quasi-Gaussian Entropy Theory Research Articles

Theoretical-Computational Modeling of Gas-State Thermodynamics in Flexible Molecular Systems: Ionic Liquids in the Gas Phase as a Case Study.

A theoretical-computational procedure based on the quasi-Gaussian entropy (QGE) theory and molecular dynamics (MD) simulations is proposed for the calculation of thermodynamic properties for molecular and supra-molecular species in the gas phase. The peculiarity of the methodology reported in this study is its ability to construct an analytical model of all the most relevant thermodynamic properties, even within a wide temperature range, based on a practically automatic sampling of the entire conformational repertoire of highly flexible systems, thereby bypassing the need for an explicit search for all possible conformers/rotamers deemed relevant. In this respect, the reliability of the presented method mainly depends on the quality of the force field used in the MD simulations and on the ability to discriminate in a physically coherent way between semi-classical and quantum degrees of freedom. The method was tested on six model systems (n-butane, n-butane, n-octanol, octadecane, 1-butyl-3-methylimidazolium hexafluorophosphate and 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ionic pairs), which, being experimentally characterized and already addressed by other theoretical-computational methods, were considered as particularly suitable to allow us to evaluate the method's accuracy and efficiency, bringing out advantages and possible drawbacks. The results demonstrate that such a physically coherent yet relatively simple method can represent a further valid computational tool that is alternative and complementary to other extremely efficient computational methods, as it is particularly suited for addressing the thermodynamics of gaseous systems with a high conformational complexity over a large range of temperature.

Theoretical-computational characterization of the temperature-dependent folding thermodynamics of a [formula omitted]-hairpin peptide

A theoretical-computational approach is presented to characterize the temperature-dependent thermodynamics of protein folding. Making use of the Quasi-Gaussian Entropy (QGE) theory and temperature exchanged molecular dynamics (TREMD) simulations, a complete picture of the folding thermodynamics can be obtained. The strategy is applied to analyze the folding thermodynamics of a β-hairpin peptide, Peptide 1, the folding process of which was experimentally characterized by means of infrared spectroscopy. The results provided by the approach here presented very well reproduce the experimental results, showing that the methodology can be successfully utilized to investigate the thermodynamics of folding processes in a wide temperature range.

Structural, thermodynamic, and kinetic properties of Gramicidin analogue GS6 studied by molecular dynamics simulations and statistical mechanics

Gramicidin S (GS) analogues belong to an important class of cyclic peptides, characterized by an antiparallel double-stranded beta-sheet structure with Type II' beta-turns. Such compounds can be used as model systems to understand the folding/unfolding process of beta-hairpins and more in general of beta-structures. In the present study, we specifically investigate the folding/unfolding behavior of the hexameric Gramicidin S analogue GS6 by using all-atoms molecular dynamics (MD) simulations at different temperatures, coupled to a statistical mechanical model based on the Quasi Gaussian Entropy theory. Such an approach permits to describe the structural, thermodynamic, and kinetic properties of the peptide and to quantitatively characterize its folding/unfolding transitions.

Solvent Electrostriction-Driven Peptide Folding Revealed by Quasi-Gaussian Entropy Theory and Molecular Dynamics Simulation

A quantitative understanding of the complex relationship between microscopic structure and the thermodynamics driving peptide and protein folding is a major goal of biophysical chemistry. Here, we present a methodology comprising the use of an extended quasi-Gaussian entropy theory parametrized using molecular dynamics simulation that provides a complete description of the thermodynamics of peptide conformational states. The strategy is applied to analyze the conformational thermodynamics of MR121-GSGSW, a peptide well characterized in experimental studies. The results demonstrate that the extended state of the peptide possesses the lowest partial molar entropy. The origin of this entropy decrease is found to be in the increase of the density and orientational order of the hydration water molecules around the peptide, induced by the "unfolding". While such a reduction of the configurational entropy is usually associated with the hydrophobic effect, it is here found to be mainly due to the interaction of the solute charges with the solvent, that is, electrostriction.

Theoretical prediction of thermodynamic equilibrium constants of chemical reactions in water

In this work we characterize the thermodynamics of two simple chemical reactions in water. Applying the quasi-gaussian entropy theory to the molecular dynamics calculations, we model the equilibrium constant and its temperature dependence along the typical water isochore. Such a theoretical–computational approach could be useful to predict the optimal condition for chemical reactions in condensed phase at a very low computational cost.

