Free volume hypothetical scanning molecular dynamics method for the absolute free energy of liquids

White, Ronald P.; Meirovitch, Hagai

doi:doi:10.1063/1.2199529

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Optimal control landscapes for quantum observables

The optimal control of quantum systems provides the means to achieve the best outcome from redirecting dynamical behavior. Quantum systems for optimal control are characterized by an evolving density matrix and a Hermitian operator associated with the observable of interest. The optimal control landscape is the observable as a functional of the control field. The features of interest over this control landscape consist of the extremum values and their topological character. For controllable fin...

Bounds on the overlap of the Hartree-Fock, optimized effective potential, and density functional approximations with the exact energy eigenstates

In this paper, we examine the limits of accuracy of the single determinant approximations (Hartree-Fock, optimized effective potential, and density functional theory) to the exact energy eigenstates of many electron systems. We show that an approximate Slater determinant of Sz = M gives maximum accuracy for states with S = M, provided that perturbation theory for the spin up minus spin down potential is applicable. The overlap with the exact energy eigenstates with S ≠ M is much smaller. Theref...

The hypothetical scanning (HS) method is a general approach for calculating the absolute entropy, S, and free energy, F, by analyzing Boltzmann samples obtained by Monte Carlo (MC) or molecular dynamics (MD) techniques. With HS applied to a fluid, each configuration i of the sample is reconstructed by gradually placing the molecules in their positions at i using transition probabilities (TPs). With our recent version of HS, called HSMC-EV, each TP is calculated from MC simulations, where the simulated particles are excluded from the volume reconstructed in previous steps. In this paper we remove the excluded volume (EV) restriction, replacing it by a “free volume” (FV) approach. For liquid argon, HSMC-FV leads to an improvement in efficiency over HSMC-EV by a factor of 2–3. Importantly, the FV treatment greatly simplifies the HS implementation for liquids, allowing a much more natural application of the method for MD simulations. Given the success and popularity of MD, the present development of the HSMD method for liquids is an important advancement for HS methodology. Results for the HSMD-FV approach presented here agree well with our HSMC and thermodynamic integration results. The efficiency of HSMD-FV is equivalent to HSMC-EV. The potential use of HSMC(MD)-FV in protein systems with explicit water is discussed.

Article Outline

INTRODUCTION
THEORY AND IMPLEMENTATION
1. Free energy and its fluctuation
2. Other free energy functionals
3. Statistical mechanics of the liquid model
4. Ideal HS strategy for liquids
  1. Ideal excluded volume HS treatment (EV)
  2. Ideal free volume HS treatment (FV)
5. The HSMC and HSMD simulation methods
  1. HSMC-EV
  2. HSMC-FV and HSMD-FV
6. Implementation details and enhancements of the method
7. Simulation details
RESULTS AND DISCUSSION
1. Results for HSMC-EV
2. Results for HSMC-FV
3. Results for HSMD-FV
4. Discussion of the FV treatment
SUMMARY AND CONCLUSIONS

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KEYWORDS and PACS

Keywords

argon, liquid theory, molecular dynamics method, Monte Carlo methods, free energy, proteins, molecular biophysics

PACS

61.20.Ja

Computer simulation of liquid structure
65.20.-w

Thermal properties of liquids

ARTICLE DATA

Digital Object Identifier

http://dx.doi.org/10.1063/1.2199529

PUBLICATION DATA

ISSN

0021-9606 (print)

1089-7690 (online)

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American Institute of Physics

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