Showing papers in "Molecular Physics in 1985"

Temperature and size dependence for Monte Carlo simulations of TIP4P water

Abstract: A series of Monte Carlo simulations has been carried out to characterize the temperature and size dependence of the results for liquid water using the TIP4P potential function. Five temperatures from -25 to 100°C and four system sizes from 64 to 512 molecules have been studied. Comparisons are made with experimental thermodynamic and structural data as well as results of prior simulations.

On the relationship of normal modes to local modes in molecular vibrations

Abstract: A simple model for the effective vibrational hamiltonian of the XH stretching vibrations in H2O, NH3 and CH4 is considered, based on a morse potential function for the bond stretches plus potential and kinetic energy coupling between pairs of bond oscillators. It is shown that this model can be set up as a matrix in local mode basis functions, or as a matrix in normal mode basis functions, leading to identical results. The energy levels obtained exhibit normal mode patterns at low vibrational excitation, and local mode patterns at high excitation. When the hamiltonian is set up in the normal mode basis it is shown that Darling-Dennison resonances must be included, and simple relations are found to exist between the xrs , gtt , and Krrss anharmonic constants (where the Darling-Dennison coefficients are denoted K) due to their contributions from morse anharmonicity in the bond stretches. The importance of the Darling-Dennison resonances is stressed. The relationship of the two alternative representations of...

Free energy functions in the extended RISM approximation

Abstract: It is shown that the free energies associated with the solutions of extended RISM integral equations can be obtained in closed form thus avoiding the necessity of numerical coupling parameter integrations. In addition, variational principles are deduced which provide a basis for efficient algorithms to solve extended RISM integral equations.

Pseudo-spectral dipole oscillator strengths and dipole-dipole and triple-dipole dispersion energy coefficients for HF, HCl, HBr, He, Ne, Ar, Kr and Xe

Abstract: Pseudo-dipole oscillator strengths and excitation energies, which are discrete representations of original continuous dipole oscillator strength distributions (DOSDs), are tabulated for the ground state HF, HCl and HBr molecules and Ne, Ar, Kr and Xe atoms. These pseudo DOSDs are used to evaluate the dipole-dipole and triple-dipole dispersion energy constants for all possible two- and three-body interactions between HF, HCl, HBr, He, Ne, Ar, Kr and Xe. The importance of these results, and of the original DOSDs, is discussed briefly.

A rapidly convergent method of solving the OZ equation

Abstract: A new method is proposed for solving numerically the Ornstein-Zernike equation for systems with a spherically symmetrical pair-potential. The method is based on expansion of the function Γ(r)=r[h(r) - c(r)] in suitable basis functions and on a combination of Newton-Raphson and direct iterations. Tests on the PY and HNC approximations for hard spheres and Lennard-Jones fluid have shown that the proposed method is three to nine times as rapid as the related and so far the most efficient method of Gillan. Other advantages besides the speed are low sensitivity to the choice of initial estimate and a relatively simple computational scheme.

The hard ellipsoid-of-revolution fluid I. Monte Carlo simulations

Abstract: We present the results of Monte Carlo simulations on a system of hard ellipsoids of revolution with length-to-breadth ratios a/b = 3, 2.75, 2, 1.25 and b/a = 3, 2.75, 2, 1.25. We identify four distinct phases, viz. isotropic fluid, nematic fluid, ordered solid and plastic solid. The coexistence points of all first order phase transitions are located by performing absolute free energy computations for all coexisting phases. We find nematic phases only for a/b ≥ 2.75 and a/b ≤ 1/2.75. A plastic solid is only observed for 1.25 ≥ a/b ≥ 0.8. It is found that the phase diagram is surprisingly symmetric under interchange of the major and minor axes of the ellipsoids.

