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 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.     

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.     

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.     

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.     

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.     

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     

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.     

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.     

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.     

Dipole,quadrupole, octupole,and dipole–octupole polarizabilities at real and imaginary frequencies for H,HE, and H2 and the dispersion-energy coefficients for interactions between them

We have calculated certain dynamic polarizabilities (for both real and imaginary frequencies) for H, He, and H₂ and the dispersion-energy coefficients for long-range interactions between them. We have done so in a sum-over-states formalism with explicitly electron-correlated wave functions to describe the states. To be precise, we have determined the dipole (α₁), quadrupole (α₂), and octupole (α₃) polarizabilities of H and He for real frequencies (ω) in a range between zero and the first electronic-transition frequency and for imaginary frequencies (iω) on a 32-point Gauss-Legendre grid running from zero to ?ω = 20 E_h, and for H₂, we have found the dipole (α), quadrupole (C), and dipole–octupole (E) polarizability tensors for the same real and imaginary frequencies. The dispersion-energy coefficients, obtained by combining the sum-over-states for-malism for the polarizabilities with analytic integration over ω, gave values of C₆, C₈, and C₁₀ for the atom–atom systems; C, C, C, C, and C for the atom–diatom systems; and C₆, C and C for the H₂? H₂ system. Nearly all the results are considered to be more reliable than those hitherto published and some have been obtained for the first time, e.g., C(iω), E(ω), and E(iω) for H₂ and C, C, and C for the H? H₂ system. © 1993 John Wiley & Sons, Inc.     

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.     

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.     

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.     

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.     

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.     

Polysila analogs of aromatic hydrocarbon ions: Structures and energies of Si3H3+, Si4H,and Si5H5−

Silicon analogs of aromatic monocyclic ions, (SiH) ( 4 ), (SiH) ( 5 ), and (SiH) ( 6 ) have been studied ab initio at MP 2(full)/6-31G *. The D_3h structure of Si₃H₃⁺ is the global minimum, whereas other two ions are nonplanar. The D_2d structure of (SiH) is less folded than the carbon analog and possesses a higher stabilization energy. Stabilization energies for the monocharged ions are diminished with respect to the corresponding carbons © 1993 John Wiley & Sons, Inc.     

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.     

Ab initio calculation of electronic states of the ions H4+ and H5+

Electronic state calculations for the ions H₄⁺ (with symmetries D ₄ and C _2v) and H (with symmetries D ₅ and D _2d) are made using the valence-bond method. All the configurations obtained from the given set of 1s-functions of Slater type are taken into account. Space functions are used throughout the computation (“spin-free quantum chemistry”). Preliminary quasidiagonalization of the secular equation is implemented by the construction of the multiplet eigenfunctions ^2S+1Γ^(α) from the initial variational functions. The results of the calculations are as follows: the ion H is unstable, the ion H is stable with equilibrium nuclear conformation of symmetry D _2d and with the energy of dissociation into H and H₂ near 4 eV.