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     

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.     

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     

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.     

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 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 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.     

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.     

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.     

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.     

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.     

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.     

Theoretical evidence of d‐orbital aromaticity in anionic metal X (X = Sc,Y, La) clusters

The equilibrium geometries, total electronic energies, and vibrational frequencies for singlet, triplet, and quinted states of three all‐metal X (X = Sc, Y, and La) anions and nine relevant neutral singlet MX₃ (M = Li, Na, K, X = Sc, Y, La) clusters are investigated with four density functional theory (DFT) and correlated ab initio methods B3LYP, B3PW91, MP2, and CCSD(T). To our knowledge, the theoretical study on these clusters composed of the transition metal Sc, Y, La is first reported here. The calculated results show that for the X clusters the singlet states with trigonal D_3h structures are the lowest energetically, while the neutral singlet MX₃ clusters each have two stable isomers: one trigonal pyramidal C_3v and one bidentate C_2v structures with the pyramidal C_3v isomer being ground state. In addition, we calculate the resonance energies (RE) and nucleus‐independent chemical shift (NICS) for the singlet trigonal X rings and show that these singlet trigonal X rings exhibit higher degree of aromaticity. The detailed molecular orbital (MO) analyses reveal that the singlet trigonal X anions have one delocalized σ‐type and one delocalized π‐type MOs, which follow the 4n + 2 electron counting rule, respectively and play an important role in rendering these species two‐fold aromaticity. Here, an explicit theoretical evidence is given to prove that the contribution to the two‐fold aromaticity of the singlet trigonal X (X = Sc, Y, and La) rings originates primarily from the d‐orbital bonding interactions of these component transition metal X atoms. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

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.     

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.     

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.     

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.     

Theoretical study of one‐electron bonds in a series of high‐spin lithium–beryllium–hydrogen clusters: “Valence shell single‐electron repulsion” rule and electron localization function analysis

A series of high‐spin clusters containing Li, H, and Be in which the valence shell molecular orbitals (MOs) are occupied by a single electron has been characterized using ab initio and density functional theory (DFT) calculations. A first type (⁵Li₂, ⁿ⁺¹LiH_n+ (n = 2–5), ⁸Li₂H) possesses only one electron pair in the lowest MO, with bond energies of ～3 kcal/mol. In a second type, all the MOs are singly occupied, which results in highly excited species that nevertheless constitute a marked minimum on their potential energy surface (PES). Thus, it is possible to design a larger panel of structures (⁸LiBe, ⁷Li₂, ⁸Li, ⁴LiH⁺, ⁶BeH, ⁿ⁺³LiH (n = 3, 4), ⁿ⁺²LiH (n = 4–6), ⁸Li₂H, ⁹Li₂H, ²²Li₃Be₃ and ²²Li₆H), single‐electron equivalent to doublet “classical” molecules ranging from CO to C₆H₆. The geometrical structure is studied in relation to the valence shell single‐electron repulsion (VSEPR) theory and the electron localization function (ELF) is analyzed, revealing a striking similarity with the corresponding structure having paired electrons. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

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.