Perturbative calculation of intermolecular interactions in orthogonalized or biorthogonal basis sets

Two versions of a many-body perturbation theory for the computation of molecular interaction energies are investigated. The methods are based on the partitioning of the second-quantized form of the dimer Hamiltonian written either in the orthogonalized basis of the monomer MOs, or, alternatively, in the original non-orthogonal dimer basis set handling the overlap by the biorthogonal formalism. The zeroth-order Hamiltonian H ⁰ is the sum of effective monomer Fockians and the zeroth-order wave functions are exact eigenfunctions of H ⁰. Full antisymmetry is ensured by the second-quantized formalism. Basis set superposition error is accounted for by the counterpoise correction recipe. Results for He₂, (H₂)₂ and (H₂O)₂ indicate the reliability of the biorthogonal technique.     

Resolution of molecular electric hyperpolarizabilities into atomic terms

Using the dipole acceleration formalism, a general theory for the resolution of molecular electric hyperpolarizabilities, at an arbitrary frequency, into atomic terms is presented. Test calculations for the molecules NH₃, H₂O and HF, at the random phase approximation level of accuracy, are reported.     

Orbital correspondence analysis in maximum symmetry: Formulation and conceptual framework

A recently proposed method for the analysis of the course of chemical reactions, based on the maximal use of available symmetry, is formulated as a set of procedural rules. The application of these rules is illustrated with a simple prototype reaction: CH₂+C₂H₄ fcyclo-C₃H₆. They are then derived, using the formalism of time-dependent perturbation theory within the Born-Oppenheimer approximation, thus bringing out the method's underlying assumptions and its relation to the widely used Woodward-Hoffmann procedure.     

Mass spectrometric fragmentation of n-alkanes: Self-consistency test of a statistical theory

The fragmentation patterns of n-paraffins in the C₁₀–C₃₀ range are accounted for using a statistical, maximal entropy, formalism. The theory can be used in a predictive manner. Particular attention is given here to a quantitative test of the theory which is independent of the uncertainties in the structure of the fragments.     

Superconductivity in the intermetallic borocarbides YPd2B2C,YPt2B2C and LaPt2B2C

We report a detailed study of the thermodynamic properties of the conventional phonon-mediated superconductors YPd₂B₂C, YPt₂B₂C and LaPt₂B₂C. Our calculations conducted within the framework of the Migdal-Eliashberg formalism show that the experimental values of the critical temperature cannot be properly reproduced using commonly accepted value of Coulomb pseudopotential. Moreover, we proved that the values of universal ratios of conventional superconductivity appearing in the Bardeen-Copper-Schrieffer (BCS) theory are inconsistent with our results obtained from the investigated borocarbides. The observed differences are connected with the strong/medium-coupling and retardation effects existing in the studied systems.     

N-electron valence state perturbation theory: a fast implementation of the strongly contracted variant

In this work we reconsider the strongly contracted variant of the n-electron valence state perturbation theory (SC NEV-PT) which uses Dyall's Hamiltonian to define the zero-order energies (SC NEV-PT(D)). We develop a formalism in which the key quantities used for the second-order perturbation correction to the energy are written in terms of the matrix elements of suitable operators evaluated on the zero-order wavefunction, without the explicit knowledge of the perturbation functions. The new formalism strongly improves the computation performances. As test cases we present two preliminary studies: (a) on N₂ where the convergence of the spectroscopic properties as a function of the basis set and CAS-CI space is discussed and (b) on Cr₂ where it is shown that the SC NEV-PT(D) method is able to provide the correct profile for the potential energy curve.     

Molecular polarization and laser photopredissociation in the presence of a magnetic field

The theory of the angular distribution of the photofragment resulting from weak predissociation in a diatomic molecule is worked out in the density matrix formalism. Special attention is given to the relationship between photofragment anisotropy, molecular polarization and fluorescence light polarization. The effect of a steady applied magnetic field is discussed and compared with classical Hanle effect. Application to the case of O₂⁺, b⁴σ_R^? state studied by fast ion beam laser spectroscopy (FIBLAS) is presented. Zeeman effect of the low J levels is observed in good agreement with theory and the angular distribution of the photofragments arising from a few selected Zeeman sublevels offers qualitative experimental confirmation of the theoretically predicted behavior.     

