Multireference perturbation CI III. Fast evaluation of the one-particle density matrix

Within the frame of multireference perturbation configuration interaction we have developed a fast algorithm, based on diagrammatic techniques, for the calculation of the first-order correction to the one-particle density matrix. As an example of an application we have chosen the evaluation of the dipole moment of the CO molecule, where utilization of the first-order density is shown to corroborate the variational calculation. Received: 4 August 1998 / Accepted: 21 September 1998 / Published online: 16 November 1998     

Equation for the direct determination of the density matrix: Time-dependent density equation and perturbation theory

The density equation proposed previously for the direct determination of the density matrix, i.e. for the wave mechanics without wave, is extended to a time-dependent case. The time-dependent density equation has been shown to be equivalent to the time-dependent Schr?dinger equation so long as the density matrix, included as a self-contained variable, is N-representable. Formally, it is obtainable from the previous time-independent equation by replacing the energy E with . The perturbation theory formulas for the density equation have also been given for both the time-dependent and time-independent cases. Received: 16 June 1998 / Accepted: 2 September 1998 / Published online: 8 February 1999     

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     

META 4. Prediction of the metabolism of polycyclic aromatic hydrocarbons

Polycyclic aromatic hydrocarbons (PAHs) are widely distributed in the environment and are often implicated as potential carcinogens. It is generally believed that the carcinogenic potential of polycyclic aromatic hydrocarbons is linked to the formation of ultimate carcinogens generated by metabolic biotransformations. In this paper we propose a methodology that consists of using both quantum chemical properties and structural features of the reaction sites to predict PAH metabolism. Two essential questions have been answered: at which sites will the reaction take place and does the transformation consist of epoxidation or hydroxylation? This methodology has been successfully implemented into an expert system, META, for the evaluation of metabolic transformations of new chemicals. Received: 3 April 1998 / Accepted: 6 July 1998 / Published online: 7 October 1998     

Determination of a set of parameters for the molecular modelling of phosphorothioate DNA

Phosphorothioate DNAs, have emerged as a new class of potent drugs. They are obtained by the replacement of the anionic oxygens of the phophodiester backbone by sulphur. A set of parameters has been developed for the FLEX force field implemented in JUMNA 10.0 to take into account the influence of sulphur on the structure of the DNA double helix. The consistency of our parameters was tested by modelling a phosphorothioate oligomer namely d(GC)8. d(GC)8. Results, obtained on both R-p_S and S-p_S diastereoisomers, were compared to the phosphodiester counterpart and are in agreement with available experimental data. Thus, our set of parameters seems suitable for further molecular modelling of other phosphorothioate oligomers. Received: 15 July 1998 / Accepted: 8 September 1998 / Published online: 10 December 1998     

A theoretical study of substituent effects on the structure of isolated and condensed three-membered rings. A comparison between radicals and parent hydrocarbons

Substituent effects on the structure of radicals and parent hydrocarbons formed by isolated or condensed three-membered rings have been investigated by Hartree-Fock, post-Hartree-Fock and density functional methods. The trends of structural parameters computed for the hydrocarbon systems are in agreement with available experimental data. Substituent effects can be rationalized in terms of interactions between localized orbitals obtained by natural bond analysis. The effects are even larger in free radicals and can be analyzed using the same model. Received: 13 March 1998 / Accepted: 13 July 1998 / Published online: 9 October 1998     

Grid-free DFT implementation of local and gradient-corrected XC functionals

Following an approach to density functional theory calculations based on the matrix representation of operators, we implemented a scheme as an alternative to traditional grid-based methods. These techniques allow integrals over exchange-correlation operators to be evaluated through matrix manipulations. Both local and gradient-corrected functionals can be treated in a similar way. After deriving all the required expressions, selected examples with various functionals are given. Received: 7 March 1998 / Accepted: 21 May 1998 / Published on line: 6 August 1998     

Temperature dependency of the intrinsic carrier density of hydrogenated amorphous silicon in MOS structures

