Unrestricted Hartree-Fock Calculations Research Articles

Semiempirical computation of homolytic O-H bond dissociation energies of alcohols: comparison of the AM1 and PM3 methods

The heats of formation of various alcohols and alkoxy radicals were calculated using the AM1 and PM3 semiempirical methods, which were then used to calculate the bond dissociation energies of the alcohols. Both restricted Hartree-Fock (RHF) and unrestricted Hartree-Fock (UHF) calculations were performed to determine which technique was most applicable to the computation of bond dissociation energies within the semiempirical frameworks. It was determined that AM1/RHF calculations gave the most accurate results for O-H bond dissociation energies of alcohols. The effect of using configuration interaction calculations to calculate bond dissociation energies within the semiempirical framework was also examined.

Comparative study of Cu K-edge x-ray-absorption and Cu 2p x-ray photoelectron spectra in copper oxide compounds.

We have measured polarization-dependent x-ray-absorption spectra (XAS) at the Cu {ital K} edge in magnetically-aligned powder samples of La{sub 2}CuO{sub 4}, Nd{sub 2}CuO{sub 4}, Bi{sub 2}CuO{sub 4}, Ca{sub 0.85}Sr{sub 0.15}CuO{sub 2}, and SrCuO{sub 2}, all of which contain Cu coordinated by four coplanar O nearest neighbors. We have also measured Cu 2{ital p}{sub 3/2} x-ray photoelectron spectra (XPS) for all except the last compound. The measurements have been analyzed in terms of unrestricted Hartree-Fock calculations for CuO{sub 6}{sup 10{minus}} and CuO{sub 12}{sup 22{minus}} clusters, with energies and Coulomb parameters, including interactions with the core hole, for the Cu 3{ital d}{sub {ital x}}{sup 2}{minus}{ital y}{sup 2}, 4{ital s}, and 4{ital p} orbitals determined in an {ital ab} {ital initio} fashion. It is well known that the intensity ratio of the two XPS peaks is sensitive to the degree of hybridization between Cu 3{ital d}{sub {ital x}}{sup 2}{minus}{ital y}{sup 2} and O 2{ital p}{sub {sigma}} orbitals in the ground state. We show both by empirical correlations and model calculations that the relative shift of the continuum absorption threshold for {cflx {epsilon}}{parallel}{bold z} (where {bold z} is perpendicular to the plane of the CuO{sub 4} units) and the shift of the main (3{italmore » d}{sup 10}{ital L}) XPS peak are also useful measures of the covalency. The Cu 4{ital p}{sub {ital z}}-like quasibound state observed in XAS is sensitive as well to 4{ital p}{sub {ital z}--}O 2{ital p} hybridization. In the cluster calculations, good agreement with the experimental features is obtained with use of a single adjustable parameter, the energy of the O 2{ital p}{sub {sigma}} level (measured relative to Cu 3{ital d}{sub {ital x}}{sup 2}{minus}{ital y}{sup 2}). We show that this energy varies linearly with the difference in Madelung energies for the O and Cu sites.« less

Ab initio study of some doublet excited states of AlH 2

Ab initio unrestricted Hartree-Fock (UHF) calculations were carried out with a relatively large basis set in order to search for the equilibrium geometries of eight doublet electronic states of the AlH 2 radical. The results indicate that among these eight states there are three unstable states and one Rydberg state. The predicted equilibrium geometries for the X 2 A 1 and 2 B 1 states are in good agreement with the available experimental and configuration interaction (CI) results. The vibrational frequencies in the five stable states were calculated under the assumptions of valence forces. On the basis of the energetic results, some qualitative predictions about the electronic spectra of AlH 2 are also presented.

