Exact on-event expressions for discrete potential systems

The properties of systems composed of atoms interacting though discrete potentials are dictated by a series of events which occur between pairs of atoms. There are only four basic event types for pairwise discrete potentials and the square-well/shoulder systems studied here exhibit them all. Closed analytical expressions are derived for the on-event kinetic energy distribution functions for an atom, which are distinct from the Maxwell-Boltzmann distribution function. Exact expressions are derived that directly relate the pressure and temperature of equilibrium discrete potential systems to the rates of each type of event. The pressure can be determined from knowledge of only the rate of core and bounce events. The temperature is given by the ratio of the number of bounce events to the number of disassociation/association events. All these expressions are validated with event-driven molecular dynamics simulations and agree with the data within the statistical precision of the simulations.     

Rotational symmetry of the molecular potential energy in the Cartesian coordinates

We consider the molecular Born-Oppenheimer potential energy as a function of atomic Cartesian coordinates and discuss the non-stationary Hessian properties arising due to rotational symmetry. A connection with the extended Hessian theory is included. New applications of Cartesian representation for examining and correcting raw numerical Hessian data and a simple formulation of harmonic vibrational analysis of partially optimized systems are proposed. Exemplary calculations for the porphyrin molecule with an internal proton transfer are reported. We also develop the normal transformation method to incorporate the rotational symmetry into the approximate analytical potentials, which are parametrized in the Cartesian coordinates. The transformation converts the coordinates from the space fixed frame to the frame which translates and rotates with the molecule and is determined by the Eckart conditions. New simple analytical formulas for the first and second derivatives of the transformed potential are derived. This fast method can be used to calculate the potential and its derivatives in the simulations of chemical reaction dynamics in the space fixed Cartesian frame without the need to constrain the molecular rotation or to define the local non-redundant internal coordinates.     

Design considerations for electrostatic microvalves with applications in poly(dimethylsiloxane)-based microfluidics

Microvalves are critical in the operation of integrated microfluidic chips for a wide range of applications. In this paper, we present an analytical model to guide the design of electrostatic microvalves that can be integrated into microfluidic chips using standard fabrication processes and can reliably operate at low actuation potentials (<250 V). Based on the analytical model, we identify design guidelines and operational considerations for elastomeric electrostatic microvalves and formulate strategies to minimize their actuation potentials, while maintaining the feasibility of fabrication and integration. We specifically explore the application of the model to design microfluidic microvalves fabricated in poly(dimethylsiloxane), using only soft-lithographic techniques. We discuss the electrostatic actuation in terms of several microscale phenomena, including squeeze-film damping and adhesion-driven microvalve collapse. The actuation potentials predicted by the model are in good agreement with experimental data obtained with a microfabricated array of electrostatic microvalves actuated in air and oil. The model can also be extended to the design of peristaltic pumps for microfluidics and to the prediction of actuation potentials of microvalves in viscous liquid environments. Additionally, due to the compact ancillaries required to generate low potentials, these electrostatic microvalves can potentially be used in portable microfluidic chips.     

Exact solutions of the Schr?dinger equation via Laplace transform approach: pseudoharmonic potential and Mie-type potentials

Exact bound state solutions and corresponding normalized eigenfunctions of the radial Schr?dinger equation are studied for the pseudoharmonic and Mie-type potentials by using the Laplace transform approach. The analytical results are obtained and seen that they are the same with the ones obtained before. The energy eigenvalues of the inverse square plus square potential and three-dimensional harmonic oscillator are given as special cases. It is shown the variation of the first six normalized wavefunctions of the above potentials. It is also given numerical results for the bound states of two diatomic molecular potentials, and compared the results with the ones obtained in literature.     

