Multiple stationary point representations in MC SCF calculations

By using a complete second-order Newton-Raphson multiconfigurational self-consistent field (MC SCF) procedure combined with the Fletcher restricted step constraint algorithm and a modification of the surface walking procedure of Simons et al., an MC SCF energy hypersurface at fixed geometry has been examined in considerably more detail than had been done previously. By calculational example, it is shown that there may exist several MC SCF stationary points which fulfill all four structural criteria we require of a state for being a “good” representation of an exact state. The problem with the existence of several stationary point solutions may be reduced if care is taken in the selection of the MC SCF configuration space. Calculational examples also demonstrate that near-lying stationary points exist which fulfill some, but not all, of these four structural criteria. Hence, stationary points should be obtained with a global MC SCF method which automatically eliminates convergence to as many as possible of these unwanted stationary points. Upon convergence, structural criteria which are not automatically fulfilled should be examined in detail.     

Automerization of pyrene a test for the mechanism of naphthalene automerization

A ¹³C-labeling experiment has revealed the scrabling or carbon atoms in pyrene at hight temperature (eq 3); comparison between the rate of this process and the rate of naphtalene automerization (eq 1) provides evidence against one plausible mechanism for the latter reaction.     

Exponentially Long Equilibrium Times in a One-Dimensional Collisional Model of Classical Gas

Around 1900, J. H. Jeans suggested that the abnormal specific heats observed in diatomic gases, specifically the lack of contribution to the heat capacity from the internal vibrational degrees of freedom, in apparent violation of the equipartition theorem, might be caused by the large separation between the time scale for the vibration and the time scale associated with a typical binary collision in the gas. We consider here a simple 1D model and show how, when these time scales are well separated, the collisional dynamics is constrained by a many- particle adiabatic invariant. The effect is that the collisional energy exchanges betgween the translational and the vibrational degrees of freedom are slowed down by an exponential factor (as Jeans conjectured). A metastable situation thus occurs, in which the fast vibrational degrees of freedom effectively do not contribute to the specific heat. Hence, the observed freezing out of the vibrational degrees of freedom could in principle be explained in terms of classical mechanics. We discuss the phenomenon analytically, on the basis of an approximation introduced by Landau and Teller (1936) for a related phenomenon, and estimate the time scale for the evolution to statistical equilibrium. The theoretical analysis is supported by numerical examples.     

De novo generation of molecular structures using optimization to select graphs on a given lattice

A recurrent problem in organic chemistry is the generation of new molecular structures that conform to some predetermined set of structural constraints that are imposed in an endeavor to build certain required properties into the newly generated structure. An example of this is the pharmacophore model, used in medicinal chemistry to guide de novo design or selection of suitable structures from compound databases. We propose here a method that efficiently links up a selected number of required atom positions while at the same time directing the emergent molecular skeleton to avoid forbidden positions. The linkage process takes place on a lattice whose unit step length and overall geometry is designed to match typical architectures of organic molecules. We use an optimization method to select from the many different graphs possible. The approach is demonstrated in an example where crystal structures of the same (in this case rigid) ligand complexed with different proteins are available.     

The trust-region self-consistent field method in Kohn-Sham density-functional theory

The trust-region self-consistent field (TRSCF) method is extended to the optimization of the Kohn-Sham energy. In the TRSCF method, both the Roothaan-Hall step and the density-subspace minimization step are replaced by trust-region optimizations of local approximations to the Kohn-Sham energy, leading to a controlled, monotonic convergence towards the optimized energy. Previously the TRSCF method has been developed for optimization of the Hartree-Fock energy, which is a simple quadratic function in the density matrix. However, since the Kohn-Sham energy is a nonquadratic function of the density matrix, the local energy functions must be generalized for use with the Kohn-Sham model. Such a generalization, which contains the Hartree-Fock model as a special case, is presented here. For comparison, a rederivation of the popular direct inversion in the iterative subspace (DIIS) algorithm is performed, demonstrating that the DIIS method may be viewed as a quasi-Newton method, explaining its fast local convergence. In the global region the convergence behavior of DIIS is less predictable. The related energy DIIS technique is also discussed and shown to be inappropriate for the optimization of the Kohn-Sham energy.     

Smooth interpolation,Fourier transformation,and two-center overlap integrals for numerical atomic orbitals

A smooth interpolation method for the calculation of Fourier transforms of numerical atomic orbitals is presented and the method is used to calculate two-center overlap integrals. Examples applying various definitions of smoothness are given.     

Geometrical derivatives of dipole moments and polarizabilities

Molecular dipole moments and polarizabilities, as well as their geometrical derivatives, are given analytical expressions for multiconfiguration self-consistent-field and configuration interaction wavefunctions. By considering the response of the electronic wavefunction induced by electric field and geometrical displacement terms in the Hamiltonian, the response of the total electronic energy to these terms is analyzed. The dipole moment and polarizability are then identified through the factors in the energy which are linear and quadratic in the electric field, respectively. Derivatives with respect to molecular deformation are obtained by identifying factors in these moments which are linear, quadratic, etc., in the distortion parameter. The analytical derivative expressions obtained here are compared to those which arise through finite-difference calculations, and it is shown how previous configuration-interaction-based finite difference dipole moment and polarizability derivatives are wrong. The proper means of treating such derivatives are detailed.     

A numerically stable procedure for calculating Møller-Plesset energy derivatives,derived using the theory of Lagrangians

Summary When Møller-Plesset energy derivatives are determined in the canonical Hartree-Fock basis, singularities or instabilities may arise due to degeneracies among the occupied or unoccupied orbitals. If a non-canonical basis is used these singularities disappear. Numerically stable expressions are presented for the molecular gradient and Hessian of the second-order Møller-Plesset energy, obtained by differentiating a fully variational Lagrangian of the energy constructed in a non-canonical representation. By using a non-canonical representation, singularities and instabilities are avoided, and the variational property of the Lagrangian ensures that Wigner's 2n + 1 rule is satisfied for the orbital derivatives and that the multipliers satisfy the stronger 2n + 2 rule. It is shown that the most expensive step in the calculation of the Hessian scales as Mn ₄o, where M is the number of independent Cartesian distortions, n the total number of orbitals, and o the number of occupied orbitals.     

Adsorption of ions to the surface of dilute electrolyte solutions: the Jones-Ray effect revisited

The controversial observation of a minimum in the surface tension of dilute aqueous electrolyte solutions by Jones and Ray in the 1930s is confirmed by new resonance-enhanced second harmonic generation (SHG) experiments demonstrating surface enhancement of simple inorganic anions in the same concentration range. New experiments show that the quadruply charged ferrocyanide, Fe(CN)(6)(4-), anion is not surface active at high concentrations, as expected, but at dilute concentrations, the anion is strongly attracted to the interface with a Gibbs free energy of adsorption of -6.8 kcal/mol. Using this value, the original Jones and Ray data are fit to a simple model of the surface tension with qualitative agreement, although better agreement is found for all 13 Jones and Ray salts with an even stronger surface adsorption.