Correlation hole for an exactly solvable problem

The probability distribution of the interparticle distance is obtained for the N-body boson problem where the potential is an attractive delta function. This is done for both the exact wave function and the Hartree wave function allowing the calculation of the correlation hole.     

Perturbation and SCF calculations for excited states

One can treat the linear variation calculation by the perturbation expansion; on the other hand, one can also relate the perturbed wave function for the mth state to the mth eigenvector and justify the upper bound nature of the perturbation calculations for excited states. One can also associate a special type linear variation wave function to the SCF calculation. The upper bound nature of the excited-state SCF calculation can then be accessed by the help of this special wave function.     

New approach to calculation of the leaky aquifer function

The leaky aquifer function W(x,y), an incomplete Bessel function which has had application in hydrology, is now also arising in electronic-structure calculations on periodic systems. This work presents an expansion which improves the efficiency of calculation of W in the range where x and y are comparable and both are larger than unity. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 913–916, 1997     

Theory of the excitation spectrum of nondiagonal disordered systems

The spectrum of a two-component solid solution with a nondiagonal disorder is studied in the framework of the average T matrix method. For a one-dimensional system in the nearest-neighbor approximation the criteria for the system parameters are given such that at an in-band resonance, one or two “impurity bands” may be realized, and the corresponding model calculation is performed. In the single-site approximation an expression of the self-energy part of a nondiagonal disordered system Green's function is found taking into account multiple occupancy corrections. The possibility of using it to describe a disordered system excitation spectrum and the calculation of state density moments are discussed.     

Addendum to “variational principle for obtaining approximate analytical solutions of the temperature-perturbed Thomas–Fermi equation for compressed atoms”

In the present work the total energy of a Ne atom at T = 0 K is calculated as a function of a spherical container radius. The calculation is based on the Thomas–Fermi (TF ) equation, which is solved approximately by an equivalent variational principle. The effect of an approximate exchange correction on the variational TF energy values is investigated.     

“Spectroscopic” Calculations of CH Bond Dissociation Energies for Ethane, Propane, Butane, Isobutane, Pentane, Hexane, and Neopentane Using Fundamental Vibration Frequencies

The fundamental spectrum and the parameters of the potential function of a number of saturated hydrocarbon molecules are calculated in an anharmonic approximation. The calculation is performed by the variational technique using a minimal Morse-harmonic basis. The potential function is taken as the sum of the Morse function for CH bonds and the harmonic function for the skeletal and deformation vibrations. The initial approximation for the potential function is found by ab initio calculations in a 6-31G basis and refined by solving the inverse problem. The calculated CH bond dissociation energies depend significantly on the molecular structure and on the position of CH bonds in the molecule. These energies correlate well with the experimental cleavage energies of these bonds. The changes in the dipole moment of the molecule induced by vibrations were found by ab initio calculations in a 6-31G basis. The calculated IR transmission curves are in good agreement with the experimental curves.     

Global optimization using bad derivatives: Derivative-free method for molecular energy minimization

A general method designed to isolate the global minimum of a multidimensional objective function with multiple minima is presented. The algorithm exploits an integral “coarse-graining” transformation of the objective function, U, into a smoothed function with few minima. When the coarse-graining is defined over a cubic neighborhood of length scale ϵ, the exact gradient of the smoothed function, 𝒰_ϵ, is a simple three-point finite difference of U. When ϵ is very large, the gradient of 𝒰_ϵ appears to be a “bad derivative” of U. Because the gradient of 𝒰_ϵ is a simple function of U, minimization on the smoothed surface requires no explicit calculation or differentiation of 𝒰_ϵ. The minimization method is “derivative-free” and may be applied to optimization problems involving functions that are not smooth or differentiable. Generalization to functions in high-dimensional space is straightforward. In the context of molecular conformational optimization, the method may be used to minimize the potential energy or, preferably, to maximize the Boltzmann probability function. The algorithm is applied to conformational optimization of a model potential, Lennard–Jones atomic clusters, and a tetrapeptide. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1445–1455, 1998     

Degrees of Chirality in Helical Structures

Long helical structures occur in both natural and synthetic polymers. Their “degree of chirality” is quantified through the calculation of an overlap‐based chirality index and an infinite hierarchy of pseudoscalar parameters. It is shown that these quantities are related, since they may be constructed from a common set of cylindrical Fourier coefficients. The formal analysis is illustrated by the application to helical ribbons. It is found that the chirality of helical ribbons is a monotonically increasing function of the ratio h/a and a decreasing function of the ratio τ/a, where h and a are the pitch and the radius of the helix, whereas τ is the height of the ribbon. Chirality achieves a maximum asymptotic value as h → ∞.     

