Effective Potential Function Research Articles

Viscous drag forces in gas operated pressure balances

Accurate determination of all forces acting on the piston in the gas operated pressure balance is a long-standing problem in high precision pressure measurements. A major contribution, responsible for the difference between the actual and the effective areas of the piston, is due to the drag force on the piston, and at a fundamental level surprisingly little is known about this force. We present here a first detailed analysis of the hydrodynamics shear forces acting at the gas–piston interface on a molecular level, using effective intermolecular potential functions and a large-scale non-equilibrium molecular dynamics simulation to model the flow of several gases. We show using the hydrodynamic approach that the drag force on the piston for force-driven plane steady-state flow is exactly one half of the external driving force independent of the boundary conditions, justifying a widely accepted assumption in pressure balance theory, and verify this result in computer simulation for a range of gas densities. The natural fall rates using different gases as the pressure transmission medium were measured experimentally for a range of generated pressures and estimated from computer simulation using force-driven Poiseuille flow. Both results, which are in excellent agreement, show pronounced species dependence. This, however, cannot explain the gas species dependence of the effective area.

Protein folding pathways from replica exchange simulations and a kinetic network model.

We present an approach to the study of protein folding that uses the combined power of replica exchange simulations and a network model for the kinetics. We carry out replica exchange simulations to generate a large ( approximately 10(6)) set of states with an all-atom effective potential function and construct a kinetic model for folding, using an ansatz that allows kinetic transitions between states based on structural similarity. We use this network to perform random walks in the state space and examine the overall network structure. Results are presented for the C-terminal peptide from the B1 domain of protein G. The kinetics is two-state after small temperature perturbations. However, the coil-to-hairpin folding is dominated by pathways that visit metastable helical conformations. We propose possible mechanisms for the alpha-helix/beta-hairpin interconversion.

Hedin’s equations and enumeration of Feynman diagrams

Hedin's equations are solved perturbatively in zero dimension to count Feynman graphs for self-energy, polarization, propagator, effective potential and vertex function in a many-body theory of fermions with two-body interaction. Counting numbers are also obtained in the GW approximation.

Critical value calculations for the screening parameter of Hulthen potential

The critical screening parameter values correspond to the zero energy states of a screened Coulomb potential and, generally, create great numerical instabilities depending on the type of the system and the methods used in the calculations. This is due to the eigenvalue problem weighted by the screening potential which becomes negligible for large arguments. Hence, the conversion of the weighted eigenvalue problem to a regular one with unit weight gains great importance. This can be accomplished via an appropriate coordinate transformation on the radial variable of the relevant Schrödinger’s equation. The transformation is constructed in such a way that the resulting ordinary differential equation differs by an effective potential function from the one which is satisfied by extended Jacobi polynomials. In this form the eigenvalue parameter is proportional to the reciprocal of the screening parameter’s critical value. This can be numerically solved via variational approximation methods. In this work, this approach is used to evaluate the critical values for the Hulthen potential systems.

Statistical mechanics of protein folding by cluster distance geometry.

This is our second type of model for protein folding where the configurational parameters and the effective potential energy function are chosen in such a way that all conformations are described and the canonical partition function can be evaluated analytically. Structure is described in terms of distances between pairs of sequentially contiguous blocks of eight residues, and all possible conformations are grouped into 71 subsets in terms of bounds on these distances. The energy is taken to be a sum of pairwise interactions between such blocks. The 210 energy parameters were adjusted so that the native folds of 32 small proteins are favored in free energy over the denatured state. We then found 146 proteins having negligible sequence similarity to any of the training proteins, yet the free energy of the respective correct native states were favored over the denatured state.

State arbitrariness of the noninteracting fermion model in quantal density functional theory

AbstractIn quantal density functional theory (Q‐DFT), any nondegenerate or degenerate ground or excited state of a system of electrons may be mapped to one of noninteracting fermions such that the equivalent density, energy, and ionization potential are obtained. As these model fermions are noninteracting, their effective potential energy, a local (multiplicative) operator, is the same for a particular state of the model system. The state of the noninteracting fermions, however, is arbitrary in that they could be in a ground or excited state. Hence, within Q‐DFT, there exist, in principle, an infinite number of local effective potential energy functions that can generate the same density as that of the interacting electrons. In this article, we demonstrate this state arbitrariness by mapping a (nondegenerate) ground state of the Hookean atom to two different noninteracting fermion systems: one in a singlet ground state (1s2) and the other in a singlet first excited state (1s2s). In each case, the density and energy determined are equivalent to that of the Hookean atom in the ground state, with the highest occupied eigenvalues of the model system being the negative of the ionization potential. The contrast with the mapping within traditional Kohn–Sham and generalized adiabatic connection Kohn–Sham density functional theories is also made. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004

Gaussian Form of Effective Core Potential and Response Function Basis Set Derived from Troullier−Martins Pseudopotential: Results for Ag and Au

We show that the Troullier-Martins scheme for constructing scalar-relativistic pseudopotentials on a particular density functional for plane-wave calculations can be applied in Gaussian-function based LCAO codes. As an example we consider the noble metals silver and gold and derive 11-electron relativistic effective core potentials, as well as a response function basis set generated by the method of Lippert et al. (J. Phys. Chem. 1996, 100, 6231). With several tests we demonstrate a better performance of these effective core potentials and basis sets as compared to non-DFT-based ECPs of equal quality.

