The frost model and perturbation theory

Symmetry-adapted double perturbation theory is applied to the Frost model. Even when used only through zero-order in the correcting ”internal“ perturbation it gives values of average electric polarizabilities in fair agreement with experiment. If the model is extended by employing clliptical gaussians rather than spherical ones, the anisotropy of the molecular polarizability can be determined.     

The modified Hartree–Fock self-consistent field equation

A one-electron correlation operator is introduced into the Hartree–Fock self-consistent field equation. The correlation operator is derived from the second-order perturbation theory. Energies of atomic and molecular systems calculated from this modified Hartree–Fock equation are equal to that from second-order perturbation of Hartree–Fock equation. The modified equation can also be solved self-consistently by the LCAO approximation. We also presented the modified expressions for other operators.     

The diagrammatic perturbation theory for the interaction of two molecular systems treated by the extended Hückel theory

The general diagrammatic perturbation theory for the interaction of two molecular systems treated by the extended Hückel method is elaborated.     

Models for strongly polar liquids. The influence of molecular polarizability

A recently proposed thermodynamic perturbation approach is used to estimate the contribution of molecular polarizability to the average dipole moments and thermodynamic properties of model HF and HC1 liquids.     

Thermodynamics of the polarizable stockmayer fluid

Pressure and internal energy of a fluid composed of polarizable Stockmayer molecules have been calculated by a molecular dynamics computation as well as by thermodynamic perturbation theory. It is found that the effect of molecular polarizability is underestimated by perturbation theory.     

The molecular basis of vision: a reply to a comment

Electrical polarizability tensors and dipole noments for closed-shell molecules are calculated using a self-consistent field perturbation theory in which each molecular orbital is written as a linear combination of electric-field-dependent atomic functions Values calculated using different sets of atomic functions are compared with experiment and with previous theoretical work.     

Relativistic perturbation theory of chemical properties

Summary Double perturbation theory is developed for the case where relativity is one perturbation and the other perturbation describes a chemically interesting observable such as molecular structure, force constant or polarizability. Relativity is treated according to Rutkowski's nonsingular perturbation approach. Expressions for four-component and two-component wave-functions and for the Hartree-Fock approximation are given. The method is applied analytically to the relativistic corrections of the electric polarizability of the H atom, and algebraically to the potential curve of the H ₂ ⁺ molecule. Second and third order double perturbation interchange relations are numerically verified. In the present formalism, terms up to third order are needed to qualitatively understand the relativistic corrections of chemical observables.     

The hydrogen perturbation in molecular connectivity computations

A new algorithm for the delta(v) number, the basic parameter of molecular connectivity indices, is proposed. The new algorithm, which is centered on graph concepts like complete graphs and general graphs, encodes the information of the bonded hydrogen on different atoms through a perturbation parameter that makes use of no new graph concepts. The model quality of the new algorithm is tested with 13 properties of seven different classes of compounds, as well as with composite classes of compounds with the same property and with composite properties of the same class of compounds. Chosen properties and classes of compounds display different percentage of bonded hydrogen atoms, which allow a checking of the importance of this parameter. A comparison is drawn with previous results with zero contribution for the hydrogen perturbation as well as among results obtained by changing the number of compounds of a property but keeping constant the percentage of hydrogen atoms. Results underline the importance of the property as well as the importance of the number of compounds in determining the level of the hydrogen perturbation. Molecular connectivity terms are in some cases more critical than the combination of indices in detecting the perturbation introduced by the hydrogen atoms.     

Theoretical development of a Gaussian potential function in the description of the radial portion of isotropic bending vibrations

Analysis of a Gaussian potential function suitable for modeling degenerate bending vibrations in weakly bound molecular complexes is presented. Approximate eigenvalues and eigenvectors are obtained by application of perturbation theory. Comparison to the “exact” eigenvalues obtained via a numerical solution shows that the first- and higher-order perturbation corrections are consistent with variational principles.     

The general theory of irreversible processes in solutions of macromolecules

The general theory of irreversible processes in solutions of macromolecules, previously formulated by the author, is reviewed. The theory is based upon the Oseen method for determining the perturbation in the hydrodynamic flow pattern produced by the frictional forces exerted by the macromolecule on the solvent, and on a generalized theory of Brownian motion in molecular configuration space. Applications of theory to viscoelastic behavior, flow birefringence, and the Kerr effect, and to dielectric dispersion are presented in outline.     

A direct approach to study radiative emission from triplet excitations in molecular semiconductors and conjugated polymers

Using the recently discovered time-dependent spin-orbit-photon interaction operator and first order perturbation theory, the rate of spontaneous emission from triplet excitations is derived within the two-level approximation for organic molecular solids and conjugated polymers. The calculated rates and corresponding radiative lifetimes agree very well with the known experimental results. Present results are compared with those obtained through the traditional approach of the second order perturbation theory in some molecular crystals and found to be in better agreement with experiments.     

