The role of d orbitals in tetrahedral hybrid orbitals of oxy-ions

The hybrid orbitals of tetrahedral oxy-ions containing some d character have been calculated by maximum overlap method. The d characters of hybrid orbitals increase in the order of SiO, PO, SO, ClO, and decrease in order of GeO, AsO, SeO, BrO. The bond strengths are also obtained for these ions. The hybrid Orbital of VO, CrO, and MnO are of the type d³s as the result of calculation.     

SCF and MC–SCF Study of CO2 with bond angle variation

Multiconfiguration (MC ) SCF calculations are reported for CO₂ for bond angles between 60° and 180°. The ground state configuration is found to be …?5a4b∣b∣a for small bending angles and …?6a3b∣b∣a for large bending angles, the change in ground state character occurring at a bond angle of about 100°. The force constant for bending obtained from the MC –SCF function is about 8.0% lower than the corresponding SCF value, and in considerably better agreement with experiment.     

Atomic integrals containing rrr with λ, μ, ν ≥ −2

In this paper, the efficient evaluation of the atomic integrals I =∫rrrrrre^{?αr1?βr2?γr3}dτ with one or two factors r is described. These integrals are necessary for a lower-bound calculation for Li-like systems using the method of variance minimization or Temple's formula. © 1993 John Wiley & Sons, Inc.     

Ab initio MO calculations on the stability of the CF,PF, SF,and MoF ions with the F1s core hole

For the CF, PF, SF, and MoF ions appearing after the F1s photoionization, the possibility of dissociation has been shown by the ab initio MO LCAO method within the Z + 1 core equivalent model. According to the calculations, the decay channel AF → AF + F(1s¹2p⁶) is energetically open for the ions. So the interpretation of the gas-phase emission FKα spectra, in which the bands are assigned to the discrete transition energies, can be unacceptable for these ions. The conditions and signs of such failure are discussed.     

Ab initio studies of negative ion-molecule(s) clusters present in the atmosphere. II. OH−(H2O)n for n = 0, 2, 3, 4

Ab initio calculations are performed with 6–31G basis set to study the geometry and binding of the H₃O, H₅O, H₇O, and H₉O complexes. The H₃O complex is also investigated with the 6–31 G* basis set and MP 2 (Moller–Plesset perturbation theory of second order).     

Geometrical and spectroscopical characterizations of some complex entities of aluminum(III) with fluoride ions by LDF-based calculations

The structure of cryolite is investigated with a theoretical approach based on LDF calculations. In fact, experimental techniques for structural studies are difficult to perform in cryolite melts because of hard experimental conditions (high temperature, corrosiveness, etc.). Use of the DMol software allows us to determine the stabilities and the vibrational frequencies of AlF, AlF, and AlF isolated complexes. The results obtained compared with published experimental works confirm that AlF should be considered in the dissociation scheme of cryolite as previously evidenced by other authors. © 1994 John Wiley & Sons, Inc.     

The formation of highly excited H in the reaction H2+(v) + H2 → H + H

A quasiclassical trajectory surface hopping method has been used to study H(v) + H₂ → H + H for v = 0, 3, 7, 10, 13, and 17 with an emphasis on determining the H internal energy and angular momentum distributions for high v. For v = 13 and 17, significant cross sections are found for producing H at energies above its dissociation energy. An average metastable H lifetime of 11.5 ps for v = 13 and 4.7 ps for v = 17 is found, but there is also a much longer lived component to the lifetime distributions that is more important for v = 13 than for v = 17. Some of the longer lived metastables correspond to high angular momentum orbiting states of H, but other sources of metastability are also present.     