MC/MO SOC-SCF calculation of parity-violating energy of l-alanine zwitterion in aqueous solution

A combination of Monte Carlo (MC) simulation and ab initio spin-orbit coupling SCF (SOC-SCF) method was used to evaluate parity-violating energy, E pv, of l-alanine zwitterion ( l-ALAZ) in aqueous solution. In the MC simulation, the effective pair potential functions, which include the effect of the polarization of l-ALAZ caused by salvation were determined and employed. The 100 solution structures were picked up at every 1 M steps of the MC simulation of the l-ALAZ aqueous solution, and the E pv energy was calculated for the l-ALAZ-(H 2O) n ( n=1–10) clusters in each solution structure by the SOC-SCF/6-31G method. The mean deviation of E pv for the l-ALAZ-(H 2O) 10 clusters was large, 2×10 −20 hartree, and this comes from the fact the coordination of H 2O at the CO 2 site brings about large effect on E pv. Although, the small change in the orientation of H 2O to the CO 2 group may change the sign of E pv, the expectation value of E pv of l-ALAZ is positive for thermally stable conformations in aqueous solution at 298 K. The present MC/MO calculations have shown that the E pv value of l-ALAZ is positive when the solvent effect is introduced by explicit H 2O molecules. This is same as that observed in previous calculations with the continuum model of solvation. The present calculations provide support for the destabilization of l-ALAZ compared to d-ALAZ at thermally accessible conformations in aqueous solution.

Radiative electroweak symmetry breaking revisited.

In the absence of a tree-level scalar-field mass, renormalization-group methods permit the explicit summation of leading-logarithm contributions to all orders of the perturbative series within the effective potential for SU(2)xU(1) electroweak symmetry. This improvement of the effective potential function is seen to reduce residual dependence on the renormalization mass scale. The all-orders summation of leading-logarithm terms involving the dominant three couplings contributing to radiative corrections is suggestive of a potential characterized by a plausible Higgs boson mass of 216 GeV. However, the tree potential's local minimum at phi=0 is restored if QCD is sufficiently strong.

Internal atomic stress near Σ5 tilt grain boundary in aluminium under tension

It is important to clarify the mechanical properties of inhomogeneous structures from the viewpoint of atomic scale to understand the mechanical behaviour of microscopic materials. Thus, the mechanical properties of local regions with inhomogeneous and non-uniform structure have been intensively investigated on the basis of the atomic stress and the elastic constant. In this study, in order to examine the mechanical behaviour of local regions under external load, we conduct atomic tensile simulations on a Σ5-(013) tilt grain boundary in aluminium using the many-body effective medium theory potential function. The structure of the grain boundary consists of two types of atomic layers, one of which has a higher elastic constant near the grain boundary and the other has a lower one. Although the grain boundary consists of identical atomic species, the local region near the grain boundary displays the mechanical properties similar to those of a composite material.

A novel algebraic scheme for describing nonrigid molecules

An algebraic scheme for describing nonrigid polyatomic molecules is introduced and used to characterize bending motion in ‘floppy’ triatomic/tetratomic species. The salient features of quasi-linear and quasi-bent molecules are classified systematically. In particular, the ( ν 5) bending vibration supported by the ground electronic state of fulminic acid (HCNO/DCNO) is shown to exhibit the predicted behavior for nonrigidity. Likewise, the ( ν 2) bending motion of magnesium hydroxide (MgOH/MgOD) demonstrates quantitative application of this novel approach to problems of spectroscopic interest. Effective potential energy functions for these large-amplitude degrees of freedom are extracted by exploiting the method of coherent states.

Correlation between electronic and molecular structure distortions and vibrational properties. I. Adiabatic approximations

Distortions of the electronic and molecular structures of a polarizable molecule in an inhomogeneous electrostatic potential were investigated by using perturbation theory. The second-order electronic energy correction term is directly related to the charge response kernel, which is a site representation of the nonlocal charge response susceptibility. Instead of using the sum-over-state expression for the charge response kernel, we discuss how a finite-field method using point charges can be used to calculate the charge response kernel. By invoking various levels of adiabatic approximations, four different coupled differential equations for the vibrational wave functions were obtained. From the effective vibrational potential functions thus obtained, the molecular structural distortion induced by the external electrostatic potential was shown to be calculable. We also present a discussion on how vibrational properties are affected by the presence of the electrostatic potential. The relationship between the vibrational frequency shift and molecular structural distortion, when a polarizable molecule is exposed to an electrostatic potential, was elucidated.

