Free Energy Variational Principle Research Articles

Waves Propagating in Nano-Layered Phononic Crystals with Flexoelectricity, Microstructure, and Micro-Inertia Effects.

The miniaturization of electronic devices is an important trend in the development of modern microelectronics information technology. However, when the size of the component or the material is reduced to the micro/nano scale, some size-dependent effects have to be taken into account. In this paper, the wave propagation in nano phononic crystals is investigated, which may have a potential application in the development of acoustic wave devices in the nanoscale. Based on the electric Gibbs free energy variational principle for nanosized dielectrics, a theoretical framework describing the size-dependent phenomenon was built, and the governing equation as well as the dispersion relation derived; the flexoelectric effect, microstructure, and micro-inertia effects are taken into consideration. To uncover the influence of these three size-dependent effects on the width and midfrequency of the band gaps of the waves propagating in periodically layered structures, some related numerical examples were shown. Comparing the present results with the results obtained with the classical elastic theory, we find that the coupled effects of flexoelectricity, microstructure, and micro-inertia have a significant or even dominant influence on the waves propagating in phononic crystals in the nanoscale. With increase in the size of the phononic crystal, the size effects gradually disappear and the corresponding dispersion curves approach the dispersion curves obtained with the conventional elastic theory, which verify the results obtained in this paper. Thus, when we study the waves propagating in phononic crystals in the micro/nano scale, the flexoelectric, microstructure, and micro-inertia effects should be considered.

A new method for estimating the relative binding free energy, derived from a free energy variational principle for the Pim-1-kinase-ligand and FKBP-ligand systems.

In this study, a new method is proposed for calculating the relative binding free energy between a ligand and a protein, derived from a free energy variational principle (FEVP). To address the shortcomings of the method used in our previous study, we incorporate the dynamical fluctuation of a ligand in the FEVP calculation. The present modified method is applied to the Pim-1-kinase-ligand system and also to the FKBP-ligand system as a comparison with our previous work. Any inhibitor of Pim-1 kinase is expected to function as an anti-cancer drug. Some improvements are observed in the results compared to the previous study. The present work also shows comparable or better results than approaches using a standard technique of binding free energy calculations, such as the LIE and the MM-PB/SA methods. The possibility of applying the present method in the drug discovery process is also discussed.

Calculation of electronic excited states of molecules using the Helmholtz free-energy minimum principle

We show that the Helmholtz free-energy variational principle is the physical principle underlying the ensemble variational theory formulated in seminal papers by Theophilou and by Gross, Oliveira, and Kohn. A method of calculating electronic excitations of atoms and molecules is then proposed, based on the constrained minimization of the free energy. It involves the search for the optimal set of Slater determinant states to describe low electronic excitations and, in a second step, the search for optimal rotations in the space spanned by these states. Boltzmann factors are used as weights of states in the ensemble since for these the free energy achieves a minimum. The proposed method is applied to the Be atom and LiH and BH molecules. The method captures static electron correlation but naturally lacks dynamic correlation. To account for the latter, we describe short-range electron-electron interaction with a density functional, while the long-range part is still expressed by a wave-function method. Using the example of the LiH molecule, we find that the resulting method is able to capture both static and dynamic electron correlations.

Estimation of relative binding free energy based on a free energy variational principle for the FKBP-ligand system

Predicting an accurate binding free energy between a target protein and a ligand can be one of the most important steps in a drug discovery process. Often, many molecules must be screened to find probable high potency ones. Thus, a computational technique with low cost is highly desirable for the estimation of binding free energies of many molecules. Several techniques have thus far been developed for estimating binding free energies. Some techniques provide accurate predictions of binding free energies but high large computational cost. Other methods give good predictions but require tuning of some parameters to predict them with high accuracy. In this study, we propose a method to predict relative binding free energies with accuracy comparable to the results of prior methods but with lower computational cost and with no parameter needing to be carefully tuned. Our technique is based on the free energy variational principle. FK506 binding protein (FKBP) with 18 ligands is taken as a test system. Our results are compared to those from other widely used techniques. Our method provides a correlation coefficient (r²) of 0.80 between experimental and calculated relative binding free energies and yields an average absolute error of 0.70 kcal/mol compared to experimental values. These results are comparable to or better than results from other techniques. We also discuss the possibility to improve our method further.

The Hartree limit of Born's ensemble for the ground state of a bosonic atom or ion

