Showing papers in "Molecular Physics in 1977"
TL;DR: In this paper, the authors investigated the application of the computer simulation method of molecular dynamics to macromolecules and compared different algorithms for integrating the equations of motion, both theoretically and in practice.
Abstract: The application of the computer simulation method of molecular dynamics to macromolecules is investigated. The protein trypsin inhibitor (BPTI), consisting of 454 united atoms, is used as an example. Different algorithms for integrating the equations of motion are compared, both theoretically and in practice. It is examined to what extent the chain structure of a macromolecule allows a reduction of the computational effort by the introduction of constraints in the dynamics of the chain. A calculational scheme is proposed, by which constraints can be incorporated in predictor-corrector algorithms. The optimum choice of an algorithm depends on the desired accuracy of the solution and on the character of the forces acting on the molecule, viz. whether these are noisy or not. For nonconstraint dynamics a Gear predictor-corrector algorithm yields the best results, whereas for constraint dynamics the Gear and Verlet algorithms produce comparable results. The application of bond-length constraints reduces the re...
1,589 citations
TL;DR: In this paper, a new algorithm is presented for the molecular dynamics simulation of rigid polyatomic molecules, which consists of solving the eulerian rigid body equations using quaternions to represent orientations, by a fifth-order predictor corrector method.
Abstract: Using a transformation of the rigid body equations of motion due to Evans [4], a new algorithm is presented for the molecular dynamics simulation of rigid polyatomic molecules. The algorithm consists of solving the eulerian rigid body equations, using quaternions to represent orientations, by a fifth-order predictor corrector method. Compared to previous methods, it is shown that this algorithm leads to an order of magnitude increase in computing speed.
436 citations
TL;DR: In this article, the Lattman metric is shown to be a scalar multiple of the metric tensor which arises naturally from the Jacobi formulation of the action principle for spherical tops.
Abstract: New sets of variables are studied which should lead to significantly improved numerical stability and efficiency for computer stimulation studies of rigid classical molecules. The search for these new variables is made by finding variables which lead to the simplest (i.e. euclidean) expressions for the metric tensor of orientation space. It is shown that the intuitively defined Lattman metric [1] is a scalar multiple of the metric tensor which arises naturally from the Jacobi formulation of the action principle for spherical tops. It is then shown that Euler's quaternion parameters lead to a euclidean form for the orientation metric. These parameters lead to many associated simplifications in the equations of motion of classical rigid bodies including the removal of singularities and spurious behaviour near θ = 0. It is felt that these benefits will translate into increased accuracy and efficiency both for numerical integration of the equations of motion and for performing Monte Carlo integrations of phas...
392 citations
TL;DR: In this article, the dependence of the properties on the molecular anisotropy defined by the reduced distance l*=l/σ between the centres in the range 0·5−0·8 was investigated.
Abstract: Molecular dynamics calculations have been carried out for model liquid systems of N (=108 or 256) molecules interacting through two Lennard-Jones (12–6) centres coinciding with the positions of the atomic masses (the ‘atom-atom’ pair potential). The objectives were (a) to study the dependence of the properties on the molecular anisotropy defined by the reduced distance l*=l/σ between the centres in the range 0·5–0·8; and (b) to compare the computed quantities with those of real liquids (F2, Cl2, Br2, CO2). This paper deals with thermodynamic and structural features. Time-dependent correlations will be treated in a future communication. In the liquid region not too far from the triple point the energy and pressure isochores are well represented by straight lines, the slopes of which increase with density and anisotropy. Thermodynamically consistent expressions for the energy and pressure as functions of density and temperature have been obtained for each system. With Lennard-Jones parameters adjusted so as...
334 citations
TL;DR: In this article, a simple general method for obtaining selection rules for the ro-vibronic states of reactant and product molecules connected in a reactive collision is discussed, neglecting only the coupling with nuclear spin, rather stringent restrictions are found to occur in systems involving three and more identical nuclei.
