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).     

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.     

Evaluation of two‐center,three‐ and four‐electron integrals over Slater‐type orbitals in elliptical coordinates

An algorithm for evaluation of two‐center, three‐electron integrals with the correlation factors of the type rr and rrr as well as four‐electron integrals with the correlation factors rrr and rrr in the Slater basis is presented. This problem has been solved here in elliptical coordinates, using the generalized and modified form of the Neumann expansion of the interelectronic distance function r for k ≥ ?1. Some numerical results are also included. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

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     

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.     

Exclusion principle and the symmetry adapted wave-functions

Wave-functions of various spin-dependent and spin-free methods are examined from the point of view of the requirements of the exclusion principle and the spin projection. It is shown that the “two-rowed” or “two-columned” requirements of the standard Young tableaux are necessary but not sufficient to replace the “antisymmetry” requirement of a wave-function and to be regarded as exclusion principle. The symmetry adapted wave-functions which are constructed from the matric basis e may not satisfy the exclusion principle and, hence, their usages are open to question. The appropriate symmetry adapted wave-functions which satisfied the exclusion principle are given for any pure spin state. We have also shown that the structure operators NP for bond functions are spin projectors in the Waller-Hartree double-antisymmetrized space only, and should not be used in the Hartree product space. Furthermore, if the corresponding matric operators PNP are used in the Hartree product space, then the wave-functions thus constructed may not be antisymmetric with respect to the permutations of indistinguishable electrons.     

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.     

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 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.     

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.     

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.     

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.     

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.     

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.