Simple physics-based analytical formulas for the potentials of mean force for the interaction of amino acid side chains in water. 2. Tests with simple spherical systems

Simple analytical functions consisting of electrostatic, polarization, Lennard-Jones or modified Lennard-Jones, and cavity terms are proposed to express the potentials of mean force analytically for spherical particles interacting in water. The cavity term was expressed either through the molecular-surface area of the solute or by using the Gaussian-overlap model of hydrophobic hydration developed in paper 1 of this series. The analytical expressions were fitted to the potentials of mean force of a methane homodimer, heterodimers composed of a methane molecule, and an ammonium cation or a chloride anion, respectively, and dimers consisting of two chloride anions, two ammonium cations, or a chloride ion and an ammonium cation. The potentials of mean force for these dimers were determined by umbrella-sampling molecular dynamics simulations with the AMBER 7.0 force field with TIP3P water either in our earlier work or in this work. For all systems, the analytical formulas fitted the potentials of mean force very well. However, using the molecular-surface area to express the cavity term provided a good fit only when the nonbonded interactions were expressed by an all-repulsive modified Lennard-Jones potential but also resulted in non-physical values of some of the parameters. Conversely, the use of our new Gaussian-overlap-based expression for the cavity term provided a good fit to the potentials of mean force (PMFs) with Lennard-Jones nonbonded potential, and the values of all parameters were physically reasonable.     

Applications of molecular dynamics simulations coupled with Harris functional approximation to argon

We have demonstrated molecular dynamics simulations using a combination of the classical molecular dynamics with density functional theory for argon clusters. Three different molecular dynamics schemes, which differ in their treatment of the potential energy and forces, have been carried out. The first uses a Lennard-Jones potential. In the second, the potential is computed using the Harris functional, and in the third, a combination of Lennard-Jones and Harris functional potentials is used. In addition to direct examination of the trajectories, the velocity autocorrelation function and its power spectrum have been computed to demonstrate the agreement between these three methods. The present studies show that a scheme that used a combination of model potentials and density functional theory provides a very useful tool for the dynamics simulation of systems that contain some fragments in which the analytical model potentials are not available. © 1994 John Wiley & Sons, Inc.     

Gaussian and finite-element Coulomb method for the fast evaluation of Coulomb integrals

The authors propose a new linear-scaling method for the fast evaluation of Coulomb integrals with Gaussian basis functions called the Gaussian and finite-element Coulomb (GFC) method. In this method, the Coulomb potential is expanded in a basis of mixed Gaussian and finite-element auxiliary functions that express the core and smooth Coulomb potentials, respectively. Coulomb integrals can be evaluated by three-center one-electron overlap integrals among two Gaussian basis functions and one mixed auxiliary function. Thus, the computational cost and scaling for large molecules are drastically reduced. Several applications to molecular systems show that the GFC method is more efficient than the analytical integration approach that requires four-center two-electron repulsion integrals. The GFC method realizes a near linear scaling for both one-dimensional alanine alpha-helix chains and three-dimensional diamond pieces.     

Efficient silicon surface and cluster modeling using quantum capping potentials

A one-electron, silicon quantum capping potential for use in capping the dangling bonds formed by artificially limiting silicon clusters or surfaces is developed. The quantum capping potentials are general and can be used directly in any computational package that can handle effective core potentials. For silicon clusters and silicon surface models, we compared the results of traditional hydrogen atom capping with those obtained from capping with quantum capping potentials. The results clearly show that cluster and surface models capped with quantum capping potentials have ionization potentials, electron affinities, and highest occupied molecular orbital-lowest unoccupied molecular orbital gaps that are in very good agreement with those of larger systems. The silicon quantum capping potentials should be applied in cases where one wishes to model processes involving charges or low-energy excitations in silicon clusters and surfaces consisting of more than ca. 150 atoms.     