Abstract: A simple general method for obtaining selection rules for the ro-vibronic states of reactant and product molecules connected in a reactive collision is discussed. Neglecting only the coupling with nuclear spin, rather stringent restrictions are found to occur in systems involving three and more identical nuclei. Several radical and ion molecule reactions of current interest are used to illustrate this finding. Even more restrictive selection rules are found when assuming weak coupling (‘ incomplete exchange of identical nuclei ’) in the intermediate reaction complex. These include the well-known selection rules for inelastic collisions of molecules with several identical nuclei, but less trivial examples with chemical reaction are also presented. The symmetry corrections and nuclear spin statistics in statistical theories of scattering (including the prior distributions for the information-theoretic approach) are derived. Further applications are discussed briefly.
292 citations
TL;DR: Improved three-parameter atomic pseudopotentials were theoretically determined from lithium to krypton in this article, and accurate expressions for the pseudopotent functions were given for the three parameters.
Abstract: Improved three-parameter atomic pseudopotentials are theoretically determined from lithium to krypton. In view of further molecular calculations, accurate expressions are given for the pseudopotent...
291 citations
TL;DR: In this paper, the orientation-averaged long-range dipole-dipole dispersion energy coefficients, C 6(A, B), have been determined for all possible pair interactions involving ground state H, Li, N, O, H2, N2, O2, NH3, H 2O, NO, and N2O.
Abstract: Accurate values for the orientation-averaged long-range dipole-dipole dispersion energy coefficients, C 6(A, B), have been determined for all possible pair interactions involving ground state H, Li, N, O, H2, N2, O2, NH3, H2O, NO, and N2O. The calculations have been carried out by employing dipole oscillator strength distributions for these species that have been constructed (except in the case of H) by using discrete oscillator strength, photo-absorption, and high energy inelastic scattering data and by requiring the distributions to reproduce the Thomas-Reiche-Kuhn sum rule and, in the case of the molecules, available accurate refractivity and dispersion measurements for the relevant dilute gases. These oscillator strength distributions were also used to evaluate the refractivity R(λ), as a function of wavelength λ in the visible and ultra-violet region below the ultra-violet absorption thresholds, and the dipole oscillator strength sums S -2l , l = 1, 2, …, 7, for each atom and molecule. The calculated...
289 citations
TL;DR: In this article, the authors explore the feasibility of widening the scope of the nonperturbative open-shell many-body formalism, which utilizes an Ursell type of cluster expansion about certain starting wavefunctions spanning a model space.
Abstract: In this paper we explore the feasibility of widening the scope of the non-perturbative open-shell many-body formalism recently developed by us [1], which utilizes an Ursell type of cluster expansion about certain starting wavefunctions spanning a model space. We show that, by generalizing the definition of the cluster expansion operator, we can incorporate into the model space (a) determinants differing widely in energy and (b) determinants differing in their number of electrons. This flexibility is useful for the calculation of difference energies of interest, like transition energies and ionization potentials of atomic and molecular systems. The generalized scheme has been tested on the 4π-electron problem trans-butadiene for which, by choosing a very general model space, we have calculated the energies of the ground, the lowest π-π* singlet and triplet and the first ionization potential by choosing a single composite cluster expansion operator for all states. Results for some more restricted choice of ...
259 citations
TL;DR: In this article, the density matrix form of Hartree-fock perturbation theory is developed for the case in which the basis functions themselves are perturbations-dependent.
Abstract: The density matrix form of Hartree-Fock perturbation theory is developed for the case in which the basis functions themselves are perturbation-dependent. Energy expressions are derived, through second order, for both single and double perturbations. The theory is applied in the calculation of electric dipole polarizabilities and hyperpolarizabilities for atoms (He, Be) and molecules (H2, LiH), with excellent results. The high computational efficiency of the method is discussed and possibilities of further development are outlined.
214 citations
TL;DR: In this paper, a supplement to Blum's theory for asymmetric electrolytes is presented. But it does not address the problem of asymmetric electrophoresis, and it cannot explain the asymmetric EH.
Abstract: (1977). Supplement to Blum's theory for asymmetric electrolytes. Molecular Physics: Vol. 33, No. 4, pp. 1195-1198.
