Statistical Mechanical Calculations Research Articles

Hydrogen bond ordering in ice V and the transition to ice XIII

The proton ordered version of ice V, ice XIII, was recently identified using Raman spectroscopy and neutron diffraction techniques. The transformation, between 108 and 117 K, only occurred in the presence of a small amount of dopant, similar to the proton ordering transition of ice Ih/XI. In this work, we investigate the hydrogen bond fluctuations in ice V and XIII with statistical mechanical techniques that use results from periodic electronic density functional theory calculations as input. We find a number of low-lying hydrogen bond configurations, approximately 20 within 10 K/water above the ground state state configuration, the structure of which agrees with fully ordered ice XIII. Using an analytic theory, graph invariants, we developed effective spin-lattice Hamiltonians governing hydrogen bond fluctuations to perform statistical mechanical calculations for a large simulation cell containing 6048 water molecules. Two models were constructed, one more elaborate than the first, to gauge the robustness of our methods when the unit cell is very complex and a large number of configurations lie close in energy to the ground state. The predicted proton ordering transitions, 62 and 72 K for the two models, are in qualitative agreement with experiment. Occupation probabilities, obtained from our simulations, compare well with values from recent neutron diffraction experiments and help verify our effective Hamiltonians. In both models, we find that a second order phase transition intervenes about 10 K above the transition to ice XIII, but its effect is negligible on the behavior of thermodynamic functions near the transition to ice XIII.

Geometrical Preferences of the Hydrogen Bonds on Protein-Ligand Binding Interface Derived from Statistical Surveys and Quantum Mechanics Calculations.

We have conducted potential of mean force (PMF) analyses to derive the geometrical parameters of various types of hydrogen bonds on protein-ligand binding interface. Our PMF analyses are based on a set of 4535 high-quality protein-ligand complex structures, which are compiled through a systematic mining of the entire Protein Data Bank. Hydrogen bond donor and acceptor atoms are classified into several basic types. Both distance- and angle-dependent statistical potentials are derived for each donor-acceptor pair, from which distance and angle cutoffs are obtained in an objective, unambiguous manner. These donor-acceptor pairs are also studied by quantum mechanics (QM) calculations at the MP2/6-311++G** level on model molecules. Comparison of the outcomes of PMF analyses and QM calculations suggests that QM calculation may serve as an alternative approach for characterizing hydrogen bond geometry. Both of our PMF analyses and QM calculations indicate that C-H···O hydrogen bonds are relatively weak as compared to common hydrogen bonds formed between nitrogen and oxygen atoms. A survey on the protein-ligand complex structures in our data set has revealed that Cα-H···O hydrogen bonds observed in protein-ligand binding are frequently accompanied by bifurcate N-H···O hydrogen bonds. Thus, the Cα-H···O hydrogen bonds in such cases would better be interpreted as secondary interactions.

Derivation of a new free energy for biological membranes

A new free energy for thin biomembranes depending on chemical composition, degree of order and membranal-bending deformations is derived in this paper. This is a result of constitutive and geometric assumptions at the three-dimensional level. The enforcement of a new symmetry group introduced in (Deseri et al., in preparation) and a 3D--2D dimension reduction procedure are among the ingredients of our methodology. Finally, the identification of the lower order term of the energy (i.e. the membranal contribution) on the basis of a bottom-up approach is performed; this relies upon standard statistical mechanics calculations. The main result is an expression of the biomembrane free energy density, whose local and non-local counterparts are weighted by different powers of the bilayer thickness. The resulting energy exhibits three striking aspects: (i) the local (purely membranal) energy counterpart turns out to be completely determined through the bottom-up approach mentioned above, which is based on experimentally available information on the nature of the constituents; (ii) the non-local energy terms, that spontaneously arise from the 3D--2D dimension reduction procedure, account for both bending and non-local membranal effects; (iii) the non-local energy contributions turn out to be uniquely determined by the knowledge of the membranal energy term, which in essence represents the only needed constitutive information of the model. It is worth noting that the coupling among the fields appearing as independent variables of the model is not heuristically forced, but it is rather consistently delivered through the adopted procedure.

