Restricted Hartree-Fock Calculations Research Articles

Spin density in the CoCl 42− ion

Unrestricted and restricted Hartree-Fock calculations for the tetrachlorocobaltate(II) ion ICoCl 4 2−) are presented. The spin density distributions from these calculations are compared with polarized neutron diffraction results through spin density plots and a population analysis.

On the structure of the tertiary butyl radical: anab initioinvestigation

The structure of the tert-butyl radical has been investigated by means of ab initio restricted Hartree-Fock calculations using a split-valence basis set augmented by polarization functions. The radical is predicted to have a pyramidal C 3v ground state geometry with an out-of-plane bending angle of circa 10°. Ionization potentials calculated in the ΔSCF approximation are in good agreement with the experimental values.

Restricted hartree—fock calculations on GeH 2 and SnH 2

Ab initio calculations using basis sets of double-zeta quality in the valence region were performed for GeH 2 and SnH 2 in the 1A 1 and 3B 1 states. The geometries found are very similar to those of SiH 2 in the respective states. By comparison of the calculated energies of GeH 2 and SnH 2 with those of CH 2 and SiH 2 the singlet—triplet separations of the former are estimated to be about 25 kcal/mol. A further estimate of the heats of formation furnishes roughly the same stability as of SiH 2.

ChemInform Abstract: RELATIVE STABILITY OF THE 2A1G AND 2EG STATES OF THE C2H6+ ION

Anab initio study of the relative stability for the states2A1g and2Eg of C2H6+ has been carried out. The results of the Open Shell Restricted Hartree-Fock calculations lead to assign the2A1g as the ground state of the molecule in agreement with previous SCF calculations.

A simulation of the exchange potential in unrestricted and restricted Hartree-Fock calculations studied on atoms

The spherical average of the Hartree-Fock exchange potential depending on each spin orbital is compared with Slater's exchange potential, V xs, as demonstrated for the phosphorus atom. It is shown that the former potential can be simulated by (a + br)V xs, where r is the radius and the constants a and b are calculated for each spin orbital. This simulation is tested for the iron atom and it is found that the results agree well with those obtained from unrestricted and restricted Hartree-Fock calculations, respectively. The applicability of this new method in energy band structure calculations is briefly discussed.

Relative stability of the2 A 1g and2 E g states of the C2H 6 + ion

Anab initio study of the relative stability for the states2 A 1g and2 E g of C2H 6 + has been carried out. The results of the Open Shell Restricted Hartree-Fock calculations lead to assign the2 A 1 g as the ground state of the molecule in agreement with previous SCF calculations. The correlation energy associated to both states has been calculated within the correlation hole model and the results, contrary to those obtained from Configuration Interaction calculations, do not alter qualitatively the conclusions from SCF.

Anab initio investigation of the inner shell excited states of the molecule Cl2

Restricted Hartree-Fock calculations of the Cl2 molecule have been carried out to investigate the X-ray excited states below Cl 2p-electron ionization potential. Some inner shell excited states are shown to have a valence or a valence-Rydberg nature that results in a considerable intensity of the appropriate transitions in the X-ray absorption spectrum. A significant interaction among some electron configurations with a 2p vacancy is predicted.

Electronic structure of silicon Rydberg series. I. The (3pnd))Do1,Do3,Fo1, andFo3series

The ($3{s}^{2}3pnd$) $^{1}D^{o}$, $^{3}D^{o}$, $^{1}F^{o}$, and $^{3}F^{o}$ Rydberg series of the silicon atom are investigated by a restricted Hartree-Fock calculation and configuration interaction (CI) calculations of various levels. The relative energies with respect to the ionized level $(3{s}^{2}3p)^{2}P^{o}$ given by the largest CI calculation in the present work are -2.63, -1.46, -0.85, -0.55, -0.38, and -0.28 eV, respectively, for the first six members of the $^{3}D^{o}$ series, while the experimental values are -2.56, -1.45, -0.85, -0.55, -0.38, and -0.27 eV. The agreement between the two is excellent. The configuration $(3s3{p}^{3})^{3}D^{o}$ is predominant in the first member of the $^{3}D^{o}$ series, and it also acts as a strong series perturber in the rest of the series. For the $^{1}D^{o}$ series the relative energies with respect to $^{2}P^{o}$ by the largest CI calculation are -2.27, -1.16, -0.70, -0.46, and -0.32 eV, respectively, whereas the experimental values are -2.31, -1.17, -0.70, -0.47, and -0.34 eV. In this series, $(3s3{p}^{3})^{1}D^{o}$ acts as a series perturber just as $3s3{p}^{3}$ does in the $^{3}D^{o}$ series. At any levels of the approximations, $(3s3{p}^{3})^{1}D^{o}$ is not found below the $^{2}P^{o}$ state. The ($3{s}^{2}3pnd$) $^{1}F^{o}$ and $^{3}F^{o}$ series are found to be pure Rydberg series.

Magnetic moments and the Skyrme interaction

The magnetic properties of the Skyrme interaction have been studied by performing a restricted Hartree-Fock calculation in order to evaluate the magnetic polarizability and the corrections to the Schmidt moments in nuclei with closed jj shells plus or minus one nucleon. Different corrections to the Schmidt values have been evaluated and discussed: the M1 core polarization, and the renormalization of the gyromagnetic factors due to exchange and spin-orbit forces. Several variants of the Skyrme interaction have been studied and discussed in detail.

Unrestricted Hartree-Fock calculations for a cluster model of NiO

Self-consistent restricted and unrestricted Hartree-Fock calculations have been performed for a NiO 6 −10 cluster embedded in a point ion field. The unrestricted Hartree-Fock calculations give rise to p-like and d-like states whose energies overlap, but which are essentially non-interacting. The calculated widths of the p-like and d-like states are 4.5 and 2.2 eV respectively, in good agreement with experiment. Furthermore, d-orbital relaxation is found to be much more important for RHF calculation as opposed to UHF calculations.