187 citations
TL;DR: In this article, a theory of vibrational relaxation in liquids is presented in which the vibrations are loosely coupled to a bath or lattice of molecular translations and rotations by intermolecular forces.
Abstract: A theory of vibrational relaxation in liquids is presented in which the vibrations are loosely coupled to a bath or lattice of molecular translations and rotations by intermolecular forces. Using the second-order perturbation expressions familiar from magnetic resonance the secular contribution to the line width is calculated. Different coupling paths are considered and expressions given for the line widths in a liquid mixture in terms of number densities and diffusion coefficients valid when reorientation is slow and translation diffusional.
TL;DR: An effective vibration-rotation hamiltonian for the ground electronic state of a diatomic molecule is derived in this paper, where the contact transformation used to account for the effect of the excited electronic states is complicated by the parametric dependence of the zerothorder electronic energies on the internuclear distance.
Abstract: An effective vibration-rotation hamiltonian for the ground electronic state of a diatomic molecule is derived. The contact transformation used to account for the effect of the excited electronic states is complicated by the parametric dependence of the zeroth-order electronic energies on the internuclear distance. The effective vibration-rotation hamiltonian contains an effective internuclear potential and two effective reduced masses, one for the vibrational and one for the rotational kinetic energies. Although the method is applied to 1Σ diatomic molecules it can readily be extended to other states and polyatomic molecules.
TL;DR: In this article, the use of Pade approximants in the theory of multipolar and ionic potentials was extended to mixed multipole terms and inclusion of polarizability.
Abstract: We extend earlier work of ours on the use of Pade approximants in the theory of multipolar and ionic potentials. The new features are (i) extension of our work to mixed multipole terms and inclusion of polarizability, (ii) formulation and implementation of a systematic means of getting analytic approximations for all the two-body and three-body terms appearing in the theory, (iii) assessment of the ionic Pade results in the low-concentration region important in ionic-solution applications, (iv) use of the Pade in a mixed perturbation theory of improved accuracy in that low-concentration regime. The results of (iii) and (iv) are used to study the remarkable lowdensity charged-sphere critical point recently discovered by Stell, Wu, and Larsen.
TL;DR: In this article, an integral equation theory based upon a simple linearization of the hypernetted-chain closure approximation is solved numerically for dipolar hard spheres, and the pair-correlation function and thermodynamic properties are found to be in excellent agreement with Monte Carlo results.
Abstract: An integral equation theory based upon a simple linearization of the hypernetted-chain closure approximation is solved numerically for dipolar hard spheres. The pair-correlation function and thermodynamic properties are found to be in excellent agreement with Monte Carlo results. The dielectric constant in this approximation is larger than that predicted by previous theories.
TL;DR: An analysis of the field dependence of CIDNP generated in reactions of flexible polymethylene biradicals is given in this article, where the nuclear polarization is calculated by a stochastic Liouville method.
Abstract: An analysis is given of the field dependence of CIDNP generated in reactions of flexible polymethylene biradicals. Nuclear polarization is calculated by a stochastic Liouville method, in which the ...
IBM1
TL;DR: In this paper, Monte Carlo values for the equation of state of the two-dimensional Lennard-Jones fluid are reported and a semi-empirical correction term to the second-order Barker-Henderson theory is constructed.
Abstract: Monte Carlo values for the equation of state of the two-dimensional Lennard-Jones fluid are reported. The agreement with previous simulations is good, with the exception of the critical point region. However, the estimates of the critical temperature and density given here are lower than those previously reported. The first and second-order Barker-Henderson and first-order Weeks-Chandler-Andersen perturbation theories are applied to this system and are found to be satisfactory only at high densities. A semiempirical correction term to the second-order Barker-Henderson theory is constructed. The resulting parameterization of the Monte Carlo data is found to be accurate and useful at all densities and temperatures for which the Monte Carlo data exist.
TL;DR: In this article, the effects of boundary conditions on Monte Carlo calculations for dipolar fluids were investigated, and it was concluded that theories giving g(12) for an infinite system should not be evaluated by direct comparison with Monte Carlo results, and two alternative methods by which meaningful comparisons can be made are described in the text.