Ground and excited electronic state thermodynamics of aqueous carbon monoxide: A theoretical study

By using the quasi Gaussian entropy theory in combination with molecular dynamics simulations and the perturbed matrix method, we investigate the ground and excited state thermodynamics of aqueous carbon monoxide. Results show that the model used is rather accurate and provides a great detail in the description of the excitation thermodynamics.

A Theoretical Model for the Folding/Unfolding Thermodynamics of Single-Domain Proteins, Based on the Quasi-Gaussian Entropy Theory

The quasi-Gaussian entropy (QGE) theory was used to formulate a statistical mechanical model describing the thermodynamics of the folding/unfolding process of single-domain proteins. The model was parametrized using experimental data obtained from differential scanning calorimetry (DSC) of a set of proteins. The results showed that the model is able to reproduce the experimental behavior in the usual temperature range, for all the analyzed proteins. Furthermore, a remarkable similarity of some parameters of the model, when normalized per residue and corresponding to well-defined physical properties, was found. Interestingly, at low temperature, the model provides cold denaturation features for all the proteins. Finally, a general description of the folding/unfolding process and stability, based on the physical view provided by the model, is discussed.

On the use of the quasi-Gaussian entropy theory in the study of simulated dilute solutions.

In a recent paper [M. D'Alessandro, M. D'Abramo, G. Brancato, A. Di Nola, and A. Amadei, J. Phys. Chem. B 106, 11843 (2002)] we showed how to combine molecular dynamics simulations with the quasi-Gaussian entropy theory, in order to model the statistical mechanics and thermodynamics of ionic (water) solutions. In this paper we extend the method to treat nonspherical solutes, describe more thoroughly its theoretical basis and apply it to a set of more complex solute molecules in water (i.e., water, methane, ethane, methanol, and ethanol). Results show that this approach can really provide an excellent theoretical description of solute-solvent systems over a wide range of temperatures.

Mixing Distributions within the Quasi-Gaussian Entropy Theory: Multistate Thermal Equations of State Valid for Large Temperature Ranges

In this article the quasi-Gaussian entropy (QGE) theory has been extended toward statistical-mechanical models that describe the temperature dependence of thermodynamic properties of fluids at fixed density over a very large temperature range, up to 15 times the critical temperature. The system's phase space is divided into multiple regions, each of which has a “potential” energy distribution that can be described by a simple model, e.g., a Gamma distribution. The overall “potential” energy distribution, which is directly related to the residual Helmholtz free energy of the system, then is a “mixture” of Gamma distributions, each with, for example, a different value of the “minimum” potential energy. Several such multistate models for the free energy were derived and tested on a series of small molecules at various densities: the hard core Yukawa fluid, the Lennard-Jones fluid, argon, methane, ammonia, water, and the extended simple point charge (SPC/E) water model. In almost all systems, a Gamma mixture of Gamma distributions provides a very accurate thermal model over a large temperature range starting at the coexistence line and applicable from ideal gas to dense liquid, even in the vicinity of the critical point. The shape of the “potential” energy distribution and its density dependence reflects the underlying molecular interactions, which are discussed by comparing different systems.

Statistical Mechanics and Thermodynamics of Simulated Ionic Solutions

In this work we combine molecular dynamics simulations with the quasi-Gaussian entropy (QGE) theory to model the statistical mechanics and thermodynamics of ionic solutions. Results showed that the use of the gamma state model provides an excellent theoretical description of the solution behavior over a wide range of temperature. Such an approach makes possible, at relatively low computational costs, the evaluation of partial molar properties such as free energy and entropy which require a heavy computational effort to be estimated with the usual procedures.

Theoretical equations of state for temperature and electromagnetic field dependence of fluid systems, based on the quasi-Gaussian entropy theory