Simple derivation of the potential energy gradient for an arbitrary electronic wave function

The magnitude of reorganization energies in the photoelectron (PE ) spectra of various transition metal compounds with Mn, Fe, and Ni as 3d center is studied by means of a variable INDO Hamiltonian. The Koopmans defects are analyzed as a function of the one-electron resonance integral β and as function of the one- and two-center electron–electron interaction integrals. β has the property of an inverse coupling constant; reorganization effects are enlarged with reduced β values. In the limit of very small resonance integrals a reduction of the calculated Koopmans defects due to modified localization properties of the orbital wave function is encountered. The two-center electron-electron interaction integrals γ have been calculated via an exponential formula with a variable range parameter. In the limit of long-range potentials with flattened γ; gradients a significant reduction of relaxation and correlation is diagnozed; large defects are predicted in the short-range limit with steep gradients in the repulsion potential. The one-center Coulomb and exchange integrals (γ, K) have been modified by a multiplicative factor. With enlarged one-center integrals enhanced Koopmans defects are encountered. The reorganization energies are determined by means of a Green's function approach with a renormalized approximation for the self-energy part.     

Convergence accelerator approach for the evaluation of some three‐electron integrals containing explicit rij factors

A simplified analysis is presented for the evaluation of the three‐electron one‐center integrals of the form ∫rrrrrred r ₁d r ₂d r ₃, for the cases i, j, k, ≥−2, l=−2, m≥−1, n≥−1. These integrals arise in the calculation of lower bounds for energy levels and certain relativistic corrections to the energy when Hylleraas‐type basis sets are employed. Convergence accelerator techniques are employed to obtain a reasonable number of digits of precision, without excessive CPU requirements. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 93–99, 1999     

Explicit expression of the franck–condon factors in terms of the potentials of the two states

The calculus of the overlap integral for two states represented by the vibrational wave functions ψ and ψ is reduced to that of the Franck–Condon integral ?(0, x) = ∫ ψψ (t) dt. It is proved that for “numerical potentials” (as well as for a Dunham potential), this integral is given on each interval by a simple analytic expression in terms of the two potentials. The Franck–Condon factors are well determined by “coupling constants” related uniquely to the coordinates of the turning points of the potentials. An application to the band system BII? XΣ of Nα₂ is compared with the usual numerical methods.     

Binding of an electron to a molecular dipole: BeF

Results of extended-basis SCF calculations indicate that BeF may exist as a metastable species. Comparison of results obtained from SCF calculations on neutral BeF₂ with those of BeF shows that the orbital occupied by the electron of BeF is well approximated by the lowest unoccupied molecular orbital of neutral BeF₂.     

A comparative quantum chemical study of ethylcarbonium ion and hydroxymethylcarbonium ion

Nonempirical molecular orbital calculations of the energies of CH₃CH (ethylcarbonium ion) and HOCH (hydroxymethylcarbonium ion) as a function of rotation about the C? C or C? O bonds and deviation from coplanarity at the carbonium ion center are reported. As expected, and in agreement with previous work, both carbonium centers are planar and there is no barrier to rotation in the planar ethylcarbonium ion. However, for the planar configuration at carbon, the conjugative interaction between oxygen and carbon produces a barrier to rotation about the C? O bond of HOCH of 19.6 Kcal/mole. When a pyramidal geometry is imposed upon the carbonium ion center of CH₃CH, a typical three-fold barrier results. As the deviation from coplanarity increases there is a regular increase in the barrier height (1.72 Kcal/mole at the tetrahedral geometry), but the energy minimum remains at the same position in each case (60°). For HOCH, imposition of a pyramidal geometry on the carbonium ion center causes a change in both rotational barriers. One decreases slightly (from 19.6 to 15.4 Kcal/mole) and the other increases to 30.5 Kcal/mole. There is an accompanying change in the position of the minimum of the rotational potential, from 90° towards the gauche structure.     