Representations of Shavitt Graphs Within the Graphical Unitary Group Approach

The Shavitt graph is a visual representation of a distinct row table (DRT) within the graphical unitary group approach. The DRT is a compact representation of the entire configuration state function expansion space within a molecular electronic structure calculation. Each node of the graph is associated with an integer triple (a _k,b _k,c _k). These integers may be mapped to other quantum numbers, including the number of orbitals, number of electrons, and spin quantum number, and used to display Shavitt graphs in various ways that emphasize different aspects of the expansion space or that reveal different aspects of computed wave functions. The features of several graph density plots are discussed, including electron–hole symmetries and the bonding–antibonding wave function character. © 2019 Wiley Periodicals, Inc.     

Thec logc contribution to the electrolyte conductance and Onsager's reciprocal relation

The differential equations and the boundary conditions for the nonequilibrium binary distribution function of an unsymmetrical binary electrolyte are derived from the Ebeling-Falkenhagen continuity equation. The connection between the Onsager reciprocal relation and the binary distribution functions is shown. Further, Feistel's result for thec logc contribution to the conductance is extended to unsymmetrical binary electrolytes. The reason for the difference between Feistel's and Chen'sc logc term is explained, and the significance of Onsager's reciprocal relation for the calculation ofc logc and higher-concentration contributions of the conductance is discussed.     

A general ab initio molecular multi-configuration self-consistent field algorithm

The ab initio multiconfiguration self-consistent-field (MC SCF ) techniques and computer programs of Basch [1, 2] and the ab initio configuration interaction (CI ) techniques and programs of Whitten and Hackmeyer [3] have been combined and generalized to form a general technique and program to yield optimized ab initio MC SCF wavefunctions for any set of Slater determinants. The Slater determinants are read in as input data to the program along with the spin parity that is being considered (optional) and the program successively does the CI calculation and one iteration of the SCF calculation, constructing the proper Fock–Hamiltonians by examining the set of Slater determinants and their CI coefficients. The Fock–Hamiltonian matrices are calculated and diagonalized in succession, a single two-dimensional array being used to store these matrices. The basis function integrals are read from a tape only once during each MC SCF iteration (one MC SCF iteration = a CI calculation followed by one iteration of the SCF calculation).     

Small-angle light scattering by random assemblies of incomplete spherulites. I. Sheaflike textures

The calculation of the scattering from a sheaflike sector of a two-dimensional spherulite has been carried out as a function of the apex angle of the sector. It is found that while for a complete spherulite the H_v scattered intensity is zero at zero scattering angle, there is an increasing intensity of scattering at 0° as the sector angle narrows. For very small values of the sector angle, the scattering becomes similar to that of a rod, with the exception that a scattering maximum is still seen at an angle close to that at which the spherulite scattering maximum occurs. The predictions of the model compare favorably with the scattering patterns observed for polymers in early stages of spherulitic growth.     

A State-dependent Division Scheme for the Potential of Simple Fluids

Abstract

A new division scheme for the pair potential into long-range and short-range parts is presented, which takes account of the dependence on the density and makes possible the extraction of the bridge function B(r) in the core region. The calculation of the correlation functions is carried out with the hybridized mean spherical approximation (HMSA). As attested by the comparison with the simulation results, HMSA used with this potential separation is suitable to produce accurate bridge function and pair correlation function for the Lennard-Jones fluid.     

Simple evaluation of Franck–Condon factors and non‐Condon effects in the Morse potential

The calculation of Franck–Condon factors between different 1‐D Morse potential eigenstates using a formula derived from the Wigner function is discussed. Our numerical calculations using a simple program written in Mathematica are compared with other calculations. We show that our results have a similar accuracy as those calculations performed with more sophisticated methods. We discuss the extension of our method to include non‐Condon effects in the calculation. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem 88: 280–295, 2002     

Study of the thermooxidative degradation kinetics of poly(tetrafluoroethene) using iso-conversional calculation procedure

The thermooxidative degradation kinetics of poly(tetrafluoroethene) (PTFE) in air flow has been studied at different heating rates (6, 10, 12 and 15 K min⁻¹) by non-isothermal differential thermal analysis (DTA). Six calculation procedures based on single TG curves and iso-conversional method, as well as 27 mechanism functions were used. The comparison of the results obtained with these calculation procedures showed that they strongly depend on the selection of proper mechanism function for the process. Therefore, it is very important to determine the most probable mechanism function. In this respect the iso-conversional calculation procedure turned out to be more appropriate. In the present work, the values of apparent activation energy E, pre-exponential factor A in Arrhenius equation, as well as the changes of entropy ΔS ^≠, enthalpy ΔH ^≠ and free Gibbs energy ΔG ^≠ for the formation of the activated complex from the reagent are calculated. All calculations were performed using programs compiled by ourselves.     