Salt Dependence of Nucleic Acid Hairpin Stability

Single-stranded junctions/loops are frequently occurring structural motifs in nucleic acid structures. Due to the polyanionic nature of the nucleic acid backbone, metal ions play a crucial role in the loop stability. Here we use the tightly bound ion theory, which can account for the possible ion correlation and ensemble (fluctuation) effects, to predict the ion-dependence of loop and stem-loop (hairpin) free energies. The predicted loop free energy is a function of the loop length, the loop end-to-end distance, and the ion (Na + and Mg 2+ in this study) concentrations. Based on the statistical mechanical calculations, we derive a set of empirical formulas for the loop thermodynamic parameters as functions of Na + and Mg 2+ concentrations. For three specific types of loops, namely, hairpin, bulge, and internal loops, the predicted free energies agree with the experimental data. Further applications of these empirical formulas to RNA and DNA hairpin stability lead to good agreements with the available experimental data. Our results indicate that the ion-dependent loop stability makes significant contribution to the overall ion-dependence of the hairpin stability.

Absorption and emission lineshapes and ultrafast solvation dynamics of NO in parahydrogen

We perform a theoretical study on the electronic spectroscopy of dilute NO impurity embedded in parahydrogen (p-H(2)). Absorption and emission lineshapes for the A (2)Sigma(+)<--X (2)Pi Rydberg transition of NO in parahydrogen have been previously measured and simulated, which yielded results for the NO/p-H(2) ground and excited state pair potentials [L. Bonacina et al., J. Chem. Phys. 125, 054507 (2006)]. Using these potentials, we performed molecular dynamics simulation, theoretical statistical mechanical calculations of absorption and emission lineshapes, and both equilibrium and nonequilibrium solvation correlation functions for NO chromophore in parahydrogen. Theory was shown to be in good agreement with simulation. Linear response treatment of solvation dynamics was shown to break down due to a dramatic change in the solute-solvent microstructure upon solute excitation to the Rydberg state and the concomitant increase of the solute size.

Voronoï cell-size distribution and Edwards’ compactivity of the parking lot model

We find by Monte Carlo simulations that the distribution of Voronoï cell sizes for the parking lot model follows a gamma distribution with shape parameter k approximately 2 for high enough packing fractions varphi . A gamma distribution of Voronoï cells sizes was found recently by Aste [Europhys. Lett. 79, 24003 (2007)] in experiments of static packings of monodisperse spheres. This statistic implies that, for high varphi , Edwards' compactivity of the parking lot model depends linearly on the average volume per cell, as predicted by the statistical mechanics calculation of Tarjus and Viot, which explicitly counted the blocked configurations of this model [Phys. Rev. E 69, 011307 (2004)].

Theoretical calculation of oxygen isotope fractionation factors in carbonate systems