Density functional calculations of structures and ionization energies for heavy group V cluster anions

The structure and electronic structure of heavy-group V cluster anions (Sb, Bi) are calculated with density functional methods within the local spin density approximation (LSDA ). The influence of gradient corrections of the exchange and correlation energy is investigated. The calculated vertical and adiabatic ionization energies are in very good agreement with data from photoelectron spectroscopy (PES ) for Sb, whereas the relatively large deviations for Bi can be reduced by the consideration of relativistic effects in a scalar-relativistic manner. Concerning the structures, a strong similarity to the corresponding P clusters was found. In particular, the negatively charged pentamers are planar rings (with similarities to the aromatic [C₅H₅]^? anion) with especially high ionization energies. © 1995 John Wiley & Sons, Inc.     

Electron–phonon coupling detection in infrared spectra of ion–radical salts based on dibenztetrathiofulvalen

The electron–phonon coupling constants in a cation radical of dibenztetrathiofulvalen (DBTTF) have been calculated. To calculate the electronic structure of DBTTF in equilibrium and distorted structures use was made of the unrestricted Hartree–Fock method as π-electron approximation for symmetrical vibrations of DBTTF. The results obtained are in good agreement with the experimental data on IR spectra of DBTTF-based cation–radical salts.     

The calculation of ligand-field multiplet states from multiple-scattering Xα wave functions

A method is outlined for the calculation of the multiplet ligand-field states of transition metal complexes. The procedure involves the use of MS-Xα wave functions, in connection with irreducible tensor operators, and allows the calculation of the elements of the many-electron CI matrices. Comparison of the calculated and experimental multiplet state energies of CrF, CrCl, and MnF allows one to conclude that the method is useful for the prediction of ligand-field spectra of transition-metal complexes.     

Limiting behavior of the ratio of 〈r〉 and 〈r〉 in the helium sequence

The limiting of the 〈r〈/〈r〈 ratio in the He sequence is critically examined at different levels of approximations leading to some interesting results.     

Ab initio calculations of many-body energy expansion in LiF− clusters

The effects of the basis-set size on many-body energy expansion in LiF^? clusters are investigated and correlated with previously reported values on LiCl^? analogs. Coulomb and non-Coulomb energies in LiF^? at different configurations are also examined. Although at the minimal STO -3G basis V^na(3, 4) and V^na(4, 4) nonadditivity terms were the smallest in the D₃h configuration, they were the largest at the extended 6-311 ++G basis. V(m, n) terms where m = n ≥ 3 were found to be playing a small role in the chemistry and physics of LiF^? clusters compared with V(3, n) terms in LiCl^? clusters.     

The role of the bond midpoint electron density in homonuclear molecular binding

Electron density theory is first employed to express the potential energy curve of the H molecular ion in terms of bond midpoint properties. For heavy homonuclear diatomics, low-ordr density gradient theory is used, but now for the chemical potential, with a similar conclusion to that for H. Homonuclear clusters of alkali atoms are then treated in some detail. Finally the dissociation of doubly charged clusters is considered, by a study of supermolecular treated in some detail. Finally the dissociation of doubly charged clusters is considered, by a study of supermolecular ions (Na)₂ and (K)₂, again using a density gradient expansion in low order. The deviation between the barrier for fission and the Coulomb barrier is linear in the bond midpoint density over a substantial range of fragment separation. © 1994 John Wiley & Sons, Inc.     

The adsorption of CO2, H2CO3, HCO3− and CO32− on Cu2O (111) surface: First‐principles study

The adsorption of CO₂, and its derivatives, H₂CO₃, HCO, and CO, on Cu₂O (111) surface has been investigated by first‐principles calculations based on the density functional theory at B3LYP hybrid functional level. The Cu₂O (111) surface has been modeled using an embedded cluster method,in which the quantum clusters plus some ab initio ion model potentials were inserted in an array of point charges. On the surface, H₂CO₃ was dissociated into an H⁺ and an HCO ion. Among the CO₂ species, HCO was the only activated species on the surface. The results suggest that the reduction of CO₂ on Cu₂O (111) surface can start from the form of HCO. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011