On a proposed radiation‐induced polaronic hole in silicon dioxide

AbstractAb‐initio self‐consistent‐field molecular‐orbital (SCF MO) Hartree–Fock (HF) calculations using the STO‐3G, 6‐31G, and 6‐31G* basis sets, were performed to model quasi‐tetrahedral silicon species in silicon dioxide. Mostly nine‐atom clusters, [Si(OH)4]qt, with charge number qt = 0 or + 1, were studied. The positions of the Si and O atoms were varied to achieve minimum total energies, while the protons were held fixed in the O‐(neighboring)Si direction to simulate the rigid crystal surroundings. The α‐quartz‐type local symmetry C2 was found to be retained for the neutral cluster, but not for the ionic one. The unrestricted HF calculations indicate that the latter paramagnetic centre, (qt = +1), has its spin population almost entirely on one short‐bonded oxygen ion bonded weakly to its neighboring Si, and is quite high in energy (9.55 eV with 6‐31G) compared to the diamagnetic centre (qt = 0). The ionization energy is much higher than the self‐trapping potential of the polaronic hole, a fact which may account for the failure so far to observe a [SiO4]+1 center in quartz by means of continuous‐wave electron paramagnetic resonance spectroscopy. Calculations on the [SiO4]+1 center agree well with ultraviolet spectra, and with the [hole portion of a] proposed radiation‐induced exciton in quartz. The hole in [Si(OH)4]+1 can be shifted from a short‐bonded to a long‐bonded oxygen to give the excited state [Si(OH)4]es+1. Conclusions reached with the nine‐atom clusters were confirmed by a series of calculations on the extended model [Si(OSiH3)4]qt. Comparisons with the known isoelectronic species [AlO4]0 were carried out.

A theoretical comparison of CO bonding on the Fe(100) surface

Unrestricted Hartree-Fock (UHF) cluster calculations with the Constrained Space Orbital Variation (CSOV) analysis are used to compare the bonding in vertical on-top, vertical bridging and tilted CO on the Fe(100) surface. Large charge transfers and strong back donation effects are found in the tilted CO cluster consistent with the expectation that this structure is a precursor to CO dissociation. The UHF calculations also reveal that mainly minority spin Fe d electrons are donated to the CO π ∗ orbitals. A qualitative interpretation of the recent spin polarized photoemission spectra for tilted CO on Fe(100) is presented.

A theoretical comparison of CO bonding on the Fe(100) surface

Unrestricted Hartree-Fock (UHF) cluster calculations with the Constrained Space Orbital Variation (CSOV) analysis are used to compare the bonding in vertical on-top, vertical bridging and tilted CO on the Fe(100) surface. Large charge transfers and strong back donation effects are found in the tilted CO cluster consistent with the expectation that this structure is a precursor to CO dissociation. The UHF calculations also reveal that mainly minority spin Fe d electrons are donated to the CO π ∗ orbitals. A qualitative interpretation of the recent spin polarized photoemission spectra for tilted CO on Fe(100) is presented.

Dynamical and spectroscopic studies of nonrigid molecules. Application to the visible spectrum of thioacetaldehyde

The methyl torsion and aldehydic hydrogen wagging modes are studied theoretically in thioacetaldehyde, in both ground and first triplet excited states. For this purpose, the potential energy surfaces were determined by ab initio restricted Hartree Fock and unrestricted Hartree Fock calculations with 4–31 basis set +d orbitals on the sulphur atom. The two electronic states were found to have different preferred conformations. The singlet state exhibits a planar eclipsed conformation, whereas the structure of the triplet state is anti-eclipsed and pyramidal. It was found that a potential function, which was constructed from a symmetry adapted double Fourier expansion of the wagging and torsional coordinates, gave a reasonable fit to the energy points. The two-dimensional Schrödinger equations for the torsion and wagging motions were solved for both singlet and triplet states, taking into account the internal symmetry and the appropriate basis. The relative band locations and the intensities (Franck–Condon factors) were evaluated from the eigenvalues and the eigenvectors. Spectra were calculated for the thioacetaldehyde CH3CHS/CH3CDS/CD3CHS/CD3CDS isotopomers. New assignments for the higher bands in the CH3CHS spectrum are proposed.