Abstract: This paper is a systematic investigation of the effects of boundary conditions upon Monte Carlo calculations for dipolar fluids. Results are reported for the minimum image (MI), spherical cut-off (SC) and uniform reaction field methods. All three approximations are shown to give different pair distribution functions, g(12), and none yields the infinite system result. It is concluded that theories giving g(12) for an infinite system should not be evaluated by direct comparison with Monte Carlo results. Two alternative methods by which meaningful comparisons can be made are described in the text. The dependence of the thermodynamic properties upon boundary conditions is important only at large values of the dipole moment. For small to moderate dipoles both MI and SC are found to give reasonable estimates of the dielectric constant.
TL;DR: In this paper, the nonlinear susceptibility tensors in irreducible spherical form are used to treat coherent anti-Stokes Raman scattering (CARS) in detail and a comparison is made with conventional RAMS.
Abstract: By putting the non-linear susceptibility tensors in irreducible spherical form it is found that orientation averaging, selection rules, and the angular dependence of intensity on field polarizations all follow in a straightforward way. These spherical tensor techniques are used to treat coherent anti-Stokes Raman scattering (CARS) in detail and a comparison is made with conventional Raman scattering. The selection rules for both processes are shown to be the same. The paper concludes with a brief discussion of the rotational structure in CARS.
TL;DR: In this paper, the polarized scattering intensity is calculated in terms of an effective isotropic polarizability α 0 eff and the ratio (α 0 eff/α 0)2, where α 0 is the gas phase anisotropy.
Abstract: The polarized scattering intensity is calculated, in the Einstein-Smoluchowski approximation, for four thermodynamic states of a model diatomic; these are the same states for which the depolarized intensity was calculated in the first article (I) of this series. The polarized intensity is discussed in terms of an ‘effective isotropic polarizability’ α 0 eff and the ratio (α 0 eff/α 0)2, where α 0 is the gas-phase isotropic polarizability, and is both expressed formally and tabulated for the four states. Similarly in (I), depolarized intensities were discussed in terms of the ratio, (γ/Δα)2, where γ is the ‘effective polarizability anisotropy’ and Δα the gas-phase anisotropy. We find that (α 0 eff/α 0)2 lies much closer to unity than does (γ/Δα)2, in agreement with existing experimental data, which indicates that the introduction of effective polarizabilities is relatively unimportant or important, respectively, as polarized or depolarized scattering is considered.
TL;DR: In this article, an extension of graph theoretical techniques developed in an earlier paper is used to analyse the pair distribution function and the dielectric constant of polarizable electric dipole with finite permanent moment.
Abstract: We examine a classical fluid composed of molecules which contain a polarizable electric dipole with finite permanent moment. The long-ranged dipolar and the short-ranged interactions are treated on a different footing by expanding relative to a reference system characterized by the absence of electrostatic interactions. Extensions of graph theoretical techniques developed in an earlier paper are used to analyse the pair distribution function and the dielectric constant. Reduction of the number of graphs and their complexity is effected by introducing renormalizations of the permanent moment and the polarizability. The analysis leads to the definition of a new function w(12), which is free of terms dependent on the shape of the sample. For polar, polarizable molecules the direct correlation function lacks translational invariance; its role as a basic quantity is ceded to w(12). The pair distribution function and the dielectric constant e are expressed in terms of w(12) and two closely related functions. At...
TL;DR: In this paper, a fully coupled SCF perturbation theory is developed in matrix form for any number of simultaneous perturbations, and explicit expressions for all energy terms up to fourth order in the SCF parameters are given.
Abstract: A fully coupled SCF perturbation theory is developed in matrix form for any number of simultaneous perturbations. Explicit expressions are given for all energy terms up to fourth order in the perturbation parameters. In succeeding papers these expressions are used to produce expressions for and values of several molecular properties dependent upon the simultaneous application of electric and magnetic fields.
