Showing papers in "Molecular Physics in 1996"
TL;DR: Explicit reversible integrators, suitable for use in large-scale computer simulations, are derived for extended systems generating the canonical and isothermal-isobaric ensembles.
Abstract: Explicit reversible integrators, suitable for use in large-scale computer simulations, are derived for extended systems generating the canonical and isothermal-isobaric ensembles. The new methods are compared with the standard implicit (iterative) integrators on some illustrative example problems. In addition, modification of the proposed algorithms for multiple time step integration is outlined.
1,564 citations
TL;DR: In this article, Rayleigh-Schrodinger perturbation theory is applied to compute second and third-order correlation energies using complete active space self-consistent field (CASSCF) zeroth-order wavefunctions.
Abstract: Rayleigh-Schrodinger perturbation theory is applied to compute second and third-order correlation energies using complete active space self-consistent field (CASSCF) zeroth-order wavefunctions. The first-order wavefunction is expanded in a basis of internally contracted configurations. The zeroth-order Hamiltonian is a sum of one-electron effective Fock operators, which are invariant to unitary transformations among the active orbitals. Comparisons with FCI data are made for the singlet-triplet splitting of CH2 and the barrier height and exothermicity of the F + H2 reaction. Potential energy functions and spectroscopic data are computed for C2, CN, CO, CF,N2, NO, O2, and F2 using large basis sets. It is demonstrated that the third-order results (CASPT3) are significantly more accurate than the second-order (CASPT2) ones. The equilibrium distances and harmonic frequencies obtained with CASPT3 are found to be as accurate as MRCI and RCCSD(T) values, while dissociation energies are generally somewhat too sma...
567 citations
TL;DR: In this article, a scheme for projection of plane wave states onto a localised basis set is proposed, which is used to calculate atomic charges and bond populations, and is illustrated by application to a selection of small molecules.
Abstract: Plane wave basis sets are widely used in ab initio electronic structure calculations even though such an expansion in terms of extended states does not provide a natural way of quantifying local atomic properties. To overcome this deficiency we have implemented a scheme for projection of plane wave states onto a localised basis set. This approach is used to calculate atomic charges and bond populations, and is illustrated by application to a selection of small molecules. Finally, we calculate the changes in these quantities induced by adsorption of a molecule onto a zeolite substrate. Thus, using the procedure described in this paper, plane wave calculations can yield the same information as traditional quantum chemical methods.
286 citations
TL;DR: In this article, a gradient-corrected exchange functional (G96) was introduced, which is similar to Becke's B88 functional and its potential in finite systems is asymptotically unbounded.
Abstract: A new gradient-corrected exchange functional (G96) is introduced. While similar to Becke's B88 functional, it is much simpler and its potential in finite systems is asymptotically unbounded. The mean absolute deviations of the B88 and G96 exchange energies from the corresponding Hartree-Fock values for the atoms H to Ar are 12⋅5 and 8⋅5 mE h, respectively. In combination with the LYP correlation functional, it yields a density functional (G-LYP) that performs similarly to B-LYP on the standard G2 benchmark and we infer that the usefulness of a functional for molecular calculations does not depend critically on its asymptotic behaviour.
232 citations
TL;DR: The Becke-Roussel (BR) exchange functional is derived by assuming a hydrogen-like exchange hole at all spatial points, and it has the attraction of being dependent on both the kinetic energy density and the Laplacian of the density and has no adjustable parameters as mentioned in this paper.
Abstract: The commonly used exchange-correlation functionals of density functional theory and their potentials are examined numerically following the first such investigation by Perdew. They are also investigated for Ne and Kr. Their behaviour for large gradients of the density and for large distances is not satisfactory. In particular, the correct asymptotic r -1 behaviour is difficult to achieve. Following van Leeuwen and Baerends, this is linked to the energy ϵmax of the highest occupied orbital arising from the Kohn-Sham equations. This deficiency is linked also with the poor prediction of molecular polarizabilities. The Becke-Roussel (BR) exchange functional is examined, which is derived by assuming a hydrogen-like exchange hole at all spatial points, and it has the attraction of being dependent on both the kinetic energy density and the Laplacian of the density and has no adjustable parameters. Becke has presented encouraging results using this functional in a hybrid manner. Fully self-consistent Kohn-Sham ca...