The admittance versus frequency of a hydrogenated amorphous silicon metal oxide semiconductor capacitor is measured at a fixed bias in inversion and for temperatures in the range of 20–50 °C. The data are fitted to theoretical capacitance and conductance curves where the time constant of inversion is the result of the fit. In turn, the time constant can be converted to the (minority) carrier lifetime so that a lifetime value for each measurement temperature is available. The conversion from the time constant to the minority carrier lifetime requires the knowledge of the temperature-dependent intrinsic carrier density or rather its activation energy. The criterion for the correct choice is a temperature-independent carrier lifetime. Three published room temperature values of the intrinsic carrier density have been tested. The carrier lifetime activation energy is E _a = 0.70 ± 0.03 eV. Received: 17 June 1998 / Accepted: 23 October 1998     

Molecular fragment approach to the study of pyrrole oligomers and polypyrrole

A molecular fragment approach is used to compute ionization potentials, transition energies and electron affinities of pyrrole oligomers. The calculations of these quantities include correlation energy contributions evaluated by integrating a functional of the two-particle Hartree-Fock density matrix. Pyrrole oligomers with chains of up to 16 rings are explicitly treated and the calculated quantities extrapolated to the limit of an infinitely long chain, to predict polymer properties. The theoretical results compare favorably with data on gas-phase ionization potentials deduced from experimental oxidation potentials, and with optical absorption peaks recorded in solution or on solid films. The large discrepancy between electron affinities obtained from the eigenvalues of an independent-particle frozen-orbital calculation and those obtained from separate, correlated calculations on the neutral system and the negative ion in shown. Received: 24 March 1998 / Accepted: 2 September 1998 / Published online: 7 December 1998     

The partial averaging Fourier path Integral approach based on the harmonic reference path

The Monte Carlo Fourier path integral approach has proved to be quite useful in calculating equilibrium thermodynamic properties. One of its advantages is that it can be formulated in such a way as to include higher order terms using the partial averaging technique, which includes the contribution from higher terms usually neglected by the discretized path integral approach. In the original approach, the Feynman path integral is evaluated via a free-particle reference state. Here, using a new expression for the Feynman paths expanded around a harmonic reference path, we derive an alternative formulation for the density matrix element and its corresponding partial averaging expression. Received: 16 September 1998 / Accepted: 30 October 1998 / Published online: 1 February 1999     

Information about the biologically relevant properties of Clostridium pasteurianum rubredoxin obtained from modeling and dynamics simulations of molecular variants

Rubredoxins are small electron transfer proteins containing one iron atom at their active site. The rubredoxin from the anaerobic bacterium Clostridium pasteurianum has been subjected to molecular dynamics studies starting from the minimized solvated structure. The results of the simulations have been compared with identical ones carried out with selected mutated forms of the protein obtained by molecular modeling. Surface residues, which are highly conserved among rubredoxins and close to the cysteine ligands, can be replaced by glutamates, i.e. long chain carboxylates. The main structural consequence is a shift of the protein backbone bearing conserved aromatic residues. Reciprocally, substitution of the aromatic residue closest to the iron atom shifts the cysteine-containing peptide fragments. These observations have been related to the changes in electron transfer and redox properties previously measured for this set of rubredoxin molecular variants. Received: 16 May 1998 / Accepted: 4 August 1998 / Published online: 2 November 1998     

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     

Chemical potential inequality principle

Regional density functional theory has been extended to treat irreversible thermodynamic electronic processes for application to adiabatic electron-transfer processes of chemical reactions. Onsager's local equilibrium hypothesis is slightly modified to take into account the quantum mechanical nature of the electron. The quantum mechanical interference effect has been demonstrated to be included in the entropy production rate formula associated with electron transfer through an interface. A new formula for the determination of the transition state of a chemical reaction has been postulated that corresponds to the maximum of the regional electron transferability. A quantum mechanical law of mass action has been established and applied to prove the regional electrochemical potential inequality principle. Received: 1 July 1998 / Accepted: 2 September 1998 / Published online: 8 February 1999     