Using established methods of statistical mechanical calculation and a recent compilation of vibrational frequency data, we have computed oxygen isotope reduced partition function ratios ( β values) for a large number of carbonate minerals. The oxygen isotope β values of carbonates are inversely correlated to both the mass and radius of the cation bonded to the carbonate anion but neither correlation is good enough to be used as a precise and accurate predictor of β values. There is an approximately 0.6% relative increase in the β values of aragonite per 10 kbar increase in pressure. These estimates of the pressure effect on β values are broadly similar to those deduced previously for calcite using the methods of mineral physics. In comparing the β values of our study with those derived recently from first-principles lattice dynamics calculations, we find near-perfect agreement for calcite and witherite (<0.3% deviation), reasonable agreement for dolomite (<0.9% deviation) and somewhat poorer agreement for aragonite and magnesite (1.5–2% deviation). In the system for which we have the most robust constraints, CO 2–calcite, there is excellent agreement between our calculations and experimental data over a broad range of temperatures (0–900 °C). Similarly, there is good to excellent correspondence between calculation and experiment for most other low to moderate atomic mass carbonate minerals (aragonite to strontianite). The agreement is not as good for high atomic mass carbonates (witherite, cerussite, otavite). In the case of witherite and cerussite, the discrepancy may be due, in part, to our calculation methodology, which does not account for the effect of cation mass on the magnitude of vibrational frequency shifts associated with heavy isotope substitution. However, the calculations also reveal an incompatibility between the high- and low-temperature experimental datasets for witherite and cerussite. Specifically, the shapes of fractionation factor versus 1/ T 2 curves in the calcite–witherite and calcite–cerussite systems do not conform to the robust constraints on the basic shape of these curves provided by theory. This suggests that either the high- or low-temperature datasets for both minerals is in error. Dolomite–calcite fractionation factors derived from our calculations fall within the wide range of fractionations for this system given by previous experimental and natural sample studies. However, our compilation of available low-temperature (25–80 °C) experimental data reveal an unusual temperature dependence of fractionations in this system; namely, the data indicate an increase in the magnitude of fractionations between dolomite (or proto-dolomite) and calcite with increasing temperature. Such a trend is incompatible with theory, which stipulates that fractionations between carbonate minerals must decrease monotonically with increasing temperature. We propose that the anomalous temperature dependence seen in the low-temperature experimental data reflect changes in the crystallinity and degree of cation ordering of the dolomite phase over this temperature interval and the effect these changes have on the vibrational frequencies of dolomite. Similar effects may be present in natural systems at low-temperature and must be considered in applying experimental or theoretical fractionation data to these systems. In nearly all cases, carbonate mineral–calcite fractionation factors given by the present calculations are in as good or better agreement with experimental data than are fractionations derived from semi-empirical bond strength methods.

Absorption and emission lineshapes and solvation dynamics of NO in supercritical Ar

We perform a theoretical study of electronic spectroscopy of dilute NO in supercritical Ar fluid. Absorption and emission lineshapes for the A(2)Sigma(+)<--X(2)Pi Rydberg transition of NO in argon have been previously measured and simulated, which yielded results for the NO/Ar ground- and excited-state pair potentials [Larregaray et al., Chem. Phys. 308, 13 (2005)]. Using these potentials, we have performed molecular dynamics simulations and theoretical statistical mechanical calculations of absorption and emission lineshapes and nonequilibrium solvation correlation functions for a wide range of solvent densities and temperatures. Theory was shown to be in good agreement with simulation. Linear response treatment of solvation dynamics was shown to break down at near-critical temperature due to dramatic change in the solute-solvent microstructure upon solute excitation to the Rydberg state and the concomitant increase of the solute size.

Theoretical Calculation of Thermodynamic Properties of Naphthalene, Methylnaphthalenes, and Dimethylnaphthalenes

For this work we performed quantum mechanical (QM) and statistical mechanical (SM) calculations to generate the entropy of 13 aromatic compoundsnaphthalene, 2 methylnaphthalene isomers, and 10 dimethylnaphthalene isomersin the ideal gas state. Density functional theory (DFT) was used to calculate the equilibrium structure and perform a full normal-mode analysis. The DFT level of theory used in this paper is B3LYP/6-31G(d,p). DFT has also been used to determine barriers for the internal rotation contribution to the entropy. For four compounds for which experimental data are available, the calculated entropies have been compared to the experimental values. The calculated entropies match experiment very well, with the percentage errors close to the experimental uncertainty, less than 0.4 %. The equilibrium distribution of dimethylnaphthalene isomers in the mixture is predicted using the calculated entropies and energies from QM and SM calculations in the 300 K to 740 K temperature range.

