Comparison of methods for point‐charge representation of electrostatic fields

The calculation of the electrostatic potential resulting from an infinite or extended array of charges in the interior of a region of interest is a frequent task in computational chemistry. In case of a periodic potential this can, for example, be done by Ewald summation or by multipole methods. An important alternative are those methods where arrays of auxiliary point charges are optimized with respect to charge and/or position to reproduce the original electrostatic potential. In the literature different variations are reported. We compare the performance of some of these with respect to their ability to reproduce the original potential and the computational effort required. Between (1) surface charges determined by the conductor‐boundary condition, (2) optimized surface charges, and (3) surface charges floating on the surface we find that (2) offers good quality with small computational costs involved. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

A new method to determine electrostatic potential around a macromolecule in solution from molecular wave functions

The three-dimensional reference interaction site model integral equation theory (3D-RISM) combined with the ab initio molecular orbital method (3D-RISM-SCF) is applied to a solvated macromolecular system. The solvation structure around a solute molecule is obtained from the 3D-RISM integral equation under the electrostatic potential of the solute molecule, calculated by the ab initio molecular orbital theory. The electrostatic potential should be calculated on each grid point in the three-dimensional real space. Therefore, the calculation of the electrostatic potential is the most time consuming part in this method. In this article, we propose a new procedure to save the computational cost for calculating the electrostatic potential and the solvated fock matrix. The strategy of this procedure is to evaluate the electrostatic potential and the solvated fock matrix in different ways, depending on the distance between solute and solvent. Inside the repulsive cores of solute atoms, it is possible to avoid the calculation of electrostatic potential and solvated Fock matrix by assuming the potential to be infinity. In the region sufficiently far from solute, they are evaluated classically by putting the effective point charge on each atom. In the intermediate region, the electrostatic potential is evaluated directly by integrating the molecular orbitals of the solute molecule. The electronic structure and the energy gradient of Methionine-Enkephalin and solvation structure are estimated by using this procedure in aqueous solution, and are compared with the results from other procedures. The results are compared also with those from the continuum model.     

Ab initio and analytic intermolecular potentials for Ar-CF4

Ab initio calculations at the CCSD(T) level of theory were performed to characterize the Ar + CF4 intermolecular potential. Potential energy curves were calculated with the aug-cc-pVTZ basis set, and with and without a correction for basis set superposition error (BSSE). Additional calculations were performed with other correlation consistent basis sets to extrapolate the Ar-CF4 potential energy minimum to the complete basis set (CBS) limit. Both the size of the basis set and BSSE have substantial effects on the Ar + CF4 potential. Calculations with the aug-cc-pVTZ basis set, and with a BSSE correction, appear to give a good representation of the BSSE corrected potential at the CBS limit. In addition, MP2 theory is found to give potential energies in very good agreement with those determined by the much higher level CCSD(T) theory. Two model analytic potential energy functions were determined for Ar + CF4. One is a fit to the aug-cc-pVTZ calculations with a BSSE correction. The second was derived by fitting an average BSSE corrected potential, which is an average of the CCSD(T)/aug-cc-pVTZ potentials with and without a BSSE correction. These analytic functions are written as a sum of two-body potentials and excellent fits to the ab initio potentials are obtained by representing each two-body interaction as a Buckingham potential.     

Dielectrophoretic choking phenomenon of a deformable particle in a converging‐diverging microchannel

The translational motion of small particles in an electrokinetic fluid flow through a constriction can be enhanced by an increase of the applied electric potential. Beyond a critical potential, however, the negative dielectrophoresis (DEP) can overpower other forces to prevent particles that are even smaller than the constriction from passing through the constriction. This DEP choking phenomenon was studied previously for rigid particles. Here, the DEP choking phenomenon is revisited for deformable particles, which are ubiquitous in many biomedical applications. Particle deformability is measured by the particle shear modulus, and the choking conditions are reported through a parametric study that includes the channel geometry, external electric potential, and particle zeta potential. The study was carried out using a numerical model based on an arbitrary Lagrangian‐Eulerican (ALE) finite‐element method.     

