Convergence of vibrational angular momentum terms within the Watson Hamiltonian

Vibrational angular momentum terms within the Watson Hamiltonian are often considered negligible or are approximated by the zeroth order term of an expansion of the inverse of the effective moment of inertia tensor. A multimode expansion of this tensor up to second order has been used to study the impact of first and second order terms on the vibrational transitions of N(2)H(2) and HBeH(2)BeH. Comparison with experimental data is provided. The expansion of the tensor can be exploited to introduce efficient prescreening techniques.     

Configuration selection within vibrational multiconfiguration self-consistent field theory: application to bridged lithium compounds

A configuration selection scheme has been used to speed up vibrational multiconfiguration self-consistent field calculations. Deviations with respect to reference calculations were found to be negligible while yielding an acceleration of about two orders of magnitude. Its application to bridged lithium compounds (Li(2)H(2), Li(2)F(2), Li(2)O(2), and Li(3)F(3)) based on high-level coupled-cluster potential energy surfaces provides accurate vibrational transitions for all fundamental modes. The explicit inclusion of 4-mode couplings was found to be important for Li(2)H(2).     

Impact of local and density fitting approximations on harmonic vibrational frequencies

Harmonic vibrational frequencies are computed using second-order M?ller-Plesset perturbation theory (MP2) with and without local (LMP2) and density fitting (DF) approximations. Results for a test set of 17 small and medium size molecules (366 normal modes) are presented, and frequency scaling factors for LMP2 in combination with two different basis sets are determined. Comparison of the MP2 and LMP2 frequencies with experimental data reveals that the introduction of local approximations leads to a slightly better agreement with experiment. This is attributed to the reduction of basis set superposition errors in local calculations. Introduction of DF approximations within the LMP2 formalism leads to negligible deviations but significantly reduces the computational cost. These facts extend the applicability of the method to larger systems with large basis sets. As an example, the method is applied to a full DF-LMP2/cc-pVTZ frequency calculation for testosterone (49 atoms).     

Sparsity in Time-Frequency Representations

We consider signals and operators in finite dimension which have sparse time-frequency representations. As main result we show that an S-sparse Gabor representation in ℂ ⁿ with respect to a random unimodular window can be recovered by Basis Pursuit with high probability provided that S≤Cn/log (n). Our results are applicable to the channel estimation problem in wireless communications and they establish the usefulness of a class of measurement matrices for compressive sensing.     

Efficient calculation of potential energy surfaces for the generation of vibrational wave functions

An automatic procedure for the generation of potential energy surfaces based on high level ab initio calculations is described. It allows us to determine the vibrational wave functions for molecules of up to ten atoms. Speedups in computer time of about four orders of magnitude in comparison to standard implementations were achieved. Effects due to introduced approximations--within the computation of the potential--on fundamental modes obtained from vibrational self-consistent field and vibrational configuration interaction calculations are discussed. Benchmark calculations are provided for formaldehyde and 1,2,5-oxadiazole (furazan).     

Photo-stabilising action of a p-hydroxybenzoate light stabiliser in polyolefins: Part III—Antioxidant behaviour and additive/pigment interactions in high density polyethylene

The effect of a number of commercial primary and secondary antioxidants, light stabilisers and pigments on the photo-stabilising action of an n-alkyl substituted p-hydroxybenzoate light stabiliser (Cyasorb® UV 2908) is examined in high density polyethylene. At the concentration levels employed here the p-hydroxybenzoate light stabiliser showed a favourable interaction with all the light stabilisers and pigments studied. Interactions with the primary and secondary antioxidants appeared to be concentration dependent. Synergism with the light stabilisers is associated with the ability of these compounds to destroy hydroperoxides and/or react with alkoxy and hydroxy radicals produced in their photolysis. Synergism with primary and secondary antioxidants is observed at low concentrations of each component (0·05% w/w each) whereas antagonism is observed at higher concentration levels, the latter being associated with unfavourable interactions between intermediate radical products of the additives. With the pigments there is strong synergism and this is associated with the known ability of the pigments to catalyse the photo-decomposition of hydroxperoxides, the resulting alkoxy and hydroxyl radicals being effectively scavenged by the p-hydroxybenzoate stabiliser. Further information on the selectivity of the p-hydroxybenzoate light stabiliser to terminate only the active free radical species in the polymer compared with conventional antioxidant structures is also provided.     

Multicenter point charge model for high-quality molecular electrostatic potentials from AM1 calculations

The natural atomic orbital/point charge (NAO-PC) model based upon the AM1 wave function has been developed to calculate molecular electrostatic potentials (MEPs). Up to nine point charges (including the core charge) are used to represent heavy atoms. The positions and magnitudes of the eight charges that represent the atomic electron cloud are calculated from the natural atomic orbitals (NAOs) and their occupations. Each hybrid NAO is represented by two point charges situated at the centroid of each lobe. The positions of the centroids and the magnitudes of the charges were obtained by numerical integration of the Slater-type hybrids and the results used to set up polynomials and look-up tables that replace the integration step in the actual MEP calculation. The MEPs calculated using this method are found to be in better agreement with those obtained using RHF/6-31G* than those obtained from the AM1 wave function using Coulson charges or with MOPAC-ESP. The MEP calculations are extremely fast and have, for instance, been incorporated into an interactive graphics package. © 1993 John Wiley & Sons, Inc.