Theory-inspired nano-engineering of photonic and electronic materials: Noncentrosymmetric charge-transfer electro-optic materials

Electronic and photonic properties of organic materials are well-known to depend on the intra- and intermolecular interaction of π-electron orbitals. We describe the systematic use of coupled quantum and statistical mechanical calculations to design materials with precisely controlled charge perturbation and charge transport (under the influence of applied electric fields) critical to the realization of desired photonic and electronic properties. Control of electro-optic activity is taken as an example because this phenomenon requires that acentric (dipolar or charge-transfer) molecules be organized in a lattice arrangement exhibiting finite noncentrosymmetric symmetry. Noncentrosymmetric organization of dipolar π-electron chromophores is also an arrangement of potential relevance to optimization of the performance of electronic, photovoltaic, and photorefractive materials. In our theoretical calculations, the roles of inter- and intramolecular electrostatic interactions and the effects of applied electrical and optical fields are explicitly taken into account. A variety of experimental tests of theoretical predictions are executed and a new class of materials is introduced and evaluated. Theoretically-inspired molecular and nanoscopic material design is shown to yield electro-optic coefficients ( r 33) at telecommunication wavelengths on the order of 500 pm/V (15 times greater than lithium niobate). The optimization of auxiliary properties including optical loss, thermal stability and conductivity is also discussed.

Lamellar Structure in Poly(Ala-Gly) Determined by Solid-State NMR and Statistical Mechanical Calculations

Lamellar structure of poly(Ala-Gly) or (AG)n in the solid was examined using 13C solid-state NMR and statistical mechanical approaches. Two doubly labeled versions, [1-13C]Gly14[1-13C]Ala15- and [1-13C]Gly18[1-13C]Ala19 of (AG)15 were examined by two-dimensional (2D) 13C spin diffusion NMR in the solid state. In addition five doubly labeled [15N,13C]-versions of the same peptide, (AG) 15 and 15 versions labeled [3-13C] in each of the successive Ala residues were utilized for REDOR and 13C CP/MAS NMR measurements, respectively. The observed spin diffusion NMR spectra were consistent with a structure containing a combination of distorted beta-turns with a large distribution of the torsion angles and antiparallel beta-sheets. The relative proportion of the distorted beta-turn form was evaluated by examination of 13C CP/MAS NMR spectra of [3-13C]Ala-(AG)15. In addition, REDOR determinations showed five kinds of atomic distances between doubly labeled 13C and 15N nuclei which were also interpreted in terms of a combination of beta-sheets and beta-turns. Our statistical mechanical analysis is in excellent agreement with our Ala Cbeta 13C CP/MAS NMR data strongly suggesting that (AG)15 has a lamellar structure.

Comment on the studies of oxygen isotope fractionation between calcium carbonates and water at low temperatures by Zhou and Zheng (2003; 2005)

Experimental and theoretical aspects of oxygen isotope fractionation in the system calcite–water at low temperatures were critically examined. Contrary to the claim made by Zhou and Zheng [Zhou G.-T., and Zheng Y.-F. (2003) An experimental study of oxygen isotope fractionation between inorganically precipitated aragonite and water at low temperatures. Geochim. Cosmochim. Acta 67, 387–399], there is excellent agreement between fractionation factors that were experimentally determined by means of slow, inorganic precipitation of calcite from solutions and those obtained largely from theoretical, statistical–mechanical calculations of the reduced partition function ratios. This agreement strongly suggests that calcite was precipitated from a solution very close to isotopic equilibrium. However, recently Zhou and Zheng [Zhou G.-T., and Zheng Y.-F. (2005) Effect of polymorphic transition on oxygen isotope fractionation between aragonite, calcite and water: a low-temperature experimental study. Am. Miner. 90, 1121–1130] presented, without any explanation, conclusions on these major aspects that contradict the previous statements of Zhou and Zheng (2003). The apparent discrepancy in calcite–water oxygen isotope fractionation between experimental and theoretical studies discussed by Zhou and Zheng (2003) originates from the “mineral–water interaction” term in the modified increment method, which was developed by one of the authors (Y.-F. Zheng). We call for evidence for the theoretical nature of the modified increment method, which has never been presented in any of Zheng’s papers. Without such evidence, great caution must be exercised in using fractionation factors derived from the modified increment method.