Diffusion Monte Carlo simulations on uracil-water using an anisotropic atom-atom potential model

We have developed an anisotropic atom-atom intermolecular potential model for the interaction of uracil with water. The potential consists of a distributed multipole analysis (DMA) model for the electrostatic energy, and a 6-exp potential to represent the repulsion-dispersion term. The repulsion-dispersion potential parameters are adjusted to yield good agreement with accurate ab initio data on the minima and transition states of the uracil-water complex. We have used this potential in diffusion Monte Carlo simulations of uracil-water, uracil-(water)2 and uracil-(water)3. The uracil-water simulations show that the theoretically based potential gives a qualitatively different picture of uracil hydration than that provided by a standard isotropic atom-atom point charge model, which is shown to underestimate the delocalized motion of the water hydrogen atoms. Plots of the vibrational probability density of the hydrogen atoms show the delocalized motion of the water hydrogen atoms that are not involved in hydrogen bonding.     

Electrochemical desorption of n-alkylthiol SAMs on polycrystalline gold: studies using a ferrocenylalkylthiol probe

The reductive voltammetric desorption of n-alkylthiol self-assembled monolayers (SAMs) was studied using ferrocenyldodecanethiol (FcC12SH) as a probe. A short (10 s) incubation in a 2 mM FcC12SH solution labels the pre-existing defect sites present in a tetradecanethiol (C14S-Au) SAM. Additional defects in a C14S-Au SAM are then created by voltammetric cycling to reductive potentials. The effects of changing the desorption potential and the hold time at the desorption potential were investigated by monitoring the change in the two characteristic FcC12S-Au peaks. These two peaks are associated with FcC12S-Au filling individual single site defects (peak I at 260 mV) and pinhole defects (peak II at 380 mV). The reductive desorption potential applied to a binary (FcC12S-/C14S-Au) SAM results in a partial desorption and a potential "remixing" of the phase-separated state.     

Study of structural and thermodynamic characteristics of adsorption layers by the density functional method: Local density in adsorption layer on planar solid surface and adsorption isotherms

The local density profiles in Lennard-Jones adsorption layers, as well as the excess (Gibbs) and absolute adsorption values, are calculated by the density functional method (weighting factor approximations). The substrate is described using the single-particle potential corresponding to the Lennard-Jones potential integrated over the half space occupied by the substrate. The Steele potential is used as a single-particle potential to consider methane adsorption on the surface of nonporous graphite as a specific system. The calculations are performed for both sub- and supercritical temperature regions. It is established that the density profiles are characterized by the existence of one to three maxima, which reflect the positional order of molecules in adsorption layers, i.e., the layered structure of an adsorbate.     

Electrostatic potential around charged finite rodlike macromolecules: nonlinear Poisson-Boltzmann theory

In this paper, we show that the far field electrostatic potential created by a highly charged finite size cylinder within the nonlinear Poisson-Boltzmann (PB) theory, is remarkably close to the potential created within the linearized PB approximation by the same object at a well-chosen fixed potential. Comparing the nonlinear electrostatic potential with its linear counterpart associated to a fixed potential boundary condition (called the effective surface potential), we deduce the effective charge of the highly charged cylinder. Values of the effective surface potential are provided as a function of the bare surface charge and Debye length of the ionic solution. This allows to compute the anisotropic electrostatic interaction energy of two distant finite rods.     

Optimized effective potential method for individual low-lying excited states

This paper presents an optimized effective potential (OEP) approach based on density functional theory (DFT) for individual excited states that implements a simple method of taking the necessary orthogonality constraints into account. The amended Kohn-Sham (KS) equations for orbitals of excited states having the same symmetry as the ground one are proposed. Using a variational principle with some orthogonality constraints, the OEP equations determining a local exchange potential for excited states are derived. Specifically, local potentials are derived whose KS determinants minimize the total energies and are simultaneously orthogonal to the determinants for states of lower energies. The parametrized form of an effective DFT potential expressed as a direct mapping of the external potential is used to simplify the OEP integral equations. A performance of the presented method is examined by exchange-only calculations of excited state energies for simple atoms and molecules.     

