Convergence of the density functional one-centre expansion for the molecular continuum: N2 and (CH3)3N

A large-scale one-centre expansion with a radial B-spline basis set is implemented for bound and continuum states. A Kohn-Sham hamiltonian is employed with Hartree and exchange-correlation potentials calculated from the SCF electron density taken from a previous LCAO calculation. An inverse iteration method is used to obtain the continuum wavefunction, from which the cross section and asymmetry parameter are calculated. The convergence with respect to angular momentum and cut-off radius is analysed for N₂. The relevance of multipolar contributions even at large distances is shown and suggestions for further improvements are given. In order to show that the present method is suitable to treat systems of moderate size, the (CH₃)₃N molecule has also been calculated and the results are compared with experiment. Received: 19 May 1998 / Accepted: 20 August 1998 / Published online: 7 December 1998     

Recombination of silicon ions by electron capture from atomic hydrogen and helium

 Ab initio potential-energy curves and coupling matrix elements of the Σ and Π molecular states involved in the collision of the Si²⁺, Si³⁺ and Si⁴⁺ multicharged ions on atomic hydrogen and helium have been determined by means of configuration interaction methods. The total and partial electron capture cross sections have been determined using a semiclassical or a quantal approach in the 0.002–0.1 au velocity range. A detailed comparison with very recent theoretical and experimental rate coefficient results is made. Received: 14 September 1999 / Accepted: 3 February 2000 / Published online: 2 May 2000     

Quantum dynamics study of Li + HF reaction

We report rigorous quantum dynamics studies of the Li + HF reaction using the time-dependent wavepacket approach. The dynamics study is carried out on a recent ab initio potential energy surface, and state-selected reaction probabilities and cross sections are calculated up to 0.4 eV of collision energy. Many long-lived resonances (as long as 10 ps) at low collision energies (below 0.1 eV) are uncovered from the dynamics calculation. These long-lived resonances play a dominant role in the title reaction at low collision energies (below 0.1 eV). At higher energies, the direct reaction process becomes very important. The reaction probabilities from even rotational states exhibit a different energy dependence than those from odd rotational states. Our calculated integral cross section exhibits a broad maximum near the collision energy of 0.26 eV with small oscillations superimposed on the broad envelope which is reminiscent of the underlying resonance structures in reaction probabilities. The energy dependence of the present CS cross section is qualitatively different from the simple J-shifting approximation, in which a monotonic increase of cross section with collision energy was obtained. Received: 8 January 1997 / Accepted: 14 January 1997     

An improved iterative solution to solve the electrostatic problem in the polarizable continuum model

 We present a discrete iterative interpolation scheme (DIIS) to improve the convergence rate of electrostatic calculations in the polarizable continuum model (PCM) to describe solvent effects on molecular solutes. The electrostatic calculations may easily become the bottleneck of the calculation when the solute size is large. For large molecules iterative procedures turn out to be computationally more convenient than matrix inversion or closure methods. The DIIS scheme is compared here to another iterative procedure (DAMP) and to the biconjugate gradient (BCG) method. The comparisons show that DIIS leads to a sizeable saving of computational time for the C-PCM and IEF-PCM methods (average 40%) compared to DAMP, and more than 50% with respect to the BCG method. Received: 5 October 2000 / Accepted: 13 November 2000 / Published online: 19 January 2001     

Multireference perturbation CI IV. Selection procedure for one-electron properties

We present in this paper a modification of the selection procedure, within the CIPSI algorithm, specifically intended for the calculation of one-electron properties. In this new procedure the determinants are selected following their contribution to a certain one-electron property. As test cases we report the calculation of the electric dipole of carbon monoxide and of the hyperfine coupling constants of the CH₃ radical. Received: 20 August 2000 / Accepted: 2 October 2000 / Published online: 21 December 2000     

Excitation energies, electron affinities and ionization potentials of the transition metals V, Cr and Mn

