Exploring the MRCI method for calculating interaction energies: application to the HeNe potential curve

A multi-reference configuration interaction (MRCI) method is described, which is devised for the calculation of interaction energies of van der Waals complexes and applied to calculating the HeNe potential energy curve. The MRCI calculations make use of a generalized Pople-correction in order to account for the lack of size consistency. The orbital space is partitioned into three subspaces: the first active space (AS1), which contains the strongly occupied orbitals; the second active space (AS2), which contains the main intra-correlating orbitals; and the external space (ES). It is shown that, to keep the error below ± 0.2 K in the excitation scheme and the active orbital space it is sufficient to include only σ-orbitals in AS2 and to use an excitation scheme (labelled Qq-MRCI) that encompasses only up to quadruply excited configurations. The final active orbital space (AS2) turned out to be 2s(He), 2pσ(He), 3s(Ne), 3σ(Ne) and 3dσ(Ne). Other MRCI variants, in which most or all quadruply excited configurations were deleted from the CI expansion (Qt- and Tt-MRCI), were found to be inadequate. Using the Qq-MRCI scheme together with a 197-orbital ‘interaction optimized’ basis set (IO197), the MRCI interaction energy at R = 5.7 _a0 was calculated to be -21.12K. The corresponding values at the MP4 and CCSD(T) levels of theory are -20.06 K and -20.99 K, respectively, indicating that the MP4 method is inappropriate for highly accurate calculations on this system. Fitting the calculated data using a generalized Morse function, including an additional C₆/R⁶ term to account for a correct long-range behaviour of the potential, the MRCI well depth was calculated to be -21.16K at R_eq = 5.73a ₀. The MRCI and CCSD(T) potentials have the same quality and are found to be in good agreement with the Hartree-Fock dispersion (HFD-B) potential of Keil, M., Danielson, L. J., and Dunlop, P. J., 1991, J. Chem. Phys., 94, 296. It is concluded that, for basis IO197, the CCSD(T) method is sufficiently accurate for calculating the HeNe interaction. To recover the small, missing contributions (a few tenths of a Kelvin), MRCI should be used.     

ON THE IMPULSIVE BEVERTON–HOLT EQUATION AND EXTINCTION CONDITIONS IN POPULATION DYNAMICS

Abstract This paper is devoted to investigate extinction and nonextinction conditions of the extended Beverton–Holt equation (BHE) for dynamics of populations in Ecology when potential discontinuities at sampling points are included in the model. The proposed model is described by means of four sequences of parameters. Two of them are the intrinsic growth rate and the carrying capacity sequences which are included in the basic BHE model. The other two ones, namely, the harvesting (i.e., the hunting or fishing quota) and the internal consumption (which can include positive and negative migrations in the considered population habitat) sequences are included to parameterize the model discontinuities. Such discontinuities are related to impulses in the corresponding continuous‐time logistic equation. The obtained results establish how the harvesting quota and/or the internal consumption has to be fixed to guarantee the population nonextinction or, eventually, its extinction. Finally, some controllability results related to the search of a carrying capacity sequence such that the solution of the proposed impulsive BHE tracks a reference one are obtained.     

THE PROTONATION OF A RETINYL SCHIFF BASE

The hydrogen bonding-protonation equilibrium for retinyl Schiff base/propionic acid or 3-chloropropionic acid systems was examined by Fourier transform infrared spectroscopy in non polar solutions at temperatures ranging from 25 degrees C to about -150 degrees C. The spectra give evidence for the gradual increase in the degree of protonation as temperature is lowered. The bearing of this on applying low temperature spectroscopic results to physiological conditions in rhodopsin research is discussed.     

Linear dynamical systems with integer constraints

We study properties of dynamic discrete-time linear systemswith the input or the state constrained to have integer components.The reachability of input-constrained systems is investigated,and consistency conditions for state-constrained systems aregiven.     

Micellar perturbation of enone reduction

The reduction of several enones using BH₄^? in the presence of cationic surfactants has been investigated. These reductions are all shifted by the micelle towards the formation of conjugate reduction products.     

Effect of γ-radiation on the molecular-topological structure of polytetrafluoroethylene

Four topological structures of polytetrafluoroethylene (PTFE): amorphous and three crystalline (high-melting, intermediate, and low-melting forms) blocks, were revealed by the technique of thermomechanical spectroscopy. The γ-irradiation of PTFE leaves both free volume and the molecular-mass characteristics in the pseudo-network structure of the amorphous block practically intact. In the crystalline phase, γ-irradiation decreases the molecular mass of crystallized chains of the low-temperature modification and leads to the disappearance of the intermediate and high-temperature crystalline phases as a result of their transformation into the amorphous phase.     

A Note on Sampling from Combinations of Distributions

A rejection technique is described for sampling from a combinationof distributions with negative weights for some of the components.     

Application of a Direct Stiffness Method to Wave Propagation in Multiphase Poroelastic Media

In this paper, it is demonstrated how a direct stiffness method for wavepropagation in multilayered saturated poroelastic media, based on integraltransform techniques, can be modified to account for a small amount of gasin the pores. Unsaturated media with small gas fractions can be treatedusing Smeulders extension of Biots poroelastic theory. The effect of thepresence of gas bubbles on the fluid bulk modulus and the dispersioncharacteristics of a water-saturated sand of Mol is demonstrated. Thedirect stiffness method is illustrated with a numerical example wheretransient wave propagation in a dry, saturated and unsaturated halfspaceis considered.     

Features of the phase behavior of gamma-irradiated polytetrafluoroethylene powder

By using the technique of thermomechanical spectroscopy, an amorphous and three crystalline (high melting, intermediate, and low melting) blocks of the topological structures of polytetrafluoroethylene (PTFE) powder were characterized and their behavior under γ-radiation up to 2420 kGy was explored. The powder has an anisotropic topological structure. Starting from a dose of 4 kGy, the structure is radically changed with the long-range orientation of chains in the intermediate and high melting crystalline blocks of PTFE being replaced by a short range orientation of cluster association structures. The temperatures of glass transition and melting point continuously decreased with an increased dose of irradiation. The influence of γ-radiation on the powder and sheet of PTFE are essentially the same, the formation of amorphous character.