3,591 research outputs found
Minimal Basis Iterative Stockholder: Atoms in Molecules for Force-Field Development
Atomic partial charges appear in the Coulomb term of many force-field models
and can be derived from electronic structure calculations with a myriad of
atoms-in-molecules (AIM) methods. More advanced models have also been proposed,
using the distributed nature of the electron cloud and atomic multipoles. In
this work, an electrostatic force field is defined through a concise
approximation of the electron density, for which the Coulomb interaction is
trivially evaluated. This approximate "pro-density" is expanded in a minimal
basis of atom-centered s-type Slater density functions, whose parameters are
optimized by minimizing the Kullback-Leibler divergence of the pro-density from
a reference electron density, e.g. obtained from an electronic structure
calculation. The proposed method, Minimal Basis Iterative Stockholder (MBIS),
is a variant of the Hirshfeld AIM method but it can also be used as a
density-fitting technique. An iterative algorithm to refine the pro-density is
easily implemented with a linear-scaling computational cost, enabling
applications to supramolecular systems. The benefits of the MBIS method are
demonstrated with systematic applications to molecular databases and extended
models of condensed phases. A comparison to 14 other AIM methods shows its
effectiveness when modeling electrostatic interactions. MBIS is also suitable
for rescaling atomic polarizabilities in the Tkatchenko-Sheffler scheme for
dispersion interactions.Comment: 61 pages, 12 figures, 2 table
Extensions of the siesta dft code for simulation of molecules
We describe extensions to the siesta density functional theory (dft) code
[30], for the simulation of isolated molecules and their absorption spectra.
The extensions allow for: - Use of a multi-grid solver for the Poisson equation
on a finite dft mesh. Non-periodic, Dirichlet boundary conditions are computed
by expansion of the electric multipoles over spherical harmonics. - Truncation
of a molecular system by the method of design atom pseudo- potentials of Xiao
and Zhang[32]. - Electrostatic potential fitting to determine effective atomic
charges. - Derivation of electronic absorption transition energies and
oscillator stren- gths from the raw spectra produced by a recently described,
order O(N3), time-dependent dft code[21]. The code is furthermore integrated
within siesta as a post-processing option
Genetic Algorithm Optimization of Point Charges in Force Field Development: Challenges and Insights
Evolutionary methods, such as genetic algorithms (GAs), provide powerful tools for optimization of the force field parameters, especially in the case of simultaneous fitting of the force field terms against extensive reference data. However, GA fitting of the nonbonded interaction parameters that includes point charges has not been explored in the literature, likely due to numerous difficulties with even a simpler problem of the least-squares fitting of the atomic point charges against a reference molecular electrostatic potential (MEP), which often demonstrates an unusually high variation of the fitted charges on buried atoms. Here, we examine the performance of the GA approach for the least-squares MEP point charge fitting, and show that the GA optimizations suffer from a magnified version of the classical buried atom effect, producing highly scattered yet correlated solutions. This effect can be understood in terms of the linearly independent, natural coordinates of the MEP fitting problem defined by the eigenvectors of the least-squares sum Hessian matrix, which are also equivalent to the eigenvectors of the covariance matrix evaluated for the scattered GA solutions. GAs quickly converge with respect to the high-curvature coordinates defined by the eigenvectors related to the leading terms of the multipole expansion, but have difficulty converging with respect to the low-curvature coordinates that mostly depend on the buried atom charges. The performance of the evolutionary techniques dramatically improves when the point charge optimization is performed using the Hessian or covariance matrix eigenvectors, an approach with a significant potential for the evolutionary optimization of the fixed-charge biomolecular force fields
Molecular modeling for physical property prediction
Multiscale modeling is becoming the standard approach for process study in a broader framework that promotes computer aided integrated product and process design. In addition to usual purity requirements, end products must meet new constraints in terms of environmental impact, safety of goods and people, specific properties. This chapter adresses the use of molecular modeling tools for the prediction of physical property usefull for chemical engineering practice
Information-theoretic approaches to atoms-in-molecules : Hirshfeld family of partitioning schemes