Mathematical Connections Between Bond-Stretching Potential Functions

Mathematical connections are useful in enabling a set of parametric data from a chemical bond-stretching potential function to be applied in a computational chemistry software that adopts a different potential function. This paper establishes connections between four potential energy functions in stretching and compression of covalent bonds. The potential functions that are mathematically connected are: (i) harmonic potential, (ii) polynomial series potential, (iii) Morse potential, and (iv) Murrell–Mottram potential. Two methods are employed in obtaining the relationships between the four potential functions. The expansion approach enables the relationships to be made at large bond-stretching, whilst the differential approach allows for the connections to be made only at infinitesimal bond-stretching. For verification, parametric data from the Murrell–Mottram potential is converted to parametric data of the harmonic, polynomial series and Morse potentials. For comparison, the bond-stretching energies for these functions are plotted. Discrepancy between the Morse and the Murrell–Mottram potentials at large bond-stretching is discussed in terms of the assumed infinitesimal deformation.     

Comparison of model potentials for molecular-dynamics simulations of silica

Structural, thermomechanical, and dynamic properties of pure silica SiO2 are calculated with three different model potentials, namely, the potential suggested by van Beest, Kramer, and van Santen (BKS) [Phys. Rev. Lett. 64, 1955 (1990)], the fluctuating-charge potential with a Morse stretch term for the short-range interactions proposed by Demiralp, Cagin, and Goddard (DCG)[Phys. Rev. Lett. 82, 1708 (1999)], and a polarizable force field proposed by Tangney and Scandolo (TS) [J. Chem. Phys. 117, 8898 (2002)]. The DCG potential had to be modified due to flaws in the original treatment. While BKS reproduces many thermomechanical properties of different polymorphs rather accurately, it also shows qualitatively wrong trends concerning the phononic density of states, an absence of the experimentally observed anomaly in the c/a ratio at the quartz alpha-beta transition, pathological instabilities in the beta-cristobalite phase, and a vastly overestimated transition pressure for the stishovite I --> II transition. These shortcomings are only partially remedied by the modified DCG potential but greatly improved by the TS potential. DCG and TS both reproduce a pressure-induced transition from alpha-quartz to quartz II, predicted theoretically based on the BKS potential.     

Global optimization study of small (10 < or = N < or = 120) Pd clusters supported on MgO(100)

Experimental evidence suggests that Pd clusters on MgO, known to be good reaction catalysts, have face centered cubic (fcc) epitaxial structures. The structure of such clusters is the result of the interplay of Pd-Pd and Pd-substrate bonds, the former inclined to favor icosahedral (Ih) and decahedral (Dh)-like structures, the latter leading to place Pd atoms on top of oxygen sites, according to an epitaxial stacking. This paper shows the results of a basin-hopping global optimization procedure applied to free and MgO-supported Pd clusters in the size range 10 < or = N < or = 120. Pd-MgO interactions are modeled by an analytical function fitted to ab initio results, while Pd-Pd interactions are modeled by a semiempirical potential. Besides the tight-binding Rosato-Guillopé-Legrand (RGL) potential, we have adopted a modified version of RGL that better reproduces the experimental surface energy of palladium, modifying the attractive part of Pd atoms potential energy. We have compared the two potential models, and as a result, the RGL potential favors clusters with epitaxial arrangements, so that cluster structures are epitaxial fcc in almost all the size ranges considered. On the contrary, the alternative potential model preserves some Ih-like characteristics typical of the free Pd clusters, and it suggests that a transition size from Ih-like to epitaxial structures can take place at about 100 atoms.     