Fourier transform general formula for systematic potentials

For calculating molecular integrals of systematic potentials, a three‐dimensional (3D) Fourier transform general formula can be derived, by the use of the Abel summation method. The present general formula contains all 3D Fourier transform formulas which are well known as Bethe–Salpeter formulas (Bethe and Salpeter, Handbuch der Physik, Bd. XXXV, 1957) as special cases. It is shown that, in several of the Bethe–Salpeter formulas, the integral does not converge in the meaning of the Riemann integral but converges in the meaning of a hyper function as the Schwartz distribution. For showing an effectiveness of the present general formula, the convergence condition of molecular integrals is derived generally for all of the present potentials. It is found that molecular integrals can be converged in the meaning of the Riemann integral for the present potentials, except for those for extra super singular potentials. It is also found that the convergence condition of molecular integrals over the Slater‐type orbitals is exactly the same as that of the corresponding integrals over the Gaussian‐type orbitals for the present systematic potentials. For showing more effectiveness, the molecular integral over the gauge‐including atomic orbitals is derived for the magnetic dipole‐same‐dipole interaction. © 2012 Wiley Periodicals, Inc.     

Energy barriers of proton transfer reactions between amino acid side chain analogs and water from ab initio calculations

Proton transfer reactions were studied in all titratable pairs of amino acid side chains where, under physiologically reasonable conditions, one amino acid may function as a donor and the other one as an acceptor. Energy barriers for shifting the proton from donor to acceptor atom were calculated by electronic structure methods at the MP2/6-31++G(d,p) level, and the well-known double-well potentials were characterized. The energy difference between both minima can be expressed by a parabola using as argument the donor-acceptor distance R(DA). In this work, the fit parameters of the quadratic expression are determined for each donor-acceptor pair. Moreover, it was found previously that the energy barriers of the reactions can be expressed by an analytical expression depending on the distance between donor and acceptor and the energy difference between donor and acceptor bound states. The validity of this approach is supported by the extensive new data set. This new parameterization of proton transfer barriers between titratable amino acid side chains allows us to very efficiently estimate proton transfer probabilities in molecular modelling studies or during classical molecular dynamics simulation of biomolecular systems.     

Universal electro-osmosis formulae for porous media

Approximate analytical formulae valid for any porous media with elongated pores are derived for the electro-osmotic coefficient alpha and for the average ionic concentration n . A macroscopic Debye-Hückel length kappa (-)(-1) based on n is introduced. Simultaneously, the electro-osmotic coefficient alpha is systematically calculated for various media, zeta potentials and electrolyte concentrations by solving the local equations. Numerical results show that kappa (-)(-1) and alpha follow universal curves valid whatever the porous medium; these curves can be approximated by the analytical formulae previously derived. These formulae can be used to provide a priori estimates of the electro-osmotic coefficient.     

Nanomicrointerface to read molecular potentials into current-voltage based electronics

Molecular potentials are unreadable and unaddressable by any present technology. It is known that the proper assembly of molecules can implement an entire numerical processing system based on digital or even analogical computation. In turn, the outputs of this molecular processing unit need to be amplified in order to be useful. We have developed a nanomicrointerface to read information encoded in molecular level potentials and to amplify this signal to microelectronic levels. The amplification is performed by making the output molecular potential slightly twist the torsional angle between two rings of a pyridazine, 3,6-bis(phenylethynyl) (aza-OPE) molecule, requiring only fractions of kcal/mol energies. In addition, even if the signal from the molecular potentials is not enough to turn the ring or even if the angles are the same for different combinations of outputs, still the current output yields results that resemble the device as a field effect transistor, providing the possibility to reduce channel lengths to the range of just 1 or 2 nm. The slight change in the torsional angle yields readable changes in the current through the aza-OPE biased by an external applied voltage. Using ab initio methods, we computationally demonstrate the amplification of molecular potential signals into currents that can be read by standard circuits.     

Linear and nonlinear excitations in a polyethylene crystal, 1. Vibrational modes and linear equations

Linear excitations in a polyethylene crystal are investigated by a new analytical method from the “first principles”. Elastic moduli are calculated from the parameters of molecular potentials of interaction. High anisotropy allows to derive comparatively simple approximate equations describing the dynamics of the crystal. Approximate expressions for the low-frequency branches of vibrational spectra are obtained. The role of internal degrees of freedom is revealed. Approximate expressions governing the dynamics of all degrees of freedom considered are obtained in analytic form suitable for nonlinear generalizations.     