 Configuration interaction calculations were carried out for neutral ground and excited states and positively and negatively ionized states of the V, Cr and Mn atoms. Energy convergence with respect to systematic expansion of both the one-electron and configuration bases was investigated for valence correlation. Contributions from core electrons to the differential correlation energies and relativistic effects were evaluated separately. Assuming additivity of these contributions, excitation energies, electron affinities and ionization potentials of the atoms were obtained. All calculated values were in excellent agreement with the observed values within a deviation of 0.056 eV except for the electron affinity of the V atom, which had a calculated value 0.110 eV larger than the experimental value. Received: 9 August 2000 / Accepted: 26 October 2000 / Published online: 3 April 2001     

Intramolecular coupling study on nonlinear optical signals

 In this contribution, we have introduced intramolecular coupling in order to study possible modifications in the topology of the resonances associated with the four-wave mixing signal emerging as a consequence of incorporating the permanent dipole moments when the rotating-wave approximation is not included. Received: 17 September 1999 / Accepted: 9 March 2000 / Published online: 21 June 2000     

Interaction energies for the water dimer by supermolecular methods and symmetry-adapted perturbation theory: the role of bond functions and convergence of basis subsets

 Using a systematic series of basis sets in supermolecular and symmetry-adapted intermolecular perturbation theory calculations it is examined how interaction energies of various water dimer structures change upon addition and shifting of bond functions. Their addition to augmented double- and triple-zeta basis sets brings the sum of the electron correlation contributions to the second-order interaction energy nearly to convergence, while accurate first-order electrostatic and exchange contributions require better than augmented quadruple-zeta quality. A scheme which combines the different perturbation energy contributions as computed in different basis subsets performs uniformly well for the various dimer structures. It yields a symmetry-adapted perturbation theory value of −21.08 kJ/mol for the energy of interaction of two vibrationally averaged water molecules compared to −21.29 kJ/mol when the full augmented triple-zeta basis set is used throughout. Received: 4 November 1999 / Accepted: 8 February 2000 / Published online: 12 May 2000     

A reexamination of virial coefficients of the Lennard-Jones fluid

The fourth-order virial coefficients have been calculated exactly to five decimal places for pure fluids of the Lennard-Jones potential at many points in the phase diagram. The calculations were performed through direct evaluation of the integrals, or diagrams, which make up the density expansion of the radial distribution function: included were the standard fast Fourier transform method of evaluating the simply connected diagrams and the evaluation of the bridge diagram for the fourth order in density by expansion in Legendre polynomials. The polynomial-order dependence of the bridge diagram calculation and the range dependence of the simply connected diagrams of the fourth order are found to have more significance than was thought from previous studies, especially in the low-temperature range. This result was confirmed by direct evaluation of the diagrams which construct the virial coefficients, as given by Rowlinson, Barker, and coworkers. This calculation confirmed that numerical convergence has not been achieved at the precision levels previously reported in the literature. These differences, though minor at higher temperatures, can be seen to be more significant at the lower temperature ranges. Received: 31 July 2000 / Accepted: 18 September 2000 / Published online: 21 December 2000     

Recognizing a triple bond between main group atoms

The electron pair density, in conjunction with the theory of an atom in a molecule, enables one to unambiguously determine the nature of the bonding between the gallium atoms in bent [HGa-GaH]²⁻. The Ga-Ga bonding in the dianion at the experimental bond length is found to be the result of the sharing of two electron pairs at the Hartree-Fock level of theory, the level consistent with the Lewis model of the electron pair. Received: 27 July 2000 / Accepted: 4 October 2000 / Published online: 19 January 2001     

Electron affinities, excitation energies and ionization potentials of the transition metals (I) Sc and Ti

The electron affinities of the Sc and Ti atoms have been obtained by configuration interaction calculations. Energy convergence with respect to the systematic expansion of both the one-electron basis set and the configuration space was investigated for valence electrons, and the inclusion of correlation contributions from core electrons and relativistic effects gave the electron affinities of 0.181 eV and 0.163 eV for Sc and Ti, respectively. These are in excellent agreement with the observed values of 0.189 ± 0.020 eV and 0.080 eV. The same approach was applied for the first excited states and positive ions of both atoms. Excellent agreement with the experimental results was also obtained for these states. Received: 16 February 1998 / Accepted: 2 April 1998 / Published online: 23 June 1998     