Potential driven deposition of poly(diallyldimethylammonium chloride) onto the surface of 3-mercaptopropionic acid monolayers assembled on gold

Electrochemical impedance spectroscopy (EIS) and quartz crystal microbalance (QCM) measurements are used to examine the ability of applied potential to drive the ionic self-assembly of poly(diallyldimethylammonium) chloride (PDDA) onto a substrate modified with a monolayer of 3-mercaptopropionic acid (3-MPA). The potential of zero charge (PZC) of the gold electrode modified with a monolayer of 3-MPA was found by differential capacitance measurements to be -0.12 (+/-0.01) V versus Ag-AgCl. Changing the substrate potential to values positive (-0.01 V vs Ag-AgCl) of the PZC induces interfacial conditions that are favorable for the electrostatic deposition of cationic polymers onto the surface of 3-MPA monolayers. This result is also consistent with experimental observations obtained when the 3-MPA-modified substrate is exposed to 0.10 mol L (-1) NaOH solutions. When potentials equal or negative to the PZC are applied to the substrate, no significant accumulation of the PDDA is found by either QCM or EIS measurement. This result is consistent with results obtained when the 3-MPA modified substrate is exposed to 0.10 mol L (-1) HCl solutions where no PDDA adsorption is expected because the monolayer is neutral under these conditions. Changes in the impedance and quartz crystal frequency obtained after potential is applied to the substrate are interpreted in terms of the applied potential creating interfacial conditions that are favorable for the deprotonation of the terminal carboxylic acid groups and the subsequent electrostatic assembly of the polycation onto the negatively charged monolayer.     

A regularized inverted perturbation approach method: potential energy curve of the 4 (1)Sigma(u) (+) state in Na(2)

We describe a modification of the inverted perturbation approach method allowing to construct physically sensible potential energy curves for electronic states of diatomic molecules even when some parts of the potential are not adequately characterized by the experimental data. The method is based on a simple regularization procedure, imposing an additional constraint on the constructed potential curve. In the present work it is applied to the double minimum 4 (1)Sigma(u) (+) state of Na(2), observed experimentally by polarization labeling spectroscopy technique.     

Ultracold collisions and reactions of vibrationally excited OH radicals with oxygen atoms

We report a quantum dynamics study of O + OH (v = 1, j = 0) collisions on its ground electronic state, employing two different potential energy surfaces: the DIMKP surface by Kendrick and Pack, and the XXZLG surface by Xu et al. A time-independent quantum mechanical method based on hyperspherical coordinates has been adopted for the dynamics calculations. Energy-dependent probabilities and rate coefficients are computed for the elastic, inelastic, and reactive channels over the collision energy range E(coll) = 10(-10)-0.35 eV, for J = 0 total angular momentum. Initial state-selected reaction rate coefficients are also calculated from the J = 0 reaction probabilities by applying a J-shifting approximation, for temperatures in the range T = 10(-6)-700 K. Our results show that the dynamics of the collisional process and its outcome are strongly influenced by long-range forces, and chemical reactivity is found to be sensitive to the choice of the potential energy surface. For O + OH (v = 1, j = 0) collisions at low temperatures, vibrational relaxation of OH competes with reactive scattering. Since long-range interactions can facilitate vibrational relaxation processes, we find that the DIMKP potential (which explicitly includes van der Waals dispersion terms) favours vibrational relaxation over chemical reaction at low temperatures. On the DIMKP potential in the ultracold regime, the reaction rate coefficient for O + OH (v = 1, j = 0) is found to be a factor of thirteen lower than that for O + OH (v = 0, j = 0). This significantly high reactivity of OH (v = 0, j = 0), compared to that of OH (v = 1, j = 0), is attributed to enhancement caused by the presence of a HO(2) quasibound state (scattering resonance) with energy near the O + OH (v = 0, j = 0) dissociation threshold. In contrast, the XXZLG potential does not contain explicit van der Waals terms, being just an extrapolation by a nearly constant function at large O-OH distances. Therefore, long-range potential couplings are absent in calculations using the XXZLG surface, which does not induce vibrational relaxation as efficiently as the DIMKP potential. The XXZLG potential leads to a slightly higher reactivity (a factor of 1.4 higher) for O + OH (v = 1, j = 0) compared to that for O + OH (v = 0, j = 0) at ultracold temperatures. Overall, both potential surfaces yield comparable values of reaction rate coefficients at low temperatures for the O + OH (v = 1, j = 0) reaction.     