The quasi-Gaussian entropy (QGE) theory employs the fact that a free-energy change can be written as the moment-generating function of the appropriate probability distribution function of macroscopic fluctuations of an extensive property. By modeling this distribution, one obtains a model of free energy and resulting thermodynamics as a function of one state variable. In this paper the QGE theory has been extended towards theoretical models or equations of state (EOS’s) of the thermodynamics of semiclassical systems as a function of two state variables. Two “monovariate” QGE models are combined in the canonical ensemble: one based on fluctuations of the excess energy (the confined gamma state giving the temperature dependence) and the other based on fluctuations of the reduced electromagnetic moment [various models as derived in the preceding paper [Apol, Amadei, and Di Nola, J. Chem. Phys. 116, 4426 (2002)], giving the external field dependence]. This provides theoretical EOS’s for fluid systems as a function of both temperature and electromagnetic field. Special limits of these EOS’s are considered: the general weak-field EOS and the limit to a Curie’s law behavior. Based on experimental data of water and simulation data using the extended simple point charge (SPC/E) water model at 45.0 and 55.51 mol/dm3, the specific EOS based on a relatively simple combination of the confined gamma state model with a discrete uniform state field model accurately reproduces the dielectric properties of water at constant density, as the temperature dependence of the weak-field dielectric constant for gases and liquids, and the field dependence of the dielectric constant of liquids.

Statistical mechanics and thermodynamics of magnetic and dielectric systems based on magnetization and polarization fluctuations: Application of the quasi-Gaussian entropy theory

The quasi-Gaussian entropy (QGE) theory employs the fact that a free-energy change can be written as the moment-generating function of the appropriate probability distribution function of macroscopic fluctuations of an extensive property. In this article we derive the relation between the free energy of a system in an external magnetic or electric field and the distribution of the “instantaneous” magnetization or polarization at zero field. The physical-mathematical conditions of these distributions are discussed, and for several continuous and discrete model distributions the corresponding thermodynamics, or “statistical state,” is derived. Some of these statistical states correspond to well-known descriptions, such as the Langevin and Brillouin models. All statistical states have been tested on several magnetic and dielectric systems: antiferromagnetic MnCl2, the two-dimensional Ising spin model, and the simulated extended simple point charge (SPC/E) water under an electric field. The results indicate that discrete modeling of magnetization and polarization is rather essential for all systems. For the Ising model the “discrete uniform” state (corresponding to a Brillouin function) gives the best description. MnCl2 is best described by a “symmetrized binomial state,” which reflects the two opposing magnetic sublattices. For simulated water it is found that the polarization, as well as the type of distribution of the fluctuations, is strongly affected by the shape of the system.

On the Use of the Quasi-Gaussian Entropy Theory in Systems of Polyatomic Flexible Molecules

In this article we show how the quasi-Gaussian entropy (QGE) theory can be used to treat systems of polyatomic flexible molecules, where the usual semirigid description is not always appropriate. We describe a completely general derivation of the QGE theory which does not make use of any semirigid approximation, and therefore it is very suited for large and flexible molecules. Using molecular dynamics simulations of flexible molecules in vacuo, we investigated the ability of the theory to describe intramolecular energy fluctuations and conformational equilibria of purely classical molecules in the ideal gas condition. Results show that the gamma state level of the theory and its generalization for treating conformational equilibria (multi-gamma state model) provide excellent theoretical models when applied to three polyatomic molecules of increasing conformational freedom.

Derivation of thermal equations of state for quantum systems using the quasi-Gaussian entropy theory

In this article, the quasi-Gaussian entropy theory is derived for pure quantum systems, along the same lines as previously done for semiclassical systems. The crucial element for the evaluation of the Helmholtz free energy and its temperature dependence is the moment generating function of the discrete probability distribution of the quantum mechanical energy. This complicated moment generating function is modeled via two distributions: the discrete distribution of the energy-level order index and the continuous distribution of the energy gap. For both distributions the corresponding physical–mathematical restrictions and possible systematic generation are discussed. The classical limit of the present derivation is mentioned in connection with the previous semiclassical derivation of the quasi-Gaussian entropy theory. Several simple statistical states are derived, and it is shown that among them are the familiar Einstein model and the one-, two-, and three-dimensional Debye models. The various statistical states are applied to copper, α-alumina, and graphite. One of these states, the beta-diverging negative binomial state, is able to provide an accurate description of the heat capacity of both isotropic crystals, like copper, and anisotropic ones, like graphite, comparable to the general Tarasov equation.