226 citations
TL;DR: Exact and local spin density approximation (LSDA) exchange energy density functionals in the Coulomb-attenuated Schrodinger equation (CASE) approximation are constructed in this paper.
Abstract: Exact and local spin density approximation (LSDA) exchange energy density functionals in the Coulomb-attenuated Schrodinger equation (CASE) approximation are constructed. When expressed as asymptotic series in the attenuation parameter ω, their leading terms are identical. If a Gaussian basis set is used, the terms in the exact series (but not the LSDA series) can be evaluated analytically, i.e. without resorting to quadrature on a grid.
203 citations
TL;DR: In this article, a symmetry-adapted perturbation theory is formulated for the calculation of Hartree-Fock interaction energies of closed-shell dimers, which leads to a basis-set independent interpretation of the Hartree Fock interaction energy in terms of basic concepts of the theory of intermolecular forces: electrostatics, exchange and induction.
Abstract: A symmetry-adapted perturbation theory is formulated for the calculation of Hartree-Fock interaction energies of closed-shell dimers. The proposed scheme leads to a basis-set-independent interpretation of the Hartree-Fock interaction energy in terms of basic concepts of the theory of intermolecular forces: electrostatics, exchange and induction. Numerical results for different geometries of HE2, Ne2, He-C2H2, He-CO, Ar-HF, (HF)2 and (H2O)2 complexes show that in the region of the van der Waals minimum the proposed perturbation theory reproduces accurately the Hartree-Fock interaction energy. This fast convergence and relatively small computational cost of the proposed perturbation scheme suggest that this method is a practical alternative for the standard supermolecular approach.
163 citations
TL;DR: In this article, a new semiclassical initial value method is derived for the calculation of bound-bound Franck-Condon spectra, combining the frozen Gaussian approximation of Herman and Kluk with the cellular dynamics algorithm of Heller, taking advantage of the best features of both approaches.
Abstract: A new semiclassical initial value method is derived for the calculation of bound-bound Franck-Condon spectra. The method combines the frozen Gaussian approximation of Herman and Kluk with the cellular dynamics algorithm of Heller, taking advantage of the best features of both approaches. In particular, it is immune to both the problems associated with chaotic trajectories that are encountered in the Herman-Kluk method and the problems associated with caustic singularities that can be encountered in the cellular dynamics method. Example applications to some model two- and three-dimensional bound state problems show that the new method is both accurate and efficient, and moreover that the effort that is required to calculate a bound-bound Franck-Condon spectrum semiclassically does not appear to increase significantly with the dimensionality of the problem.
145 citations
TL;DR: In this article, a detailed analysis of the results obtained with various types of boundary condition was carried out by carrying out Ewald calculations carried out with a central simulation cell adapted to describe the slab geometry of interest.
Abstract: In computer simulations of water between hydrophobic walls the results exhibit a strong dependence upon the boundary conditions applied. With the minimum image (MI) convention the water molecules tend to be orientationally ordered throughout the simulation cell (Valleau, J. P., and Gardner, A. A., 1987, J. chem. Phys., 86, 4162) whereas, if a spherical cut-off (SC) is applied, strong orientational order is found only in the immediate vicinity of the surface (Lee, C. Y., McCammon, J. A., and Rossky, P. J., 1984, J. chem. Phys., 80, 4448). These conflicting observations have remained unresolved, and clearly raise troubling questions concerning the validity of simulation results for water between surfaces of all types. In the present paper we explore this problem by carrying out a detailed analysis of the results obtained with various types of boundary condition. These include Ewald calculations carried out with a central simulation cell adapted to describe the slab geometry of interest. It is shown that the...
