Phonon spectra and thermodynamic properties of rare gas solids based on empirical and semi-empirical (ab initio) two-body potentials : a comparative study /

We study the phonon dispersion, cohesive and thermal properties of raxe gas solids Ne, Ar, Kr, and Xe, using a variety of potentials obtained from different approaches; such as, fitting to crystal properties, purely ab initio calculations for molecules and dimers or ab initio calculations for solid crystalline phase, a combination of ab initio calculations and fitting to either gas phase data or sohd state properties. We explore whether potentials derived with a certain approaxih have any obvious benefit over the others in reproducing the solid state properties. In particular, we study phonon dispersion, isothermal ajid adiabatic bulk moduli, thermal expansion, and elastic (shear) constants as a function of temperatiue. Anharmonic effects on thermal expansion, specific heat, and bulk moduli have been studied using A^ perturbation theory in the high temperature limit using the neaxest-neighbor central force (nncf) model as developed by Shukla and MacDonald [4]. In our study, we find that potentials based on fitting to the crystal properties have some advantage, particularly for Kr and Xe, in terms of reproducing the thermodynamic properties over an extended range of temperatiures, but agreement with the phonon frequencies with the measured values is not guaranteed. For the lighter element Ne, the LJ potential which is based on fitting to the gas phase data produces best results for the thermodynamic properties; however, the Eggenberger potential for Ne, where the potential is based on combining ab initio quantum chemical calculations and molecular dynamics simulations, produces results that have better agreement with the measured dispersion, and elastic (shear) values. For At, the Morse-type potential, which is based on M0ller-Plesset perturbation theory to fourth order (MP4) ab initio calculations, yields the best results for the thermodynamic properties, elastic (shear) constants, and the phonon dispersion curves.

Fluorescence spectra and ab initio theoretical studies of HCOOH /

A fluorescence excitation spectrum of formic acid monomer (HCOOH) , has been recorded in the 278-246 nm region and has been attributed to an n >7r* electron promotion in the anti conformer. The S^< S^ electronic origins of the HCOOH/HCOOD/DCOOH/DCOOD isotopomers were assigned to weak bands observed at 37431.5/37461.5/37445.5/37479.3 cm'''. From a band contour analysis of the 0°^ band of HCOOH, the rotational constants for the excited state were estimated: A'=1.8619, B'=0.4073, and C'=0.3730 cm'\ Four vibrational modes, 1/3(0=0), j/^(0-C=0) , J/g(C-H^^^) and i/,(0-H^yJ were observed in the spectrum. The activity of the antisymmetric aldehyde wagging and hydroxyl torsional modes in forming progressions is central to the analysis, leading to the conclusion that the two hydrogens are distorted from the molecular plane, 0-C=0, in the upper S. state. Ab initio calculations were performed at the 6-3 IG* SCF level using the Gaussian 86 system of programs to aid in the vibrational assignments. The computations show that the potential surface which describes the low frequency OH torsion (twisting motion) and the CH wagging (molecular inversion) motions is complex in the S^ excited electronic state. The OH and CH bonds were calculated to be twisted with respect to the 0-C=0 molecular frame by 63.66 and 4 5.76 degrees, respectively. The calculations predicted the existence of the second (syn) rotamer which is 338 cm'^ above the equilibrium configuration with OH and CH angles displaced from the plane by 47.91 and 41.32 degrees.