Derivation of a general fluid equation of state based on the quasi-Gaussian entropy theory: application to the Lennard-Jones fluid

In this article we present an equation of state for fluids, based on the quasi-Gaussian entropy theory. The temperature dependence along isochores is described by a confined Gamma state, previously introduced, combined with a simple perturbation term. The 11 parameters occurring in the free energy and pressure expressions along the isochores are obtained from molecular dynamics simulation data. The equation of state has been parametrized for the Lennard-Jones fluid in the (reduced) density range 0–1.0 and (reduced) temperature range 1.0–20.0 using (partly new) NVT molecular dynamics simulation data. An excellent agreement for both energy and pressure was obtained. To test the ability to extrapolate to unknown state points, the parametrization was also performed on a smaller set of data in the temperature range 1.0–6.0. The results in the two cases are remarkably close, even in the high temperature range, and are often almost indistinguishable, in contrast to a pure empirical equation of state, like for example the modified Benedict—Webb—Rubin equation. The coexistence line agrees in general very well with Gibbs ensemble and NpT simulation results, and only very close to the critical point there are deviations. Our estimate of the critical point for both parametrizations is somewhat different from the best estimate based on Gibbs ensemble simulations, but is in excellent agreement with other estimates based on NVT simulations and integral equations.

Derivation of a general fluid equation of state based on the quasiGaussian entropy theory: application to the Lennard-Jones fluid

Derivation of a general fluid equation of state based on the quasiGaussian entropy theory: application to the Lennard-Jones fluid

Application of the quasi-Gaussian entropy theory to molecular dynamics simulations of Lennard-Jones fluids

The quasi-Gaussian entropy theory has been applied to reproduce the temperature dependence of the internal energy, pressure and isochoric heat capacity of a molecular dynamics simulated Lennard-Jones (LJ) fluid at density ρ=1 (reduced units). The results show that the gamma state level of the theory is an excellent approximation, able to predict the behavior of these properties over a large temperature range. This application of the theory to the simulated LJ fluid confirms previous results, obtained using experimental fluid data, and shows that the gamma state level of the theory, in combination with molecular simulation techniques, can be used as a general model to obtain accurate and physically consistent equations of state for fluid systems.

On the use of the quasi-Gaussian entropy theory in noncanonical ensembles. II. Prediction of density dependence of thermodynamic properties

In previous articles we derived and tested the quasi-Gaussian entropy theory, a description of the excess free energy in terms of the potential or full internal energy or enthalpy probability distribution, instead of the (configurational) partition function. We obtained in this way the temperature dependence of thermodynamic functions in the NVT, NpT and μVT ensembles assuming a Gaussian, Gamma or Inverse Gaussian distribution. In this article we extend the theory to describe the density dependence of thermodynamic properties, using the distribution of volume and number of particles in the isothermal-isobaric and grand canonical ensemble, respectively. In both ensembles pressure-density expressions for a Gaussian and various Gamma distributions are derived and applied to water. A Gamma description for the volume distribution turns out to be a good model in the gas range, which is in accordance with the volume distribution of an ideal gas. A Gamma description for the particle number distribution works well for liquid densities.

On the use of the quasi-Gaussian entropy theory in noncanonical ensembles. I. Prediction of temperature dependence of thermodynamic properties

In previous articles we derived and tested the quasi-Gaussian entropy theory, a description of the excess Helmholtz free energy in terms of the potential energy distribution, instead of the configurational partition function. We obtained in this way the temperature dependence of thermodynamic functions in the canonical ensemble assuming a Gaussian, Gamma or Inverse Gaussian distribution. In this article we extend the theory to describe the temperature dependence of thermodynamic properties in an exact way in the isothermal-isobaric and grand canonical ensemble, using the distribution of the appropriate heat function. For both ensembles restrictions on and implications of these distributions are discussed, and the thermodynamics assuming a Gaussian or (diverging) Gamma distribution is derived. These cases have been tested for water at constant pressure, and the results for the latter case are satisfactory. Also the distribution of the heat function of some theoretical model systems is considered.

Extensions of the quasi-Gaussian entropy theory

In this paper we present the quasi-Gaussian entropy theory in a comprehensive and consistent way, introducing a new derivation of the theory very suited for applications to molecular systems, and addressing its use in the case of multi-phase systems. A general derivation of the possible confinement of the system within a part of phase space is given, and for water it is shown that for this a hard sphere excluded volume model can be used. To obtain the temperature dependence of the pressure, a new differential equation is derived, and besides the previously introduced Gaussian and Gamma states, in this paper we also describe a new statistical state, the Inverse Gaussian state. We discuss the properties of these different statistical states and for water compare their thermodynamics with experimental data, finding that both the Gamma and Inverse Gaussian states are excellent descriptions.