125 citations
TL;DR: The detailed stereodynamics of the H+CO2 system have been studied using polarized Doppler resolved laser induced fluorescence to state selectively probe the OH product as discussed by the authors, where lambda-doublet specific differential cross-sections and translational energy distributions were measured, along with the scattering angle dependence of the rotational angular momentum polarization.
Abstract: The detailed stereodynamics of the H+CO2 system have been studied using polarized Doppler resolved laser induced fluorescence to state selectively probe the OH product The lambda-doublet specific differential cross-sections and translational energy distributions were measured, along with the scattering angle dependence of the rotational angular momentum polarization The observed centre-of-mass differential cross-section has significant contributions in both the forward and backward hemispheres, with a small preference for backward scattering, and the measured fraction of available energy released as translational energy is greater than that predicted by statistical models The rotational angular mometum vector of the OH product displays a polarized angular distribution, measured with respect to the reagent relative velocity vector k and the kk' scattering plane, with the π(A'') lambda-doublet component being significantly more strongly polarized than the π(A') level In addition, those products scattere
110 citations
TL;DR: In this paper, a relatively simple expression for intermolecular exchange repulsion based on the isolated wavefunctions of the two overlapping species is proposed, which is based on a simple expression based on isolated wave functions.
Abstract: The exchange repulsion formula proposed by Murrell and co-workers (Proc. Roy. Soc. (Lond.) 1965, A284, 566; J. chem. Phys., 1967, 47, 4916) is considered in detail. Potentially important terms missing in the formalism of Murrell and co-workers are identified and evaluated for the water dimer using several basis sets. Insights into the contributing terms are obtained by using localized molecular orbitals. The results point towards a relatively simple expression for intermolecular exchange repulsion, based on the isolated wavefunctions of the two overlapping species.
TL;DR: In this paper, an integration algorithm using an analytical representation of the interatomic surface is proposed, which is implemented in the program MORPHY 2.0, allowing automatic integration of all atoms in one input deck without external topological information.
Abstract: The theory of atoms in molecules rigorously defines reliable, accurate, consistent and stable average atomic properties. Obtaining these properties poses a complicated integration which is revisited in this paper and critically examined ab ovo. An integration algorithm using an analytical representation of the interatomic surface is proposed. This new technique is implemented in the program MORPHY 2.0, allowing automatic integration of all atoms in one input deck without external topological information. The present algorithm is illustrated via a few selected molecules with emphasis on the accuracy of (high) atomic electrostatic moments. It is shown that the theory of ‘atoms in molecules’ yields sufficiently accurate moments to reproduce the exact ab initio electrostatic potential.
TL;DR: In this article, a two-referencefluid equation of state is developed to describe the pressure-volume-temperature properties of square-well and Lennard-Jones chains, and phase envelopes predicted by such an equation are in good agreement with results of simulations.
Abstract: Monte Carlo simulations of phase equilibria for Lennard-Jones chains of intermediate length are performed in the Gibbs ensemble using configurational bias sampling. Simulations of phase equilibria for square-well chains of up to 100 segments are performed using the NPT-μ method and newly proposed Monte Carlo moves. A two-reference-fluid equation of state is developed to describe the pressure-volume-temperature properties of square-well and Lennard-Jones chains. The phase envelopes predicted by such an equation are in good agreement with results of simulations. This equation is also shown to be superior to models derived from first-order thermodynamic perturbation theory (TPT1).
TL;DR: In this article, total energy pseudopotential calculations were performed on talc and pyrophyllite to assess the success of the method in determining the structure of layered silicates.
Abstract: Ab-initio total energy pseudopotential calculations were performed on talc and pyrophyllite to assess the success of the method in determining the structure of layered silicates. The calculated relative atomic coordinates were in good agreement with experiment. Further calculations were undertaken to determine the probable position of water in hydrated 10 A talc. It was found that the water molecule does not react with the clay's hydroxyl group to form H3O+, as has previously been suggested. Instead it is loosely bound midway between the talc layers, with its oxygen lying above the hydroxyl group. No equivalent hydrated phase was found for pyrophyllite.