A molecular dynamics study of the structure of water around the ions Li+, Na+, K+, Ca++, Ni++ and Cl-

Abstract: This paper reports a molecular dynamics study of the structure of water around Li+, Na+, K+, Ca++, Ni++ and Cl- ions. Jorgensen's TIP4P potential is used for the water-water interaction, and new ab initio SCF potentials have been obtained for Ca++/H2O and Ni++/H2O using the recently developed gradient method. In most cases where experimental results are available the positions of the peaks associated with the coordination shells, the ion-water geometries, and the coordination numbers are in satisfactory agreement. However, we believe that more precise neutron measurements of the coordination number of Ni++ in dilute solution are needed. The main effects of high pressure on the structure of water around Cl- occur in the second coordination shell. High temperature and high pressure are found to have little effect on the structure around Ca++.

Special geometrical constraints in the molecular dynamics of chain molecules

Abstract: The molecular dynamics simulation of chain molecules with a full atomic description is considered in the particular case of a n-alkane molecule. In order (a) to keep the time step in the numerical integration of the equations of motions to a reasonable value (10-15-10-14s) and (b) to describe such flexible systems with a minimum number of degrees of freedom, it is useful to impose geometrical constraints in order to freeze the fastest intramolecular motions of the chain. Given the large number and the nature of the geometrical constraints involved in this model, the method of constraints used to solve the dynamics in terms of atomic cartesian coordinates needs to be generalized to arbitrary constraints and solved in an iterative way. Such a method is proposed and illustrated on a ring alkane chain, namely cyclo-tetradecane (C14H28).

Distributed multipole analysis: Methods and applications

Abstract: The conventional multipole expansion gives a description of electrostatic interactions which is only useful at long distances. Distributed multipole analysis gives a description which is accurate at all accessible distances, and also gives a much more detailed and instructive picture of the charge distribution. We report our recent investigations into the method and comment on its limitations.

Calculations of rate constants for ion-molecule reactions using a combined capture and centrifugal sudden approximation

Abstract: Rate constant calculations are reported for the gas-phase reactions of HCN with H-, D- and H+ 3 ions. The technique used in the computations involves a combination of adiabatic capture and centrifugal sudden approximations. The convergence of the calculated cross sections, with respect to rotational basis functions, is improved by use of localized functions of the form exp (A cos θ), where θ is the atom-molecule orientation angle. These functions localize the hindered rotational wavefunctions about the collinear configuration, which is appropriate for the collisions of ions with molecules possessing dipole moments. Excellent agreement with experimental room temperature rate constants is obtained. The theory predicts sharply increasing rate constants as the temperature decreases, and this is related to the strong sensitivity of rotationally selected rate constants to the initial rotational state.

Surface enhancement of optical fields

Abstract: The enhancement of electromagnetic processes on metallic surfaces is discussed in view of applications in surface photochemistry and surface analytics. The strongest enhancements are found on substrates that consist of discrete metal particles. A theoretical description for plasmon resonances of such particles is developed, which includes the effects of finite particle size and of dipolar interactions between the particles. Spheroidal particles with dimensions in the range 10–100 nm are found to produce the strongest enhancements; the role of particle interactions in shifting and broadening the plasmon resonances is discussed. Potential applications of the amplified local fields for chemical processes include photochemistry, chemical vapour deposition, and etching. Storage of excitation energy in the bonds to be transformed is necessary for these reactions. The enhanced excitation rate is competing with radiationless energy transfer to the substrate. This rate must be reduced by a spacer layer between met...

The hard ellipsoid-of-revolution fluid II. The y-expansion equation of state

Abstract: The γ-expansion as introduced by Barboy and Gelbart is applied to a system of hard ellipsoids-of-revolution. The expansion is truncated after the third order term yielding an approximate theory requiring the second- and third-virial coefficients as inputs. As the third virial coefficient is not known analytically, numerical results are obtained for this quantity. The equation of state is obtained from a free-energy variational calculation. The results are compared with Monte Carlo data taken from the preceding paper in this series. The application of scaled particle theory to the same system is discussed, and shown to have serious shortcomings.

Constant pressure-constant temperature molecular dynamics for rigid and partially rigid molecular systems

Abstract: The method of molecular dynamics at fixed pressure and/or temperature is adapted to rigid or partly rigid molecular systems with geometrical constraints using the cartesian coordinate approach. Both isotropic and anisotropic volume fluctuations, allowing for shape variation, are considered. The simulation of a benzene crystal at zero pressure and various temperatures is given as an illustration.