The non-relativistic bosonic ground state is studied for quantum N-body systems with Coulomb interactions, modeling atoms or ions made of N “bosonic point electrons” bound to an atomic point nucleus of Z absolute “electron” charges, treated in Born–Oppenheimer approximation (the nuclear mass M = ∞). By adapting an argument of Hogreve, it is shown that the (negative) \documentclass[12pt]{minimal}\begin{document}${\mathscr B}$\end{document}Bosonic ground state energy \documentclass[12pt]{minimal}\begin{document}${\cal E}_{{\infty }}^{{\mathscr B}}(Z,N)$\end{document}E∞B(Z,N) yields the monotone non-decreasing function \documentclass[12pt]{minimal}\begin{document}$N\mapsto {\cal E}_{{\infty }}^{{\mathscr B}}(\lambda N,N)/N^3$\end{document}N↦E∞B(λN,N)/N3 for any λ > 0. The main part of the paper furnishes a proof that whenever λ ⩾ λ* ≈ 1/1.21, then the limit \documentclass[12pt]{minimal}\begin{document}$\varepsilon (\lambda ):=\lim _{N\rightarrow \infty }{\cal E}_{{\infty }}^{{\mathscr B}}(\lambda N,N)/N^3$\end{document}ɛ(λ):=limN→∞E∞B(λN,N)/N3 is governed by Hartree theory, and the rescaled bosonic ground state wave function factors into an infinite product of identical one-body wave functions determined by the Hartree equation. The proof resembles the construction of the thermodynamic mean-field limit of the classical ensembles with thermodynamically unstable interactions, except that here the ensemble is Born's, with |ψ|2 as ensemble probability density function on \documentclass[12pt]{minimal}\begin{document}$\mathbb {R}^{3N}$\end{document}R3N, with the Fisher information functional in the variational principle for Born's ensemble playing the role of the negative Gibbs entropy functional in the free-energy variational principle for the classical petit-canonical configurational ensemble.

Pseudocritical behavior of ferromagnetic pure and random diluted nanoparticles with competing interactions: Variational and Monte Carlo approaches

The magnetic properties and critical behavior of both ferromagnetic pure and metallic nanoparticles having concurrently atomic disorder, dilution and competing interactions, are studied in the framework of an Ising model. We have used both the free energy variational principle based on the Bogoliubov inequality and Monte Carlo simulation. As a case of study for random diluted nanoparticles we have considered the Fe$_{0.5}$Mn$_{0.1}$Al$_{0.4}$ alloy characterized for exhibiting, under bulk conditions, low temperature reentrant spin glass (RSG) behavior and for which experimental and simulation results are available. Our results allow concluding that the variational model is successful in reproducing features of the particle size dependence of the Curie temperature for both pure and random diluted particles. In this last case, low temperature magnetization reduction was consistent with the same type of RSG behavior observed in bulk in accordance with the Almeida-Thouless line at low fields and a linear dependence of the freezing temperature with the reciprocal of the particle diameter was also obtained. Computation of the correlation length critical exponent yielded the values $\nu=0.926\pm 0.004$ via Bogoliubov and$ \nu =0.71\pm 0.04$ via Monte Carlo. This fact indicates that even though thermodynamical models can be indeed used in the study of nanostructures and they can reproduce experimental features, special attention must be paid regarding critical behavior. From both approaches, differences in the $\nu$ exponent with respect to the pure Ising model agree with Harris and Fisher arguments.

2P085 種々の分子指標による化合物分類に基づく結合自由エネルギー予測における自由エネルギー変分原理の有効性の検討(蛋白質-機能(反応機構,生物活性など),第48回日本生物物理学会年会)

2P085 種々の分子指標による化合物分類に基づく結合自由エネルギー予測における自由エネルギー変分原理の有効性の検討(蛋白質-機能(反応機構,生物活性など),第48回日本生物物理学会年会)

Estimation of relative binding free energy based on a free energy variational principle for quantitative structure activity relationship analyses

In the present study, we try to estimate values of relative binding free energy of ligands to a protein based on a free energy variational principle. Results are used for quantitative structure activity relationship (QSAR) analyses. The aim of our study is to construct a procedure free from adjustable empirical parameters and expensive computational costs, and fast enough for use in QSAR. We apply our procedure to inhibitors of dehydrofolate reductase for which values of binding free energy have been studied extensively with both experimental and theoretical techniques. We demonstrate in this paper that we can obtain fairly good values when we can categorize ligands based on structural similarity or on the Log P values of substituents. The present results indicate that our procedure is valid and applicable to QSAR analyses for drug discovery when major differences in ligand structures can be regarded as small perturbations.

3P-035 自由エネルギー変分原理に基づく結合自由エネルギー予測と化学性質によるリガンドの分類(蛋白質-構造機能相関,第47回日本生物物理学会年会)

3P-035 自由エネルギー変分原理に基づく結合自由エネルギー予測と化学性質によるリガンドの分類(蛋白質-構造機能相関,第47回日本生物物理学会年会)

Internal energy variational principles and governing equations in electroelastic analysis

The first thermodynamic law contains a universal thermodynamic variational principle. The complete internal energy variational principle in the electroelastic analysis is not discussed in previous papers. In this paper this principle will be discussed. From this principle the simple complete governing equations can be deduced, and the Maxwell stress can be naturally derived from this variational principle. It is shown that the Maxwell stress has slightly different forms determined by using internal energy or electric Gibbs free energy variational principle, but substantially they are the same. In the second-order precision the Maxwell stress is uniquely determined, and its expression has the same form for all deformable and rigid dielectrics. The electroelastic analyses in the dielectric should be studied together with its environment, because the electric field exists in all materials except the ideal conductor. The complete governing equations under finite deformation in the initial configuration are also discussed.

