Representation of square-cell configurations in the complex plane: Tools for the characterization of molecular monolayers and cross sections of molecular surfaces

Two numerical codes, a complex face vector F and a real face vector D are developed for the characterization of square-cell configurations (lattice animals), used for representing the shapes of molecular monolayers and cross sections of molecular surfaces. The real face vector D represents all the intrinsic properties, size, and shape of the lattice animal. The complex face vector F contains complete information about the size, the shape, and also the placement of the particular lattice animal with respect to the lattice. Based on the properties of the face vectors, a method is developed for the classification of similar animals into equivalence classes. The face vector method is proposed for an algorithmic, nonvisual computer analysis of similarity of shapes of molecular monolayers and planar domains of cross sections of molecular surfaces, approximated by lattice animals.     

Algorithms for clustering molecular dynamics configurations

Two traditional clustering algorithms are applied to configurations from a long molecular dynamics trajectory and compared using two sets of test data. First, a subset of atoms was chosen to present conformations which naturally fall into a number of clusters. Second, a subset of atoms was selected to span a relatively continuous region of conformational space rather than form discrete conformational classes. Of the two algorithms used, the single linkage method is inappropriate for this kind of data. The divisive hierarchical method, based on minimizing the difference between cluster centroids and extrema, is successful but also prone to imposing clustering hierarchy where none can be justified. © 1994 by John Wiley & Sons, Inc.     

Stationary molecular wave packets at nonequilibrium nuclear configurations

We study different schemes that allow laser controlled adiabatic manipulation of the bond in diatomic molecules by using sequences of nonresonant time-delayed chirped pulses. The schemes rely on adiabatic passage of the vibrational wave packet by laser-induced potential shaping from the ground electronic state to a laser-stabilized dissociative electronic state by two-photon absorption. The degree of control that is possible over the position (bond length) and width (bond spread) of the vibrational wave packet is compared for the different schemes. The dynamics is analyzed detailing the role of the different control knobs and the conditions that allow or break the adiabatic passage.     

Modification of the superposition of correlated configurations method

Introduction of a modified correlation factor in the place of r eliminates the problem of multiple infinite summations in Hamiltonian matrix elements. Calculations performed for several He states show that the introduction of the modified correlation factor does not change energies of the states by more than 1 cm^?1.     

The consistent force field: Representation of molecular structure by potential energy functions

The principles are outlined, but the presentation concentrates on: the choice of structures on which to optimise; accuracy of post-dicted structure; reliability of pre-dicted structure; model building from graphic data.     

Representation of molecular electrostatic potentials of biopolymer by self‐organizing feature map

The Kohonen self‐organizing map was introduced to map the protein molecular surface features. The protein or polypeptide properties, such as shape and molecular electrostatic potential, can be visualized by self‐organizing map, which was trained by the 3D surface coordinates. Such maps allow the visual comparison of molecular properties between proteins having common topological or chemical features.     

A reassignment of molecular orbital configurations of the electronic states of ScF

Ab initio molecular orbital calculations have been performed on low-lying electronic states of ScF. The calculations suggest a reassignment of the molecular orbital configurations of the lowest lying Φ states, and suggest also that some of the low-lying Π states may not be well described by single configuration wavefunctions.     

Reduced interaction matrix for doubly-excited configurations and the correlation energy by a partitioning method

Analyses of the correlation energy of an N-electron system by Nesbet and Löwdin are extended to obtain a reduced interaction matrix for doubly-excited configurations and an exact expression for correlation energy; the latter is separable in a basis diagonalizing this matrix.     

Determination of molecular properties by the method of moments

The method of moments and the method of least squares is applied to electron scattering on a simple model potential. Some general problems connected with treatment of scattering problems by the method of moments and the method of least squares are discussed. The calculations give an example of the random sampling type error estimates discussed in previous papers of the series, and present a possible way of optimizing nonlinear parameters in the framework of the method of moments and the method of least squares.

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Zusammenfassung Die Momentenmethode und die Methode der kleinsten Quadrate wird auf die Elektronenstreuung an einem einfachen Modellpotential angewandt. Einige allgemeine Probleme bei der Anwendung dieser beiden Methoden auf Streuprobleme wurden diskutiert. Die Berechnungen geben ein Beispiel der Fehlerabschätzung vom Stichproben-Typ, der in vorhergehenden Artikeln dieser Serie untersucht wurde; sie stellen eine Möglichkeit der Optimierung nicht-linearer Parameter bei den genannten zwei Methoden dar.