Formation characteristics of nano-clusters during rapid solidification process of liquid metal Al

Recently, a lot of work, both experimental and theoretical, is focused on nano-clusters formed by evaporation, ionic spray methods and so on [1–6], however, the other kind of nano-clusters, formed in liquid metallic systems during solidification processes, is still neglected up to now. It is well known that for investigating the formation characteristics of nanoclusters during solidification processes of liquid metals, it is necessary to trace the transition processes of microstructural configurations in the system step by step. Under present experimental conditions, it is difficult to complete such a tracking research. Fortunately, due to the rapid development of computer technique, the molecular dynamics method has been used to make such a tracking study, and some very clear physical pictures of the instantaneous processes of microstructure in a small liquid metal system consisting of 500 Al atoms have been obtained in the past years [7–12]. However, in the small system, it is still difficult to research the clusters, especially the nano-clusters. In this paper, based on the author’s works [10–12], a large-scale liquid system consisting of 400 000 Al atoms has been used to perform a simulation study on the formation process of nano-clusters during rapid solidification by using constant-pressure molecular dynamics method and parallel algorithm on the Clare supercomputer. The conditions for simulation calculation are as follows: at first, the 400 000 Al atoms are placed in a cubic box and their calculation task is distributed into 40 machines, and then the system runs under periodic boundary condition. The interatomic potential adopted here is the effective pair potential function of the generalized energy independent non-local model–pseudopotential theory developed by Wang et al. [13, 14], and the function is

An effective potential function with enhanced charge-transfer-type interaction for hydrogen-bonding liquids

The potential energy function (PEF) has been derived to perform the liquid simulations using the Monte Carlo method for three hydrogen-bonding systems, water, hydrogen fluoride, and ammonia. The PEF is a pair potential function of the overlap integrals between molecules and of the Coulomb interactions between atomic fractional charges. The parameters of the PEF are easily determined in order to reproduce the ab initio pair interaction energies. The lack of many-body interactions, however, prevents the reproduction of the liquid structures. The PEF consists of some physically meaningful terms, and using the characteristics of the function, it is found that the enhancement of a component in the PEF reasonably succeeds in producing the liquid structures. The general procedure for obtaining an effective pair potential function for the hydrogen-bonding systems is reported by a simple modification to the PEF.

Puddle-skimming: An efficient sampling of multidimensional configuration space

We examine the effectiveness of a simple method for surmounting energy barriers and enhancing the exploration of configuration space in Monte Carlo (MC) and molecular dynamics (MD) simulations. Proposed previously for treating surface diffusion [M. M. Steiner, P.-A. Genilloud, and J. W. Wilkins, Phys. Rev. B 57, 10236 (1998)], the method has widespread applicability and is particularly advantageous for systems with potential energy landscapes whose features are not known a priori. The algorithm requires selection of a single parameter, a “boost energy” EB. The MC or MD simulation is carried out on an effective potential energy function that is equal to the true potential energy when it is greater than EB, but is equal to EB otherwise. Since the effective potential energy is, therefore, never less than EB, deep energy minima are removed analogous to a rough landscape that has been flooded with water. The bias introduced by altering the potential energy function in this way is easily and rigorously removed “on-the-fly.” We test the method with a MD simulation of the equilibrium populations of conformations of n-pentane. The method recovers the canonical equilibrium distribution with dramatically increased sampling efficiency and modest additional computational overhead, over a range of temperatures. In cases for which the potential energy function can be written as a sum of terms, the energy boost can be applied to the selected terms rather than to the entire potential energy function. We illustrate this by application to the dihedral angle term only of the empirical n-pentane potential energy function and show that this further enhances sampling efficiency. The simple nature of this algorithm allows it to be readily scaled to high-dimensional systems. We discuss the prognosis for applying this method to more complex systems such as liquids and macromolecules.

On the Anharmonic XCN Bending Modes of the Quasilinear Molecules BrCNO and ClCNO

The millimeter-wave spectra of the unstable halofulminates BrCNO and ClCNO were recorded at room temperature in several frequency intervals between 52 and 230 GHz. Besides rotational transitions in the vibrational ground state, transitions in numerous thermally excited states of the XCN bending mode (X = Br or Cl) could be observed. The irregular sequence of these satellites indicated that in both molecules, the XCN bending mode is highly anharmonic. Indeed, the XCNO molecules exhibit truly quasilinear behavior. From semirigid bender analyses of the rotational data, the effective potential functions and their barriers to linearity were determined. The barrier heights were found to be 130.82 (56) cm-1 for BrCNO and 166.86 (84) cm-1 for ClCNO, resulting in quasilinearity parameters γ0 of +0.362 and +0.416, respectively.

