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.     

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 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.     

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.     

A Flory–Huggins thermodynamic approach for predicting sorption equilibrium in ternary polymer systems

The Flory–Huggins theory as modified by Pouchlý has been applied to calculate preferential (λ) and total (Y) sorption coefficients for a ternary polymer system. The ternary interaction function (?₁?₂?₃G_T(u₁, ?₃)) is described as the product of three independent binary functions. This expression allows prediction of λ and Y from binary interaction parameters χ, χ, g, g, and g₁₂(?₁₀). Three ternary polymer systems are used to check the validity of the expression. Moreover for polymer systems in which the parameters g and/or g are unknown, a procedure to evaluate them has been developed and verified on systems for which sufficient experimental information is available.     

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.     

Explicitly correlated Gaussian functions with r factors for calculations of the ground state of the helium atom

Explicitly correlated Gaussian functions with r exp( ? β r ) factors have been used in variational calculations of the ground state of the helium atom. Additional correlation factors in the form of even powers of r _ij were introduced to the Gaussian functions with exponential correlation components by differentiating these functions with respect to the correlation exponent β. The algorithm of this method and its computational implementation is described. A number of calculations were performed for the ground state of helium atom to test the performance of the basis sets comparising different numbers of the Gaussians with the exp( ? β r ) and r exp( ? β r ) correlation factors. The numerical results indicate that including functions with r factors does not lead to improved results, contrary to what was anticipated initially. © 1994 by John Wiley & Sons, Inc.     

Laser ablation of AgSbS2 and cluster analysis by time‐of‐flight mass spectrometry

Thin films of AgSbS₂ are important for phase‐change memory applications. This solid is deposited by various techniques, such as metal organic chemical vapour deposition or laser ablation deposition, and the structure of AgSbS₂(s), as either amorphous or crystalline, is already well characterized. The pulsed laser ablation deposition (PLD) of solid AgSbS₂ is also used as a manufacturing process. However, the processes in plasma have not been well studied. We have studied the laser ablation of synthesized AgSbS₂(s) using a nitrogen laser of 337 nm and the clusters formed in the laser plume were identified. The ablation leads to the formation of various single charged ternary Ag_pSb_qS_r clusters. Negatively charged AgSbS, AgSb₂S, AgSb₂S, AgSb₂S and positively charged ternary AgSbS⁺, AgSb₂S⁺, AgSb₂S, AgSb₂S clusters were identified. The formation of several singly charged Ag⁺, Ag, Ag, Sb, Sb, S ions and binary Ag_pS_r clusters such as AgSb, Ag₃S^?, SbS (r = 1–5), Sb₂S^?, Sb₂S, Sb₃S (r = 1–4) and AgS, SbS⁺, SbS, Sb₂S⁺, Sb₂S, Sb₃S (r = 1–4), AgSb was also observed. The stoichiometry of the clusters was determined via isotopic envelope analysis and computer modeling. The relation of the composition of the clusters to the crystal structure of AgSbS₂ is discussed. Copyright © 2009 John Wiley & Sons, Ltd.     

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.     

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     

Thermodynamic molecular mechanics force field: Modified QCFF program

The QCFF program originated by Warshel and Karplus^4a was modified to compute accurate thermodynamic properties S^o, C, (H – H)/T, and ΔH for various acyclic and cyclic alkenes and alkadienes. Modifications consisted of adjusted bond angle, dihedral angle, bond stretch, and bond energy parameters that improved calculated vibrational frequencies, zero point energies, and thermodynamic functions. Supplemental torsional potential energy functions that were added to existing torsional functions led to greatly improved relative conformer energies and ΔH values. It was shown that inclusion of hindered internal rotation leads to significantly better agreement of calculated thermodynamic functions with observed values for acyclic alkenes at high temperatures. The calculated thermodynamic properties of the alkenes and alkadienes were deemed sufficiently accurate for calculation of standard enthalpies and Gibbs free energies of gas phase chemical reactions at various temperatures. © 1994 by John Wiley & Sons, Inc.     