Biogas Production Potential and Kinetics of Microwave and Conventional Thermal Pretreatment of Grass

Pretreatment methods play an important role in the improvement of biogas production from the anaerobic digestion of energy grass. In this study, conventional thermal and microwave methods were performed on raw material, namely, Pennisetum hybrid, to analyze the effect of pretreatment on anaerobic digestion by the calculation of performance parameters using Logistic function, modified Gompertz equation, and transference function. Results indicated that thermal pretreatment improved the biogas production of Pennisetum hybrid, whereas microwave method had an adverse effect on the performance. All the models fit the experimental data with R ² > 0.980, and the Reaction Curve presented the best agreement in the fitting process. Conventional thermal pretreatment showed an increasing effect on maximum production rate and total methane produced, with an improvement of around 7% and 8%, respectively. With regard to microwave pretreatment, maximum production rate and total methane produced decreased by 18% and 12%, respectively.     

Exact ground state for a Herndon–Simpson model via resonance–theoretic cluster expansion

The Herndon–Simpson model for a particular catacondensed polyphene chain is considered as a nontrivial many-body Hamiltonian, defined on a space with a basis of orthonormal Kekulé structures. An Explicitly correlated cluster expanded resonance–theoretic wave function is described for this model, and its quality is judged by calculation of the standard deviation for the energy expectation. The quality is found to be high. Indeed, for a particular parameter ratio within the range of experimental interest, the wave function ansatz is found to be exact. This very accurate solution is then used to gauge the quality of the common ansatz with equally weighted Kekulé structures, and it is found to be reasonably good.     

Dynamical properties of S(3P) + HD reaction on 13A″state and their quantum wavepacket calculation

The time‐dependent wavepacket method is used to study the reaction dynamics of S(³P) + HD (v = 0, 1, 2) on the adiabatic 1³A″ potential energy surface constructed by Han and coworkers [J. Chem. Phys. 2012, 136, 094308]. The reaction probabilities and integral cross sections as a function of collision energy are obtained and discussed. The results calculated by using the CC and the CS approximation have been compared, which suggests that for this direct abstraction reaction, the cheaper CS approximation calculation is valid enough in the quantum calculation. The investigation also shows that the reaction probabilities and integral cross sections tend to increase with collision energy. By analyzing the v‐dependent behavior of the integral cross sections, the significant effect of the vibrational excitation of HD is found. Also found in the calculation is a significant resonance feature in the reaction probabilities versus collision energy. © 2014 Wiley Periodicals, Inc.     

Energy deposition mechanisms and biochemical aspects of DNA strand breaks by ionizing radiation

A theoretical model based on physical, chemical, and biochemical mechanisms has been presented to evaluate the yields of DNA strand breaks (single and double) as a function of linear energy transfer (LET ) or ?dE/dx. Energetic heavy charged particles are considered explicitly to provide a general theory for low- as well as for high-LET radiation. There are three main features of the calculation: (a) track structure considerations for the energy deposition pattern, (b) three-dimensional structure of DNA molecules to provide information on the exact location of damage, and (c) a Monte-Carlo scheme to simulate the diffusion processes of water radicals. To avoid the complexities of a cellular medium, an aqueous solution of DNA is considered in the calculation. When the results of the calculations are compared with experimental measurements of the yields of strand breaks in mammalian DNA (exposed in a cellular complex), reasonable agreement is obtained. However, only those experimental data have been compared where there were no enzyme repair processes. The method of calculation has also been extended to study breaks in higher-order structures of DNA molecules such as chromatin. Specific limitations of the present model have been pointed out for making further improvements.     

Vibrational energy transfer in near resonance due to dipole–dipole interactions

The contribution of long-range forces to the observed rates of V → V energy transfer processes has been studied. The theoretical model uses the first order perturbation approximation to generate a probability function, with the dipole–dipole perturbing potential as given by Margenau: V_if = [(1/6)^1/2_{μ1 · μ2}]R^?3. The probability function derived is shown to be a strong function of the energy mismatch between the IR bands of the colliding molecules. The calculation emphasizes the importance of rotational state population effects, the most important J states being those which minimize the energy mismatch. A complete analysis of energy transfer between CO(v) and COS(000) where v = 1,2, ? 13 is presented. The calculation reveals the importance of combination bands in the energy transfer mechanism of polyatomics. The temperature dependence for near-resonant processes is also studied and the importance of the V → R energy transfer leads to the classification of ω₀ (band-center energy mismatch) into three categories small, medium, and large, according to the temperature dependence that the corresponding processes exhibit. The predictions of the theoretical model are compared to experimental data for the same system.