Density functional study on zerovalent lanthanide bis(arene)-sandwich complexes

Several zerovalent lanthanide bis(arene)-sandwich complexes, Ln(η⁶-C₆H₆)₂, Ln = La, Ce, Eu, Gd and Lu, have been studied by means of density functional theory. The calculated geometries are in good agreement with experiment. The calculated dissociation energies of the bond Ln-(η⁶-C₆H₆) may be considerably underestimated, but they correctly reveal the variation regularity. The bonding in these molecules can be described in terms of a relatively weak π-electron donation from benzene to Ln and a stronger electron back-donation from Ln 5d to the benzene π* orbitals. During bond formation, there is electron promotion from Ln 6s to 5d instead of from 4f to 5d, in opposition to the proposal of Anderson et al. The relativistic effect only slightly influences the molecular geometry, but decreases the bonding energy considerably through lowering the Ln 6s level and raising the 5d level. It enhances the trend of the bonding energy to decrease along the lanthanide series. Received: 22 June 1998 / Accepted: 9 September 1998 / Published online: 17 December 1998     

The structure and energetics of cryolite melts

A method of solvation energy computation is proposed for ions and molecules in the environment of an ionic melt, based on the approximation of the ionic melt as an ideal conductor. The method is used to compute equilibrium constants of some equilibria in cryolite melt. Theoretically obtained results predict that aluminium is bound in tetrafluorocomplexes AlF₄ ⁻. Received: 16 March 1998 / Accepted: 19 June 1998 / Published online: 7 October 1998     

Parallel implementation of a divide and conquer semiempirical algorithm

We have implemented a parallel version of the semiempirical divide and conquer program DivCon previously developed in our laboratory. By utilizing a parallel machine we are able to leverage the linear scaling of the divide and conquer algorithm itself to perform semiempirical calculations on large bio-molecules. The utility of the implementation is demonstrated with a partial geometry optimization of hen egg white lysozyme in the gas phase. Received: 5 December 1997 / Accepted: 13 February 1998 / Published online: 17 June 1998     

Evaluation of the proton transfer kinetics of potential electrolytes in non-aqueous solutions using electrochemical techniques Part 1. Kinetic analysis of the general CE mechanism at stationary and rotating electrodes

The transport and kinetics of potential electrolytes (such as weak organic acids) at stationary and rotating electrodes have been examined in detail. A coherent mathematical analysis enabling the normalised current response to be evaluated has been developed, and various rate limiting scenarios have been identified and examined. Received: 13 March 1998 / Accepted: 31 July 1998     

Reaction path following by quadratic steepest descent

An efficient steepest descent algorithm for the integration of minimum energy paths, based on local quadratic approximations of the potential energy surface, is presented. The algorithm incorporates a selection procedure for the points at which the second derivatives of the energy are calculated fully or partially, thus minimizing the computational effort while maintaining high accuracy. This makes the method especially well suited for application in variational transition state theory calculations with tunnelling corrections, which have very high accuracy requirements. The performance of the algorithm is illustrated by ab initio calculations for four chemical reactions of differing complexity. The overall computational cost is less than for, or comparable to that of, first- or second-order algorithms published previously. Received: 28 July 1998 / Accepted: 10 August 1998 / Published online: 28 October 1998     

Global geometry optimization of small silicon clusters at the level of density functional theory

By an application to small silicon clusters Si _N (with N = 4,5,7,10) it is shown that truly global geometry optimization on an ab initio or density functional theory level can be achieved, at a computational cost of approximately 1–5 traditional local optimization runs (depending on cluster size). This extends global optimization from the limited area of empirical potentials into the realm of ab initio quantum chemistry. Received: 24 February 1998 / Accepted: 6 March 1998 / Published online: 17 June 1998     

Identification of deadwood in configuration spaces through general direct configuration interaction

 In order to identify ineffective and, hence, superfluous configurations in algorithmically generated configuration spaces, a direct configuration interaction (CI) method has been developed for determining completely general configurational expansions based on arbitrary determinantal configuration lists. While based on the determinantal ordering scheme of Knowles and Handy, our direct CI algorithm differs from previous ones by the use of the Slater–Condon expressions in direct conjunction with single and double replacements. A full, as well as a completely general selected, CI program has been implemented. With it, full configuration spaces of Ne, C₂, CO and H₂O with up to about 40 million determinants have been investigated. It has been found that, in all cases, fewer than 1% of the configurations in a natural-orbital-based configuration expansion reproduce the exact results within chemical accuracy. Received: 19 December 2000 / Accepted: 9 May 2001 / Published online: 11 October 2001