TL;DR: In this paper, the Silvera-Goldman potential is used to compare simulation results with experimental data for computing the density and internal energy of normal and para-hydrogen, and the Gibbs free energy is calculated from the PIHMC simulations by an adaptation of Widom's particle insertion technique to a path integral fluid.
Abstract: The thermodynamic properties of normal and para-hydrogen are computed from multiple time-step path integral hybrid Monte Carlo (PIHMC) simulations. Four different isotropic pair potentials are evaluated by comparing simulation results with experimental data. The Silvera–Goldman potential is found to be the most accurate of the potentials tested for computing the density and internal energy of fluid hydrogen. Using the Silvera–Goldman potential, simulation and experimental data are compared on isobars ranging from 0.1 to 100 MPa and for temperatures from 18 to 300 K. The Gibbs free energy is calculated from the PIHMC simulations by an adaptation of Widom's particle insertion technique to a path integral fluid. A new method is developed for computing phase equilibria for quantum fluids directly by combining PIHMC with the Gibbs ensemble technique. This Gibbs–PIHMC method is used to calculate the vapour–liquid phase diagram of hydrogen from simulations. Agreement with experimental data is good.
TL;DR: In this article, the authors conducted an ensemble molecular dynamics simulation of methane and ethane in an atomistic model of AlPO4-5, a molecular sieve with approximately cylindrical channels of diameter 7·3 A.
Abstract: Canonical ensemble molecular dynamics simulations of Lennard-Jones methane and ethane are conducted in an atomistic model of AlPO4-5, a molecular sieve with approximately cylindrical channels of diameter 7·3 A. Methane molecules are able to pass each other in the nanopore and exhibit unidirectional but otherwise ordinary diffusion along the channel axis, with the mean-square displacement directly proportional to time, and a diffusion coefficient calculated at a loading of 0·7 molecules per unit cell at 295 K of 4·70 × 10-4 cm2 s-1. Ethane molecules cannot pass each other easily in the nanopore and for short times exhibit single-file diffusion, i.e., the mean-square displacement is proportional to the square root of the time. After longer times, contributions of ordinary unidirectional diffusion are observed due to the nonzero probability of passing. A slightly larger molecule exhibits pure single-file diffusion. The single-file mobility for the large molecule at 0·7 molecule per unit cell and 295 K is 1·5...
TL;DR: In this article, a series of halogen-substituted carbenes and silylenes were analyzed using the difference-dedicated configuration interaction method, including the singlet-triplet separation.
Abstract: Ab initio calculations including correlation energy are reported on a series of halogen-substituted carbenes and silylenes: CH2, CHF, CF2, CHCl, CCl2, CHBr, CBr2, SiH2, SiHF, SiF2, using the difference-dedicated configuration interaction method. All these compounds with the exception of CH2 have singlet ground states. The singlet-triplet energy differences are in very good agreement with experiment when available, as well as with other high level calculations. The singlet-triplet separation is also determined in trifluoromethyl carbenes, CHCF3, CFCF3, CClCF3 and CBrCF3. The CF3 substituent has little influence on the energy gap since CHCF3 like CH2 has a triplet ground state, with a gap of 11·1 kcal mol-1, and CFCF3, CClCF3 and CBrCF3 have singlet ground states, like CHF, CHCl and CHBr, with gaps of -17·6, -5·4, and -3·5 kcal mol-1.
TL;DR: An extension to chiral phases of a model derived previously to interpret orientational properties in liquid crystal solvents of molecules with arbitrary shape leads, quite naturally, to the definition of a traceless chirality tensor, useful for predicting the structures of twisted nematics induced by chiral solutes as discussed by the authors.
Abstract: An extension to chiral phases of a model derived previously to interpret orientational properties in liquid crystal solvents of molecules with arbitrary shape leads, quite naturally, to the definition of a traceless chirality tensor, useful for predicting the structures of twisted nematics induced by chiral solutes. The magnitude and handedness of the helical pitch in the induced chiral phase depend on the interplay of the chirality tensor components and the ordering of the different axes of the chiral probe in a given nematic solvent. The effect of changing the molecular structure of the solute and the temperature is discussed for a number of typical dopants, including biphenyl, binaphthyl and heptalene derivatives. Although the model has been derived in a form suitable for application to induced cholesteric structures, it contains the basic ingredients to account for the physical behaviour of chiral smectic-C* mesophases.
