Eigenvalues of model Hamiltonian matrices from spectral density distribution moments: The Heisenberg spin Hamiltonian

An approach aimed at approximating the extreme (the lowest and/or the highest) eigenvalues of matrices representing many-electron model Hamiltonians from a knowledge of several spectral density distribution moments is proposed. A detailed discussion of the Heisenberg spin Hamiltonian spectrum is presented as an example of an application. © 1996 John Wiley & Sons, Inc.     

Commutator perturbation method in the study of vibrational–rotational spectra of diatomic molecules

The commutator perturbation method, an algebraic version of the Van Vleck–Primas perturbation method, expressed in terms of ladder operators, has been applied to solving the eigenvalue problem of the Hamiltonian describing the vibrational–rotational motion of a diatomic molecule. The physical model used in this work is based on Dunham's approach. The method facilitates obtaining both energies and eigenvectors in an algebraic way. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 721–726, 2000     

Exact matrix elements for general two-body central-force interactions,expressed as sums of products

ABSTRACT

In a manner similar to but distinct from concurrent tensor efforts in electronic structure, it is shown that the Laplace transform can serve as a generator for a sum-of-products (SOP) form that allows one to write essentially any function of distance between two particles (i.e. any central force potential) as an exact two-body matrix. In particular, exact expressions for the Coulomb, Yukawa and long-range Ewald two-body operators are evaluated in a band-limited (Sinc function) basis. The resultant exact, full-basis, SOP representations for these interaction potentials – acting in conjunction with an external harmonic confining field – are validated via comparison with energy eigenstate solutions obtained via an independent calculation based on separation of variables. The new two-body matrix representations may have substantial impact in any of the many disciplines in which pair-wise central force interactions are relevant – especially, electronic structure and dynamics.     

The influence of (5′R) and (5′S)-5′,8-cyclo-2′-deoxyadenosine for the electronic properties of nucleosides pairs. The theoretical quantum mechanics studies

Oxidatively generated damage to DNA frequently appears in the human genome as the effect of aerobic metabolism or as the result of exposure to exogenous oxidizing agents such as ionization radiation. In this paper, for the first time, the electronic properties of nucleoside pairs containing 5′,8-cyclo-2′-deoxyadenosine (cdA) in their 5′R and 5′S diastereomeric forms (cdA(R)::T and cdA(S)::T) as the simplest model of ds-DNA have been discussed. The following values of the selected electronic parameters, measured in eV, were found for cdA(R)::T, cdA(S)::T, and dA::T, respectively, adiabatic/vertical electron affinity: 0.39/0.24, 0.35/0.18, 0.33/0.21; and adiabatic/vertical ionization potential: 7.27/7.50, 7.7.25/7.49, 7.03/7.27. Moreover, based on the results of the relaxation energy, the presence of cdA(S)::T should provide the highest barrier for electron transfer in ds-DNA. Analyses of hydrogen bond length deviations reveal that the formation of cationic forms results in higher elongation than that of anionic forms. Moreover, during the electron attachment or detachment for the investigated cdA(R)::T, cdA(S)::T, and dA::T nucleoside pairs, the same scheme of changes in hydrogen bond length was noted.      

New mineralogical phases identified by Mössbauer measurements in Morasko meteorite

The 0.9FeTiO₃–0.1Fe₂O₃ solid solution was prepared by solid state reaction with FeTiO₃ and α-Fe₂O₃ powders, and studied by x-ray diffraction, Mössbauer spectroscopy, and vibrating sample magnetometer (VSM). The crystalline structure was found to be single phase rhombohedral structure with lattice constant a?=?5.089 Å and c?=?14.051 Å. Mössbauer spectra of 0.9FeTiO₃–0.1Fe₂O₃ solid solution were taken at various temperatures ranging from 4.5 to 300 K. The anomalous absorption curves at low temperature are observed. Mössbauer spectra at 4.5 K was fitted to four six-line hyperfine pattern with magnetic hyperfine fields H _hf?=?504, 424, 115, and 58 kOe, respectively. At 40 K the spectrum shows the mixture of ferromagnetic six-line pattern and paramagnetic two-line and above 50 K it show asymmetry two-line patterns. The fitted curves at room temperature are obtained by superimposing two doublets corresponding to Fe^2?+ and Fe^3?+. The isomer shift δ and quadrupole splitting ΔE _Q of sample are 0.92 and 0.69 mm/s for Fe^2?+ and 0.14 and ??0.29 mm/s for Fe^3?+, respectively. Corresponding relative absorption subspectral areas are 89.2% for Fe^2?+ and 10.8% for Fe^3?+. Magnetization measurements indicate ferromagnetic behaviour with 92 Oe coercivity value at 50 K but at 300 K it show no hysteresis loop.     

Trace Formula for p-Adics

We give a p-adic analogue of Selberg's trace formula relating the trace of a semigroup generated by a natural elliptic operator with a sum over contributions coming from closed geodesics. The construction uses probabilistic methods to define the generator.     

Grad’s 13 Moment Equations in a Modified Form

We describe a hierarchy of formal expansions that represent the Fourier transform of a solution of the Boltzmann equation. The constructed approximations are based on the family of weighted Taylor expansions. The first two representations correspond to the Maxwellian and to the Gaussian expansions. The third representation has a weight that generalizes the Gaussian and it depends on the first 13 moments of the Boltzmann density f. It can be shown that this weight is Galilean invariant and it is close to the Gaussian, providing that the heat fluxes are not too large. The 13 moment weight yields a revised form of Grad’s 13 moment expansion for the Boltzmann equation. In search for the entropy dissipation inequality, we also examine the relation between Levermore’s 14 moment density and Grad’s 13 moment expansion. First, we show that the coefficients of the Godunov potential are described by a system of partial differential equations, with coefficients that depend on the Fourier transform of the Levermore’s density f _Λ itself. Then, we argue that the same Taylor expansion exploited in the Grad’s scheme, can be used to approximate Levermore’s 14 moment density. We also show that the weighted Taylor expansions are related to a formal solution of the Hamburger problem.     

A multireference direct CI program based on the symmetric group graphical approach

Specific features of an SGGA-based multireference direct CI program working in large internal spaces are discussed. In particular, advantages resulting from the explicit separation of the orbital and the spin spaces are explored. Concepts allowing for the efficient creation of a flexible and symmetry-adapted CI basis, for the high-speed generation of the coupling coefficients and for structuring a simple permutation driven algorithm to handle the orbital space are briefly discussed.Alexander von Humboldt Fellow 1985/87     

On the closability of some positive definite symmetric differential forms on c0∞(ω)

Let $\text{S}$ be a Dirichlet form in $\text{L}{}^2\text{(Ω; m)}$, where Ω is an open subset of $\text{R}$ⁿ, n ? 2, and m a Radon measure on Ω; for each integer k with 1 ? k < n, let $\text{S}$_k be a Dirichlet form on some k-dimensional submanifold $\text{Ω}{}_{\mathrm{k}}$ of Ω. The paper is devoted to the study of the closability of the forms E with domain $\text{C}{}_0{}^{\mathrm{\infty }}\text{(Ω)}$ and defined by: $\text{(?,g)=}$$\text{E}$$\text{(?, g)+}\text{∑}\text{i}\text{p}\text{=1}$$\text{E}$k_i where 1 ? k_p < ? < n, and where , g^k_i denote restrictions of ?, g in $\text{C}{}_0{}^{\mathrm{\infty }}\text{(Ω)}$ to . Conditions are given for E to be closable if, for each i = 1,…, p, one has k_i = n ? i. Other conditions are given for E to be nonclosable if, for some i, k_i < n ? i.