FIRE: predicting the spatial proximity of protein residues from 3D NOESY–HSQC

 We address the problem of the prediction of residue spatial proximity in a protein, through the automatic processing of a 3D ¹⁵N NOESY–HSQC. The spatial distance between residues is estimated from a spectral match value calculated using a comparison of the resonances involving the amide hydrogens. The method is shown to provide a good estimation of a large number of residue spatial proximities, in the case of two experimental 3D spectra, recorded on proteins of α and β secondary structures. It is tested on simulated data sets against the protein size, secondary structure and the quality of the signal. More than 70% of the sequential assignment is correctly predicted, and the prediction is better for the α than for the β secondary structure. The medium- and long-range correlations seem equally well predicted for all the secondary structures. The efficiency of the method is compared to a previously proposed spectral correlation approach. Received: 5 July 2000 / Accepted: 8 September 2000 / Published online: 19 January 2001     

Nature and importance of three-body interactions in the (H2O)2HCl trimer

 The nature and importance of nonadditive three-body interactions in the (H₂O)₂HCl cluster have been studied by the supermolecule coupled-cluster method and by symmetry-adapted perturbation theory (SAPT). The convergence of the SAPT expansion was tested by comparison with the results obtained from the supermolecule coupled-cluster calculations including single, double, and noniterative triple excitations [CCSD(T)]. It is shown that the SAPT results reproduce the converged CCSD(T) results within 3% at worst. The SAPT method has been used to analyze the three-body interactions for various geometries of the (H₂O)₂HCl cluster. It is shown that the induction nonadditivity is dominant, but it is partly quenched by the first-order Heitler–London-type exchange and higher-order exchange–induction/deformation terms. This implies that the classical induction term alone is not a reliable approximation to the nonadditive energy and that it will be difficult to approximate the three-body potential for (H₂O)₂HCl by a simple analytical expression. The three-body energy represents as much as 21–27% of the pair CCSD(T) intermolecular energy. Received: 15 September 1999 / Accepted: 3 February 2000 / Published online: 2 May 2000     

Stabilization centers and protein stability

The well-balanced stability of protein structures allows large-scale fluctuations, which are indispensable in many biochemical functions, ensures the long-term persistence of the equilibrium structure and it regulates the degradation of proteins to provide amino acids for biosynthesis. This balance is studied in the present work with two sets of proteins by analyzing stabilization centers, defined as certain clusters of residues involved in cooperative long-range interactions. One data set contains 56 proteins, which belong to 16 families of homologous proteins, derived from organisms of various physiological temperatures. The other set is composed of 31 major histocompatibility complex (MHC)–peptide complexes, which represent peptide transporters complexed with peptide ligands that apparently contribute to the stabilization of the MHC proteins themselves. We show here that stabilization centers, which had been identified as special clusters of residues that protect the protein structure, evolved to serve also as regulators of function – related degradation of useless protein as part of protein housekeeping. Received: 25 August 2000 / Accepted: 6 September 2000 / Published online: 21 December 2000     

Contracted basis sets for electrical property calculations derived from Second-order Møller–Plesset theory atomic natural orbitals

 Using established methods based on correlated atomic natural orbitals (ANOs), sets of contracted polarization functions are derived for use in calculations of atomic and molecular electrical properties (especially electric moments, dipole polarizabilities and related property hypersurfaces). Through test calculations on Ne, Ar, NH₃ and CO₂, these polarization functions are shown to reproduce the accuracy of larger basis sets, to incorporate dynamical electron correlation effects and are economical to use in conjunction with sophisticated electron-correlation treatments. We also show how triple-zeta polarized ANO and double-zeta polarized ANO basis sets are constructed from these contracted polarization functions for use in the calculation of reliable zero-point vibrational averages of electrical properties. Received: 20 December 1999 / Accepted: 15 February 2000 / Published online: 12 May 2000     

