Improved efficiency of focal point conformational analysis with truncated correlation consistent basis sets

It has been suggested that the computational cost of correlated ab initio calculations could be reduced efficiently by using truncated basis sets on hydrogen atoms (Mintz et al., J Chem Phys 2004, 121, 5629). We now explore this proposal in the context of conformational analysis of small molecules, such as hydrogen peroxide, dimethyl ether, ethyl methyl ether, formic acid, methyl formate, and several small alcohols. It is found that truncated correlation consistent basis sets that lack certain higher angular momentum functions on hydrogen atoms offer accuracy similar to traditional Dunning's basis sets for conformational analysis. Combination of such basis sets with the basis set extrapolation technique to estimate Hartree-Fock and M?ller-Plesset second order energies provides composite extrapolation model chemistries that are significantly more accurate and faster than analogous single point calculations with traditional correlation consistent basis sets. Root mean square errors of best composite extrapolation model chemistries on the used set of molecules are within 0.03 kcal/mol of traditional focal point conformational energies. The applicability of composite extrapolation methods is illustrated by performing conformational analysis of tert-butanol and cyclohexanol. For comparison, conformational energies calculated with popular molecular mechanics force fields are also given.     

Mathematical aspects of the LCAO MO first order density function (1): atomic partition, metric structure and practical applications

Partition of the first order density function within LCAO MO theory permits the definition of Mulliken and Minkowski metric spaces. The metric matrices obtained become useful to connect density atomic partition with quantum similarity measures, Mulliken populations, EHT, expectation values of Hermitian operators and the comparison of two density distributions.     

Generically there is but one self homeomorphism of the Cantor set

We describe a self homeomorphism of the Cantor set and then show that its conjugacy class in the Polish group of all homeomorphisms of forms a dense subset of . We also provide an example of a locally compact, second countable topological group which has a dense conjugacy class.

     

Some results on best approximation in spaces with convex structure

Some generalizations of the result proved by S.P Singh[J.Approx.Theory 25(1979),89-90]are presented in convex metric spaces.The results proved contain several known results on the subject.     

An Enumeration of Certain Projective Ternary Two‐Weight Codes

We detail the enumeration of all two‐intersection sets of the five‐dimensional projective space over the field of order 3 that are invariant under an element of order 7, which include the examples of Hill (1973) and Gulliver (1996). Up to projective equivalence, there are 6,635 such two‐intersection sets.     

(s,l)-叠加码的构作及其性质

一个二元叠加(s,l)-码在许多领域有着极为广泛的应用.利用有限集[n]的子集构作了一个(0,1)-矩阵C,并证明了它是一个(s,l)-码,给出了(s,l)-码的性质.