Multipole molecular

It is worthwhile to mention that the projected oscillator orbitals bear some similarities to the trial perturbed wave function in the variation-perturbational technique associated with the names of Kirkwood [30], Pople and Schofield [31] (KPS), to calculate multipole molecular polarizabilities. The closely related Karplus-Kolker [32, 33] (KK) method and its variants [34, 35] use a similar Ansatz for the perturbed orbitals. In these latter methods, which were formulated originally as simplified perturbed Hartree-Fock theories, the first-order perturbed... 

Stone A J 1981 Distributed multipole analysis or how to describe a molecular charge distribution Chem. Phys. Lett. 83 233... 

At distances of a few molecular diameters, the interaction will be dominated by electric multipole interactions for dipolar molecules, such as water, the dominant tenn will be the dipole-dipole interaction ... 

Abstract. Molecular dynamics (MD) simulations of proteins provide descriptions of atomic motions, which allow to relate observable properties of proteins to microscopic processes. Unfortunately, such MD simulations require an enormous amount of computer time and, therefore, are limited to time scales of nanoseconds. We describe first a fast multiple time step structure adapted multipole method (FA-MUSAMM) to speed up the evaluation of the computationally most demanding Coulomb interactions in solvated protein models, secondly an application of this method aiming at a microscopic understanding of single molecule atomic force microscopy experiments, and, thirdly, a new method to predict slow conformational motions at microsecond time scales. 

R. Zhou and B. J. Berne. A new molecular dynamics method combining the reference system propagator algorithm with a fast multipole method for simulating proteins and other complex systems. J. Phys. Chem., 103 9444-9459, 1995. 

T. Bishop, R. D. Skeel, and K. Schulten. Difficulties with multiple timestepping and the fast multipole algorithm in molecular dynamics. J. Comput. Chem., 18 1785-1791, 1997. 

J. F. Leathrum, Jr. Scalable implementations of multipole-accelerated algorithms for molecular dynamics. In Proceedings of the Scalable High-Performance Computing Conference, pages 87-94, Los Alamitos, Calif., 1994. IEEE Computer Society Press. 

J. A. Board, Jr. et al.. Scalable variants of Multipole-Accelerated Algorithms for Molecular Dynamics Applications, Proceedings, Seventh SIAM Conference on Parallel Processing for Scientific Computing, SIAM, Philadelphia (1995), pp. 295-300. 

C. G. Lambert, Multipole-based Algorithms in Molecular Biophysics and Non-parametric Statistics, Ph.D. Dissertation, Duke University Department of Computer Science, 1997. 

NAMD [7] was born of frustration with the maintainability of previous locally developed parallel molecular dynamics codes. The primary goal of being able to hand the program down to the next generation of developers is reflected in the acronym NAMD Not (just) Another Molecular Dynamics code. Specific design requirements for NAMD were to run in parallel on the group s then recently purchased workstation cluster [8] and to use the fast multipole algorithm [9] for efficient full electrostatics evaluation as implemented in DPMTA [10]. 

Molecular dipole moments are often used as descriptors in QPSR models. They are calculated reliably by most quantum mechanical techniques, not least because they are part of the parameterization data for semi-empirical MO techniques. Higher multipole moments are especially easily available from semi-empirical calculations using the natural atomic orbital-point charge (NAO-PC) technique [40], but can also be calculated rehably using ab-initio or DFT methods. They have been used for some QSPR models. 

Fig. 4.18 The most favourable orientations of various multipoles. (Figure adapted from Buckingham A D 1959. Molecular Quadrupole Moments. Quarterly Reviews of the Chemical Society 13 183-214.)...

Distributed multipole models for Nj and HF. (Figure adapted from Stone A j and M Alderton 19S5. ibuted Multipole Analysis Methods and Applications. Molecular Physics 56 3 047-1064.)... 

Stone A J 1981. Distributed Multipole Analysis, or How to Describe a Molecular Charge Distribution. Chemical Physics Letters 83 233-239. 

Zhou R and B J Berne 1995. A New Molecular Dynamics Method Combining the Reference Sys Propagator Algorithm with a Fast Multipole Method for Simulating Proteins and Ol Complex Systems. Journal of Chemical Physics 103 9444-9459. 

Cartesian coordinates system for locating points in space based on three coordinates, which are usually given the symbols x, y, z or i, j, k CBS (complete basis set) an ah initio method CC (coupled cluster) a correlated ah initio method CFF (consistent force field) a class of molecular mechanics force fields CFMM (continuous fast multipole method) a method for fast DFT calculations on large molecules... 

The molecular dipole moment is perhaps the simplest experimental measure of charge density in a molecule. The accuracy of the overall distribution of electrons in a molecule is hard to quantify, since it involves all of the multipole moments. Experimental measures of accuracy are necessary to evaluate results. The values for the magnitudes of dipole moments from AMI calculations for a small sample of molecules (Table 4) indicate the accuracy you may... 

The first simulation studies of full double layers with molecular models of ions and solvent were performed by Philpott and coworkers [51,54,158] for the NaCl solution, using the fast multipole method for the calculation of Coulomb interactions. The authors studied the screening of a negative surface charge by free ions in several highly concentrated NaCl solutions. A combination of (9-3) LJ potential and image charges was used to describe the metal surface. 

Gaussian also predicts dipole moments and higher multipole moments (through hexadecapole). The dipole moment is the first derivative of the energy with respect to an applied electric field. It is a measure of the asymmetry in the molecular charge distribution, and is given as a vector in three dimensions. For Hartree-Fock calculations, this is equivalent to the expectation value of X, Y, and Z, which are the quantities reported in the output. 

Molecular energies and structures Energies and structures of transition states Bond and reaction energies Molecular orbitals Multipole moments... 

Much of our knowledge of molecules is obtained from experimental studies of the way they interact with electromagnetic radiation, and the recent growth in non-linear spectroscopies and molecular electronics has focused attention on our ability (or otherwise) to predict and rationalize the electric properties of molecules. The idea of an electric multipole is an important one, so let s begin the discussion there. 

Since the electric field (F = —dV/dr) normally is fairly uniform at the molecular level, it is useful to write as a multipole expansion. 

Given the diversity of different SCRF models, and the fact that solvation energies in water may range from a few kcal/mol for say ethane to perhaps 100 kcal/mol for an ion, it is difficult to evaluate just how accurately continuum methods may in principle be able to represent solvation. It seems clear, however, that molecular shaped cavities must be employed, the electiostatic polarization needs a description either in terms of atomic charges or quite high-order multipoles, and cavity and dispersion terms must be included. Properly parameterized, such models appear to be able to give absolute values with an accuracy of a few kcal/mol." Molecular properties are in many cases also sensitive to the environment, but a detailed discussion of this is outside the scope of this book. ... 

Molecular polarisability anisotropy and high order multipoles... 

A common feature of many mesogenic molecules is the presence of polar substituents and aromatic cores [3]. The electrostatic interactions between such groups can be incorporated into a molecular potential with the addition of dipolar and quadrupolar terms, respectively. Rather than represent these permanent electrostatic interactions by using a model in which a charge distribution is scattered over the surface of the molecule, it is very common to use one (or more) point multipoles [2,29]. Thus for an electrostatic Gay-Berne model, the pair potential is given by the sum... 

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