TL;DR: Experimental and theoretical photo-absorption and high energy inelastic electron scattering cross sections, together with refractivity and sum rule constraints, are used to construct the non-relati....
Abstract: Experimental and theoretical photo-absorption and high energy inelastic electron scattering cross sections, together with refractivity and sum rule constraints, are used to construct the non-relati...
TL;DR: In this paper, the vibrational relaxation rates of the ν1(A 1)C-H and C-D stretching fundamentals in liquid CHCl3 and CDCl3 have been measured as a function of pressure from 1 bar to 4·5 kbar within the temperature range 30°C to 90°C.
Abstract: The Raman line shapes of the ν1(A 1)C-H and C-D stretching fundamentals in liquid CHCl3 and CDCl3 have been measured as a function of pressure from 1 bar to 4·5 kbar within the temperature range 30°C to 90°C. Densities have also been determined under the same experimental conditions. The vibrational relaxation rates are obtained from the isotropic component of the Raman band and the experimental results can be summarized as follows: (i) as T increases at constant density the vibrational relaxation rate increases; (ii) at constant T, the increase in density produces an increase in the relaxation rate; (iii) an increase in temperature at constant pressure results in an increased relaxation rate. The above three cases hold for the CDCl3 liquid, whereas only (ii) may be stated for the CHCl3 liquid. The experimental vibrational data are interpreted in terms of the Kubo stochastic line-shape theory and the collinear-isolated-binary-collision model proposed by Fischer and Laubereau. Application of the Kubo forma...
TL;DR: In this article, an orbital justification to the use of the phenomenological spin hamiltonian of the Heisenberg-Dirac-Van Vleck model is given, and the exchange interaction parameter J is expressed as a function of orbital integrals related to the real mechanism of the phenomenon.
Abstract: Exchange interaction in ring chains of N transition ions with n unpaired electrons per ion is investigated. The study is focused on the case where N becomes very great, i.e. on the case of one-dimensional magnetic compounds. The main results are the following: (i) An orbital justification to the use of the phenomenological spin hamiltonian of the Heisenberg-Dirac-Van Vleck model is given. (ii) The exchange interaction parameter J is expressed as a function of orbital integrals related to the real mechanism of the phenomenon. The key expression is in which Sμμ is the overlap integral between two magnetic orbitals of the same symmetry centred on nearest-neighbour transition ions, Δμ is the width of the molecular orbital band built from the magnetic orbitals of symmetry μ for the spectroscopic term of highest spin multiplicity. Finally J μν is the two-electron exchange integral between magnetic orbitals of symmetry μ and ν respectively, centred on nearest-neighbour ions.
TL;DR: In this paper, density-dependent 13C nuclear magnetic shielding has been found for each of the pure gases CH4, C2H6, C 2H4, CO and CO2, and for several binary mixtures of gases.
Abstract: Density-dependent 13C nuclear magnetic shielding has been found for each of the pure gases CH4, C2H6, C2H4, CO and CO2, and for several binary mixtures of gases. For methane gas the density dependence is greater at higher temperatures in contrast to expectation and the observed temperature dependence of the shielding at zero density is attributable to nuclear motion. 13C magnetic shielding is considerably higher in the gas phase than in the liquid phase and the difference varies for chemically non-equivalent 13C nuclei by amounts which are well above the level of experimental error.
TL;DR: In this paper, the properties of a particle undergoing circular rotational motion in an N-fold cosine potential are investigated in detail and the rate equation for the probability function is given and order parameters are defined.
Abstract: The properties of a particle undergoing circular rotational motion in an N-fold cosine potential is investigated in detail. The rate equation for the probability function is given and order parameters are defined. The self-correlation functions of cos nϕ and sin nϕ (ϕ is the azimuthal angle) are calculated. The neutron incoherent scattering law is derived. The elastic incoherent structure factor is calculated directly. The jump model among N equidistant sites and the continuous rotational diffusion model are found as limiting cases. The problem of a more general potential is also discussed.
TL;DR: In this article, the authors considered the problem of moving an axially symmetric rod, 2, about another, 1, such that their relative orientation Θ 12 never changes and they never penetrate each other.