Thermophysical behaviour of monofunctional acrylate and liquid crystal systems

The phase behavior of monofunctional acrylate and low molecular weight nematic liquid crystals (LC) is considered. Systems involving the monomeric 2-ethylhexylacrylate (2-EHA), the eutectic LC mixture known as E7 and the 4-cyano-4^′-n-pentyl-biphenyl (5CB) are investigated. A similar investigation is performed on mixtures involving a polymer poly-2-EHA with molecular weight M_w=48,000 g/mol and both LCs. The experimental phase diagrams are established using polarized optical microscopy and analyzed using a theoretical formalism which combines the Flory-Huggins theory of isotropic mixing and the Maier-Saupe theory of nematic order. The results lead to characterization of the miscibility of E7 and 5CB with monomeric and analogous polymeric 2-EHA systems.     

Approximate molecular orbital theory: the ese mo formalism. II. Direct comparison with ab initio results

The utility of the ESE MO formalism is examined in relation to ab initio results, when a typical small gaussian basis is employed. Good electronic structure predictions result from simplified schemes based on the ESE MO formalism, despite adverse features of the chosen basis set, for the diverse group of molecules FH, OH₂, NH₃, FCN, O₃ and OF₂.     

Semiclassical wavepacket construction of quantum resonance states from classical resonant orbits for the F + H2 reaction

The semiclassical interpretation of reactive resonances as dynamically confined orbits is extended for the F + H₂ reaction by construction of resonant-state wavefunctions according to a time-dependent formalism for Gaussian wavepacket dynamics. The partitioning of nodal curves between entrance and exit channels for the collinear resonances agrees with adiabatic theory and nodal surfaces for the 3D probability density distribution qualitatively agree with quantal calculations.     

Excess enthalpies and apparent molar volumes of aqueous solutions of crown ethers and cryptand(222) at 25°C

The enthalpies of dilution and densities of aqueous solutions of 12-crown-4, 15-crown-5, 18-crown-6, 1,10-diaza-18-crown-6 and cryptand (222) were measured at 25°C. The excess enthalpies and enthalpic coefficients of solute-solute interactions were calculated by the McMillan-Mayer theory formalism. Values for the apparent molar volumes at infinite dilution were determined by extrapolation. The contributions of the-CH₂CH₂O-group to values of h₂ and to the limiting partial molar volume were calculated for the series of crown ethers studied. It is concluded that the hydrophobic hydration and the hydrophobic solute-solute interaction are predominant in the solutions investigated.     

Solution thermodynamics of first row transition elements. 3. Apparent molal volumes of aqueous ZnCl2 and Zn(CIO4)2 from 15 to 55°C and an examination of solute-solute and solute-solvent interactions

The apparent molal volumes of aqueous ZnCl₂ and Zn(ClO₄)₂ solutions have been measured from 15–55°C. The dilute solution data are extrapolated to infinite dilution using the Redlich-Meyer equation. The full concentration range data are fitted with the Pitzer formalism. The data are then compared with the data on the previously measured salts of Mn²⁺, Fe²⁺, Co²⁺, Ni²⁺, and Cu²⁺. The effect of complex ion formation is easily seen in the Cu²⁺ and Zn²⁺ salt data. A new approach to single ion volumes from salt volumes is proposed. The calculated ionic volumes at infinite dilution are compared, and it is clear that crystal field effects must be considered in any quantitative theory of transition element volumes.     

The variation of spectroscopic properties with numbers of electrons

A formalism that describes the variation of the spectroscopic properties, D_e, R_e, and k_e, of homonuclear, diatomic molecules, with the number of molecular electrons has been developed. The theory describes the interrelation of these properties and predicts “critical” behavior in sequences of “isonuclear” and neutral molecules. Detailed calculations are possible with the help of experimental data in lieu of a deeper, dynamical theory of molecular behavior with respect to electron number. The present work points the way toward a first-principle's theory. © 1992 John Wiley & Sons, Inc.     