Interaction-induced contributions to Rayleigh and allowed Raman bands

Abstract: Molecular dynamics simulations of a model of CS2 have been analysed to calculate the shapes and intensities of the Rayleigh and allowed Raman bands of the liquid. The calculations are performed using the first order dipole induced dipole mechanism (DID). There is a clear time scale separation between the collision induced and reorientational components of the spectrum which becomes more marked at lower temperatures. The projection factors which determine the effective polarizabilities are large for CS2 at first order DID and second order DID terms calculated for the Raman polarizabilities are also substantial. An empirical renormalization scheme to incorporate higher order DID effects for the Raman intensities is described. A simple model which neglects orientational correlations and orientational translational correlations provides a semi quantitative prediction of the collision induced intensities.

Momentum, quasi-momentum and hamiltonian operators in terms of arbitrary curvilinear coordinates, with special emphasis on molecular hamiltonians

Abstract: Since the conformation of physical systems is often advantageously described with the help of generalized (i.e. curvilinear) coordinates, the following questions are raised and general answers given to them: (i) What are the components of the momentum operators, those of the adjoint momentum operators and those of the hermitian momentum operators? (ii) What is the general form of the hamiltonian operator? (iii) What do the general forms of the momentum and hamiltonian operators become when expressed in terms of quasi-momentum operators (e.g. angular momentum component operators)? (iv) How are the answers to the above questions affected by an arbitrary choice of normalization convention for the total wave-function? A complete set of formulae (whatever the independent choices of coordinates, quasi-momentum operators and normalization) is given and various ‘historical’ formulae are shown to be particular instances of the general formulae proposed.

Two-dimensional, fully numerical molecular calculations

Abstract: Fully numerical two-dimensional Hartree-Fock calculations are reported for the ground states of the diatomic systems He2, Li2, Be2, HF, OH-, N2, CO, BF, NO+ and CN-. total energies, electric multipole moments and electric field gradients are given. A close agreement with the seminumerical results by McCullough is obtained. High multipole moments, up to Q 10, are reported and compared to LCAO ones. The role of correlation in nuclear quadrupole coupling constants is discussed.

The form of the density profile at a liquid-gas interface

Abstract: The form of the density profile at the liquid-gas interface of some model fluids is investigated using a simple free-energy functional For fluids with attractive Yukawa potentials we find that the profile decays exponentially into the bulk regions with a decay length greater than the appropriate bulk correlation length; the two lengths become closer and diverge in the same fashion at the critical temperature We contrast this decay with that found for fluids with attractive van der Waals potentials where the profile decays asymptotically as z -3 The results of numerical calculations suggest that the effects of van der Waals' potentials would be difficult to observe in experiments or in computer simulations of liquid-gas interfaces We compare the results of our calculations for fluids with truncated Lennard-Jones potentials with those of recent simulations The theory provides a rather good account of the interfacial width and surface tension as a function of temperature Our results show that truncatio

The parity violating energy differences between the enantiomers of α-amino acids

Abstract: The parity-violating weak neutral current perturbation of the groundstate electronic energy has been calculated, using ab initio methods, for the series of α-amino acids glycine, alanine, valine, serine and aspartic acid. It is found that the WNC energy shifts for these fundamental biomolecules consistently favour the existence of the natural L-enantiomers in preference to the unnatural mirror image D-enantiomers for the molecular conformations preferred in aqueous media. The parity violating energy differences between enantiomers are small, of the order 10-14 J mol-1, and highly sensitive to molecular conformation. The significance of the energy difference between enantionmers arising from the electroweak interactions with reference to the transition from a prebiotic racemic geochemistry to the terrestrial homochiral biochemistry is discussed.

The freezing of hard spheres: The density functional theory revisited

Abstract: We have analysed the recent theories of freezing and found that all results obtained hitherto are biased numerically by the early truncation of slowly converging series. As a result the local density of the solid is shown to become very negative in the interstitial regions. Therefore we have reconsidered the theory of freezing starting from formally exact equations, making three physical approximations and testing all numerical methods for the case of the freezing of hard spheres. A fluid-solid transition is found which is in fair agreement with the known computer experiments.

