Efficient solvent boundary potential for hybrid potential simulations

A common challenge in computational biophysics is to obtain statistical properties similar to those of an infinite bulk system from simulations of a system of finite size. In this work we describe a computationally efficient algorithm for performing hybrid quantum chemical/molecular mechanical (QC/MM) calculations with a solvent boundary potential. The system is partitioned into a QC region within which catalytic reactions occur, a spherical region with explicit solvent that envelops the quantum region and is treated with a MM model, and the surrounding bulk solvent that is treated implicitly by the boundary potential. The latter is constructed to reproduce the solvation free energy of a finite number of atoms embedded inside a low-dielectric sphere with variable radius, and takes into account electrostatic and van der Waals interactions between the implicit solvent and the QC and MM atoms in the central region. The method was implemented in the simulation program pDynamo and tested by examining elementary steps in the reaction mechanisms of two enzymes, citrate synthase and lactate dehydrogenase. Good agreement is found for the energies and geometries of the species along the reaction profiles calculated with the method and those obtained by previous experimental and computational studies. Directions in which the utility of the method can be further improved are discussed.     

Evaluation of surface potential from single crystal electrode potential

The new method of evaluation of the point of zero potential for the metal oxide exhibiting a saddle-like surface potential function Ψ ₀(pH), as obtained by acid base potentiometric titration using Single Crystal Electrode, was proposed. The electrode potential of sapphire single crystal electrode (A crystal plane, $11\bar{2}0$ ) was measured, point of zero potential and surface potentials were evaluated, and the results were analyzed using the Surface Complexation Model. The electroneutrality point corresponding to the point of zero potential was found to be at pH_pzp=7.0. Thermodynamic protonation equilibrium constants for the first and the second step of protonation were obtained as $\lg K_{1}^{\circ} = 12.7$ ; $\lg K_{2}^{\circ} = 1.2$ .     

Chemical potential for harmonically interacting particles in a harmonic potential

The chemical potential μ, as it appears in density functional theory, is examined extensively for harmonically interacting spin-½ fermions in three dimensions. For this system the energy and chemical potential are discontinuous functions of the particle number if the most straightforward equation is used to define the energy for a noninteger particle number.     

The surface potential of solvent and the intraphase pre-existing potential

Using own and literature data, the differences of real solvation energy for ferricenium and ferrocene in six solvents are found. These quantities are confronted with the calculated difference of the dielectric response energies plus nonelectrostatic energies for the redox couple. Such a comparison allows determining the sum of the surface and intraphase potentials. The comparison of these sums with the experimental values of the surface potential differences obtained by the measuring of Volta potentials allowed determining the differences of pre-existing intraphase potentials formed by solvent molecules on the ferrocene molecule. Thus, the intraphase potentials are evaluated for the first time, using an approach not based on the molecular-dynamic modeling. Using some approximations, the surface potentials of the studied solvents are found.     

Fermionic chemical potential

This paper gives a critical review of the physical meaning of the chemical potential, perhaps the most abstract of all thermodynamic quantities. To show its basic behavior, thereby to illustrate its physical significance, we have derived the chemical potential of a system of free electrons as a function of the density and temperature in different spatial dimensions. We have shown how to obtain the isothermal compressibility given the chemical potential. To emphasize the usefulness of the knowledge of dimensional dependence, both the compressibility and average kinetic energy are expressed as simple dimensional relationships of the density and, hence, the chemical potential. Finally, there is a certain temperature at which the chemical potential should identically vanish. Physical implications of zero chemical potential are discussed.     

On-the-energy-shell optical potential

The on-the-energy-shell optical potential is derived for the vibrational excitation in atom-diatom collisions. A “comparison” potential is employed to avoid possible numerical difficulties. It is shown that the on. the-energy-shell optical potential can be expressed in a closed analytical form and that the potential is non-local, energy dependent and complex     

Complete error potential

The complete error potential is a function of electronic and nuclear coordinates which has to be added to the physical potential in order to obtain the eigenfunctions of the molecular Hamiltonian in an a priori specified approximation. This potential is essential for the error theory, in particular it furnishes a simple justification of the Born-Oppenheimer approximation. It is given as a sum of the electronic error potential and that of the intramolecular forces, whose importance is discussed.Dedicated to Professor J. Koutecký on the occasion of his 65th birthday     

Controlled potential electroanalysis

Some fundamental principles involved in controlled potential electroanalysis are discussed. A potentiostat is described which automatically maintains the potential of a working electrode constant during an electrolysis. Cells for different applications of controlled potential electrolysis are described. Some typical applications are reviewed, including electrogravimetric determinations of metals, electrolytic separation of metals with mercury and platinum cathodes prior to polarographic analysis, coulometric analysis, identification of the oxidation states that correspond to polarographic waves, and electrolytic preparation of organic and inorganic compounds.     