Abstract: We consider moving an axially symmetric rod, 2, about another, 1, such that (A) their relative orientation Θ12 never changes and (B) they never penetrate each other. These constraints define uniquely a closed surface S inside which the second rod's centre can never be found. We determine S explicitly as a function of the rod dimensions and of the fixed angle ϑ12 (Θ12) between their axes. We then treat fluids of anisotropic molecules whose pair interaction energy can be written as the sum of a hard rod (h.r.) repulsion, v h.r., and a dispersional attraction, v attr. The effective one-body potential is given approximately by where ρ is the number density and f(Θ) is the fraction of molecules having orientation Θ. Using our results for the surface S ϑ12 we evaluate this mean field for typical ratios of molecular length (l) to width (w). Even when the attractive part of the pair potential consists only of the familiar Ψ(Θ) can be expressed in the form where the bars over the Pn 's denote averages over the ori...
TL;DR: In this paper, it is pointed out that it is more advantageous to express the Franck-Condon factors in terms of the gradient of the final state potential energy surface at the equilibrium geometry of the initial electronic state.
Abstract: In the customary calculation of vibrational intensity distribution in electronic spectra of polyatomic molecules, the Franck-Condon factors are expressed in terms of the difference of the equilibrium geometries of the initial and the final state. It is pointed out that it is more advantageous to express the Franck-Condon factors in terms of the gradient of the final state potential energy surface at the equilibrium geometry of the initial electronic state. The ionization and excitation of the NH3 molecule are considered to illustrate this fact. Although the change in geometry is known accurately in this case, rather poor Franck-Condon factors are obtained with the customary harmonic method. Remarkably enough, even the use of anharmonic potential energy functions, though rather laborious, does not improve the situation. The reason for this failure is discussed. Expanding, on the other hand, the final state potential energy around the initial state equilibrium geometry, we obtain satisfactory Franck-Condon ...
TL;DR: In this paper, the authors derived a kinetic equation for the description of the relaxation of the isotropic (rotational invariant) part of the Raman polarizability correlation function, with a goal to aid interpretations of experimental results.
Abstract: This paper is concerned with the derivation of a kinetic equation for the description of the relaxation of the isotropic (rotational invariant) part of the Raman polarizability correlation function, with a goal to aid interpretations of experimental results. The isotropic polarizability correlation function is closely associated with the Raman spectral line-shape of a totally symmetric mode of an ensemble of molecules in a liquid. The kinetic equation was derived for an interaction potential consisting of two parts: one associated with a hard-core potential which is assumed to be unaffected by the intramolecular vibrations, and another associated with a potential which is modulated by molecular vibrations. The interaction potential chosen for this work is applicable to the intermolecular dipole-dipole interaction, hydrogen bonding interaction and other types of interactions. While we have included in the derivation the mechanism of the vibrational energy dissipation to nonvibrational degrees of freedom an...
TL;DR: In this article, a proton magnetic relaxation investigation has been carried out on a further six polycrystalline amino acids from 130 to 500 K at 60·2 MHz and in two cases at 20·0 MHz also Asparagine and glutamine with amide side chains.
Abstract: A proton magnetic relaxation investigation has been carried out on a further six polycrystalline amino acids from 130 to 500 K at 60·2 MHz and in two cases at 20·0 MHz also Asparagine and glutamine with amide side chains exhibit closely similar relaxation minima well accounted for in terms of the Kubo-Tomita relaxation theory by NH3 group reorientation in the zwitterion form of the molecules Cysteine and phenylalanine exhibit two relaxation mechanisms, one at higher temperatures due to NH3 group reorientation and a weaker mechanism at lower temperatures ascribed to motion of their side chains The unusual relaxation behaviour of arginine arises from the protonation of the guadinium side group, so generating three reorienting amino groups in the molecule The exceptionally long relaxation times of proline stem from the rigidity of its ring structure Relaxation constants, activation energies and time factors for all the amino acids studied in this series are tabulated and discussed For 18 amino acids th