Chiral effect in the sechenov parameters of argon solubility in aqueous α-valine and α-phenylalanine solutions

Data on the solubility of argon in water and aqueous solutions of L and D enantiomers of α-valine and α-phenylalanine at T = 283–328 K and partial pressure of argon p ₂ = 0.1 MPa are used to calculate the standard parameters of the Sechenov salt effect. Parameters of the solute-solute pair interaction are estimated within the formalism of the McMillan-Mayer theory. Evidence is provided for the presence of the chiral effect in the Sechenov parameters.     

An Experimental Evidence of a Metal−Metal Bond in μ‐Carbonylhexacarbonyl[μ‐(5‐oxofuran‐2(5H)‐ylidene‐κC,κC)]‐dicobalt(Co−Co)[Co2(CO)6(μ‐CO)(μ‐C4O2H2)]

The orthorhombic crystal structure of [Co₂(CO)₆(μ‐CO)(μ‐C₄O₂H₂)] ( 1 ) was determined at 150 K (Fig. 1). Two C−H⋅⋅⋅O bonds connect the molecules, forming waving ribbons along the b axis. The experimental electron density, determined with the aspherical‐atom formalism, was analyzed with the topological theory of molecular structure. The presence of the Co−Co bond critical point indicates for the first time the existence of a metal−metal bond in a system with bridged ligands. The bond critical properties of the intramolecular bonds and of the intermolecular interactions show features similar to those found in [Mn₂(CO)₁₀], confirming our previously established bonding classification for organometallic and coordination compounds.     

Faint features of the rotationalS 0(0) andS 0(1) transitions of H2

The complete collision induced absorption spectrum of H₂ - H₂ pairs at a temperature of 77 K, including the faint features due to bound and quasi-bound (H₂)₂ dimers, has been calculated from first principles and compared in detail with recently published laboratory measurements. An empirical anisotropic intermolecular potential energy surface (“F84”), and an ab initio induced dipole moment function due to Meyer were used in the calculations. The close coupled formalism was applied to determine the multiple-component scattering and bound-state wave functions. Comparisons between experiment and theory show very good general agreement: all the faint hydrogen dimer features that are observed are reproduced theoretically. The observed pressure broadening of sharper dimer features could also be partially accounted for in the calculations. The remaining disagreements between theory and experiment in the intensities and positions of the features are very useful for deriving the small modifications required to further improve the F 84 surface, especially in the region of the attractive potential well.     

Effects of electrolyte concentration,temperature, and pressure on the sechenov salt-effect parameter: He-NaCl-H<Subscript>2</Subscript>O system

The data on the solubility of helium in water and aqueous solutions of sodium chloride at a temperature of T = 293–353 K and a He partial pressure of p ₂ = 0.1–20 MPa are used to calculate the standard parameters of the Sechenov salt effect and estimate, within the formalism of the McMillan-Mayer theory, the parameters of the pairwise solute-solute interaction.     

Angle-resolved photoelectron spectroscopy of the chloro-substituted methanes

The angular distribution parameter, β, was determined for the valence orbitals (IP ′ 21.2 eV) of CCl₄, CHCl₃, CH₂Cl₂, and CH₃Cl in the 10–30 eV photon energy range using dispersed polarized synchrotron radiation. The energy dependence of β in the photoelectron energy range of 2 to 10 eV for the non-bonding chlorine n(Cl) orbitals of these molecules was found to be similar for all n(Cl) orbitals investigated. The energy dependence of β for the σ orbitals in these molecules was similar to that observed previously for other σ orbitals. The experimental CCl₄ results were compared with theoretical CCl₄ results obtained using the Xα multiple scattering formalism. Theory predicts the existence of two strong shape resonances in each of the valence orbitals of CCl₄. The overall agreement between experiment and theory is evaluated along with the experimental evidence concerning the verification of the predicted shape resonances.     

Orbital functional theory of linear response and excitation

Orbital functional theory (OFT) is based on a rule that determines a single‐determinant reference state Φ for any exact N‐electron eigenstate Ψ. An OFT model postulates an explicit correlation energy functional E_c of occupied orbital functions {?_i} and occupation numbers {n_i}. The orbital Euler–Lagrange equations are analogous to Kohn–Sham equations, but do not in general contain local potential functions. Time‐dependent Hartree–Fock theory is generalized in OFT to a formally exact linear response theory that includes electronic correlation. In the exchange‐only limit, the theory reduces to the random‐phase approximation of many‐body theory. The formalism determines excitation energies. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001