The collision induced spectroscopies

Abstract: Classical spectral line shapes are symmetric and easy to compute. Measured broad profiles, on the other hand, are asymmetric (principle of detailed balance) and can be reproduced from a much more involved quantum theory. Various desymmetrization procedures are known which, when applied to classical profiles, result in a line shape that is formally consistent with the asymmetry required by detailed balance. It is an interesting fact that various desymmetrization procedures known give rise to very different profiles. Little is known about which (if any) results in a simple but accurate substitute for the quantum shape. An ab initio quantum calculation is in close agreement with a measurement of the binary collision induced, translational Raman spectrum of helium at 30 amagat. To a classical line shape based on the same input, four common desymmetrization procedures are applied. The comparison shows that the Egelstaff procedure simulates the quantum profile most closely and should have broad applications in ...

The role of inter-state Renner-Teller coupling in the dissociation of triatomic molecules

Abstract: An evolving wavepacket study has been made of the rate of radiationless transition from a linear excited electronic state of a triatomic molecule to a lower dissociative bent state, brought about by vibronic interaction (the Renner-Teller effect) where both states correlate with a Π state in the linear configuration. The rate is found to increase (i) with decrease in the quantum number π2 of the upper state bending vibration, (ii) with increase in the quantum number K for the axial component of the total rotational angular momentum, and (iii) with increase in the divergence between the two Born-Oppenheimer potential curves upon bending. There is a maximum crossing probability of 50 per cent during one half-period of the bending vibration. The model is validated by calculating the rate of dissociation of HCO ⪷A 2 A″ → H + CO, giving close agreement with experiment. It is then applied in a discussion of the dissociation pathways for the [Btilde] 1 A 1 state of H2O, providing an explanation for the low quant...

A Monte Carlo study of crystal structure transformations

Abstract: The Metropolis algorithm has been generalized to allow for the variation of shape and size of the MC cell. A calculation using different potentials illustrates how the generalized method can be used for the study of crystal structure transformations. A restricted MC integration in the nine dimensional space of the cell components also leads to the stable structure for the Lennard-Jones potential.

The shear viscosity of a Lennard-Jones fluid calculated by equilibrium molecular dynamics

Abstract: Using the Green-Kubo relation we have calculated the shear viscosities for 14 different fluid states by molecular dynamics (MD) simulations. The common Lennard-Jones interaction potential was employed, and the statistical significance of the correlation function as well as the particle number dependence have been investigated. Some of the main results are the following: (i) the values obtained are estimated to be accurate within 5 per cent; (ii) for particle numbers larger 256, no significant number dependence could be found (checked up to 2048); (iii) for the number of states studied up until now, good agreement is evident with the values obtained by Heyes [1] using non-equilibrium MD; (iv) a noticeable tail of the time correlation function appears for states near the phase boundary to the solid state, however, the function decreases to practically zero within about 2·5 ps; (v) the computational effort necessary for the performance of equilibrium MD is comparable with that needed for nonequilibrium MD.

A model for density oscillations in liquids between solid walls

Abstract: A simple model of a binary alloy in a one-dimensional lattice is used to map the phenomena observed in a fluid filling a planar capillary. It is proposed that the presence of oscillating forces acting on the walls is due to the constructive/destructive interference between the local ordering induced by the boundaries. The numerical results agree with the deduced analytical ones and are compared with the reported experimental results.