Investigation of molecular polarizabilities and derivatives in halomethanes

The research undertaken was to obtain absolute Raman intensities for the symmetric stretching vibrations of the methyl halides, CH3X with (X=F, CI, Br), by experiment and theory. The intensities were experimentally measured using the Ar+ ion gas laser as excitation source, a Spex 14018 double monochromator and a RCA C-31034 photomultiplier tube as detector. These intensities arise from changes in the derivative of the polarizability (8 a'), with respect to vibration along a normal coordinate (8qi). It was intended that these derivatives obtained with respect to normal coordinates would be converted to derivatives with respect to internal coordinates, for a quantitative comparison with theory. Theoretical numerical polarizability derivatives for the stretching vibrations are obtained using the following procedure. A vibration was simulated in the molecule by increasi.ng and decreasing the respective bond by the amount ±o.oosA for the C-H bonds and ±o.oIA for the C-X (X=F, CI, Br) bond. The derivative was obtained by taking the difference in the polarizability for the equilibrium geometry and the geometry when a particular bond is changed. This difference, when divided by the amount of change in each bond and the number of bonds present results in the derivative of the polarizability with respect to internal coordinate i.e., !1u/!1r. These derivatives were obtained by two methods: I} ab initio molecular orbital calculation and 2} theory of atoms in molecules (AIM) analysis. Due to errors in the experimental setup only a qualitative analysis of the results was undertaken relative to the theory. Theoretically it is predicted that the symmetric carbonhalogen stretch vibrations are more intense than the respective carbon-hydrogen stretch, but only for the methyl chloride and bromide. The carbon fluorine stretch is less intense than the carbon-hydrogen stretch, a fact which is attributed to the small size and high electronegativity of the fluorine atom. The experimental observations are seen to agree qualitatively with the theory results. It is hoped that when the experiment is repeated, a quantitative comparison can be made. The analysis by the theory of atoms in molecules, along with providing polarizabilities and polarizability derivatives, gives additional information outlined below. The theory provides a pictorial description of the main factors contributing to the molecular polarizability and polarizability derivative. These contributions are from the charge transfer and atomic dipole terms i.e., transfer of charge from one atom to another and the reorganization of atomic electronic charge distribution due to presence of an electric field. The linear relationship between polarizability and molecular volume was also observed.

Molecular dynamics calculation of mean square displacement in alkali metals and rare gas solids and comparison with lattice dynamics

Molec ul ar dynamics calculations of the mean sq ua re displacement have been carried out for the alkali metals Na, K and Cs and for an fcc nearest neighbour Lennard-Jones model applicable to rare gas solids. The computations for the alkalis were done for several temperatures for temperature vol ume a swell as for the the ze r 0 pressure ze ro zero pressure volume corresponding to each temperature. In the fcc case, results were obtained for a wide range of both the temperature and density. Lattice dynamics calculations of the harmonic and the lowe s t order anharmonic (cubic and quartic) contributions to the mean square displacement were performed for the same potential models as in the molecular dynamics calculations. The Brillouin zone sums arising in the harmonic and the quartic terms were computed for very large numbers of points in q-space, and were extrapolated to obtain results ful converged with respect to the number of points in the Brillouin zone.An excellent agreement between the lattice dynamics results was observed molecular dynamics and in the case of all the alkali metals, e~ept for the zero pressure case of CSt where the difference is about 15 % near the melting temperature. It was concluded that for the alkalis, the lowest order perturbation theory works well even at temperat ures close to the melting temperat ure. For the fcc nearest neighbour model it was found that the number of particles (256) used for the molecular dynamics calculations, produces a result which is somewhere between 10 and 20 % smaller than the value converged with respect to the number of particles. However, the general temperature dependence of the mean square displacement is the same in molecular dynamics and lattice dynamics for all temperatures at the highest densities examined, while at higher volumes and high temperatures the results diverge. This indicates the importance of the higher order (eg. ~* ) perturbation theory contributions in these cases.

Assessing the Reproducibility of Clustering of Molecular Dynamics Conformations on Self-Organizing Maps

The goal of most clustering algorithms is to find the optimal number of clusters (i.e. fewest number of clusters). However, analysis of molecular conformations of biological macromolecules obtained from computer simulations may benefit from a larger array of clusters. The Self-Organizing Map (SOM) clustering method has the advantage of generating large numbers of clusters, but often gives ambiguous results. In this work, SOMs have been shown to be reproducible when the same conformational dataset is independently clustered multiple times (~100), with the help of the Cramérs V-index (C_v). The ability of C_v to determine which SOMs are reproduced is generalizable across different SOM source codes. The conformational ensembles produced from MD (molecular dynamics) and REMD (replica exchange molecular dynamics) simulations of the penta peptide Met-enkephalin (MET) and the 34 amino acid protein human Parathyroid Hormone (hPTH) were used to evaluate SOM reproducibility. The training length for the SOM has a huge impact on the reproducibility. Analysis of MET conformational data definitively determined that toroidal SOMs cluster data better than bordered maps due to the fact that toroidal maps do not have an edge effect. For the source code from MATLAB, it was determined that the learning rate function should be LINEAR with an initial learning rate factor of 0.05 and the SOM should be trained by a sequential algorithm. The trained SOMs can be used as a supervised classification for another dataset. The toroidal 10×10 hexagonal SOMs produced from the MATLAB program for hPTH conformational data produced three sets of reproducible clusters (27%, 15%, and 13% of 100 independent runs) which find similar partitionings to those of smaller 6×6 SOMs. The χ^2 values produced as part of the C_v calculation were used to locate clusters with identical conformational memberships on independently trained SOMs, even those with different dimensions. The χ^2 values could relate the different SOM partitionings to each other.

