Identification and thermodynamic treatment of several types of large-amplitude motions

We present a partially automated method for the thermodynamic treatment of large-amplitude motions. Starting from the molecular geometry and the Hessian matrix, we evaluate anharmonic partition functions for selected vibrational degrees of freedom. Supported anharmonic vibration types are internal rotation and inversion (oscillation in a double-well potential). By heuristic algorithms, we identify internal rotations in most cases automatically from the Hessian eigenvectors, and we also estimate the parameters of anharmonic partition functions (e.g., potential barrier, periodicity, and symmetry number) with thermodynamically sufficient precision. We demonstrate the validity of our schemes by comparison to pointwise calculated ab initio potential curves.     

Atoms-in-molecules from the Stockholder Partition of the Molecular Two-electron Distribution

The effective one-electron distributions of bonded atoms obtained from the “stockholder” partition of the molecular two-electron density are reported. These two-electron stockholder (S) atoms are compared with their one-electron analogs represented by the corresponding Hirshfeld (H) one-electron stockholder pieces of the molecular electron density. The influence of the exchange (Fermi) and Coulomb correlation between electrons on the resultant shapes of bonded atoms is investigated The vertical (for the fixed molecular electron density) and horizontal (involving the electron density displacement) correlation influences on the two-electron stockholder atoms are examined. The two sets of bonded stockholder atoms in the near-dissociation bond-elongated diatomics are compared for different approximations of the electron correlation effects. The cluster components in atomic resolution of the S-partitioning scheme are investigated for illustrative homonuclear and heteronuclear diatomics: H₂, LiH, HF, LiF, and N₂. This framework facilitates an understanding of the origins of the observed differences between the S and H variants of Atoms-in-Molecules. With the exception of hydrogen atoms, especially in light molecules, the two sets of bonded atoms were found to be practically identical. For H₂ and LiH the S atoms were shown to exhibit a distinctly higher degree of the bonding character, compared to their H analogs. The main electron correlation effects have been found to be well represented already at the exchange-only level, e.g., in the unrestricted Hartree–Fock (UHF) theory. An inclusion of the extra vertical Coulomb correlation exerts a marginal moderating influence on the ionic/covalent composition of the chemical bond already predicted by the UHF approximation, in the direction of a slightly more covalent (less ionic) bond character. The horizontal shifts of the molecular density due to Coulomb correlation, relative to the UHF reference, often act in the opposite direction.     

胶束及反胶束微环境中的槲皮素金属配合物

无机金属元素可与中药活性有机化合物通过配位键结合形成配合物,进而影响药物的生理活性[1]。但配合物的形成往往改变了原有机成分的溶解性能(如水溶性或脂溶性),而表面活性胶束体系可使金属有机配合物的水溶性或脂溶性得到明显改善,从而提高药物的生物利用度和改善药物的吸收。然而,胶束体系中已有的研究多是针对单纯的有机化合物[2]或生物分子如蛋白质[3]等,而涉及金属配合物胶束溶液的则很少,尤其是反胶束微环境中的中药金属配合物。反胶束亦称W/O型微乳液,是双亲物质在非极性有机溶剂中自发形成的具有纳米尺寸的含有水核的微小胶团聚集…     

Entropy for Random Partitions and Its Applications

Asymptotic properties of partitions of the unit interval are studied through the entropy for random partition

Applications of pseudo-monotone operators with some kind of upper semicontinuity in generalized quasi-variational inequalities on non-compact sets

Let be a topological vector space and be a non-empty subset of . Let and be two maps. Then the generalized quasi-variational inequality (GQVI) problem is to find a point and a point such that for all . We shall use Chowdhury and Tan's 1996 generalized version of Ky Fan's minimax inequality as a tool to obtain some general theorems on solutions of the GQVI on a paracompact set in a Hausdorff locally convex space where the set-valued operator is either strongly pseudo-monotone or pseudo-monotone and is upper semicontinuous from to the weak-topology on for each non-empty finite subset of .

     

On Equivalence Relations in Ordered Sets

A relationship between equivalence relations in finite ordered sets and linear decompositions is presented.     

A polarized partition relation for cardinals of countable cofinality

We prove that if and , then

for all . This polarized partition relation holds if for every partition either there are and with or there are and with .

     

Superconvergence of mixed finite element methods for optimal control problems

In this paper, we investigate the superconvergence property of the numerical solution of a quadratic convex optimal control problem by using rectangular mixed finite element methods. The state and co-state variables are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions. Some realistic regularity assumptions are presented and applied to error estimation by using an operator interpolation technique. We derive superconvergence properties for the flux functions along the Gauss lines and for the scalar functions at the Gauss points via mixed projections. Moreover, global superconvergence results are obtained by virtue of an interpolation postprocessing technique. Thus, based on these superconvergence estimates, some asymptotic exactness a posteriori error estimators are presented for the mixed finite element methods. Finally, some numerical examples are given to demonstrate the practical side of the theoretical results about superconvergence.

     

A new proof of the Ramanujan congruences for the partition function

Let p(n) denote the number of partitions of n. Recall Ramanujan’s three congruences for the partition function,

Reflection positivity, rank connectivity, and homomorphism of graphs

It is shown that a graph parameter can be realized as the number of homomorphisms into a fixed (weighted) graph if and only if it satisfies two linear algebraic conditions: reflection positivity and exponential rank connectivity. In terms of statistical physics, this can be viewed as a characterization of partition functions of vertex coloring models.