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Résumé La méthode des moments et la méthode des moindres carrés sont appliquées à l'étude de la diffusion électronique sur un potentiel modèle simple. Discussion de certains problèmes généraux liés à l'emploi de ces méthodes à l'étude de la diffusion. Les calculs donnet un exemple de l'estimation d'erreur par échantillonage discutée dans les articles précédents, et présentent une méthode pour optimiser des paramètres non linéaires dans le cadre des méthodes des moments et des moindres carrés.

     

Determination of molecular properties by the method of moments

Basic principles of a possibility of simplifying the unrestricted spin-projected Hartree-Fock equations by means of the method of moments are outlined.     

Determination of molecular properties by the method of moments

Some precautions needed in the choice of weight functions when calculating wave functions by the method of moments are analysed. It appears that an important criterion for good weight functions is that the difference between the total and the truncated overlaps (both defined in the paper) be high.The method of moments is applied to wave functions involving Hylleraas-type correlation factors using weight functions made up of products of single-particle orbitals. The aim of the calculations is partly to test the criteria for good weight functions, partly a preparation of more extended calculations of a similar type.The new name of the institute is: Computer Application Research and Development Center of the Chemical Industries.     

Atomic and molecular quantum mechanics by the path integral molecular dynamics method

The quantum path integral molecular dynamics method was applied to studies of excess electron localization by a Na⁺ ion and by a NaCl molecule. Spatial and energetic characterization of the ground state of the excess electron compare favorably with results of model potential calculations for Na and with SCF Cl calculations for NaCl⁻.     

The fruitful introduction of chirality and control of absolute configurations in molecular magnets

In this critical review, it is shown how the introduction of chirality and the control of the absolute configurations of chiral elements in molecular magnets allow obtaining enantiopure chiral magnets (ECM), an archetype of multifunctional materials. This task has been recognised as a major challenge for both chemists and physicists of molecular magnetism. To reach this goal, the former have combined the rational approaches towards molecular-based magnets and of enantiopure metal-organic frameworks. They have used enantiopure stable radicals, ligands from the chiral pool, enantiopure coligands associated with achiral connectors or enantioselective self-assembly to successfully reach their synthetic targets. They were motivated by the will to obtain suitable systems for the experimental demonstration of the influence of enantiomeric purity on the physico-chemical properties. This influence can be found in the magnetic properties themselves but, most interestingly, in the coexistence and interaction between the properties arising from controlled non-centrosymmetry. Thus the combination of natural circular dichroism, second harmonic generation or ferroelectricity with long-range magnetic ordering can give birth to new properties like magneto-chiral dichroism, magnetisation induced second harmonic generation or multiferroicity. The two former synergetic effects have already been demonstrated in enantiopure chiral magnets. The third one remains a challenging target that can be reached by adapting strategies developed towards enantiopure molecular ferroelectrics (119 references).     

Calculation of molecular energies by atom-bond electronegativity equalization method

The atom-bond electronegativity equalization method (ABEEM), based on the equalization of the “effective electronegativity” of an atom or a bond in a molecule, allows the direct calculation of the charge distribution and the molecular electronegativity of a large molecule. We now demonstrate how the another important quantity, the total molecular energy, can be computed directly and rapidly. It is shown that, based on the ABEEM, the corresponding ab initio values of the total molecular energy can be reproduced with very satisfactory accuracy. In addition, it has been found that in the expression of the energy functional E[ρ] of the ABEEM, the charge-dependent term C correlates quite well with the total molecular bonding energy.     

Nonadiabatic treatment of molecular systems by the wavepackets method

We have already developed the many-electron wavepackets (MEWP) method in order to study the dynamics and electronic structure of molecular systems. We extended the MEWP method to study the nonadiabatic effects and formulated a nonadiabatic molecular theory, where both electron and nucleus are treated equivalently. Then we applied our method to the isotope series of hydrogen molecule i.e., H₂, HD, and D₂, and calculated the total energy and the average distance between nucleus-nucleus, electron-electron, and nucleus-electron in order to analyze numerically the nonadiabatic effect in the molecule. Finally we calculated the real-time evolution of the polarization by means of Chebyshev scheme; and by Fourier transforming this, we found out the excitation spectrum of the system, which corresponds to the electronic excitation and the nuclear vibrational frequency. © 1996 John Wiley & Sons, Inc.