Quantum state-selected photodissociation dynamics in h2o and d2o

Abstract: Two photon excitation, tunable near 248·5 nm, has been used to dissociate H2O/D2O via the [Ctilde] 1 B 1 and [Btilde] 1 A 1 states. Rotationally resolved OH/OD(A 2Σ+) photofragment excitation spectra are reported, following excitation to predissociated levels of [Ctilde] 1 B 1. Rotational resolution of the OH/OD(A 2Σ+ → X 2Π) fluorescence, generated from individual J′ K a K c levels of [Ctilde] 1 B 1, allows full quantum state selection in both the entry and exit channels. The OH/OD(A 2Σ+) fragment is formed rotationally hot as a result of the large change in bond angle in going from [Xtilde] 1 A 1 (or [Ctilde] 1 B 1) to the linear dissociative [Btilde] 1 A 1 surface. Product alignment measurements allow assignment of the two photon continuum absorption to [Btilde] 1 A 1: a-axis rotation in [Ctilde] 1 B 1 destroys product alignment from these levels. Electronic branching from ⪷B 1 A 1 to A 1 B 1 (and/or [Xtilde] 1 A 1) during the dissociation forms ground state OH/OD(X 2Π). Relative branching ratios are o...

Calculations of two- and three-body dispersion coefficients for ions in crystals

Abstract: Coupled Hartree-Fock theory is used to calculate two and three body dispersion coefficients for in-crystal ions (Li+, Na+, K+, Rb+, Mg2+, Ca2+, F-, Cl-, O2-) subject to both electrostatic and overlap interactions. For anions the reduction of the dispersion coefficients in the crystalline environment parallels the decrease of the static polarizability. From comparison of ab initio results with those of the Slater-Kirkwood formula we propose an empirical scheme for calculating in-crystal dispersion coefficients from accurate static polarizabilities. We find that two-body dispersion forces are not responsible for the greater stability of the 8 : 8 compared to the 6 : 6 polymorph of CsCl. A correlated Moller-Plesset calculation of the static polarizability of Rb+ confirms our previous scheme for deriving polarizabilities from experiment.

Statistical mechanical models of chemical reactions

Abstract: The statistical mechanical study of chemically reactive fluids via the analytic solution of integral equation approximations for such fluids (Cummings, P. T., and Stell, G., 1984, Molec. Phys., 51, 253; 1985, Ibid., 55, 33) is extended to a consideration of solvent effects. This is achieved by studying mixtures of molecular species some of which can undergo reaction (the solute(s)) and one of which is inert (the solvent). The results obtained near infinite dilution of the reacting solute in the inert solvent are similar in magnitude to those observed in experiments on the dissociation equilibrium of dinitrogen tetroxide.

Long-range potentials for the X 1Σ+ and a 3Σ+ states of the NaK molecule

Abstract: Fluorescence spectra of the NaK molecule excited by the 4765 A and 4880 A lines of an argon-ion laser have been recorded at high resolution by Fourier-transform spectrometry. Constants for the ground state X 1Σ+ and for the first excited state, a 3Σ+, have been determined from a simultaneous least-squares fit to a total of 1758 lines assigned to five systems. Rotationless potentials for these two states have been calculated at internuclear distances out to about 9·3 A for the ground state and to about 9·1 A for the triplet state. The dissociation energy, D e (NaK), is found to be 5274·9 ± 0·5 cm-1, and the long-range potential for X 1Σ+ is given by with V in cm-1, r in A. Values of the potential constants are in satisfactory agreement with the results of recent calculations.

Theoretical prediction of vibrational spectra

Abstract: The complete harmonic force field and the diagonal and first off-diagonal cubic constants of aniline have been calculated ab initio using a 4–21 basis set augmented by addition of d functions to the nitrogen atom. The force constants were then scaled using scale factors optimized previously to give the best fit to the similarly computed vibrational spectra of benzene and its deuterated isotopomers. The vibrational spectra of aniline, aniline-NHD, and aniline-ND2 were then calculated from this scaled quantum mechanical (SQM) force field and compared with experimentally observed spectra. Several corrections were made to previously proposed empirical spectral assignments. Because of computational difficulties, no definitive statement can be made about the torsion or inversion modes of the amino group. Aside from these and the C-H stretching frequencies for which the detailed assignment is still quite uncertain, the average deviation between the observed frequencies and those obtained entirely from the scaled...

Isothermal response theory

Abstract: We derive expressions for the isothermal response of N-particle systems to a mechanical perturbation. Thermostating is achieved using gaussian isothermal equations of motion. Our theory is ergodically consistent in the sense that ensemble averages over the initial phases of the system are equivalent to time averages of the isothermal steady state response.