Rapid determination of surface-active substances by fast-scan differential-pulse voltammetry

Fast-scan differential-pulse voltammograms of air-saturated acetate buffer and mercury nitrate solutions are presented. The current-voltage curves obtained are markedly influenced by surface-active substances (SAS). The peak potential of the voltammogram shifts to more positive potentials with increasing concentration of the SAS. This effect can be utilized for analytical purposes.     

Point charge representation of multicenter multipole moments in calculation of electrostatic properties

Summary Distributed Point Charge Models (PCM) for CO, (H₂O)₂, and HS-SH molecules have been computed from analytical expressions using multicenter multipole moments. The point charges (set of charges including both atomic and non-atomic positions) exactly reproduce both molecular and segmental multipole moments, thus constituting an accurate representation of the local anisotropy of electrostatic properties. In contrast to other known point charge models, PCM can be used to calculate not only intermolecular, but also intramolecular interactions. Comparison of these results with more accurate calculations demonstrated that PCM can correctly represent both weak and strong (intramolecular) interactions, thus indicating the merit of extending PCM to obtain improved potentials for molecular mechanics and molecular dynamics computational methods.Dedicated to Prof. Alberte PullmanPacific Northwest Laboratory is operated for the US Department of Energy by Battelle Memorial Institute under contract DE-ACO6-76RLO 1830     

Electrostatic potentials and fields from density expansions of deformed atoms in molecules

The exact representation of the molecular density by means of atomic expansions, consisting in spherical harmonics times analytical radial factors, is employed for the calculation of electrostatic potentials, fields, and forces. The resulting procedure is equivalent to an atomic multipolar expansion in the long-range regions, but works with similar efficiency and accuracy in the short-range region, where multipolar expansions are not valid. The performances of this procedure are tested on the calculation of the electrostatic potential contour maps and electrostatic field flux lines of water and nitrobenzene, computed from high-quality molecular electron densities obtained with Slater basis sets.     

Consistent treatment of inter- and intramolecular polarization in molecular mechanics calculations

A protocol is described for the treatment of molecular polarization in force field calculations. The resulting model is consistent in that both inter- and intramolecular polarization are handled within a single scheme. An analytical formula for removing intramolecular polarization from a set of atomic multipoles for an arbitrary static structure or conformation is given. With the help of the intramolecular polarization, these permanent atomic multipoles can then be applied in modeling alternative conformations of a molecule. Equipped with this simple technique, one can derive transferable electrostatic parameters for peptides and proteins using flexible model compounds such as dipeptides. The proposed procedure is tested for its ability to describe the electrostatic potential around various configurations of the N-methylacetamide dimer. The effect of different intramolecular polarization schemes on the accuracy of a force field model of the electrostatic potential of alanine dipeptide is investigated. A group-based scheme for including direct intramolecular polarization is shown to be most successful in accounting for the conformational dependence of electrostatic potentials.     

Mixed quantum-classical dynamics in the adiabatic representation to simulate molecules driven by strong laser pulses

The dynamics of molecules under strong laser pulses is characterized by large Stark effects that modify and reshape the electronic potentials, known as laser-induced potentials (LIPs). If the time scale of the interaction is slow enough that the nuclear positions can adapt to these externally driven changes, the dynamics proceeds by adiabatic following, where the nuclei gain very little kinetic energy during the process. In this regime we show that the molecular dynamics can be simulated quite accurately by a semiclassical surface-hopping scheme formulated in the adiabatic representation. The nuclear motion is then influenced by the gradients of the laser-modified potentials, and nonadiabatic couplings are seen as transitions between the LIPs. As an example, we simulate the process of adiabatic passage by light induced potentials in Na(2) using the surface-hopping technique both in the diabatic representation based on molecular potentials and in the adiabatic representation based on LIPs, showing how the choice of the representation is crucial in reproducing the results obtained by exact quantum dynamical calculations.