Experimental and theoretical study of thermodynamic excess properties of associating liquid alkanol + 4-picoline mixtures based on quantum mechanical ab initio calculations

Experimental data of the molar enthalpy of mixing H m E of 6 alkanol + 4-picoline systems obtained by flow calorimetric measurements have been compared with statistical–mechanical calculations based on the ERAS-model. The original version of the model has been extended by accounting for results obtained by quantum mechanical ab initio calculations of energetic and structural properties of about 50 molecular clusters, each containing up to 4 molecules associated by hydrogen bonding. The essential results obtained from these calculations are cooperative effects concerning the hydrogen bonding energies of linearly associated alkanol clusters and the quantitative specification of particularly stabilized cyclic alkanol tetrameric clusters. Furthermore, results for the structure and energy of cross-associating clusters containing alkanols and 4-picoline molecules have revealed that the cross-associating energy of the alkanol + 4-picoline hydrogen bonding exceeds the self associating energy of alkanol molecules also leading to an additional cooperative energetic effect when more than two molecules are involved. These quantum mechanical results have directly been incorporated as molecular parameters into the extended ERAS-model without increasing the number of freely adjustable parameters compared to previous versions of the model. An excellent description of the thermodynamic mixture properties has been achieved. The molar excess enthalpy H m E is negative for all 1-alkanol + 4-picoline mixtures while isomeric 2-alkanol + 4-picoline mixtures show positive H m E values quantitatively described by the theory. An explanation of this effect is given on the basis of the ab initio results.

On the theory of the mechanochemical sorption-striction phenomenon in nanoporous bodies with dispersion forces

The soption-striction phenomenon is a change in the dimensions of a porous body in the course of sorption due to the strain caused by the action of molecular forces. The formulation of the theory of the phenomenon includes the following problems: the statistical-mechanical calculation of the pressure tensor in the pore interior as a function of the pore shape and size; the analysis of the role of surface tension in the mechanical equilibrium condition at the pore wall and producing strain at various mechanisms (physical or chemical) of sorption; the calculation of the body strain within the theory of elasticity. The calculation of the pressure tensor was performed for spherical, cylindrical, and flat (slit-like) pores using asymptotic relations for ordinary dispersion forces (in the context of the nano-scaled pore size) and dispersion forces with electromagnetic retardation (for micropores of larger dimensions), with the pair potential exponents −6 and −7, respectively. The results obtained consider both an initial contraction of a porous body in a vacuum and an additional contraction, if any, or the body expansion on the initial stage of the gas sorption. The exact calculation of strain is given for a cylindrical and spherical pore. The role of surface tension is shown to be reduced, first, to the initial contractive strain of a porous body in a vacuum and, second, to the body dilatation in the course of the gas sorption. A small additional contraction of a porous body on the initial stage of sorption (that, as is shown, cannot be caused by surface tension) is explained by the peculiarities of the sorbate pressure tensor in a pore. The effect is more pronounced the smaller the pore size and the lower the temperature, and is typical for nanoporous bodies. A general consideration based on the Irving-Kirkwood pressure tensor qualitatively confirms the regularities established for any kind of molecular interaction.

On the disordered SAW model for DNA denaturation

We investigate numerically the transition properties for models of DNA denaturation, which can be relevant for certain classes of disordered systems. The investigation follows two, complementary, numerical approaches: on-lattice Monte Carlo like simulations or off-lattice statistical mechanics calculations, which can extend very significantly the affordable lengths for the sequences. The on-lattice model consists of two interacting self-avoiding walks with the same origin on a three-dimensional cubic lattice. We introduce two different contact energies, for the adenine–thymine coupling and the guanine–cytosine one, respectively, distributed according to a bimodal law. Whereas the transition is recognized to be of first order in the pure (homopolymer) case, the behaviour of quantities averaged over disorder suggests that the random system undergoes a second-order transition.

