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Register a new userExact electrostatic energy calculation for charged systems neutralized by uniformly distributed background charge using fast multipole method and its application to efficient free energy calculation
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In the molecular dynamics calculations for the free energy of ions and ionic molecules, we often encounter wet charged molecular systems where electrical neutrality condition is broken. This causes a problem in the evaluation of electrostatic interaction under periodic boundary condition. A standard remedy for the problem is to consider a hypothetical homogeneous background charge density to neutralize the total system. Here, we present a new expression for the evaluation of electrostatic interactions for the system including the background charge by fast multipole method (FMM). Further, an efficient scheme to evaluate solute-solvent interaction energy by FMM has been developed to reduce the computation of far-field part. We have calculated hydration free energy of ions, Mg$^{2+}$, Na$^{+}$, and Cl$^{-}$ dissolved in neutral solvent using the new expression. The calculated free energy showed a good agreement with the result using well-established particle mesh Ewald method, demonstrating the validity of the present expression in the framework of FMM. An advantage of the present scheme is in an efficient free energy calculation of a large-scale charged systems (particularly over million particles) based on highly parallel computations.
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Solvation free energy is an important quantity in Computational Chemistry with a variety of applications, especially in drug discovery and design. The accurate prediction of solvation free energies of small molecules in water is still a largely unsolved problem, which is mainly due to the complex nature of the water-solute interactions. In this letter we develop a scheme for the determination of the electrostatic contribution to the solvation free energy of charged molecules based on nonlocal electrostatics involving a minimal parameter set which in particular allows to introduce atomic radii in a consistent way. We test our approach on simple ions and small molecules for which both experimental results and other theoretical descriptions are available for quantitative comparison. We conclude that our approach is both physically transparent and quantitatively reliable.
The trace amplitude method (TAM) provides us a straightforward way to calculate the helicity amplitudes with massive fermions analytically. In this work, we review the basic idea of this method, and then discuss how it can be applied to next-to-leading order (NLO) quantum chromodynamics (QCD) calculations, which has not been explored before. By analyzing the singularity structures of both virtual and real corrections, we show that the TAM can be generalized to NLO QCD calculations straightforwardly, the only caution is that the unitarity should be guaranteed. We also present a simple example to demonstrate the application of this method.
An efficient real space method is derived for the evaluation of the Madelungs potential of ionic crystals. The proposed method is an extension of the Evjens method. It takes advantage of a general analysis for the potential convergence in real space. Indeed, we show that the series convergence is exponential as a function of the number of annulled multipolar momenta in the unit cell. The method proposed in this work reaches such an exponential convergence rate. Its efficiency is comparable to the Ewalds method, however unlike the latter, it uses only simple algebraic functions.
Light nuclei at room temperature and below exhibit a kinetic energy which significantly deviates from the predictions of classical statistical mechanics. This quantum kinetic energy is responsible for a wide variety of isotope effects of interest in fields ranging from chemistry to climatology. It also furnishes the second moment of the nuclear momentum distribution, which contains subtle information about the chemical environment and has recently become accessible to deep inelastic neutron scattering experiments. Here we show how, by combining imaginary time path integral dynamics with a carefully designed generalized Langevin equation, it is possible to dramatically reduce the expense of computing the quantum kinetic energy. We also introduce a transient anisotropic Gaussian approximation to the nuclear momentum distribution which can be calculated with negligible additional effort. As an example, we evaluate the structural properties, the quantum kinetic energy, and the nuclear momentum distribution for a first-principles simulation of liquid water.
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