Charge, spin and theoretical densities in transition metal complexes

The results of diffraction experiments, of X-rays to give charge density and of polarised neutrons to give spin density, are compared between themselves and with the theoretical density obtained by a local density unrestricted Hartree-Fock calculation. The systems studied include in particular the archetypal M(CN)63− and M(OH2)62+ ions. Electron-electron correlation effects on their distribution can be as large as covalent bonding transfers, so there may be no simple relationship between the charge and the spin densities. Covalence appears to be appreciable even for the most ionic of crystals, but its effects are often masked by the correlation terms. The local density calculations can give a good account of the densities and of spectra in complexes in which the ground state is not orbitally degenerate. Orbital degeneracy emphasises the correlation problem and theory beyond the UHF treatment will be required.

Ab initio molecular orbital calculations of effective exchange integrals for transition metal oxides and halides: Strong superexchange interactions and high T c superconductivity

Ab initio unrestricted Hartree-Fock (UHF) calculations involving the correlation corrections by the Møller-Plesset (MP) perturbation method are carried out for K 2NiF 4-type transition-metal halides and related copper oxides. The magnitude of effective exchange integrals (Jab) obtained by the spin-projected UHF MP method is found to be particularly large for copper oxides, in agreement with recent experiments. Implications of these results are discussed in relation to spin-mediated theories for the mechanism of high-T c superconductivity of copper oxides.

Ab initio study of the interaction of polyoxymethylene with polyoxymethylene, ammonium perchlorate, and the aluminum (100) surface.

Self-consistent restricted and unrestricted Hartree-Fock calculations have been performed for the microscopic interactions in particle-filled polymeric suspensions. First, we have investigated the elongation and the torsion potential of a single infinite polyoxymethylene chain. It is found that the 9/5 helix is \ensuremath{\sim}4.5 kcal/mol lower in energy than the planar zigzag conformation. A Young's modulus of 80\ifmmode\pm\else\textpm\fi{}20 GPa is obtained for the chain-direction deformation. The potential-energy curve for the van der Waals interaction between two 2/1 helical polyoxymethylene chains has a minimum for a chain separation of \ensuremath{\sim}4.3 A\r{} with a binding energy of \ensuremath{\sim}1.3 kcal per (${\mathrm{CH}}_{2}$O${)}_{2}$ translational unit. For the chain-direction slip of two polyoxymethylene chains a barrier of \ensuremath{\sim}5.1 kcal is calculated. To study polymer-particle interactions, cluster calculations for the interaction of polyoxymethylene fragments with ammonium perchlorate and the aluminum (100) surface have been performed. The oxygen in the polyoxymethylene backbone forms a hydrogen bond with ammonium perchlorate. For an O-H distance of 1.62 A\r{} a binding energy of 23.7 kcal is obtained. This strong coordination of the ammonium ion with the oxygen in the polyether backbone is in agreement with the experimentally observed increase in viscosity of polyether lacquers upon dissolution of ammonium perchlorate. The potential energy curve for the bonding of a ${\mathrm{H}}_{3}$C-O-${\mathrm{CH}}_{2}$-O-${\mathrm{CH}}_{2}$-O-${\mathrm{CH}}_{3}$ fragment at the on-top sites of an ${\mathrm{Al}}_{5}$ cluster has a minimum for an O-Al separation of 2.3 A\r{} with a binding energy of 17.1 kcal (8.55 kcal per O-Al bonding).This binding energy is of the same order of magnitude as the energy of 4.5 kcal per ${\mathrm{CH}}_{2}$O unit needed to stretch the polyoxymethylene 9/5 helix to a helix whose next-nearest oxygen atoms are commensurate with the aluminum lattice constant of 4.05 A\r{}. Therefore the coating of aluminum particles with polyoxymethylene polymers is possible. The quantum-mechanical results of these microscopic static-model studies provide an estimate for polymer-particle forces needed for a macroscopic dynamic model of particle-filled polymeric suspensions.