Can rare SAT formulae be easily recognized? On the efficiency of message-passing algorithms for K-SAT at large clause-to-variable ratios

For large clause-to-variable ratios, typical K-SAT instances drawn from the uniform distribution have no solution. We argue, based on statistical mechanics calculations using the replica and cavity methods, that rare satisfiable instances from the uniform distribution are very similar to typical instances drawn from the so-called planted distribution, where instances are chosen uniformly between the ones that admit a given solution. It then follows, from a recent article by Feige, Mossel and Vilenchik (2006 Complete convergence of message passing algorithms for some satisfiability problems Proc. Random 2006 pp 339–50), that these rare instances can be easily recognized (in O(log N) time and with probability close to 1) by a simple message-passing algorithm.

A comparison between entropies of aromatic compounds from quantum mechanical calculations and experiment

In this work, we perform a set of quantum mechanical and statistical mechanical calculations to generate the entropy of five simple, aromatic compounds—benzene, toluene, p-xylene, m-xylene and o-xylene—in the ideal gas state. We systematically examine how the choice of quantum mechanical level of theory and size of basis set impact the agreement between theory and experiment. Regardless of level of theory and basis set, all calculations require an empirical scaling factor to correct the vibrational contribution to the entropy. Once this scaling factor is applied, there is at most nominal advantage in more sophisticated levels of theory or increased basis set size, while a heavy computational penalty is paid for the more advanced theory. We find that the variation in scaling factor across these aromatic compounds is on average 0.3%. Across a range from 250 to 540 K, the difference in the entropies obtained from all quantum mechanical calculations and from experiment is less than half a percent.

Modeling of Protein Interactions with Surface-Grafted Charged Polymers. Correlations between Statistical Molecular Modeling and a Mean Field Approach

Ion exchange media involving charge groups attached to flexible polymers are widely used for protein purification. Such media often provide enhanced target protein purity and yield. Yet, little is understood about protein interaction with such media at the molecular level, or how different media architectures might affect separation performance. To gain a better understanding of such adsorptive systems, statistical mechanical perturbation calculations, utilizing a Debye-Hückel potential, were performed on surface-grafted charged polymers and their interaction with model proteins. The studied systems were weakly charged, and the polymers were linear and relatively short (degree of polymerization is 30). Segment distributions from the surface were also determined. The interaction of spherical model protein particles of 12-30 A radius were investigated with respect to polymer grafting density, distance from matrix surface, protein charge, and ionic strength. The partitioning coefficient of the model proteins was determined for different distances from the surface. An empirical mean field theory that scales the entropy of the protein with the square of the protein radius correlates well to Monte Carlo statistical modeling results. Upon adsorption to the polymer layers, the model proteins exhibit a critical surface charge density that is proportional to the ionic strength, independent of the grafting density, and appears to be a fundamental determinant of protein adsorption. Partitioning of protein-like nanoparticles to the charged polymer surface is only favored above the particle critical charge density.

First-principle Thoery of Phase Stability, Phase Equilibria and Phase Transition of Ordered Compounds

AbstractFirst-principles theory of alloys is based on electronic structure calculation at the ground state and statistical mechanics calculation at finite temperatures. The former clarifies the stability of an ordered compound against competing phases and the latter is employed mainly to derive a phase diagram. The author performed a series of first-principles investigations on binary alloy systems including noble metal alloys, semiconductor alloys and Fe-based alloy systems by combining FLAPW electronic structure total energy calculations with Cluster Variation Method. Recently, the theoretical framework is extended even to calculate microstructural evolution process. By exemplifying Fe-based alloy systems, the progress of the first-principles calculation is reviewed and future prospect is discussed.

P1-3 Statistical Mechanical calculation of the ultrasonic relaxation of salt solutions(Poster session 1)

P1-3 Statistical Mechanical calculation of the ultrasonic relaxation of salt solutions(Poster session 1)