Prediction of SAMPL2 aqueous solvation free energies and tautomeric ratios using the SM8, SM8AD,and SMD solvation models

We applied the solvation models SM8, SM8AD, and SMD in combination with the Minnesota M06-2X density functional to predict vacuum-water transfer free energies (Task 1) and tautomeric ratios in aqueous solution (Task 2) for the SAMPL2 test set. The bulk-electrostatic contribution to the free energy of solvation is treated as follows: SM8 employs the generalized Born model with the Coulomb field approximation, SM8AD employs the generalized Born approximation with asymmetric descreening, and SMD solves the nonhomogeneous Poisson equation. The non-bulk-electrostatic contribution arising from short-range interactions between the solute and solvent molecules in the first solvation shell is treated as a sum of terms that are products of geometry-dependent atomic surface tensions and solvent-accessible surface areas of the individual atoms of the solute. On average, three models tested in the present work perform similarly. In particular, we achieved mean unsigned errors of 1.3 (SM8), 2.0 (SM8AD), and 2.6 kcal/mol (SMD) for the aqueous free energies of 30 out of 31 compounds with known reference data involved in Task 1 and mean unsigned errors of 2.7 (SM8), 1.8 (SM8AD), and 2.4 kcal/mol (SMD) in the free energy differences (tautomeric ratios) for 21 tautomeric pairs in aqueous solution involved in Task 2.     

On connection of the geometry of a four-dimensional open manifold with the topology of its ideal boundaries

The research was supported by the Russian Foundation for Fundamental Research (grant 93-011-179).     

Manifolds with minimal radial curvature bounded from below and big volume

We prove that a convergence in the Gromov-Hausdorff distance of manifolds with minimal radial curvature bounded from below by 1 to the standard sphere is equivalent to a volume convergence.

     

Invertibility of binary functions

Translated from Matematicheskie Zametki, Vol. 52, No. 5, pp. 75–82, November, 1992.     

Isomerism and Vibrational Spectra of Alkali Metal Perrhenates: Ab Initio CISD+Q Calculations

The equilibrium geometric parameters, isomerization energies, force fields, vibrational frequencies and intensities in the IR spectra of MReO₄ molecules (M = Li, Na, K) are calculated by the configuration interaction method including all singly and doubly excited configurations with Davidson's correction for quartic excitations in expanded basis sets using effective relativistic core potentials. The calculations indicate that the chemical bonds between the metal atoms and the ReO₄ anion group are highly polar. It is found that the MReO₄ molecule has two isomers. The basic isomer with C_2v symmetry has bidentate b coordination of the M⁺ cation to the ReO ₄ ^- anion. The excited isomer is of C_3v symmetry and corresponds to monodentate m coordination of M⁺. The low relative energies of the m isomers (17-29 kJ/mole) and the low energy barriers to the intramolecular mb rearrangements (5-11 kJ/mole) indicate that MReO₄ molecules are structurally nonrigid systems where the M–XO₄ chemical bonds are polytopic. The results of calculations are compared with the available literature data on the structure and vibrational spectra of MReO₄ molecules.     

Isomerism and Vibration Spectra of M2XO4 Molecules (M = Li,Na, K; X = S,Se, Te,Cr, Mo,W)

The equilibrium geometries, isomerization energies, force fields, vibration frequencies, and band intensities in the IR spectra of M₂XO₄ molecules (M = Li, Na, K; X = S, Se, Te, Cr, Mo, W) were calculated ab initio by the Hartree-Fock method in extended basis sets using relativistic effective core potentials. The relative energies of alternative structures were refined by the configuration interaction method taking into account single- and double-excited configurations, with the Davidson correction for quartic excitations. The results show that the chemical bonds between the metal atom and the acid residue XO₄ are highly polar. The majority of M₂XO₄ molecules have two isomers. In both isomers the XO₄ ^{2 -} anion coordinates the metal cations M⁺ in the bisbidentate (bb) fashion. The equilibrium configurations ofthe nuclei in the ground (bb) and excited (bb') isomers have the D ₂ d and C _s symmetry, respectively. In the bb isomer, the cations coordinate at the opposite, and in the bb' isomer, at the adjacent edges of the XO₄ ^{2 -} anion, having the shape of a distorted tetrahedron. The relative energy of the bb' isomer is 9-28 kJ mol^{- 1}. The energy barriers to intramolecular rearrangements bb'(C _4s) bb(D _{2 d}) are also low: 15-35 kJ mol^{- 1}. These results show that the M₂XO₄ molecules are structurally nonrigid, with a polytopic character of the M-XO₄ chemical bonds. The calculation results were compared to the published experimental data on the structure and vibration spectra of the M₂XO₄ molecules.     

Factoriality of the projective limit of factorial rings

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 41, No. 9, pp. 1231–1234, September, 1989.     

Electrical transport and magnetic ordering in R 2Ti3Ge4 (R=Dy, Ho and Er) compounds

New R ₂Ti₃Ge₄ (R=Dy, Ho and Er) intermetallic compounds have been synthesized and characterized by X-ray diffraction and low temperature ac magnetic susceptibility, electrical resistivity and thermoelectric power measurements were carried out. The compounds crystallize in the parent, Sm₅Ge₄-type orthorhombic structure (space group Pnma) and lanthanide contraction is observed as one moves along the rare-earth series. The changeover from paramagnetic to antiferromagnetic phase happens at low temperatures and the ordering temperature scales with the de Gennes factor. The electrical resistivity is metallic with a negative curvature above 100 K. Thermopower displays a weak maximum at temperatures less than 50 K signifying the possible phonon and magnon drag effects.