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  • 1
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 113 (2000), S. 10464-10476 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The application of the particle–particle—particle–mesh (P3M) method for computing electrostatic interactions in molecular simulations relies on the use of a charge-shaping function to split the potential into two contributions, evaluated in real and reciprocal space, respectively. Although the charge-shaping function is traditionally taken to be a Gaussian, many other choices are possible. In the present study, we investigate the accuracy of the P3M method employing, as charge-shaping functions, polynomials truncated to a finite spacial range (TP functions). We first discuss and test analytical estimates of the P3M root-mean-square force error for both types of shaping functions. These estimates are then used to find the optimal values of the free parameters defining the two types of charge-shaping function (width of the Gaussian or coefficients of the TP function). Finally, we compare the accuracy properties of these optimized functions, using both analytical estimates and numerical results for a model ionic system. It is concluded that the use of specific TP functions instead of the traditional Gaussian function leads to improvements in terms of computational speed, simplicity of use, and accuracy of results. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 110 (1999), S. 10679-10692 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: In order to reduce computational effort and to allow for the use of periodic boundary conditions, electrostatic interactions in explicit solvent simulations of molecular systems do not obey Coulomb's law. Instead, a number of "effective potentials" have been proposed, including truncated Coulomb, shifted, switched, reaction-field corrected, or Ewald potentials. The present study compares the performance of these schemes in the context of ionic solvation. To this purpose, a generalized form of the Born continuum model for ion solvation is developed, where ion–solvent and solvent–solvent interactions are determined by these effective potentials instead of Coulomb's law. An integral equation is formulated for calculating the polarization around a spherical ion from which the solvation free energy can be extracted. Comparison of the polarizations and free energies calculated for specific effective potentials and the exact Born result permits an assessment of the accuracy of these different schemes. Additionally, the present formalism can be used to develop corrections to the ionic solvation free energies calculated by molecular simulations implementing such effective potentials. Finally, an arbitrary effective potential is optimized to reproduce the Born polarization. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 110 (1999), S. 1856-1872 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The use of Ewald and related methods to handle electrostatic interactions in explicit-solvent simulations of solutions imposes an artificial periodicity on systems which are inherently nonperiodic. The consequences of this approximation should be assessed, since they may crucially affect the reliability of those computer simulations. In the present study, we propose a general method based on continuum electrostatics to investigate the nature and magnitude of periodicity-induced artifacts. As a first example, this scheme is applied to the solvation free-energy of a spherical ion. It is found that artificial periodicity reduces the magnitude of the ionic solvation free-energy, because the solvent in the periodic copies of the central unit cell is perturbed by the periodic copies of the ion, thus less available to solvate the central ion. In the limit of zero ionic radius and infinite solvent permittivity, this undersolvation can be corrected by adding the Wigner self-energy term to the solvation free-energy. For ions of a finite size or a solvent of finite permittivity, a further correction is needed. An analytical expression for this correction is derived using continuum electrostatics. As a second example, the effect of artificial periodicity on the potential of mean force for the interaction between two spherical ions is investigated. It is found that artificial periodicity results in an attractive force between ions of like charges, and a repulsive force between ions of opposite charges. The analysis of these two simple test cases reveals that two individually large terms, the periodicity-induced perturbations of the Coulomb and solvation contributions, often cancel each other significantly, resulting in an overall small perturbation. Three factors may prevent this cancellation to occur and enhance the magnitude of periodicity-induced artifacts: (i) a solvent of low dielectric permittivity, (ii) a solute cavity of non-negligible size compared to the unit cell size, and (iii) a solute bearing a large overall charge. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 4
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Different schemes for treating the electrostatic interactions in molecular dynamics simulations are investigated: charge-group truncation with or without reaction-field correction, atomic truncation with or without reaction-field correction, and Ewald summation. When a reaction-field correction is applied, the influence of the size of the radius selected for the spherical boundary to the continuum is also considered. The different schemes are applied to simple point charge water simulations, and simulated energetic, transport, structural, and dielectric properties are compared. It is concluded that (i) the inclusion of a reaction-field correction in a charge-group truncation scheme induces significant changes in different types of properties, and that a number of properties are not identical to those observed using the Ewald scheme, (ii) when the reaction-field correction is included in an atomic truncation scheme instead, the agreement with the Ewald results is in general improved, and (iii) the increase (decrease) of the radius of the boundary to the continuum by 0.1 (nm) with respect to the cutoff radius induces in both cases a degradation of the simulated properties. Special attention is paid to the calculation of the dielectric permittivity from the simulations. Due to the finite size of the statistical ensembles considered, this property is not assumed to be isotropic, and the degree of anisotropy is used instead as a test for convergence. Since the incorporation of the reaction-field correction into an atomic truncation scheme leads, when systems of high dielectric permittivity are considered, to electrostatic interactions which implicitly contain a (physically reasonable) shifting function and properties which are comparable to those obtained using the Ewald method, this scheme is a clear improvement over a charge-group-based truncation when a reaction-field correction is used in molecular dynamics simulations of noncharged systems. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    Chemical research in toxicology 3 (1990), S. 566-573 
