol 79 (2) ◽  
pp. 121-123 ◽  
Author(s):  
R Centoducatte ◽  
E VR de Castro ◽  
F E Jorge
Keyword(s):  
Key Words ◽  
Ground State ◽  
Basis Sets ◽  
Gaussian Basis Sets ◽  
Hartree Fock ◽  
Generator Coordinate ◽  
Discretization Technique ◽  
Total Energies

An improved generator coordinate Hartree-Fock (IGCHF) method is used to generate Gaussian basis sets for the atoms from K (Z = 19) through Xe (Z = 54). The Griffin-Hill-Wheeler-HF equations are integrated using the integral discretization technique. The ground state HF total energies obtained by us are compared with those calculated with the original GCHF method and with other approaches reported in the literature. The largest difference between our energy values and the corresponding ones computed with a numerical HF method is equal to 6.003 mhartree for Kr (Z = 36).Key words: improved generator coordinate Hartree-Fock method, Gaussian basis sets, total energies.

Gaussian basis sets for CO2 molecule generated with the molecular improved generator coordinate Hartree?Fock method

2005 ◽  
Vol 113 (2) ◽  
pp. 69-72 ◽  
Author(s):  
M. T. Barreto ◽  
E. P. Muniz ◽  
F. E. Jorge ◽  
A. G. Cunha
Keyword(s):  
Basis Sets ◽  
Gaussian Basis Sets ◽  
Hartree Fock ◽  
Generator Coordinate

Polarization consistent basis sets using the projector augmented wave method: a renovation brought by PAW into Gaussian basis sets

2020 ◽  
Vol 22 (46) ◽  
pp. 27037-27052
Author(s):  
Quan Manh Phung ◽  
Masaya Hagai ◽  
Xiao-Gen Xiong ◽  
Takeshi Yanai
Keyword(s):  
Dft Calculations ◽  
Basis Set ◽  
Basis Sets ◽  
Wave Method ◽  
Gaussian Basis Sets ◽  
New Family ◽  
Consistent Basis ◽  
Projector Augmented Wave

A new family of polarization consistent basis set, combined with the projector augmented wave method, was introduced. The basis sets are compact and have good performance as compared to conventional all-electron basis sets in DFT calculations.

From Atomic Orbitals to Molecular Orbitals and Chemical Bonds

2020 ◽  
pp. 150-187
Author(s):  
Jochen Autschbach
Keyword(s):  
Hydrogen Molecule ◽  
Atomic Orbital ◽  
Plane Waves ◽  
Basis Set ◽  
Orbital Method ◽  
Chemical Bonds ◽  
Atomic Orbitals ◽  
Hartree Fock ◽  
Generalized Matrix

It is shown how an aufbau principle for atoms arises from the Hartree-Fock (HF) treatment with increasing numbers of electrons. The Slater screening rules are introduced. The HF equations for general molecules are not separable in the spatial variables. This requires another approximation, such as the linear combination of atomic orbitals (LCAO) molecular orbital method. The orbitals of molecules are represented in a basis set of known functions, for example atomic orbital (AO)-like functions or plane waves. The HF equation then becomes a generalized matrix pseudo-eigenvalue problem. Solutions are obtained for the hydrogen molecule ion and H2 with a minimal AO basis. The Slater rule for 1s shells is rationalized via the optimal exponent in a minimal 1s basis. The nature of the chemical bond, and specifically the role of the kinetic energy in covalent bonding, are discussed in details with the example of the hydrogen molecule ion.

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