Convergence properties of Hartree–Fock SCF molecular calculations

Hartree-Fock equations are viewed as nonlinear algebraic equations that can be solved iteratively. Provided we assume the existence of a solution, valuable properties of convergence may be assessed. The close connection between convergence of the SCF procedure and stability properties of the solution is shown from a nonapproximate standpoint. The convergence features of level-shifting convergence-forcing techniques are analyzed. The connection between this nonlinear algebraic approach and the related gap equation is displayed and the example of the restricted Hartree-Fock hydrogen molecule is discussed.     

Genetic algorithms: A robust scheme for geometry optimizations and global minimum structure problems

A Genetic Algorithm for Geometry Optimizations (GALGO) program has been developed to study the efficiency of this method of finding global minimum structures. Using a semiempirical tight-binding potential, the behavior of different genetic algorithm (GA) operators has been tested for the linear chain isomer of a C₈ cluster. An optimum set of parameters for the GA operators is proposed for this problem and afterward is used to obtain the global minimum structure of rare-gas atomic clusters of up to 13 atoms using the 12–6 Lennard-Jones interatomic pair potential. © 1995 by John Wiley & Sons, Inc.     

A complete shape characterization for molecular charge densities represented by Gaussian-type functions

An algorithm for a detailed 3-D characterization of the shapes of molecular charge distributions is implemented, tested and applied for a family of AB₂ molecules. The characterization is performed by computing a number of topological invariants (“shape groups”) associated with a continuum of molecular surfaces: the complete family of all electronic isodensity contours for the given molecules. These shape groups (the homology groups of truncated surfaces derived from isodensity contours) depend continuously on two parameters: a density value defining the density contour, and a reference curvature value, to which the local curvatures of the isodensity contours are compared. The electronic charge distribution is modeled by means of Gaussian-type functions. The method employs an explicit form of the charge density function in order to compute the curvature properties for the molecular surfaces analytically, from which the shape groups are derived by the algorithm. No visual inspection is required for the characterization and comparison of shapes of molecular charge densities, as these are done algorithmically by the computer. However, visual inspection of the results of the shape analysis is a possible option. For a given molecule, in a given nuclear configuration, the technique provides a two-dimensional shape map, displaying the distribution of shape groups as a function of the local curvature and the level set value (the value of the charge density at the contour). The computer program GSHAPE performs the analysis of shape maps automatically. This feature makes it potentially useful in the context of computer-aided drug design, where unbiased, automated shape characterization methods are valuable tools. As examples, several two-dimensional shape maps for simple systems are discussed. The changes induced in these maps by a change in the nuclear geometry, as well as by the changes of the nuclear charge, are also analyzed. The method is applicable to large biomolecules of interest if charge density information is available.     

Chalcogenide Exchange Reaction of [RGa(μ3-Te)]4 with Elemental Sulfur and Selenium: A Density Functional Theory Study

Thermodynamic and mechanistic features of the chalcogen exchange reaction between [RGa( ₃-Te)]₄ and elemental sulfur or selenium have been studied employing density functional theory (DFT) calculations using the BL3YP basis set and Stuttgart pseudopotentials. For [MeGa( ₃-E)]₄ (E=S, Se, Te) the correlation between the calculated parameters and diffraction data for their isolable analogs is greater than 98%. Each step of the conversion of [MeGa( ₃-Te)]₄ to [MeGa( ₃-E)]₄ via [Me₄Ga₄( ₃-Te)_4–x ( ₃-E) _x ] (E=S, Se) is predicted to occur as a series of isolated reactions. The entropy change for each chalcogen exchange is small in magnitude and corresponds to the degree of cage distortion within the cubane molecules. Calculations performed on [MeGa( ₃-Te)]₄...S₈ and [MeGa( ₃-Te)]₄-S suggest that an increase in electrophilicity of the gallium next to a surface bound tellurium may result in nucleophilic cage opening for which intermediate structures are calculated.     

Solid-state versus solution preparation of two crystal forms of [HN(CH2CH2)3NH][OOC(CH2)COOH]2. Polymorphs or hydrogen bond isomers?

The reaction of [N(CH2CH2)3N] with malonic acid [HOOC(CH2)COOH] in the molar 1:2 ratio yields two different crystal forms of the salt [HN(CH2CH2)3NH][OOC(CH2)COOH]2 depending on the preparation technique and crystallization speed: form I, containing malonate anions with intramolecular hydrogen bonds, is obtained by solid-state co-grinding or by rapid crystallization, whereas form II containing intermolecular hydrogen bonds is obtained by slow crystallization. Form I and II do not interconvert, and form I undergoes an order-disorder phase transition on cooling.     

Gold(III) complexes with imidazole,benzoxazole, purine and pyrimidine derivatives

Summary The synthesis and characterization of Au^III complexes with several heterocyclic ligands are reported. The compounds have general formula [AuX₃(L)], where L =N-methylimidazole (N-MeIz),N-ethylimidazole (N-EtIz),N-propylimidazole (N-PrIz), benzoxazole (BO), 2-methylbenzoxazole (2-MeBO), 2,5-dimethylbenzoxazole (2,5-diMeBO), 2-amino-pyrimidine (2-APm), 4(6) -hydroxy-pyrimidine [4(6)-hydrPm] or hypoxanthine (Hypox) and X = Cl or Br. Elemental analysis, conductivity measurements and spectral studies were used for the characterization of the complexes. A square-planar geometry withN-bonded heterocyclic ligands is suggested.     

An algebraic method that includes Gibbs minimization for performing phase equilibrium calculations for any number of components or phases

The most widely used technique for performing phase equilibria calculations is the K-value method (equality of chemical potentials). This paper proposes a more efficient algorithm to achieve the results that includes Gibbs minimization when we know the number of phases. Using the orthogonal derivatives, the tangent plane equation and mass balances, it is possible to reduce the Gibbs minimization procedure to the task of finding the solution of a system of non-linear equations. Such an operation is easier and faster than finding tangents or areas, and appears to converge as fast as the K-value method. Examples illustrate application of the new technique to two and three phases in equilibrium for binary and ternary mixtures.     

Single wall carbon nanotubes density of states: comparison of experiment and theory

We study the electronic structure of a variety of single wall carbon nanotubes and report density of states obtained with the Perdew–Burke–Ernzerhof (PBE) generalized gradient approximation and hybrid PBE0 approximation of density functional theory using Gaussian orbitals and periodic boundary conditions. PBE gives very good results for metallic tubes but the addition of a portion of exact exchange in the hybrid PBE0 functional worsens the agreement between experiment and theory. On the other hand, the PBE0 hybrid significantly improves the theoretical predictions (compared to PBE) for semiconducting tubes.