    ISSN: 1520-5010
    Source: ACS Legacy Archives
    Topics: Medicine
    Type of Medium: Electronic Resource
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  • 6
    ISSN: 1520-5010
    Source: ACS Legacy Archives
    Topics: Medicine
    Type of Medium: Electronic Resource
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  • 7
    ISSN: 1520-5010
    Source: ACS Legacy Archives
    Topics: Medicine
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 115 (2001), S. 1125-1136 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Four methods to compute the dielectric permittivity ε of a liquid from molecular simulations are compared in the context of the simple point charge (SPC) water model. In the first method (unrestrained method), ε is evaluated from the fluctuations of the box dipole moment M, monitored during a single equilibrium simulation. In the three other methods, ε is evaluated from the probability distribution p(M) of the dipole moment norm. This distribution is itself evaluated in three different ways: (i) from multiple simulations involving a M-dependent biasing potential (umbrella-sampling method), (ii) from multiple simulations involving a constrained dipole moment norm (M-constraint method), or (iii) from fitting of incomplete p(M) estimates to a Maxwell distribution (fitting method). The four methods are shown to converge to an identical estimate of ε=61±1 for SPC water (256 molecules, reaction-field electrostatics). The convergence properties, advantages, and drawbacks of the different methods are analyzed in detail. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 116 (2002), S. 7434-7451 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: An iterative algorithm based on fast Fourier transforms is proposed to solve the Poisson equation for systems of heterogeneous permittivity (e.g., solute cavity in a solvent) under periodic boundary conditions. The method makes explicit use of the dipole–dipole interaction tensor, and is thus easily generalizable to arbitrary forms of electrostatic interactions (e.g., Coulomb's law with straight or smooth cutoff truncation). The convergence properties of the algorithm and the influence of various model parameters are investigated in detail, and a set of appropriate values for these parameters is determined. The algorithm is further tested by application to three types of systems (a single spherical ion, two spherical ions, and small biomolecules), and comparison with analytical results (single ion) and with results obtained using a finite-difference solver under periodic boundary conditions. The proposed algorithm performs very well in terms of accuracy and convergence properties, with an overall speed comparable in the current implementation to that of a typical finite-difference solver. Future developments and applications of the algorithm will include: (i) the assessment of periodicity- and cutoff-induced artifacts in explicit-solvent simulations; (ii) the design of new electrostatic schemes for explicit-solvent simulations mimicking more accurately bulk solution; (iii) a faster evaluation of solvation free energies based on continuum electrostatics in cases where periodicity-induced artifacts can be neglected. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 116 (2002), S. 6880-6897 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A general formulation is given for the calculation of the isotropic or anisotropic group-based instantaneous pressure in molecular simulations under periodic boundary conditions. The equations, derived from the statistical mechanical definition of the pressure, apply to groups defined as single atoms (atomic pressure) or whole molecules (molecular pressure), but also to any other arbitrary atom grouping. Different definitions lead to different pressure fluctuations, but to the same average pressure. Two sets of equations are derived for the calculation of the group-based virial. The "traditional" set, which is the one commonly used to compute molecular pressures in simulations, has two main drawbacks: (i) it requires bookkeeping of group definitions in the inner loop of the nonbonded interaction calculation, (ii) it cannot be applied when electrostatic interactions are computed through lattice-sum methods. The "alternative" set is based on the remarkable result that any group-based virial can be computed from the atomic virial by adding a computationally inexpensive correction term to account for atom grouping. This new formalism presents the following advantages: (i) it requires no bookkeeping of group definitions in the inner loop of the nonbonded interaction calculation, (ii) the isotropic virial corresponding to each homogeneous pairwise interaction term can be computed directly from the corresponding interaction energy contribution without knowledge of the pairwise forces, (iii) application to lattice-sum electrostatics is straightforward. Traditional and alternative virial expressions are derived for all terms typical of interaction functions used in molecular simulations, namely covalent, Lennard-Jones (and long-range correction), truncated electrostatic (and reaction-field correction), and lattice-sum electrostatic (Ewald and particle-particle–particle-mesh including self-energy) terms. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
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