Theoretical study of the geometry of Mn5

The geometry of Mn5 in rare gas matrices has been proposed to be a planar pentagon with 25 unpaired electrons. Simple unrestricted Hartree-Fock (UHF) calculations have been carried out using a basis of STO-6G for 1s, 2s, and 2p orbitals with STO-4G for 3s, 3p, 3d, 4s, and 4p in the HONDO5 program. The structure is optimized at the UHF level using the analytic gradient formalism for a planar pentagon. Binding energies and spinmixing are given for the optimized structure.

Spin densities and covalency in transition-metal complexes: A comparison of discrete variational Xα calculations with polarised neutron diffraction data

Spin-unrestricted discrete variational Xα self-consistent charge (DVXα SCC) calculations for the cubic transition-metal complexes [CoCl 4] 2−, [CoBr 4] 2−, [FeCl 4] −, [CrF 6] 3− and [Cr(CN) 6] 3− are reported. The calculated covalencies exhibit the same trends predicted by empirical nephelauxetic parameters. However, agreement between the experimental ligand-field splittings and theoretical values determined via Koopman's theorem is poorer, particularly for the tetrahedral species. The computed spin densities are compared in detail with experimental results derived from polarised neutron diffraction (PND) studies and with unrestricted Hartree-Fock (UHF) calculations. The qualitative agreement with the PND data is good and for [CoCl 4] 2− and [CrF 6] 3− the DVXα SCC and UHF models give almost identical spin densities. However, quantitative agreement with experiment is not obtained because the calculations ignore the real molecular site symmetry, the crystalline environment and configuration interaction (CI). These features appear to influence significantly the experimental spin and charge densities and, except for CI, can be readily included in DVXα SCC calculations. The present work suggests that the DVXα SCC scheme gives a sufficiently accurate description of electron distributions to provide a useful tool for further examination of these effects.

Use of local-density pseudopotentials in Hartree-Fock calculations.

Norm-conserving pseudopotentials obtained from a local-density approximation (LDA) are implemented in an unrestricted Hartree-Fock (UHF) formalism. A series of tests is devised to ascertain the utility and validity of this methodology. Calculations using LDA and coreless Hartree-Fock (CHF) pseudopotentials are contrasted and compared to full-core Hartree-Fock results. We find that for light atoms (Zl21) the LDA-derived potentials yield accurate results when used in UHF calculations. The methodology reproduces experimental results as accurately as full-core calculations. LDA pseudopotentials are found to yield accurate wave functions for use in many-body-theory corrections to the correlation energy. By including correlation corrections in this manner the methodology reproduces experimental results to within 0.2 eV.

Investigation of soliton-like excitations in t r a n s-polyacetylene

In the study reported here, unrestricted Hartree–Fock calculations were performed on the ground state and several soliton-like defect states of the model large polyene, trans-polyacetylene. The calculations included the use of the random phase approximation to obtain screened electron repulsion integrals and projection of the UHF eigenfunctions to obtain pure spin states. The trans-polyacetylene ground state geometry is characterized here by alternating double and single bonds with lengths of 1.456 and 1.369 Å, respectively. Calculations on model soliton-like defect states yielded functional forms for the bond alternation, spin density, and charge density defects which are consistent with the soliton model for trans-polyacetylene and are similar to those reported elsewhere. The average positive and average negative spin density on chains containing neutral kink defects are 0.045 and −0.011, respectively. These values are in fair agreement with the best experimental estimates of 0.06 and −0.02.

Unrestricted Hartree—Fock calculations of methoxyl-substituted semiquinone radicals and the proton hyperfine coupling constants

Using the ab initio unrestricted Hartree—Fock method, spin densities are calculated for various members of the family of methoxyl-substituted p-semi, respectively, p-hydrosemiquinones. The empirical McConnell relation has been applied to estimate from these results the proton isotropic hyperfine splittings measured in electron spin resonance (ESR) experiments. The principle of additivity, which in general accurately describes the changes in the hyperfine coupling constants is violated on substituting two neighboring ring protons in p-semiquinone by the bulky methoxyl groups according to the experimental results. The breakdown of this concept, however, is not observed when the theoretically calculated spin densities are used. Therefore, solvent effects cannot be excluded to explain the determined anomalous ESR in the case of two adjacent methoxyl substituents in the ring. Furthermore, the general problem of the interpretation of spin-densities obtained from an unrestricted Hartree—Fock wave function which is not an eigenstate of spin is discussed using a projection operator technique. From the results it is obvious that the UHF-wavefunction obtained for all systems almost corresponds to the pure doublet spin state.

