Force Field Equations Research Articles

Molecular Mechanics Parameterization of Anesthetic Molecules.

Anesthetic drug molecules are being increasingly studied through the use of computational methods such as molecular dynamics (MD). Molecular mechanics force fields require the investigator to supply parameters for the force field equation, which are not available for novel molecules. Careful selection of these parameters is critical for simulations to produce meaningful results. Therefore, this chapter presents a state-of-the-art method for determining these parameters by comparison to quantum mechanics calculations and experimental quantities. Ketamine is used as an example to demonstrate the process.

Effect of Basis Sets on the Selection of the Level of Theory Toward the Development of Quantum-Based Force Field Equation for Ionic Liquids

The chemical industry is under considerable pressure to replace many of the volatile organic compounds. Volatile organic compounds are a major contributor to air pollution, but out of necessity, they are still frequently used in many chemical and industrial processes. A new class of solvents, referred to as ionic liquids, may offer at least a partial solution to the pollution problem caused by volatile organic compounds. Ionic liquids are generally considered "green" solvents because of their environment-friendly properties. However, the main problem that hinders the chemical industry from using ionic liquids is that, compared to conventional organic solvents, relatively little is known about their thermodynamic and transport properties. Since there are large possible combinations of ionic liquids, it would be very expensive if the study were conducted in the laboratory. The more appropriate approach in studying the properties of ionic liquids is to engage in a computational method, which uses a computer software that evaluates ionic liquids' thermophysical quantities via quantum mechanical and molecular mechanical simulations. In this study, a computer simulation, with the aid of SPARTAN '02 software, is used to study the effect of basis sets on the selection of the appropriate level of theory, which would be employed later in developing a quantum-based force field equation for predicting the properties of ionic liquids. Using the Hartree-Fock self-consistent filled (HF-SCF) molecular orbital model with different basis sets, a single point energy calculations were carried out for the chosen ionic liquid. With the exception of the minimal basis set, the SCF total energies for the other basis sets agree with each other in terms of magnitude. The SCF total energy is not affected as the basis set varies from minimal to split valence and as it polarizes. The most appropriate basis set was found to be 6-31G*. Keywords: Basis sets, Hartree-Fock, ionic liquids, force field equation, level of theory, and SPARTAN '02.

Limitations of the force field equation to describe cosmic ray modulation

The force field approximation to the transport equation which describes cosmic ray modulation in the heliosphere is a widely used tool. It is popular because it provides an easy to use, quasi‐analytical method to describe the level of modulation with a single parameter. A simple numerical solution of the one‐dimensional cosmic ray transport equation is used to show that this is a good approximation for galactic cosmic rays in the inner heliosphere but that its accuracy decreases toward the outer heliosphere. On the other hand, the even simpler convection‐diffusion approximation improves with radial distance. The reason for the complementary behavior of these two approximations is that energy losses are relatively important in the inner heliosphere but not in the outer heliosphere. The force field approximation is worse for anomalous cosmic rays at all radial distances due to the exponential cutoff of these spectra at high energies. The ranges of validity are quantified. Since both approximations have their limitations, a simple numerical solution of the one‐dimensional transport equation is provided for general use.

Development and parametrization of continuum solvent models. I. Models based on the boundary element method

A series of different simplifications of the boundary element method (BEM) for solving the Poisson–Boltzmann equation is investigated in an effort to obtain an accurate and fast enough treatment of electrostatic effects to be incorporated in Monte-Carlo and molecular dynamics simulation methods. The tested simplifications include increasing the size of Boundary Elements, decreasing the surface dot density, and ignoring the interactions between the polarization charges. Combined with terms describing the nonelectrostatic solvation effects, the simplified BEM polarization terms were built into expressions for the solvation potential. The solvation potential is treated as empirical consistent force field equations. The intervening parameters, including atomic and probe radii, are derived by different fitting strategies of calculated vs experimental vacuum to water transfer energies of 173 charged, polar, and nonpolar small molecules. These fits are shown to yield very good correlations (rms ∼1.4 kcal/mol), even when the interactions between the polarization charges are neglected, proving that the most time-consuming step in BEM, which involves solving the linear system, can be successfully avoided. Finally, the computing efficiency of the method is tested on macromolecules and is found to be convenient for implementation in molecular dynamics or Monte Carlo simulations.