A first principles study of Pd deposition on the TiO2(1 1 0) surface

 The adsorption of isolated Pd atoms on the (1 1 0) surface of rutile TiO₂ was investigated through ab initio embedded-cluster calculations performed at the Hartree–Fock, second-order M?ller–Plesset and Becke's three parameter hybrid method with the Lee–Yang–Parr correlation functional levels. The role played by the magnitude of the surrounding charges used in the embedding procedure was carefully analyzed. The most stable site for adsorption consisted of a fourfold hollow site in which the Pd atom was coordinated to a fivefold Ti atom, two basal oxygens, and a protruding oxygen atom. However, the adsorption energies computed after basis set superposition error corrections seemed to favor a bridge site in which the Pd atom binds two protruding oxygen atoms. A periodic slab calculation using gradient-corrected functionals and plane-wave basis sets confirmed that for full coverage, the hollow site was more stable, although Pd displacement along the fivefold Ti channels was almost free. These results agree with the experimental data obtained from scanning tunneling microscopy. Finally, the adsorption energy computed from the periodic calculations was found to be 1.88 eV. Received: 14 September 1999 / Accepted: 3 February 2000 / Published online: 19 April 2000     

The hierarchy of localization basins: a tool for the understanding of chemical bonding exemplified by the analysis of the VOx and VOx+ (x=1–4) systems

The hierarchy of the electron localization basins is a powerful tool of analysis of the bonding in molecules and solids within the “elfological” framework. It is a generalization of the molecular isodensity contour analysis originally proposed by Mezey. In this approach the basins are ordered with respect to the electron localization function values at the critical points which determine the reduction of the reducible localization domains. The procedure enabling the corresponding tree diagrams to be built is described and it is shown how the method can be used as a generator of mathematical definitions of chemical concepts. The possibility offered by this simple tool is illustrated by a study of the VO _x and VO _x ⁺ (x=1–4) oxides in their ground state and in some excited states. Received: 20 July 2000 / Accepted: 20 October 2000 / Published online: 23 January 2001     

The generalized hybrid orbital method for combined quantum mechanical/molecular mechanical calculations: formulation and tests of the analytical derivatives

 Hybrid quantum mechanical (QM) and molecular mechanical (MM) potentials are becoming increasingly important for studying condensed-phase systems but one of the outstanding problems in the field has been how to treat covalent bonds between atoms of the QM and MM regions. Recently, we presented a generalized hybrid orbital (GHO) method that was designed to tackle this problem for hybrid potentials using semiempirical QM methods [Gao et al. (1998) J Phys Chem A 102: 4714–4721]. We tested the method on some small molecules and showed that it performed well when compared to the purely QM or MM potentials. In this article, we describe the formalism for the determination of the GHO energy derivatives and then present the results of more tests aimed at validating the model. These tests, involving the calculation of the proton affinities of some model compounds and a molecular dynamics simulation of a protein, indicate that the GHO method will prove useful for the application of hybrid potentials to solution-phase macromolecular systems. Received: 4 October 1999 / Accepted: 18 December 1999 / Published online: 5 June 2000     

Harmonic analysis and discrete polynomials. From semiclassical angular momentum theory to the hyperquantization algorithm

Orthogonal polynomials of a discrete variable have been widely investigated as fundamental tools of numerical analysis. This work aims to propose the extension of their use to quantum mechanical problems. By exploiting both their connection with coupling and recoupling coefficients of angular momentum theory and their asymptotic relationships (semiclassical limit) with spherical and hyperspherical harmonics, a discretization procedure, the hyperquantization algorithm, has been developed and applied to the study of anisotropic interactions and of reactive scattering. One of the most appealing features of this method turns out to be a drastic reduction of memory requirements and computing time for extensive dynamical calculations. Examples of the application of this technique to stereodirected dynamics via an exact representation for the S matrix as well as to the characterization of molecular beam polarization are also illustrated. Received: 17 September 1999 / Accepted: 3 February 2000 / Published online: 5 June 2000     

Calculation of three-center electric and magnetic multipole moment integrals using translation formulas for Slater-type orbitals

 By the use of translation formulas for the expansion of Slater-type orbitals (STOs) in terms of STOs at a new origin, three-center electric and magnetic multipole moment integrals are expressed in terms of two-center multipole moment integrals for the evaluation of which closed analytical formulas are used. The convergence of the series is tested by calculating concrete cases. Computer results with an accuracy of 10⁻⁷ are obtained for 2^ν– pole electric and magnetic multipole moment integrals for 1≤ν≤5 and for arbitrary values of screening constants of atomic orbitals and internuclear distances. Received: 28 October 1999 / Accepted: 15 February 2000 / Published online: 5 June 2000