Many population analysis methods are based on the precept that molecules should be built from fragments (typically atoms) that maximally resemble the isolated fragment. The resulting molecular building blocks are intuitive (because they maximally resemble well-understood systems) and transferable (because if two molecular fragments both resemble an isolated fragment, they necessarily resemble each other). Information theory is one way to measure the deviation between molecular fragments and their isolated counterparts, and it is a way that lends itself to interpretation. For example, one can analyze the relative importance of electron transfer and polarization of the fragments. We present key features, advantages, and disadvantages of the information-theoretic approach. We also codify existing information-theoretic partitioning methods in a way, that clarifies the enormous freedom one has within the information-theoretic ansatz
Influence of polarizability on metal oxide properties studied by molecular dynamics simulations
We have studied the dependence of metal oxide properties in molecular
dynamics (MD) simulations on the polarizability of oxygen ions. We present
studies of both liquid and crystalline structures of silica (SiO2), magnesia
(MgO) and alumina (Al2O3). For each of the three oxides, two separately
optimized sets of force fields were used: (i) Long-range Coulomb interactions
between oxide and metal ions combined with a short-range pair potential. (ii)
Extension of force field (i) by adding polarizability to the oxygen ions. We
show that while an effective potential of type (i) without polarizable oxygen
ions can describe radial distributions and lattice constants reasonably well,
potentials of type (ii) are required to obtain correct values for bond angles
and the equation of state. The importance of polarizability for metal oxide
properties decreases with increasing temperature.Comment: 8 pages, 7 figure
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Point Charges Optimally Placed to Represent the Multipole Expansion of Charge Distributions
We propose an approach for approximating electrostatic charge distributions with a small number of point charges to optimally represent the original charge distribution. By construction, the proposed optimal point charge approximation (OPCA) retains many of the useful properties of point multipole expansion, including the same far-field asymptotic behavior of the approximate potential. A general framework for numerically computing OPCA, for any given number of approximating charges, is described. We then derive a 2-charge practical point charge approximation, PPCA, which approximates the 2-charge OPCA via closed form analytical expressions, and test the PPCA on a set of charge distributions relevant to biomolecular modeling. We measure the accuracy of the new approximations as the RMS error in the electrostatic potential relative to that produced by the original charge distribution, at a distance the extent of the charge distributionâthe mid-field. The error for the 2-charge PPCA is found to be on average 23% smaller than that of optimally placed point dipole approximation, and comparable to that of the point quadrupole approximation. The standard deviation in RMS error for the 2-charge PPCA is 53% lower than that of the optimal point dipole approximation, and comparable to that of the point quadrupole approximation. We also calculate the 3-charge OPCA for representing the gas phase quantum mechanical charge distribution of a water molecule. The electrostatic potential calculated by the 3-charge OPCA for water, in the mid-field (2.8 Ă
from the oxygen atom), is on average 33.3% more accurate than the potential due to the point multipole expansion up to the octupole order. Compared to a 3 point charge approximation in which the charges are placed on the atom centers, the 3-charge OPCA is seven times more accurate, by RMS error. The maximum error at the oxygen-Na distance (2.23 Ă
) is half that of the point multipole expansion up to the octupole order
Atomic radius and charge parameter uncertainty in biomolecular solvation energy calculations
Atomic radii and charges are two major parameters used in implicit solvent
electrostatics and energy calculations. The optimization problem for charges
and radii is under-determined, leading to uncertainty in the values of these
parameters and in the results of solvation energy calculations using these
parameters. This paper presents a new method for quantifying this uncertainty
in implicit solvation calculations of small molecules using surrogate models
based on generalized polynomial chaos (gPC) expansions. There are relatively
few atom types used to specify radii parameters in implicit solvation
calculations; therefore, surrogate models for these low-dimensional spaces
could be constructed using least-squares fitting. However, there are many more
types of atomic charges; therefore, construction of surrogate models for the
charge parameter space requires compressed sensing combined with an iterative
rotation method to enhance problem sparsity. We demonstrate the application of
the method by presenting results for the uncertainties in small molecule
solvation energies based on these approaches. The method presented in this
paper is a promising approach for efficiently quantifying uncertainty in a wide
range of force field parameterization problems, including those beyond
continuum solvation calculations.The intent of this study is to provide a way
for developers of implicit solvent model parameter sets to understand the
sensitivity of their target properties (solvation energy) on underlying choices
for solute radius and charge parameters
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