Mass spectrometric studies on aryltin compounds and alkali halides /

The fragmentation behavior of aryltin compounds [(p-ThAnis)nSnPh4.n (n=l-4); (p-ThAnis)3SnX (X=C1, Br, I); (o-CH30C6H4)3SnCl; Ph3Sn(o-pyr)] have been studied comparatively under EI and FAB ionization modes. Alkali halides were run under FAB mode. For the aryltin compounds, the effect of ligand type on the spectra have been explored in both EI and FAB modes. The fragmentation mechanisms have been examined with linked scans, such as fragment ion scans (B/E) and parent ion scans (B^/E). Ab Initio molecular orbital calculations were used to determine the structures of the fragments by comparing their relative stabilities. In the EI MS studies, negative ion EI mode has also been used for some of the aryltin compounds, to examine the possible ion molecule reactions under low pressures at 70eV. In the positive ion FAB MS studies, matrix optimization experiments have been carried out. Negative ion FAB experiments of all the compounds have been done in two different ways. Finally, the comparison of the two methods, EI MS and FAB MS, have been made.For alkali halides, the studies focused on the FAB MS behavior under different conditions. The intensities of cluster ions were reported, and the anomalies in the intensity distribution was also discussed.

An analysis of the methyl rotation dynamics in the So (x' A) and T (a A) states of thioacetaldehyde from Pyrolysis jet spectra /

Jet-cooled, laser-induced phosphorescence excitation spectra (LIP) of thioacetaldehyde CH3CHS, CH3CDS, CD3CHS and CD3CDS have been observed over the region 15800 - 17300 cm"^ in a continuous pyrolysis jet. The vibronic band structure of the singlet-triplet n -* n* transition were attributed to the strong coupling of the methyl torsion and aldehydic hydrogen wagging modes . The vibronic peaks have been assigned in terms of two upper electronic state (T^) vibrations; the methyl torsion mode v^g, and the aldehydic hydrogen wagging mode v^^. The electronic origin O^a^ is unequivocally assigned as follows: CH3CHS (16294.9 cm"'' ), CH3CDS (16360.9 cm"'' ), CD3CHS (16299.7 cm"^ ), and CD3CDS (16367.2 cm"'' ). To obtain structural and dynamical information about the two electronic states, potential surfaces V(e,a) for the 6 (methyl torsion) and a (hydrogen wagging) motions were generated by ab initio quantum mechanical calculations with a 6-3 IG* basis in which the structural parameters were fully relaxed. The kinetic energy coefficients BQ(a,e) , B^(a,G) , and the cross coupling term B^(a,e) , were accurately represented as functions of the two active coordinates, a and 9. The calculations reveal that the molecule adopts an eclipsed conformation for the lower Sq electronic state (a=0°,e=0"') with a barrier height to internal rotation of 541.5 cm"^ which is to be compared to 549.8 cm"^ obtained from the microwave experiment. The conformation of the upper T^ electronic state was found to be staggered (a=24 . 68° ,e=-45. 66° ) . The saddle point in the path traced out by the aldehyde wagging motion was calculated to be 175 cm"^ above the equilibrium configuration. The corresponding maxima in the path taken by methyl torsion was found to be 322 cm'\ The small amplitude normal vibrational modes were also calculated to aid in the assignment of the spectra. Torsional-wagging energy manifolds for the two states were derived from the Hamiltonian H(a,e) which was solved variationally using an extended two dimensional Fourier expansion as a basis set. A torsionalinversion band spectrum was derived from the calculated energy levels and Franck-Condon factors, and was compared with the experimental supersonic-jet spectra. Most of the anomalies which were associated with the interpretation of the observed spectrum could be accounted for by the band profiles derived from ab initio SCF calculations. A model describing the jet spectra was derived by scaling the ab initio potential functions. The global least squares fitting generates a triplet state potential which has a minimum at (a=22.38° ,e=-41.08°) . The flatter potential in the scaled model yielded excellent agreement between the observed and calculated frequency intervals.