TL;DR: In this paper, the melting of structure I methane clathrate hydrate has been investigated using NVT molecular dynamics simulations, for a number of potential energy models for water and methane.
Abstract: The melting of structure I methane clathrate hydrate has been investigated using NVT molecular dynamics simulations, for a number of potential energy models for water and methane. The equilibrated hydrate crystal has been heated carefully from 270 K, in steps of 5 K, until a well defined phase instability appears. At a density of 0⋅92 g cm-3, an upper bound for the mechanical stability of the methane hydrate lattice over a timescale of 11 nanoseconds is 330 K. Finite size effects have been investigated by simulating systems of 1 and 8 units cells of methane hydrate. The properties of the melted system upon cooling are examined.
TL;DR: In this article, the authors simulate the permeation of Lennard-Jones gases across a zeolite model membrane using a newly developed dual control volume grand canonical molecular dynamics technique, creating spatial variation in the chemical potential in a dynamical system and hence an accurate simulation of steady-state pressure-driven diffusion.
Abstract: In this work we simulate the permeation of Lennard-Jones gases across a zeolite model membrane. Using a newly developed dual control volume grand canonical molecular dynamics technique, we create spatial variation in the chemical potential in a dynamical system and hence an accurate simulation of steady-state pressure-driven diffusion. The molecular sieving nature of microporous zeolites is discussed, and the results from the simulation are compared very favourably with recent experimentalresults of He, H2 and CH4 permeation through ZSM-5 polycrystalline membranes. A massively parallel algorithm is utilized to give a quick and insightful study of this and other microporous materials for use as membranes.
TL;DR: In this article, a symmetry-adapted perturbation theory (SAPT) is formulated for interaction-induced electrical properties of weakly bound complexes, and asymptotic (large R) expressions are reported for the contributions to the collision-induced dipole moments and polarizabilities up to and including second order in the intermolecular potential.
Abstract: A symmetry-adapted perturbation theory (SAPT) is formulated for interaction-induced electrical properties of weakly bound complexes. Asymptotic (large R) expressions are reported for the contributions to the collision-induced dipole moments and polarizabilities up to and including second order in the intermolecular potential. These long-range expressions require knowledge only of the multipole moments and (hyper)polarizabilities of the isolated monomers. Numerical results are given for the dipole moment of He-H2 and the polarizability of He2 and the accuracy of the SAPT approach is examined by comparison with full configuration interaction results. The role of various physical contributions to the dipole moment of He-H2 and the polarizability of He2 is investigated. The validity of the long-range approximation and the importance of charge penetration (damping) effects are discussed.
TL;DR: In this paper, the chemical potentials of hard-sphere fluids up to very high densities by computer simulation is applied to the case of binary additive hardsphere mixtures.
Abstract: An efficient, recently proposed, method for calculating the chemical potentials of hard-sphere fluids up to very high densities by computer simulation is applied to the case of binary additive hard-sphere mixtures. Mixtures are studied with diameter ratios 0·9, 0·6, and 0·3 at packing fractions up to η = 0·49, for several mole fractions. This paper is believed to give the first direct calculation of the chemical potentials of such mixtures by computer simulation techniques. In addition, pair distribution functions are simulated and compressibility factors calculated from the contact values of these. More particles are used than in earlier works and many more configurations generated. The results are used to test the BMCSL equation of state and systematic deviations are found whose magnitudes increase in systems with large sphere size ratios at small concentrations of the larger component. Two additional routes are explored for calculating the chemical potentials. One is based on a new version of the Gibbs...
TL;DR: In this article, a theoretical investigation of the weakly bound complex formed between benzene and water is presented, where diffusion quantum Monte Carlo methods are used to describe the nuclear motion plus two potentials which give quite good agreement with DZP/MP2 ab initio calculations.