Effect of the Ar-Ni(s) potential on the cross section for Ar+CH4/Ni{111} collision-induced desorption and the need for a more accurate CH4/Ni{111} potential

In a previous paper [L. Sun, P. de Sainte Claire, O. Meroueh, and W. L Hase, J. Chem. Phys. 114, 535 (2001)], a classical trajectory simulation was reported of CH(4) desorption from Ni{111} by Ar-atom collisions. At an incident angle theta(i) of 60 degrees (with respect to the surface normal), the calculated collision-induced desorption (CID) cross sections are in excellent agreement with experiment. However, for smaller incident angles the calculated cross sections are larger than the experimental values and for normal collisions, theta(i)=0 degrees , the calculated cross sections are approximately a factor of 2 larger. This trajectory study used an analytic function for the Ar+Ni(s) intermolecular potential which gives an Ar-Ni{111} potential energy minimum which is an order of magnitude too deep. In the work reported here, the previous trajectory study is repeated with an Ar+Ni(s) analytic intermolecular potential which gives an accurate Ar-Ni{111} potential energy minimum and also has a different surface corrugation than the previous potential. Though there are significant differences between the two Ar+Ni(s) analytic potentials, they have no important effects on the CID dynamics and the cross sections reported here are nearly identical to the previous values. Zero-point energy motions of the surface and the CH(4)-Ni(s) intermolecular modes are considered in the simulation and they are found to have a negligible effect on the CID cross sections. Calculations of the intermolecular potential between CH(4) and a Ni atom, at various levels of theory, suggest that there are substantial approximations in the ab initio calculation used to develop the CH(4)+Ni{111} potential. The implication is that the differences between the trajectory and experimental CID cross sections may arise from an inaccurate CH(4)+Ni{111} potential used in the trajectory simulation.     

Effective potential in density matrix functional theory

In the previous paper it was shown that in the ground state the diagonal of the spin independent second-order density matrix n can be determined by solving a single auxiliary equation of a two-particle problem. Thus the problem of an arbitrary system with even electrons can be reduced to a two-particle problem. The effective potential of the two-particle equation contains a term v(p) of completely kinetic origin. Virial theorem and hierarchy of equations are derived for v(p) and simple approximations are proposed. A relationship between the effective potential u(p) of the shape function equation and the potential v(p) is established.     

Self-assembled monolayers on mercury probed in a modified surface force apparatus

Self-assembled monolayers (SAMs) of three thiol compounds formed on mercury are investigated by a combination of cyclic voltammetry, electrocapillary curves, and a novel method of measuring electrical double-layer properties. The last method involves a modified surface force apparatus in which a flat mica surface is pressed down toward a fixed mercury drop held beneath it, while both are immersed in aqueous electrolyte solution. Optical interference measurements are made of the mica-mercury separation as a function of electrical potential applied to the mercury, which yields information on the double-layer interaction between the two surfaces. Mercury is decorated by SAMs of 11-mercapto-1-undecanoic acid, which is shown to bring negative charge to the mercury/aqueous interface due to dissociation of the carboxylic acid groups; 11-mercapto-1-undecanol, which although it is uncharged changes the dipole potential of the interface; and 1-undecanethiol, which likewise changes the dipole potential, but by a different amount. The difference between the changes in dipole potential (90 mV) can be related to the different terminal groups of these two SAMs, -CH3 compared to -OH, that are in contact with the aqueous phase.     

Semiempirical studies of inner-core energy levels: IX. Esca shifts of silicon atoms in various chemical environments by the scc-mo method

The semiempirical self-consistent charge molecular orbital (SCC-MO) method has been applied to a number of representative molecules involving Si atoms in various chemical environments. The calculated point charges were correlated with Si(2p) inner-core energy level shifts by using ground state potential, relaxation potential and transition potential models (GPM, RPM and TPM). The results are in good agreement with experimental data. Various contributions to the relaxation energy are briefly discussed.