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     

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.     

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.     

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.     

Correlated n1,3S states for coulomb three‐body systems

n^1,3S (n = 1 ? 4) states for atomic three‐body systems are studied with the Angular Correlated Configuration Interaction method. A recently proposed angularly correlated basis set is used to construct, simultaneously and with a single diagonalization, ground and excited states wave functions which: (i) satisfy exactly Kato cusp conditions at the two‐body coalescence points; (ii) involve only linear parameters; (iii) show a fast convergency rate for the energy; and (iv) form an orthogonal set. The efficiency of the method is illustrated by the study a variety of three‐body atomic systems [m m m] with two negatively charged light particles, with diverse masses m and m, and a heavy positively charged nucleus m. The calculated ground 1¹S and excited n^1,3S (n = 2 ? 4) state energies are compared with those given in the literature, when available. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

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.     

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.     

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.     

D∞h B2(BS)2−/2− and Td B(BS)4−: Boron sulfide clusters containing BB multiple bonds and B− tetrahedral centers

A density functional theory investigation on the geometrical and electronic properties of B₄S (B₂(BS)) and B₅S (B(BS)) clusters has been performed in this work. Both the doublet B₂(BS) ([S?B? BB? B?S]^?) (D_∞h, ²Π_u) and the singlet B₂(BS) ([S?B? B?B? B?S]^2?) (D_∞h, ¹Σ) proved to have perfect linear ground‐state structures containing a multiply bonded BB core (BB or B?B) terminated with two BS groups, while T_d B(BS) turned out to possess a perfect B^? tetrahedral center directly corrected to four BS groups, similar to the corresponding boron hydride molecules of D_∞h B₂H, D_∞h B₂H, and T_d BH, respectively. B₄S₂ and B₅S₄ neutrals, however, appeared to be much different: they favor a planar fan‐shaped C_2v B₄S₂ (a di‐S‐bridged B₄ rhombus) and a planar kite‐like C_2v B₅S₄ (a di‐S‐bridged B₃ triangle bonded to two BS groups), respectively. One‐electron detachment energies and symmetrical stretching vibrational frequencies are calculated for D_∞h B₂(BS) and T_d B(BS) monoanions to facilitate their future characterizations. Neutral salts of B₂(BS)₂Li₂ with an elusive B?B triple bond and B(BS)₄Li containing a tetrahedral B^? center are predicted possible to be targeted in experiments. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

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 EPR study of S and Se defects in alkali halides

Calculations using density functional theory are performed to study the electron paramagnetic resonance (EPR) and electron nuclear double resonance (ENDOR) properties of S and Se impurities in alkali halide lattices. Cluster in vacuo models are used to describe the defect and the lattice surroundings. The trivacancy defect model proposed in the literature is able to reproduce both the experimental principal values and directions of the g tensor for S and Se defects doped in alkali halides. The alternative monovacancy model gives rise to important discrepancies with experiment and can be discarded. For the KCl lattice, the hyperfine tensors of the S and Se molecular ions also agree well with the available experimental data, giving further evidence to the trivacancy model. In addition, for NaCl:S and KCl:S computational results for the ²³Na and ³⁵Cl superhyperfine and quadrupole tensors are compared with experimental ENDOR parameters. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Aromaticity of ionic structures: Investigation and application of NICS value and 4n + 2 rule

At DFT/B3LYP/6‐31G** theoretical level, C₆H and C (n = 0, ?2, and +2), C₆H and C (n = 0, ±2, ±4, and ±6), C₆H (n = 0–6), as well as C₆H₆‐A and C₆‐A (A = Be, B, N, O, Mg, Al, Si, S, and Fe) structures were investigated. Comparing NICS values of C₆H and C (n = 0, ?2, and +2), we discovered that C₆H, C₆H were antiaromatic, and C₆H₆, C₆, C, C had aromaticity with negative NICS values. According to research of C₆H and C (n = 0, ±2, ±4, ±6), C₆H (n = 0–6), we sustained that their σ and π orbit were different and the locations of electrons were difficult to confirm in ionic structures. Thus, neither 4n + 2 rule nor NICS values can precisely estimate the aromaticity of ionic structures. Besides, through WBI (NBO) research of C₆H₆‐A and C₆‐A (A = Be, B, N, O, Mg, Al, Si, S, and Fe) structures, we found that C₆H₆ was easy to accept electrons, contrarily, C₆ was prone to bestowing electrons. Moreover, C₆H₆ took the symmetrical carbon atoms form feeble interaction or bond, and C₆ used all carbon atoms to impact with other atom. C₆H₆ generated two contrapuntal single bonds with oxygen, sulfur, and nitrogen atoms, whereas C₆ molecule formed double bond with oxygen and nitrogen atoms, two conjoint single bonds with sulfur atom. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

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.     

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.     

Structure and stability of B6, B,and B clusters

We investigated various isomers of B₆, B, and B clusters with ab initio [Hartree–Fock (HF), MP2)] and density functional theory (DFT) methods. Ten B₆ isomers, 6 B isomers, and 6 B isomers are determined to be local minima on their potential energy hypersurfaces by the HF, B3LYP, B3PW91, and MP2 methods. Fourteen of these structures are first reported. The most stable neutral B₆ cluster is the capped pentagonal pyramid (C_5v), in agreement with the results reported previously. Hexagon B (C_2h) isomer and fan‐shaped B (C_2v) isomer are found to be the most stable on the cationic and anionic energy hypersurfaces, respectively. Natural bond orbital analysis suggests that there are three‐centered bonds in the most stable B₆ neutral and ionic clusters. The multicentered bonds are responsible for the special stability of the lowest‐energy isomer. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 94: 269–278, 2003     

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.     

Leading‐order behavior of the correlation energy in the uniform electron gas

We show that, in the high‐density limit, restricted Møller‐Plesset (RMP) perturbation theory yields E = π^?2(1 ? ln 2) ln r_s + O(r) for the correlation energy per electron in the uniform electron gas, where r_s is the Seitz radius. This contradicts an earlier derivation which yielded E = O(ln|ln r_s|). The reason for the discrepancy is explained. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012