Local effective potential theory: nonuniqueness of potential and wave function

In local effective potential energy theories such as the Hohenberg-Kohn-Sham density functional theory (HKS-DFT) and quantal density functional theory (Q-DFT), electronic systems in their ground or excited states are mapped to model systems of noninteracting fermions with equivalent density. From these models, the equivalent total energy and ionization potential are also obtained. This paper concerns (i) the nonuniqueness of the local effective potential energy function of the model system in the mapping from a nondegenerate ground state, (ii) the nonuniqueness of the local effective potential energy function in the mapping from a nondegenerate excited state, and (iii) in the mapping to a model system in an excited state, the nonuniqueness of the model system wave function. According to nondegenerate ground state HKS-DFT, there exists only one local effective potential energy function, obtained as the functional derivative of the unique ground state energy functional, that can generate the ground state density. Since the theorems of ground state HKS-DFT cannot be generalized to nondegenerate excited states, there could exist different local potential energy functions that generate the excited state density. The constrained-search version of HKS-DFT selects one of these functions as the functional derivative of a bidensity energy functional. In this paper, the authors show via Q-DFT that there exist an infinite number of local potential energy functions that can generate both the nondegenerate ground and excited state densities of an interacting system. This is accomplished by constructing model systems in configurations different from those of the interacting system. Further, they prove that the difference between the various potential energy functions lies solely in their correlation-kinetic contributions. The component of these functions due to the Pauli exclusion principle and Coulomb repulsion remains the same. The existence of the different potential energy functions as viewed from the perspective of Q-DFT reaffirms that there can be no equivalent to the ground state HKS-DFT theorems for excited states. Additionally, the lack of such theorems for excited states is attributable to correlation-kinetic effects. Finally, they show that in the mapping to a model system in an excited state, there is a nonuniqueness of the model system wave function. Different wave functions lead to the same density, each thereby satisfying the sole requirement of reproducing the interacting system density. Examples of the nonuniqueness of the potential energy functions for the mapping from both ground and excited states and the nonuniqueness of the wave function are provided for the exactly solvable Hooke's atom. The work of others is also discussed.     

Modelling of potential energy curves for diatomics: Reference molecular potential method

A method is suggested for modelling the potential energy curves of diatomics. It involves a search for the mapping which transfers the structural details from an analytically prescribed reference potential. For the ground-state potentials of seven covalent molecules, the accuracy in describing the spectroscopic region is comparable with the best empirical potentials, and the correct asymptotic behaviour at R → 0 and R → ∞ are also obtained.     

Zeta potential of particle bilayers on mica: a streaming potential study

The streaming potential of mica covered by bilayers of latex particles was measured using the parallel-plate channel cell. The size of the first latex (A500) bearing amidine charged groups was 503 nm and the second latex (L800) bearing sulfonate groups was 810 nm (at pH 5.5 and an ionic strength of 10(-2)M). The A500 latex exhibited an isoelectric point at pH 10.5, whereas the L800 latex was strongly negative at all pH. Mica sheets were precovered first by the A500 latex particles under diffusion transport conditions. The coverage of this supporting layer was regulated between 0.02 and 0.5 by changing the bulk concentration of latex and the deposition time. Then, the second layer of the L800 latex of regulated coverage up to 0.55 was deposited under the diffusion transport. The coverage of particles and their distributions in both layers were determined by a direct enumeration of particles by optical microscopy under wet conditions and by AFM. It was shown that the structure of the L800 particle layers and the maximum coverage were in accordance with theoretical simulations performed according to the random sequential adsorption (RSA) model. After forming bilayers of desired composition and structure, streaming potential measurements were carried out. The influence of the mica substrate, the supporting layer coverage, and its zeta potential on the apparent zeta potential of bilayers was systematically studied. It was established that for a bilayer coverage exceeding 0.20, the net zeta potential became independent of the substrate and the supporting layer zeta potentials. Then, the asymptotic values of the zeta potential of the bilayer approach 1/√2=0.71 of the bulk zeta potential of the particles forming the external (second) layer. This behavior was interpreted theoretically in terms of the electrokinetic model derived previously for monolayers. It was also concluded that results obtained in this work can be exploited for interpretation of polyelectrolyte film formation in the layer by layer (LbL) processes and protein adsorption pertinent to the antigen/antibody interactions.     