On the use of symmetry in first-order perturbed Hartree–Fock theory

A method for the determination of the symmetry of first-order vectors in Hartree–Fock perturbation theory is developed. This leads to the definition of symmetry-adapted basis vectors to be employed at first order in the perturbation. It is shown that computer time can be saved, to some extent, in the calculation of second-order properties, by exploiting molecular symmetry. Specific examples are given for methane, ammonia, and water.     

Non-empirical molecular orbital theory of the electronic structure of molecular crystals

A non-empirical molecular orbital treatment of molecular crystals, based on SCF perturbation theory and matrix partitioning methods is presented.     

Errors in the calculations of first-order and second-order energy perturbations

We consider the calculation of first-order and second-order atomic and molecular properties from approximate ground-state wave-functions by using variational procedures for solving the first- and second-order perturbation equations. We evaluate the errors in the final results due to the error in the unperturbed wave-function and to the errors caused by the approximations in solving the perturbation equations. By combining slightly different results we can eliminate all first-order errors. Our analysis covers situations where perturbation expansions of the error in the ground-state wave-function are not feasible and it includes the effects due to approximations in solving the perturbation equations.     

Theoretical Study on Divergence Problems of Single Reference Perturbation Theories

Divergences of the single reference perturbation theories due to the addition of diffusion basis functions have been investigated for both closed-shell and open-shell molecular systems. It is found that the oscillatory range of perturbation energies of open-shell systems increases as the spin multiplicity of systems changes from 2 to 4. Feenberg transformation is exploited to treat the divergence problems. It is found numerically that within the interval of Feenberg parameter there exists a minimum perturbation order at which the perturbation series become convergent. It is also found for the open-shell systems that the magnitude of the corresponding Feenberg parameter becomes larger as the spin multiplicity of the system of interest changes from 2 to 4.     

Electronic aspects of enzymatic catalysis

Enzymes are large aperiodic structures and this hinders both ab initio molecular orbital and Bloch-type band theory of calculations. A frontier orbital perturbation theory of catalysis is applied to enzymes. Reasons are given for proposing that the induced-fit conformational changes, essential to enzymatic catalysis, leads to an increase in the electronic eigenvalue density at the active site, enhancing the necessary catalytic orbital perturbation.     

The calculation of ground and excited doublet state molecular polarizabilities by the CNDO/S-CI method

The calculation of ground and excited state molecular polarizabilities by the CNDO/S-CI method has been extended to include doublet states. As incorporated, the second order perturbation scheme usually predicts average state polarizabilities of molecular cation ground states to be lower than the corresponding singlet ground states. Average anion polarizabilities are generally found to be higher than those of the corresponding singlet states. Excited doublet state polarizabilities are presented for the molecular cation of formaldehyde, benzene, 1,3,5-trans-hexatriene, and naphthalene. Due to the unavailability of experimental data it is currently impossible to assess appropriately the quality of these results.     

One-electron properties of molecules calculated using second-order multireference perturbation theory

A new form of second-order multireference perturbation theory coupled with finite-field perturbation theory is applied to evaluate some one-electron molecular properties. Several possible definitions of the zeroth-order Hamiltonian are considered and results tested against bench-mark full CI calculations. © 1995 John Wiley & Sons, Inc.     

Understanding relativistic effects of chemical bonding

To elucidate the physical origin of relativistic changes of molecular properties, exact theorems, perturbation theory, and Hartree-Fock-Slater-Pauli calculations are exploited. The relativistic molecular virial theorem offers insight into the relativistic and nonrelativistic, kinetic, and potential energy contributions to the bond energy. In general, there exist two contributions to the relativistic correction of a molecular property: the relativistic change at the nonrelativistic equilibrium geometry and the change of the nonrelativistic property due to the relativistic change of the equilibrium geometry. Sometimes the first and sometimes the second contribution is the dominant one. Accurate numerical results for H⁺₂-like systems are obtained using direct relativistic double perturbation theory. In some cases, near-degenerate perturbation theory is mandatory. Relativistic changes of chemical bond energies are often proportional to the density change in the K-shell when the bond is formed. Relativistic corrections to many properties (and also to the 1s²-correlation energy) are often proportional to Z²α². © 1996 John Wiley & Sons, Inc.     

Explaining the “large numbers” via a unified (classical) theory of strong and gravitational interactions

An advantage of modified virtual orbitals of Hartree–Fock method is discussed in the calculation of the second-order perturbation energy. All the modified virtual orbitals can be fitted for the intermediate virtual states in the perturbation expansion, only if the molecular orbitals are expanded in terms of infinite basis functions and the set of molecular orbitals is infinite and complete. If the molecular orbitals are expanded in terms of finite basis functions, only the modified virtual orbitals with lower energies are appropriate to describe the intermediate virtual states, but the modified virtual orbitals with higher energies become inadequate. To explain the usefulness of the modified virtual orbitals, the calculation by the modified Hartree–Fock method without CI are compared with the calculation by the traditional Hartree–Fock method with complete CI .