Restricted Hartree-Fock calculations on the interaction of an olefine with a titanium compound

Ab-initio, all electron, restricted Hartree-Fock calculations are performed on various configurations of a molecular compounds stimulating the reaction TiCl 4 · Al(CH 3) 3+C 2H 4 → TiCl 4 · Al(CH 3) 2 · C 3H 7. A minimal basis set of contracted gaussians has been used to describe the molecular orbitals. The results indicate that the Ti exerts weak attraction on the olefine and that a concerted motion of the olefin and the alkyl group is basic to explain the reaction mechanism.

Theoretical condiserations regarding the existence of PsO and PsS+

At has been proposed from experimental studies and in analogy with hydrogen compounds that PsO may be an entity of some importance, or an intermediate, in the reaction of positronium, Ps, with aqueous oxyacid species such as H2PO−4, HSO−4, ClO−4, and NO−3. This communication explores the stability of PsO and PsS, or [0−: e+] and [S−:e+], respectively, relative to dissociation into Ps and O(3P) or S(3P) on the basis of restricted Hartree-Fock calculations for the PsO and PsS systems and certain correlation correction arguments. We obtain a reasonable lower estimate of the dissociation energy to Y + Ps of ⪢ −0.47 eV for PsO and ⪢ −0.70 eV for PsS. It is suggested that a modest correlation correction to the positron affinity (PA) of O− would very probably lead to a bound state system for PsO.

The electronic structure and positron annihilation characteristics of positronium halides, [X−; e+]. I. Hartree–Fock calculations and stability

The electronic structure of the atom/positron systems [F−;e+], [Cl−;e+], [Br−;e+], and [I−;e+] are examined by means of restricted Hartree–Fock calculations on the ...ns2np6(nl)+, 2L and...ns2np5 (n+1) sls+, 2P,4P states. A modified version of the numerical MCHF72 program of Froese–Fischer was used in these calculations. Our theoretical investigations suggest that...ns2np61s+, 2S is the ground state of the system. It is shown that X− ions have a substantial positron affinity (e.g. ∼5 eV for F− to 3.3 eV for I−) and arguments based on pair-correlation and many-electron perturbation theory are used to obtain hard lower limit estimates of the binding energy of Ps to the X atom. We thus find that the ground state of [X−:e+] is stable with respect to dissociation into X and Ps with binding energies of at least 1.66, 0.80, 0.19, and −0.45 eV for [F−:e+], [Cl−:e+], [Br−:e+], and [I−:e+], respectively. The details of the positronic orbitals are presented and discussed.

A configuration interaction calculation of the potential energy surface of Li3

Large-scale configuration interaction calculations of the potential energy surface of Li3 are described. The major prediction which emerges is that triangular configurations are more stable than linear ones, with the 2B2 and 2A1 states having different equilibrium geometries but essentially the same energies. It is found that the most stable linear configuration is symmetric, unlike the prediction of restricted Hartree-Fock calculations. A fit of our calculated surface to a semi-empirical LEPS function is presented.

SCF Calculations on excited states

The formalism recently developed by Pople and co-workers for restricted Hartree—Fock calculations on high spin open shells is extended to a general treatment of singly excited states. The limitations of the method and possible alternative approaches are briefly discussed.

A theoretical interpretation of the satellite peaks associated with core electron ionization of N2O

The satellite spectra associated with both oxygen and nitrogen 1s ionization of nitrous oxide are interpreted using configuration interaction calculations whose basis orbitals are the MO's of the corresponding core hole state, obtained by restricted Hartree—Fock calculations. The most intense peaks in the spectra are assigned to π → π transitions, and their intensities are correlated with the atomic character of the π MO's of N2O.

Variational study of a closed shell plus one particle using zero-range interaction

Restricted Hartree-Fock calculations are done for a closed shell plus one particle using zero-range interactions. Oscillator wave functions, with different length parameters for the valence particle and the core, are used. Radial and quadrupole distortions are considered. The most novel feature of our results is that the valence nucleon moves in towards the core. However the introduction of finite-range interactions tends to move the valence nucleon away from the core. Isoscalar effective E2 charge corrections are near unity.

Configuration interaction calculations of the Auger spectrum of CH4, HF, H2O and CO

Configuration interaction calculations of the doubly-ionized states of CH4, HF, H2O and CO are described and the results correlated with the Auger spectra of these molecules. The basis M.O.'s for the configuration interaction calculations are obtained from restricted Hartree-Fock calculations on a low-lying state of the doubly ionized molecule. In general, these calculations allow an assignment of the quite complex Auger spectra of these molecules.

Ab initio calculations of the ground, excited and ionic states of titanium and vanadium tetrachlorides

Ab initio restricted Hartree-Fock calculations of the ground states of TiC14, v c h , and vc14+ are described. The excited states of these molecules are calculated by means of configuration interaction calculations and are used to interpret the absorption spectra of Tic14 and vc14 and the photoelectron spectrum of vc14. The photoelectron spectrum of Tic14 is discussed with the aid of Koopmans’ theorem. These calculations lead to a generally satisfactory interpretation of the spectroscopic data.

Self-consistent-field wavefunctions using a symmetry-restricted annihilation of single-excitations procedure

The form of Brillouin’s theorem appropriate for restricted Hartree–Fock calculations is used to determine rigorous self-consistent-field wavefunctions for the 3A1, 3E, 3A2, 1A2, and 1E states of the ... 2e3 3e manifold of CH3CO+, a manifold for which traditional Fock operator techniques are unsuitable. The results of an approximate method previously reported are compared with these exact results are found to be in quite good agreement.