Characteristic operators and unitarily invariant decomposition of hermitian operators

A set of characteristic operators {F} is proposed for performing the decomposition of p-particle Hermitian operators {D^p} to constitute irreducible components {D} of the unitary group D = FD^p, q = 0,1,2,…,p. For a deeper expolration of the properties of the characteristic operators, a few theorems are presented. As an illustration, the expected values for symmetric p-particle Hermitian operators are obtained as a number of terms having invariant group-theoretical meaning.     

Expansion of r12 and r in terms of analytical functions

Expansions in terms of the spherical coordinates of two particles are given for the interparticle distance and its inverse. The expansions are characterized in that each term is a product of analytical one-variable functions. While it is possible to find acceptable expansions for r₁₂, those obtained for r exhibit extremely slow convergence, unacceptable for practical use. The same objections must be raised against related expansions of multi-centered molecular integrals.     

Ab initio MO calculations of hyperfine coupling constants. A basis set study for 19F, 35Cl, 19F,and 35Cl

Hyperfine coupling constants (HFCC ) of the ¹⁹F and ³⁵Cl atoms and the ¹⁹F and ³⁵Cl radical anions have been calculated by the unrestricted Hartree–Fock (UHF ) method using polarization and diffuse functions with contracted double-zeta as well as uncontracted basis sets. The A_dip values are fairly insensitive to changes in the basis set and show good accordance with experimental and other theoretical studies. The isotropic HFCCS a_N of ¹⁹F, ¹⁹F, and ³⁵Cl show strong dependence on d functions and the state of contraction of the s, p set. Spin-projected UHF wave functions lead to better agreement with experiment.     

Structures and Electrical Properties of Some New Organic Conductors Derived from the Donor Molecule TMET (S,S,S,S,-Bis(dimethylethylenedithio) tetrathiafulvalene)

Crystal structures and electrical properties of radical-cation salts of the chiral organic donor TMET (S,S,S,S,-bis-(dimethylethylenedithio)tetrathiafulvalene) are described. Two structural types, 2:1 with octahedral anions Pf, AsF, SbF, I (incommensurate), and 3:2 with tetrahedral anions BF^?₄, CIO^?₄, ReO^?₄ are observed. Resistivity measurements between 2 and 298 K indicate that the 3:2 types are organic metals, while the other compounds are semiconductors. (TMET)₃(CIO₄)₂ is metallic down to about 120 K at ambient pressure and remains metallic down to 2 K at 8 kbar.     

Gaussian wave functions for CH3 and NH

Ground state single determinant LCAO-MO-SCF wave functions, using a large contracted Gaussian basis set (6^s, 2^p, 1^d/3^s, 1^p), have been computed for the 9 electron molecular systems of CH₃ and NH. The minimum energies obtained using Roothaan's open shell SCF procedure for the planar equilibrium geometries were ?39.5703 Hartree for CH₃ and ?55.8945 Hartree for NH. Additional properties such as electron populations and multiple moments were calculated from the planar wave functions.     

Atomic integrals in Hylleraas–CI calculations with double-linked correlation terms

Atomic Hylleraas-CI calculations with linked correlation terms of the form r r are discussed. Formulas for the integration of the radial part and the arising auxiliary integrals are deduced and convergence proofs are given. © 1995 John Wiley & Sons, Inc.     

Oxidation of thallium(I) by hexacyanoferrate(III) in aqueous acetic acid

The hexacyanoferrate(III)-thallium(I) reaction in aqueous acetic acid containing large concentrations of hydrochloric acid is considerably accelerated both by hydrogen and chloride ions as well as increasing acetic acid in the medium. The experimental results obey the rate law (1) where β₁ to β₆ are the cumulative stability constants of the species TlCl, TlCl, TlCl, HFe(CN), H₂Fe(CN) and H₃Fe(CN)₆ respectively and k_a and k_b are the rate constants associated with the mono- and di-protonated oxidant species. The main active species are H₂Fe(CN) and TlCl.