Abstract: A theoretical investigation is presented of the weakly bound complex formed between benzene and water. Diffusion quantum Monte Carlo methods are used to describe the nuclear motion plus two potentials which give quite good agreement with DZP/MP2 ab initio calculations, and simulations were performed for four isotopomers of C6H6H⋅⋅⋅H2O. Although the minimum energy structure can be considered to have only a single hydrogen bond, vibrational averaging renders the hydrogens indistinguishable, a prediction in agreement with the experimental observation that the complex is a symmetric top. The results include zero-point energies, vibrationally averaged structures, rotational constants and wavefunctions. By calculating transition states and rearrangement mechanisms, it is possible to characterize the tunnelling dynamics and calculate the associated tunnelling splittings.
TL;DR: In this paper, the G2,G2(MP2) and G2 (MP2,SVP) levels of theory for benzene, cyclohexane, and other selected hydrocarbons, along with the heats of several isodesmic and isogyric reactions involving these species, are reported at the G 2, G2(G2,MP2)-level of theory.
Abstract: Heats of formation for benzene, cyclohexane and other selected hydrocarbons, along with the heats of several isodesmic and isogyric reactions involving these species, are reported at the G2,G2(MP2) and G2(MP2,SVP) levels of theory. All three models predict heats of isodesmic reactions very accurately. G2 heats of isogyric non-isodesmic reactions are also reliable, but G2(MP2,SVP) heats of such reactions (e.g. hydrogenation) can be significantly in error. In the case of 'large' hydrocarbons, an accumulation of small component errors can cause G2,G2(MP2) and (surprisingly to a lesser extent) G2(MP2,SVP) heats of formation evaluated from atomization energies to be unreliable. However, the accumulated error in the heat of formation can be estimated in advance. In cases where the predicted error is large, more accurate heats of formation can generally be obtained with the help of isodesmic (and to a lesser degree isogyric) reactions rather than by following the standard procedure based on heats of atomization.
TL;DR: In this paper, a density functional theory (DFT) methodology for the ab initio calculation of atomic axial tensors (AATs) using direct, analytical derivative methods and gauge-invariant atomic orbital (GIAO) basis sets is presented.
Abstract: We document a new density functional theory (DFT) methodology for the ab initio calculation of atomic axial tensors (AATs) using direct, analytical derivative methods and gauge-invariant atomic orbital (GIAO) basis sets. AATs are calculated for ethylene oxide. Their accuracy is assessed using AAT sum rules and the experimental electric dipole moment and paramagnetic susceptibility tensor. AATs calculated for the chiral molecule 6,8-dioxabicyclo[3.2.1]octane, in combination with DFT harmonic force fields and atomic polar tensors, are used to predict vibrational rotational strengths and vibrational circular dichroism (VCD) spectra. Their accuracy is assessed by comparison with the experimental rotational strengths and VCD spectrum.The dependence of calculated results on density functional and basis set is explored. The DFT calculations are compared to SCF (Hartree-Fock) calculations carried out in parallel.
TL;DR: The near ultraviolet photolysis of H2S has been investigated further, at nine different excitation wavelengths in the range 244-198 nm and at yet higher resolution than hitherto, using the technique of H (Rydberg) atom photo-fragment translational spectroscopy.
Abstract: The near ultraviolet photolysis of H2S has been investigated further, at nine different excitation wavelengths in the range 244-198 nm and at yet higher resolution than hitherto, using the technique of H (Rydberg) atom photo-fragment translational spectroscopy. Analyses of the total kinetic energy release spectra of the primary H + SH fragments has allowed further refinement of the parent bond dissociation energy, D00(HS-H) = 31440 ± 20 cm-1, and revealed a marked correlation between the wavelength dependence of , the fraction of the available energy partitioned into SH(X) product vibration, and the first of the diffuse vibronic structures evident in the UV absorption spectrum of the H2S parent. Secondary photolysis of the primary SH(X) fragments has also been investigated further. 2 + 1 Resonance enhanced multiphoton ionization spectroscopy has been used to confirm that the S(3P) atoms resulting from 218⋅2 nm photolysis of the primary SH(X) fragments are formed in all three spin-orbit states, with...