Covalent-ionic nature of the potential energy surface of the Li-CO2 complex

Unrestricted Hartree-Fock calculations with large basis sets, including d-functions, and the estimation of the correlation energy, show that the potential energy surface for the Li-CO2 complex is built from the crossing of two states, each of them corresponding to a different electron arrangement. One has a strong ionic character and the other is of van der Waals type. Each portion of the energy surface presents a minimum, which is stable in respect to the dissociation limit.

UHF RPA calculations on large model polyene systems

Unrestricted Hartree-Fock calculations have been performed on even and odd polyenes and both neutral and charged species. The calculations include projection of the pure spin states and the use of the random-phase approximation to obtain screened electron-repulsion integrals. Calculations on even, neutral molecules containing up to seventy-four carbon atoms provide a single-bond length of 1.456 Å and a double-bond length of 1.369 Å for a Δ R∞ value of 0.087 Å, which compares well with experimental data. The functional forms of the bond-alternation, spin-density, and charge-density defects are similar to those reported from earlier treatments. For the odd polyene, the width of the soliton spin-density wave is comparable with the SSH results and the ratio of the total negative spin density to the total positive spin density is 0.25. However, the width of the bond-alternation defect is found to be larger than that found by other investigators.

Calculation of ESR coupling constants by means of the unrestricted Hartree-Fock method

We present a simple and straightforward procedure for the derivation of ESR coupling constants from the results of unrestricted Hartree-Fock calculations. We combine the spin orbitals into α-β pairs with similar but slightly different orbital parts; in addition there is a single unpaired orbital. After correcting the UHF results for spin contamination, the spin density is obtained as the sum of the contribution from the unpaired orbital and one-third of the contributions from all the paired orbitals. As an example we present calculations for the methyl, ethyl, vinyl, and allyl radicals based on ab initio wave functions, and we obtain satisfactory agreement with the experimental data.

Theoretical study of O chemisorption on NiO. Perfect surfaces and cation vacancies

Self-consistent unrestricted Hartree-Fock calculations are presented for the adsorption of atomic oxygen onto the nickel oxide (100) surface. The perfect surface is shown to be nonreactive, but enhanced binding is found for vacancy sites in the first two atomic layers. Of particular interest is a second-layer anion-vacancy site. Various charge states are examined and charge transfer between adsorbate and surface are noted. A calculation for molecular oxygen in the neighborhood of a second-layer anion vacancy is also presented. ${\mathrm{O}}_{2}$ is found to bind to the surface less strongly than atomic oxygen, and accordingly a dissociation site is postulated. Analysis of the character of the electrons on the transition-metal atom indicates that bonding is localized in the $s$- and $p$-character electrons rather than in the $d$ electrons.

Broken symmetry in valence molecular region within Hartree-Fock calculations

Symmetry restricted and unrestricted Hartree-Fock calculations at theab initio LCAO-MO-SCF level have been carried out on the ground, core and valence hole states of N2 at various N-N distances. A one-particle criterion for symmetry breaking is discussed. Strong broken-symmetry effects in the inner valence molecular region of N2 have been found at larger N-N distances. This breaking of symmetry accompanying the symmetry unrestricted Hartree-Fock calculations of the inner valence hole states at large internuclear separations can be considered to be a common phenomenon with all highly symmetric molecules. The outer valence broken-symmetry effects with N2 have showed some deviations as compared with these effects in the inner valence and core molecular regions.