Electromagnetic and Force Field Equations

In classical physics the electromagnetic equations are described by Maxwell's equations. Maxwell's equations proved to be invariant under gauge, or Lorentz transformations. Also, Einstein's equations of the special theory of relativity are invariant under Lorentz transformations. On the other hand classical mechanics and quantum mechanics laws are invariant under Galilean transformations. This means that, there are two different dynamical structures describing our universe. Einstein's unified field theory failled in putting our universe in one dynamical structure. New electromagnetic and force field equations are going to be derived. They have the same shape like Maxwell's equations, but with different dynamical structure. Those equations are invariant under Galilean transformations and in the density matrix formalism of quantum mechanics.

TheFolded LC-Circuit

The folded LC-circuit is studied from quantum mechanical point of view. New equations relating the current, voltage, electric, magnetic, and force fields are derived. The dynamical electromagnetic and force field equations are proved to be invariant under Galilean transformation.

Carbonization of anthracene and phenanthrene. 2. Spectroscopy and mechanisms

The C, H analysis and FTIR and 1 H NMR data on the carbonization products from anthracene and phenanthrene showed remarkable differences in reaction chemistry and mechanisms for these isomers. As different from phenanthrene, anthracene involves extensive hydrogenation reactions which lead to the formation of hydroaromatic compounds in the liquid phase during carbonization. Dreiding models of reaction products based on the C, H contents and spectroscopic data along with the minimization of the force field equation showed that anthracene produced planar oligomers more readily than phenanthrene. A mechanism is proposed for the two dimensional growth of discotic mesogens using Huckel molecular orbital calculations combined with structural modeling

A new strategy for the evaluation of force parameters from quantum mechanical computations

AbstractA new strategy for the determination of force parameters is presented. The equilibrium values appearing in the force field equations representing the “stretching” and “bending” of bonds are directly determined from quantum mechanical calculations without geometrical restrictions. The determination of the force parameters is carried out by means of a rigorous fitting between the quantum mechanic and the molecular mechanical energy variations arising from the perturbation of the geometric variables. The strategy presented here has been incorporated into a computer program named PAPQMD, which was developed in order to provide nonquantum mechanical experts with a powerful tool for the determination of approximate force parameters. The program was developed upon the assumption that force parameters are not universal, but they strongly depend on the molecular environment. This implies that the parametrization procedure should be done in a molecular model close to the molecule or molecules to be studied by means of molecular mechanical or dynamic methods, and consequently, it is no longer supposed that the variation of one geometrical parameter does not affect the rest of the molecular geometry. PAPQMD performs the fitting between molecular mechanics and quantum mechanical energies considering all the perturbations that the modification in one geometric variable causes in all the others, enabling the parametrization even of large molecules. The ability of our method to reproduce experimentally derived force parameters is discussed and compared with the widely used Hopfinger's strategy. The study of the behavior of PAPQMD and Hopfinger's strategies for reproducing the force parameters of two complex molecules demonstrates the superiority of the methodology presented here.

The force field equation for the propagation of galactic cosmic rays applied to neutron monitor measurements

The modulation of galactic cosmic rays is described in terms of a generalized force field equation for a mixture of particles to which a neutron monitor is sensitive. The force field solution is used to derive the modulation parameters from observations inside the atmosphere in an energy region well above the effective high-energy limit of satellite observations. The parameters are calculated in the rigidity range ∼2–15 GV and provide statistically accurate extensions in rigidity to existing results. The limitations of the modified convection-diffusion approximation for modulation studies in the rigidity range ∼2–15 GV are indicated.

A study of the force-field equation for the propagation of galactic cosmic rays

A new development is given of the solution of the equation of the force-field approximation for the propagation of galactic cosmic rays in the interplanetary region. It leads to simpler methods for determining the force-field parameters. A method is given for determining the separable diffusion coefficient from observations of galactic electron spectrum and near-Earth electron spectra; it is shown that this diffusion coefficient is not unique but may have a periodic-like dependence upon rigidity; and the method is used to obtain diffusion coefficients for 1965 and 1968. Approximate formulae relating small changes in intensity and diffusion coefficient are developed and some applications of these noted; in one it is shown that the form of, and changes in, diffusion coefficient deduced previously for a neutron monitor event during June–September 1969 are unnecessarily constrained and therefore probably not correct.