Thermodynamic perturbation theory of simple liquids

It was proven that after averaging over the canonical Gibbs ensemble, the mean perturbation energy was singled out of the classical partition function before the expansion in a series of perturbation theory. Therefore, the term that formally coincides with first order perturbation theory in a decomposition of the Helmholtz free energy bears no relationship to perturbation theory. Then the proper series of the thermodynamic perturbation theory always starts with a second order infinitesimal. Therefore, the wellknown condition of applicability of the thermodynamic perturbation theory, “...the requirement that the perturbation energy per particle be small compared with T...” (L. D. Landau and E. M. Livshits, Statistical Physics, Vol. V, Pt. I), can be substantially weakened. The most important factor for applicability of thermodynamic perturbation theory is the value of many-particle correlations in an unperturbed system, but not the smallness of the perturbation potential.     

Thermodynamic perturbation theory of simple liquids: Monte Carlo simulation of a hard sphere system and the Helmholtz free energy of SW fluids

The Monte Carlo method is used to simulate similar sized hard sphere systems in a wide range of densities (from η 0.005 to 0.530 with a step of η = 0.005). The models are used to calculate the coefficients of the thermodynamic perturbation theory series for SW fluids up to the fourth order. The width of the attraction zone of the SW potential λ is varied from 1 to 2.5 sphere diameters. The analytical expressions approximating the obtained coefficients by polynomials with respect to the variables η and λ are determined. The absolute accuracy of the approximation is estimated to be better than ±0.001. All the necessary data for the calculation of the Helmholtz free energy of SW fluids up to the fourth-order perturbation theory are given.     

Stationary perturbation theory for non-Hamiltonian eigenvalue equations

Second-order perturbation theory is developed for equations of the Klein-Gordon typeK(E, V, ?²) Ψ=0, in which the eigenvalueE occurs in various powers. The result is a simple generalization of Schrödinger's.     

A new single-center perturbation theory for the treatment of simple hydrides

The perturbation expansion of Hartree-Fock potential energy surfaces of simple hydrides in a single-center scale 1/Z-expansion is carried out using diagrammatic methods. Diagrams having the topological structure of third-order diagrams are summed to all orders using an integral equation technique. The resulting one-electron wavefunction is used to generate a resummed perturbation series correct through fourth order.     

Convergence of the perturbation theory expansion for spin-spin coupling constants

The convergence of the full perturbation theory expansion for the Fermi contact term in the spin-spin coupling constant of hydrogen fluoride has been studied. By examining the contribution of higher virtual states as the basis set is expanded to 18 atomic orbitals, it is shown that at this level of approximation the expansion does not converge. The need to also establish convergence before accepting values calculated from configuration interaction wavefunctions is discussed.The Puerto Rico Nuclear Center is operated by the University of Puerto Rico for the United States Atomic Energy Commission under Contract No. AT(40-1)-1833.     

Thermodynamic properties of nitrogen from a perturbation theory for ISM fluids

A first-order Barker-Henderson perturbation theory for interaction-site model (ISM) fluids has been applied to calculate the Helmholtz free energy, entropy and internal energy of liquid nitrogen. Comparison with experiment reinforces the idea that the theory is accurate over a wide range of temperatures and densities corresponding to the liquid state, except for the critical region.     

Thermodynamic perturbation theory for fused sphere hard chain fluids using nonadditive interactions

A model is developed for the equation of state of fused chains based on Wertheim thermodynamic perturbation theory and nonadditive size interactions. The model also assumes that the structure (represented by the radial distribution function) of the fused chain fluid is the same as that of the touching hard sphere chain fluid. The model is completely based on spherical additive and nonadditive size interactions. The model has the advantage of offering good agreement with simulation data while at the same time being independent of fitted parameters. The model is most accurate for short chains, small values of Delta (slightly fused spheres) and at intermediate (liquidlike) densities.     

Thermodynamic analysis of fluorescence enhancement and Quenching theory equations

The action of the three kinds of new third generation cephalosporin-class drugs, cefepime hydrochroride, cefpiramide and ceftizoxime with HSA and BSA was studied at different temperatures through the fluorescence method. First, the binding constants were calculated by using fluorescence quenching and enhancement theoretical equations. Their thermodynamic functions were also calculated. Because the K _A corresponding to the different theoretical equations are not completely the same, the thermodynamic parameters calculated are also different. In this paper, the differences among these thermodynamic data obtained from the different theoretical equations were analyzed and the results show that the thermodynamic data deduced from fluorescence enhancement are more reasonable. Thus, we propose that even when the fluorescence quenching action of the acceptorsubstrate is studied, more realistic data can be obtained by using the fluorescence enhancement equation. __________ Translated from Acta Chimica Sinica, 2007, 65(19): 2109–2116 [译自: 化学学报]     

A real-space perturbation theory for electronic correlation

We introduce a method for treating electronic correlation in which a correlation factor is optimized using Hylleraas variational perturbation theory. The factor is defined by a number of parameters which grows only linearly with system size. We test the theory on two-electron atoms using the shielded-nucleus Hamiltonian at zeroth order, obtaining −2.9035 a.u. for helium. The convergence of the method is investigated, and energies and intracule densities are compared with accurate variational results. The application of the theory to an N-electron problem with a Hartree–Fock Hamiltonian at zeroth order is discussed.     