Synthesis of potential antimalarials

A series of quinoline derivatives containing a 2-thienyl ring in the 2-position and CO₂H, CH₂OH, CHO, CH(OH)CN, CH(OH)CO₂H, CO₂C₂H₅, COCH[N(C₂H₅)₂]CO₂C₂H₅, COCH₂N(C₂H₅)₂, COCH₃, substituents in the 4-position was synthesized. Both intermediate and target compounds were tested for antimalarial activity. A second series with a 5-bromo-2-thienyl group in the 2-position and CHOHCH₂N(C₂H₅)₂, CHOHCH₂N(CH₂)₆, and CHOHCH₂N(CH₂C₆H₅)₂ substituents in the 4-position was also prepared, it was found that, although these quinoline methanols were moderately active antimalarials, they exhibited a high degree of phototoxicity. A third series of compounds with 2-alkyl substituents (methyl, t-butyl) was also synthesized, and these were found to combine a modest degree of antimalarial activity with low phototoxicity. Several novel synthetic routes to the above compounds were developed and are detailed.     

Chemical potential inequality principle

Regional density functional theory has been extended to treat irreversible thermodynamic electronic processes for application to adiabatic electron-transfer processes of chemical reactions. Onsager's local equilibrium hypothesis is slightly modified to take into account the quantum mechanical nature of the electron. The quantum mechanical interference effect has been demonstrated to be included in the entropy production rate formula associated with electron transfer through an interface. A new formula for the determination of the transition state of a chemical reaction has been postulated that corresponds to the maximum of the regional electron transferability. A quantum mechanical law of mass action has been established and applied to prove the regional electrochemical potential inequality principle. Received: 1 July 1998 / Accepted: 2 September 1998 / Published online: 8 February 1999     

Analytical carbon-oxygen reactive potential

We present a reactive empirical potential with environment-dependent bond strengths for the carbon-oxygen (CO) system. The distinct feature of the potential is the use of three adjustable parameters characterizing the bond: the strength, length, and force constant, rather than a single bond order parameter, as often employed in these types of potentials. The values of the parameters are calculated by fitting results obtained from density functional theory. The potential is tested in a simulation of oxidative unzipping of graphene sheets and carbon nanotubes. Previous higher-level theoretical predictions of graphene unzipping by adsorbed oxygen atoms are confirmed. Moreover, nanotubes with externally placed oxygen atoms are found to unzip much faster than flat graphene sheets.     

The beryllium dimer potential

The convergence of ab initio calculations of the beryllium dimer potential is examined with several basis sets orders of perturbation theory. When the atomic pair natural orbital basis set calculations are extrapolated to the complete basis set and full CI limits, the calculated parameters: R_e=2.447 Å, D_e=827 cm⁻¹, ν₀₁=212.7 cm⁻¹, ν₁₂=167.2 cm⁻¹, ν₂₃=121.5 cm⁻¹ and ν₃₄=77.7 cm⁻¹ are in good agreement with the experimental parameters: R_e=2.45 Å, D_e=839±10 cm⁻¹, ν₀₁=223.2 cm⁻¹, ν₁₂=169.7 cm⁻¹, ν₂₃=122.5 cm⁻¹, and ν₃₄=79 cm⁻¹.     

Mapping potential energy surfaces

A recently proposed dynamical method [A. Laio and M. Parrinello, Proc. Natl. Acad. Sci. U.S.A. 99, 12562 (2002)] allows us to globally sample the free energy surface. This approach uses a coarse-grained non-Markovian dynamics to bias microscopic atomic trajectories. After a sufficiently long simulation time, the global free energy surface can be reconstructed from the non-Markovian dynamics. Here we apply this scheme to study the T=0 free energy surface, i.e., the potential energy surface in coarse-grained space. We show that the accuracy of the reconstructed potential energy surface can be dramatically improved by a simple postprocessing procedure with only minor computational overhead. We illustrate this approach by conducting conformational analysis on a small organic molecule, demonstrating its superiority over traditional unbiased approaches in sampling potential energy surfaces in coarse-grained space.     

Local redox potential measurement

A local potential measurement method that can be easily used in an anaerobic solution was settled and the potential probe was tested with a simple and fast electrochemical system. From the local potential value, plotted versus the distance to the working electrode, the concentration profile of the electrochemically consumed species can be calculated. The comparison of this experimental concentration profile to the theoretical one, which is based on Nernst hypothesis, enables us to assess the screening effect induced by the potential probe on the potential and current distributions. Thus, it is possible to calculate the potential profile that would be recorded by an ideal probe.