TL;DR: In this paper, three different types of prediction for electron affinities determined in this work are: the adiabatic electron affinity, the vertical electron affinity and the vertical detachment energy of the anion.
Abstract: Predictions of molecular structure and energies have been made for each of the members in the ClF n /ClF n - (n = 1-7) series of molecules using density functional theory (DFT). The three different types of prediction for electron affinities determined in this work are: the adiabatic electron affinity (EAad), the vertical electron affinity (EAvert), and the vertical detachment energy (VDE) of the anion. Also reported are the first Cl-F dissociation energies for both the neutral and the anion (D CIFn ). Self-consistent Kohn-Sham orbitals were obtained using four different functional forms and a double-ζ plus polarization (DZP) basis set. When diffuse s- and p-type functions were added to the basis set, the anions were stabilized significantly with respect to the neutrals, and the electron affinity values were increased significantly. Overall, the best agreement with experimental structures was obtained with the DZP++ BHLYP method based upon Becke's half-and-half exchange functional and the Lee-Yang-Parr co...
TL;DR: In this article, the brace notation is applied to formulate the general nth-order Cartesian derivatives of internal coordinates, and to provide closed forms for general, nthorder transformation equations of anharmonic force fields, expressed as Taylor series, from internal to Cartesian or normal coordinate spaces.
Abstract: The brace notation, introduced by Allen and Csaszar (1993, J. chem. Phys., 98 2983), provides a simple and compact way to deal with derivatives of arbitrary non-tensorial quantities. One of its main advantages is that it builds the permutational symmetry of the derivatives directly into the formalism. The brace notation is applied to formulate the general nth-order Cartesian derivatives of internal coordinates, and to provide closed forms for general, nth-order transformation equations of anharmonic force fields, expressed as Taylor series, from internal to Cartesian or normal coordinate spaces.
TL;DR: In this paper, a model tetravalent network fluid, crystal and many glasses are studied by molecular dynamics simulation, and the free energy and pressure of the dense fluid can be simply expressed in terms of the properties of the glasses.
Abstract: A model tetravalent network fluid, crystal and many glasses are studied by molecular dynamics simulation. 171 glasses were made by compressing the fluid with five orders of magnitude variation in the quench rate. The pressure and entropy of each glass are expressed as functions of a single variable, the quench rate dependent limiting density, z 0 of the rigidly jammed state where the pressure diverges. The number of possible glasses with limiting density z0 is approximated by a Gaussian distribution N g(z 0)dz0 = exp{1·2N}exp(-123N(Δz 0)2}dz0, where Δz 0 = z 0 −0·766 and N is the number of molecules. That distribution implies that In {N g(z 0)}/N → 0 as z 0 → 0·864, which suggests that an ideal glass transition would occur to a glass with z 0 = 0·864 with slow compression rates, if the fluid did not freeze. We show that the free energy and pressure of the dense fluid can be simply expressed in terms of the properties of the glasses.
TL;DR: In this article, the role of individual energy components in the total interaction energy involved in the formation of the weakly bound ground state X1Sigma+g of the Hg2 molecule is investigated.
Abstract: Relativistic and non-relativistic all-electron, ab initio methods are used to investigate the role of the individual energy components in the total interaction energy involved in the formation of the weakly bound ground state X1Sigma+g of the Hg2 molecule. The interaction energy is partitioned according to a hybrid approach into a supermolecular repulsive potential and the damped dispersion energy derived from perturbation theory. Both parts are then computed individually and their dependence on relativity and electron correlation investigated. From this analysis, hybrid potentials that comprise different physical interactions are constructed and the importance of specific features is evaluated by comparison of the appropriate hybrid potentials with each other and with the experimental curve. The most detailed model is based on a CASSCF supermolecular potential to which the damped intramonomer correlated dispersion energy series is added. In the relativistic case it yields a potential with quantitatively ...