The relationship between coefficients of expansion and heat capacities of simple metals

The authors of this paper, being intrigued by statements in the literature that the coefficients of expansion of metals are proportional to the heat capacities, have put these statements to the test. This paper shows that the experimental ratios of coefficients of expansion and heat capacities at constant pressure are indeed a constant for each metal over wide temperature ranges and the constants are in fair agreement with the values computed from theory.     

Application of second order BWEN perturbation theory to some simple reactions

The second order Brillouin-Wigner perturbation expansion with the Epstein-Nesbet partitioning is applied to some isomerization and insertion reactions, using the 6-31G^* basis set. BWEN2 is found to be comparable in accuracy with RSMP2 for predictions of energy barriers and isomerization energies.     

Partial summation of various subsets of low-temperature terms to all orders in the direct correlation function based thermodynamic perturbation theory of simple liquids

Various subsets of a new thermodynamic perturbation expansion for simple liquids [PHYSICAL REVIEW E 83, 021203 (2011)] is summed up by a new method to all orders which yield explicit formulas for the structure and thermodynamic of simple fluids. The formulas then have been tested successfully against computer simulations results for hard-core Yukawa potential.     

A constant denominator perturbation theory for molecular energy

A constant denominator perturbation theory is developed based on a zeroth order Hamiltonian characterized by degenerate subsets of orbitals. Such a formulation allows for a decoupling of the numerators of the perturbation sequence, allowing for much more rapid evaluation of the resultant sums. For example, the full fourth order theory can be evaluated as an N ⁶ step rather than N ⁷, where N is proportional to the basis set.Although the theory is general, a constant denominator is chosen for this study as the difference between the average occupied and average virtual orbital energies scaled so that the first order wavefunction yields the lowest possible variational bound. The third order correction then appears naturally as a scaled Langhoff-Davidson correction. The full fourth order with this partitioning is developed. Results are presented within the localized bond model utilizing both the Pariser-Parr-Pople and CNDO/2 model Hamiltonians. The second order theory presents a useful bound, usually containing a good deal of the basis set correlation. In all cases examined the fourth order theory shows remarkable stability, even in those cases in which the Nesbet-Epstein partitioning seems poorly convergent, and the Moller-Plesset theory uncertain.     

Thermodynamic properties of pure liquids within a generalized version of the hole theory

A generalized hole theory for computing the thermodynamic and acoustic properties of liquids and liquid mixtures has been developed. Ultrasonic velocity, isothermal compressibility and thermal expansivity of different pure liquids at 293.15 and 298.15?K are evaluated by using hole theory. The calculated values of ultrasonic velocities, isothermal compressibilities, and thermal expansivities are compared with the experimental findings. A fairly good agreement between experimental and calculated values is observed.     

Self-consistent field equations in the distribution function theory of polymeric liquids

In the distribution function approach to the conformational and thermodynamic properties of polymeric liquids site-site (pair) distribution functions are essential components of the theory. These site-site pair distribution functions are basically mean fields obeying integral equations. In our recent works, a set of self-consistent field equations has been proposed for site-site pair correlation functions which allow us to study conformational and thermodynamic properties of polymeric liquids. In this article, we present a short review of the theory and its applications to a number of aspects of polymeric liquids we have made until now. We also present a self-consistent version of the polymer reference interaction site model where the integral equations for the intramolecular site-site correlation functions are obtained from the Kirkwood hierarchy on the basis of the present theory. The present theory is shown to predict correctly the scaling properties associated with swollen and collapsed polymers in good and poor solvents, respectively. At finite densities, self-consistent solutions of the intra- and intermolecular equations yield the structures and thermodynamics of polymer melts which are favorably compared with Monte Carlo simulation results. Self-consistent theory results are found to be more accurate than the non-self-consistent approaches that use an ideal Gaussian chain conformation distribution function. © 1995 John Wiley & Sons, Inc.     

Bounds for Hartree-Fock perturbation theory

Upper and lower bounds for the second-order energy in both coupled and uncoupled Hartree-Fock perturbation theories are derived. Using these bounds inequalities are derived for the error in the geometric approximation.     

Erratum: Thermodynamic perturbation theory of a dense fluid of polar and polarizable spheres

A method is described for determination of the dissociation energy D₀ for hydrogen bonded dimers B…H-A using only measurements of rotational transition intensities at a single temperature. Application in the particular case HCN…HF gives D₀ = 18.5 ± 1.1 kJ mol^?1. By taking account of the vibrational modes of HCN…HF in the harmonic oscillator approximation, D_e is estimated as 25.6 ± 1.6 kJ mol^?1.     

New finite-difference method for solving the pair radial equations of the many electron perturbation theory

A new convenient and efficient finite-difference (FD ) method is developed for solving the pair radial equations (PRE ) of many electron perturbation theory (MPT ). This method can be interpreted as the FD analog of the well-known Fourier method. The method is used to solve PRE arising in the second order of MPT based on the hydrogenic and Hartree–Fock (HF ) zero approximations. Being very simple programmed our method gives results comparable with the most accurate variational calculations.