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.     

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     

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).     

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.     

Variation of the polarizability of the hydrogen molecule ion and the hydrogen molecule with internuclear separation

The variation of the polarizability of H and H₂ with internuclear separation R = 1.6 – R = 2.4 a.u. for H and R = 1.0 – R = 2.0 a.u. for H₂ is determined using a variational method suggested by Das and Bersohn. From these data, values of 〈α〉_0,J for which nuclear motion due to zero point vibration and centrifugal stretching is taken into account, are calculated at 300°K. The relative percent increases of the motion averaged values compared to the equilibrium values are as follows: 10.50% for H and 6.52% for H₂.     

The spin-density-functional formalism for quantum mechanical calculations: Test on diatomic molecules with an efficient numerical method

We have applied the spin-density-functional (SDF ) formalism with the local-spin-density (LSD ) approximation to a number of small molecules with the primary aim of testing the approximation for molecular applications. A new numerical method to solve the one-electron wave equation is developed, utilizing the special features of the SDF formalism. We have calculated energy curves, dissociation energies, and equilibrium distances for some diatomic molecules [H (²Σ, ²Σ), H₂(¹Σ, ³Σ), He (¹Σ), and He₂(¹Σ)] and the vibrational frequencies of H₂. The deviations from the experimental results are typically 1/2 eV for the energies and ≤ 0.1 Å for the distances. We discuss the LSD approximation using the concept of an exchange-correlation hole and make predictions about the applicability to other molecules. The LSD approximation is compared with the Hartree-Fock and multiple-scattering-Xα methods and some difficulties in the latter methods are pointed out. It is argued that the SDF formalism within the LSD approximation has physical advantages compared to the Hartree-Fock and Xα methods and that it should provide a simple and useful method for a broad range of applications.     

Hylleraas–CI with linked correlation terms

Hylleraas–CI calculations with linked correlation terms of the form rr are discussed. Formulas for the integration of the angular part are deduced and a method for the reduction of the radial part to auxiliary integrals is given. In the case of the Li atom, it is shown that for the calculation of the ground-state energy an ansatz for the wave function with at most two factors rr is sufficient to achieve spectroscopic accuracy. © 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.     

Long- and intermediate-range interaction between hydrogen atoms in the B 1Σ state

The energy of the hydrogen molecule in the B ¹Σ state, for internuclear separations 12 ≦ R ≦ 20 a.u., has been computed using an 80-term variational wave function depending explicitly on the interelectronic distance. The same type of wave function has been employed in the perturbation theory approach. Using the polarization approximation, and not expanding the interaction Hamiltonian, the first-, second- and third-order energies have been computed and higher-order corrections have been estimated. The results show that in the region under consideration E and E represent the dominant contributions to the interaction energy in the B state.     

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.     

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.     

An insight into optical and EPR properties of AgCl and AgF complexes through MS–Xα and SCCEH calculations

MS-Xα and SCCEH calculations on the Ag²⁺ complexes AgF and AgCl (displaying an elongated D_4h symmetry) have been carried out for a better understanding of their experimental optical and EPR properties. As salient features, the present work supports that the unpaired electron in AgCl spends a little more time on ligands than on Ag²⁺, in agreement with the previous analysis of EPR and optical data for KCl:Ag²⁺. Furthermore, the five experimental optical transitions observed in that case are reasonably assigned. The first transition (observed at 12,500 cm^?1) is assigned to a jump involving the 5a_1g orbital built mainly (∽70%) from 3p orbitals of axial ligands, a fact that reflects the distinct level scheme for AgCl when compared to that for more ionic complexes. Calculations on AgF and AgF performed as a function of the equatorial Ag²⁺ –F^? distance led to a reasonable understanding of experimental gyromagnetic and superhyperfine tensors displayed by Ag²⁺ in fluorides. The different relative decrease undergone by g‖– go (8%) and g ? – go (28%) on passing from CsCdF₃:Ag²⁺ to RbCdF₃:Ag²⁺ is shown to be consistent with the formation of AgF and AgF complexes, respectively, related to the different substitutional position of Ag²⁺ in such lattices. The decrement of about 8.5% experienced by both g‖ – go and g? – go values on going from CsCdF₃:Ag²⁺ to NaF:Ag²⁺ is pointed out to reflect the different electrostatic potential (exerted by the rest of the lattice upon the complex) seen by AgF embedded in NaCl or perovskite-type lattices. © 1994 John Wiley & Sons, Inc.     

Ab initio Hartree–Fock–Slater calculations of polysulfanes H2Sn (n = 1–4) and the ions HS and S

An ab initio Hartree–Fock–Slater procedure was applied to the calculation of the electronic structure of polysulfanes, H₂S_n (n = 1–4) and the ions HS and S. Charge densities, overlap populations, and deprotonation energies are calculated; the latter appear well correlated with the first and second acidity constants.     

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.     

The proton affinity and the structure of protonated species of methylsilane

An ab initio LCAO-MO-SCF calculation was made on the proton affinity (PA ) of methylsilane (CH₃SiH₃) by using STO -3G, MIDI -1, and MIDI -1* basis sets. Three types of protonated methylsilane are taken into account, and their geometrical parameters are optimized. The calculated PA of CH₃SiH₃ is 160.5 kcal/mol, which exceeds that of SiH₄ by 11.5 kcal/mol. The protonated species (I) which refers to Si—C bond protonation is shown to be most favorable, and to be a weak σ-complex between CH₄ and SiH. Other two species are also σ-complexes between H₂ molecule and SiH₃CH or CH₃SiH, and similar to CH, SiH, GeH, and C₂H.     

Continuum states of the hydrogen molecule with the R-Matrix method

The interaction of low-energy electrons with H and ligh with H₂ is analyzed using the R-matrix method including both coupled state and polarization effects ab initio. Particular attention is paid to the energy region containing low-lying H*₂ resonances which converge to H A ²Σ. Resonances in both elastic scattering and the photoionization asymmetry parameter, β, are presented. At low photon eneries, satisfactory results for vibrationally resolved photoionization are obtained using the adiabatic nuclei approximation. The use of nonadiabatic techniques for higher energies is discussed.     

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.     

Dipole,quadrupole, octupole,and dipole–dipole–quandrupole polarizabilities and second hyperpolarizabilities at real and imaginary frequencies for helium in the 23S state: Dispersion-energy coefficients for interactions between He(23S) and H(12S), He(11S), He(23S), or H2(X1∑g+)

We have determined the dynamic dipole (α₁), quadrupole (α₂), octupole (α₃), and dipole–dipole–quadrupole (B) polarizabilities and the second hyperpolarizability tensor (γ) for the helium atom in its lowest triplet state (2³S). We have done so for both real and imaginary frequencies: in the former case, for a range of frequencies (ω) between zero and the first electronic-transition frequency, and in the latter case for a 32-point Gauss–Legendre grid running from zero to ?ω = 20 E_h. We have also determined the dispersion-energy coefficients C₆, C₈, and C₁₀ for the systems H(1²S)? He(2³S), He(1¹S)? He(2³S), and He(2³S)? He(2³S) and the C, C, C, C, and C coefficients for the interaction He(2³S)? H₂(X¹∑). Our values of the higher-order multipolar polarizabilities and of γ for the 2³S state of helium are, we believe, the first to be published. © 1993 John Wiley & Sons, Inc.     

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.