On the Low-Lying CCN Bending Mode of the Nearly Linear Molecule NCCNO

The low-lying CCN bending mode of cyanofulminate, NCCNO, was characterized by rotational spectroscopy in the millimeter-wave and submillimeter-wave range as well as by rovibrational spectroscopy in the far-infrared range. The spectra exhibit the gross features of a linear molecule. However, a closer qualitative analysis regarding the low-lying CCN bending mode revealed significant deviations from a harmonic bending mode that is normally found in a linear molecule. This result was confirmed by a quantitative analysis of the combined data with an effective Hamiltonian for a linear molecule. In linear molecule notation, the term value of the first excited state ν7 is 80.524 182 (10) cm-1, and the term values for the l7 = 0 and l7 = 2 levels of the second excited state 2ν7 are 166.118 254 (16) and 164.604 243 (22) cm-1. A semirigid bender analysis of our data, including rotational transitions of the isotopomers 15NCCNO, N13CCNO, NCC15NO, and NCCN18O observed in natural abundance, yielded a considerable quartic contribution to the effective CCN bending potential function V(ρ)/cm-1 = 747.40 (81) × (ρ/rad)2 + 959.2 (24) × (ρ/rad)4.

Generation of converging Regge-pole bounds: a new formulation of complex rotation quantization

We propose an unprecedented bounding theory which generates converging bounds to the Regge poles of rational fraction scattering potentials. This is made possible by the recent work of Handy ( 2001 J. Phys. A: Math. Gen. 34 L271) and Handy and Wang (2001 J. Phys. A: Math. Gen. 34 8297) which transforms the Schrödinger equation into an equivalent fourth-order, lineardifferential equation for the probability density. This new representation is better suited for numerical considerations, since the rapid oscillations of the Regge-pole wavefunction are factored out. More importantly, the moments of the probability density can be constrained (and thereby the underlying complex angular momentum parameter of the effective potential function) through appropriate moment problem theorems, as incorporated within the eigenvalue moment method of Handy and Bessis (1985 Phys. Rev. Lett. 55 931) and Handy et al (1988 Phys. Rev. Lett. 60 253).

Application of Integral Equation Joined with the Chain Association Theory to Study Molecular Association in Sub- and Supercritical Water

In this report, the Percus−Yevick and the Ornestein-Zernike integral equations are solved simultaneously for the radial distribution functions of water at various state conditions, including sub- and supercritical states. The intermolecular potential function used in this study consists of an effective Kihara potential, which is derived for associated fluids. For derivation of the effective potential function, water is considered as a mixture of associated species due to hydrogen bonding. The contribution of hydrogen bonding is considered in the formulation of the effective Kihara potential parameters through the application of the analytic chain association theory. There is a good agreement between the present calculations and the experimental data in predicting the oxygen−oxygen radial distribution function near the critical point and at supercritical conditions for which experimental data are available. It is also concluded that at supercritical conditions a considerable degree of hydrogen bonding may be still present in the form of linear chain association. Therefore, the chain association model is valid near the critical point and at supercritical conditions instead of other structure models for the investigations on molecular structure of water.

Internal dynamics in azetidine: A microwave and ab initio study

The internal dynamics of interconversion between equivalent conformations due to the coupling between ring puckering and NH inversion in azetidine has been investigated by rotational spectroscopy and ab initio computations. Analysis of the rotational spectra in the 8–220 GHz region has been completed for the ground state and first four excited states of the ring-puckering vibration. Rotational transitions exhibit a characteristic doubling originated by tunneling between equivalent conformations through a C2v barrier, which is related to symmetric (A1) and antisymmetric (B1) inversion states. Additionally, nuclear quadrupole hyperfine structure arising from the N nucleus could be resolved for low-J transitions. Accurate rotational and centrifugal distortion parameters together with the energy difference between inversion states derived from μc-type inversion transitions have been derived for each ring-puckering state using a two-state Hamiltonian. An effective monodimensional reduced potential function for the ring-puckering vibration V(X)=10.82(X4+14.29X−8.93X2−0.28X3) has been found consistent with the observed experimental variation of the rotational and centrifugal distortion constants with ring-puckering. This asymmetric single minimum potential function supports the existence of only one stable equatorial form. The barrier to interconversion between equivalent equatorial conformers, related to the C2v conformation of azetidine in which the ring atoms and the NH group are coplanar, has been estimated to range between 1900 and 2600 cm−1. The strong dependence of the dipole moment and quadrupole coupling constants with ring-puckering vibrational state evidence structural changes that occur along the ring-puckering coordinate.