1P-052 自由エネルギー変分原理を用いたFKBP阻害剤の結合自由エネルギー予測とリガンドの分類(蛋白質・構造機能相関(1),第46回日本生物物理学会年会)

1P-052 自由エネルギー変分原理を用いたFKBP阻害剤の結合自由エネルギー予測とリガンドの分類(蛋白質・構造機能相関(1),第46回日本生物物理学会年会)

2P006 自由エネルギー変分原理に基づく相対的結合自由エネルギー計算とそのFK506結合タンパク阻害剤への応用(蛋白質(構造・構造機能相関),口頭発表,第45回日本生物物理学会年会)

2P006 自由エネルギー変分原理に基づく相対的結合自由エネルギー計算とそのFK506結合タンパク阻害剤への応用(蛋白質(構造・構造機能相関),口頭発表,第45回日本生物物理学会年会)

2P583 On the Calculation Relative Binding Free Energy Between a Receptor and a Ligand based on a Free Energy Variational Principle(55. Drug design and delivery,Poster Session,Abstract,Meeting Program of EABS &BSJ 2006)

2P583 On the Calculation Relative Binding Free Energy Between a Receptor and a Ligand based on a Free Energy Variational Principle(55. Drug design and delivery,Poster Session,Abstract,Meeting Program of EABS &BSJ 2006)

THE THREE-STATE CHIRAL CLOCK MODEL

We give a brief summary of our recent works on the three-state chiral clock model. In these works, we use improved effective field theories with clusters being strips, infinite in the chiral direction and finite in the non-chiral direction. Hence, effective-field transfer matrix methods can be employed in these studies. The effective fields are determined by the Gibbs-Bogoliubov free energy variational principle, leading to Weiss or Bethe approximations in different studies respectively. By systematic improvement of these approximations, i.e. widening the strips, these studies point to the conclusion that there is no Lifshitz point existing at finite non-zero chirality.

Variational model for micelle structure

A free energy variational principle is proposed for the study of aggregation structures in amphiphile solutions. For nonionic amphiphiles the postulated free energy functional depends on the scalar concentration fields for solvophilic head groups (H) and solvophobic tail groups (T); it has a form appropriate for a binary mixture of head-group chains and tail-group chains supplemented by a term that enforces chemical bond connection between pairs of those chains. Numerical solutions to the Euler equations for the variational principle are presented for molecules with formal constitution (H)10 (T)10, under conditions of spherical aggregate symmetry. These solutions include globular micelles, hollow vesicles, and a type of point defect in a smectic A lamellar system.

Principle of compensation of dangerous diagrams for boson systems. III. Finite temperature

The principle of compensation of dangerous diagrams (PCDD) is derived at finite temperature for boson systems by minimizing the average number of Bogoliubov quasiparticles in the system. The conditions obtained state that (a) the amplitude for the creation (or annihilation) of a single quasiparticle is zero and (b) the amplitude for the creation (or annihilation) of a pair of quasiparticles is zero. These conditions are expanded in finite-temperature perturbation theory, using both the density matrix and Green's function methods. In first order the resulting equations are the Hartree-Fock-Bogoliubov equations for a homogeneous boson system at finite temperature which can also be obtained from a free energy variational principle.

Consistency of variational approximations in statistical thermodynamics

It is shown that a large class of approximations in statistical thermodynamics that are based on the free-energy variational principle for the density operator yield expressions for the macroscopic quantities of the system that are consistent from both the statistical-mechanical and thermodynamical points of view. This corrects some erroneous statements in the literature.

Localized versus Extended Holes in a Two-Band Model for Semiconductor-Metal Transitions

We consider essentially the two-band Hubbard-type model of a nonmagnetic semiconductor studied recently by Falicov and Kimball (FK), but we allow the bandwidth ${\ensuremath{\Delta}}_{v}$ of the valence band to be nonzero and the Coulomb repulsion ${U}_{11}$ between holes to be noninfinite. FK treated this model in an approximation based to some extent on the free-energy variational principle, and they used one-electron wave functions which are localized (Wannier) functions for the valence band, and extended (Bloch) functions for the conductior band. This problem is formulated within the framework of the recently introduced thermal single-determinant approximation. The limit ${U}_{11}\ensuremath{\rightarrow}\ensuremath{\infty}$, ${\ensuremath{\Delta}}_{v}\ensuremath{\rightarrow}0$ then provides a strictly variational derivation of the FK results. We then show that for ${\ensuremath{\Delta}}_{v}\ensuremath{\ne}0$, ${U}_{11}<\ensuremath{\infty}$, and temperature sufficiently small ($T<{T}_{0}$), a lower free energy is obtained when valence-band Bloch functions are substituted for the Wannier functions. That ${T}_{0}$ can be appreciable even when $\frac{{U}_{11}}{{\ensuremath{\Delta}}_{v}}\ensuremath{\gg}1$ and the possibility of a transition to the localized picture at ${T}_{0}$ are pointed out. It is shown that magnetic inelastic neutron scattering (arising from the magnetic dipolar interaction between neutrons and electrons) and distinguish, at least in principle, between the extended and the localized pictures. The fact that band gaps occur in the thermal-neutron range for interesting materials is noted.