Dispersion interactions of carbohydrates with condensate aromatic moieties: theoretical study on the CH-π interaction additive properties

In this article we present the first systematic study of the additive properties (i.e. degree of additivity) of the carbohydrate-aromatic moiety CH-π dispersion interaction. The additive properties were studied on the β-D-glucopyranose, β-D-mannopyranose and α-L-fucopyranose complexes with the naphthalene molecule by comparing the monodentate (single CH-π) and bidentate (two CH-π) complexes. All model complexes were optimized using the DFT-D approach, at the BP/def2-TZVPP level of theory. The interaction energies were refined using single point calculations at highly correlated ab initio methods at the CCSD(T)/CBS level, calculated as E + (E(CCSD(T))-E(MP2))(Small Basis). Bidentate complexes show very strong interactions in the range from -10.79 up to -7.15 and -8.20 up to -6.14 kcal mol(-1) for the DFT-D and CCSD(T)/CBS level, respectively. These values were compared with the sum of interaction energies of the appropriate monodentate carbohydrate-naphthalene complexes. The comparison reveals that the bidentate complex interaction energy is higher (interaction is weaker) than the sum of monodentate complex interaction energies. Bidentate complex interaction energy corresponds to 2/3 of the sum of the appropriate monodentate complex interaction energies (averaging over all modeled carbohydrate complexes). The observed interaction energies were also compared with the sum of interaction energies of the corresponding previously published carbohydrate-benzene complexes. Also in this case the interaction energy of the bidentate complex was higher (i.e. weaker interaction) than the sum of interaction energies of the corresponding benzene complexes. However, the obtained difference is lower than before, while the bidentate complex interaction energy corresponds to 4/5 of the sum of interaction energy of the benzene complexes, averaged over all structures. The mentioned comparison might aid protein engineering efforts where amino acid residues phenylalanine or tyrosine are to be replaced by a tryptophan and can help to predict the changes in the interactions. The observed results also show that DFT-D correctly describes the CH-π interaction energy and their additive properties in comparison to CCSD(T)/CBS calculated interaction energies. Thus, the DFT-D approach might be used for calculation of larger complexes of biological interest, where dispersion interaction plays an important role.     

On the minimum order of graphs with given semigroup

Denote by M(n) the smallest positive integer such that for every n-element monoid M there is a graph G with at most M(n) vertices such that End(G) is isomorphic to M. It is proved that $\text{2}\text{(1 + o(1))n}\text{log}{}_2\text{n}\text{≤M(n)≤n ·}\text{2n}\text{+ O(n)}$. Moreover, for almost all n-element monoids M there is a graph G with at most 12 · n · log₂n + n vertices such that End(G) is isomorphic to M.     

Spin-adapted wave functions of the serber type and time reversal

A procedure is proposed for generating Serber-type spin eigenfunctions withM _s = 0. The procedure uses the time-reversal invariance of these functions to increase the efficiency and to reduce the storage requirements. Simplifications in calculating the matrix elements of an observable operator which follow from the use of the time-reversal symmetry are briefly discussed.     

сОДЕРжАНИь РАБОт, ОпУБлИкОВАННых тОлькО В ЧЕшскОМ ИжДАНИИ НАстОьЩЕгО жУРНАлА

---

Abstracts of Papers which have appeared only in the Czech Edition of this Journal

     

The Ramsey property for graphs with forbidden complete subgraphs

The following theorem is proved: Let G be a finite graph with cl(G) = m, where cl(G) is the maximum size of a clique in G. Then for any integer r ≥ 1, there is a finite graph H, also with cl(H) = m, such that if the edges of H are r-colored in any way, then H contains an induced subgraph G′ isomorphic to G with all its edges the same color.     

Sharp Bounds For Some Multicolor Ramsey Numbers

Let H ₁,H ₂, . . .,H _k+1 be a sequence of k+1 finite, undirected, simple graphs. The (multicolored) Ramsey number r(H ₁,H ₂,...,H _k+1) is the minimum integer r such that in every edge-coloring of the complete graph on r vertices by k+1 colors, there is a monochromatic copy of H _i in color i for some 1ik+1. We describe a general technique that supplies tight lower bounds for several numbers r(H ₁,H ₂,...,H _k+1) when k2, and the last graph H _k+1 is the complete graph K _m on m vertices. This technique enables us to determine the asymptotic behaviour of these numbers, up to a polylogarithmic factor, in various cases. In particular we show that r(K ₃,K ₃,K _m ) = (m ³ poly logm), thus solving (in a strong form) a conjecture of Erdos and Sós raised in 1979. Another special case of our result implies that r(C ₄,C ₄,K _m ) = (m ² poly logm) and that r(C ₄,C ₄,C ₄,K _m ) = (m ²/log² m). The proofs combine combinatorial and probabilistic arguments with spectral techniques and certain estimates of character sums.* Research supported in part by a State of New Jersey grant, by a USA Israeli BSF grant and by a grant from the Israel Science Foundation. Research supported by NSF grant DMS 9704114.     

Internal magnetic fields in submicron particles of barium hexaferrite detected by 57Fe NMR

⁵⁷Fe nuclear magnetic resonance (NMR) spectra of hexaferrite BaFe₁₂O₁₉ powder samples prepared by glass crystallization method were measured at 4.2 K and analyzed in comparison to spectra of single crystals. Samples with various mean particle dimensions were tested. NMR spectral lines corresponding to individual iron sublattices showed pronounced frequency shifts of their positions and a significant line broadening compared to single crystals. The significant contribution to the line shifts and line shape had a uniform macroscopic origin giving identical absolute value of shifts and the same line shapes for all measured lines of a particular sample. Estimations of demagnetization fields based on mean particle dimensions reasonably corresponded to the observed frequency shifts for particle mean diameter 67 nm, or had a higher value for a sample with mean diameter of 340 nm, for which a presence of domain walls was detected by NMR. In the spectrum of a sample with the smallest particles (～16 nm), an additional contribution having broader lines and faster spin-spin relaxations was found. It could be assigned to weaker exchange interactions or deviations of magnetic moment directions from the hexagonal axis in a surface layer.     

Code loops in both parities

We present equivalent definitions of code loops in any characteristic p≠0. The most natural definition is via combinatorial polarization, but we also show how to realize code loops by linear codes and as a class of symplectic conjugacy closed loops. For p odd, it is possible to define code loops via characteristic trilinear forms. Related concepts are discussed.