Free energy functional expansion as the generalized approach to the equation of state of dense fluids

A version of the thermodynamic perturbation theory based on a scaling transformation of the partition function has been applied to the statistical derivation of the equation of state in a highpressure region. Two modifications of the equations of state have been obtained on the basis of the free energy functional perturbation series. The comparative analysis of the experimental PV T- data on the isothermal compression for the supercritical fluids of inert gases has been carried out. © 2012.

Path Optimization in Free Energy Calculations

Free energy calculations are a computational method for determining thermodynamic quantities, such as free energies of binding, via simulation.

Currently, due to computational and algorithmic limitations, free energy calculations are limited in scope.

In this work, we propose two methods for improving the efficiency of free energy calculations.

First, we expand the state space of alchemical intermediates, and show that this expansion enables us to calculate free energies along lower variance paths.

We use Q-learning, a reinforcement learning technique, to discover and optimize paths at low computational cost.

Second, we reduce the cost of sampling along a given path by using sequential Monte Carlo samplers.

We develop a new free energy estimator, pCrooks (pairwise Crooks), a variant on the Crooks fluctuation theorem (CFT), which enables decomposition of the variance of the free energy estimate for discrete paths, while retaining beneficial characteristics of CFT.

Combining these two advancements, we show that for some test models, optimal expanded-space paths have a nearly 80% reduction in variance relative to the standard path.

Additionally, our free energy estimator converges at a more consistent rate and on average 1.8 times faster when we enable path searching, even when the cost of path discovery and refinement is considered.

Understanding Co-translational Protein Targeting and Lithium Dendrite Formation through Free Energy Simulations and Coarse-Grained Models

We describe the application of alchemical free energy methods and coarse-grained models to study two key problems: (i) co-translational protein targeting and insertion to direct membrane proteins to the endoplasmic reticulum for proper localization and folding, (ii) lithium dendrite formation during recharging of lithium metal batteries. We show that conformational changes in the signal recognition particle, a central component of the protein targeting machinery, confer additional specificity during the the recognition of signal sequences. We then develop a three-dimensional coarse-grained model to study the long-timescale dynamics of membrane protein integration at the translocon and a framework for the calculation of binding free energies between the ribosome and translocon. Finally, we develop a coarse-grained model to capture the dynamics of lithium deposition and dissolution at the electrode interface with time-dependent voltages to show that pulse plating and reverse pulse plating methods can mitigate dendrite growth.

Metal-free graphitic carbon nitride as mechano-catalyst for hydrogen evolution reaction

Graphitic carbon nitride (g-C3N4), as a promising metal-free catalyst for photo-catalytic and electrochemical water splitting, has recently attracted tremendous research interest. However, the underlying catalytic mechanism for the hydrogen evolution reaction (HER) is not fully understood. By using density functional theory calculations, here we have established that the binding free energy of hydrogen atom (ΔGH∗0) on g-C3N4 is very sensitive to mechanical strain, leading to substantial tuning of the HER performance of g-C3N4 at different coverages. The experimentally-observed high HER activity in N-doped graphene supported g-C3N4 (Zheng et al., 2014) is actually attributed to electron-transfer induced strain. A more practical strategy to induce mechanical strain in g-C3N4 is also proposed by doping a bridge carbon atom in g-C3N4 with an isoelectronic silicon atom. The calculated ΔGH∗0 on the Si-doped g-C3N4 is ideal for HER. Our results indicate that g-C3N4 would be an excellent metal-free mechano-catalyst for HER and this finding is expected to guide future experiments to efficiently split water into hydrogen based on the g-C3N4 materials.

Gibbs Energy of Formation of Cobalt Divanadium Tetroxide

The Gibbs energy of formation of V2O3-saturated spinel CoV2O4 has been measured in the temperature range 900–1700 K using a solid state galvanic cell, which can be represented as Pt, Co + CoV2O4 + V2O3/(CaO) ZrO2/Co + CoO, Pt. The standard free energy of formation of cobalt vanadite from component oxides can be represented as CoO (rs) + V2O3 (cor) → CoV2O4 (sp), ΔG° = −30,125 − 5.06T (± 150) J mole−1. Cation mixing on crystallographically nonequivalent sites of the spinel is responsible for the decrease in free energy with increasing temperature. A correlation between “second law” entropies of formation of cubic 2–3 spinels from component oxides with rock salt and corundum structures and cation distribution is presented. Based on the information obtained in this study and trends in the stability of aluminate and chromite spinels, it can be deduced that copper vanadite is unstable.

Phase Relations in the System Cu-Gd-O and Gibbs Energy of Formation of CuGd204

The phase relations in the system Cu-Gd-O have been determined at 1273 K by X-ray diffrac- tion, optical microscopy, and electron microprobe analysis of samples equilibrated in quartz ampules and in pure oxygen. Only one ternary compound, CuGd2O4, was found to be stable. The Gibbs free energy of formation of this compound has been measured using the solid-state cell Pt, Cu2O + CuGd2O4 + Gd2O3 // (Y2O3) ZrO2 // CuO + Cu2O, Pt in the temperature range of 900 to 1350 K. For the formation of CuGd2O4 from its binary component oxides, CuO (s) + Gd2O3 (s) → CuGd2O4 (s) ΔG° = 8230 - 11.2T (±50) J mol-1 Since the formation is endothermic, CuGd2O4 becomes thermodynamically unstable with respect to CuO and Gd2O3 below 735 K. When the oxygen partial pressure over CuGd2O4 is lowered, it decomposes according to the reaction 4CuGd2O4 (s) → 4Gd2O3 (s) + 2Cu2O (s) + O2 (g) for which the equilibrium oxygen potential is given by Δμo 2 = −227,970 + 143.2T (±500) J mol−1 An oxygen potential diagram for the system Cu-Gd-O at 1273 K is presented.

Gibbs energy of formation of orthorhombic CaZrO3

The Gibbs free energy of formation of the orthorhombic form of CaZrO3(o) from monoclinic ZrO2(m) and periclase CaO(p) has been determined as a function of temperature in the range 950-1225 K, using an electrochemical cell incorporating single-crystal CaF2 as the solid electrolyte. The results are corrected for the small solid solubility of CaO in ZrO2. For the reaction, ZrO2(m) + CaO(p) --> CaZrO3(o), DELTAG(phi) = -31590 -13.9T(+/- 180) J mol-1. The ''second-law'' enthalpy of formation of CaZrO3 obtained from the results of this study at a mean temperature of 1090 K is in excellent agreement with the high-temperature solution calorimetric measurements of Muromachi and Navrotsky at 1068 K (J. Solid State Chem., 72 (1988) 244), and the average value of the bomb and acid solution calorimetric studies of Lvova and Feodosev (Zh. Fiz. Khim., 38 (1964) 28), Korneev et al. (Izv. Akad. Nauk SSSR, Neorg. Mater., 7 (1971) 886) and Brown and Bennington (Thermochim. Acta, 106 (1986) 183). The standard entropy of CaZrO3(o) at 298.15 K from the free energy data is 96.4 (+/- 3.5) J K-1 mol-1. The results of this study are discussed in comparison with high-temperture e.m.f. measurements reported in the literature on cubic zirconia solid solutions.

Determination of the Gibbs energy of diamond using a solid state cell

he chemical potential of carbon in diamond, relative to its value in graphite, has been directly determined using a solid state electrochemical cell incorporating single crystal CaF2 as the solid electrolyte. The cell can be represented as Pt, C(graphite) + CaC2 + CaF2double vertical barCaF2double vertical barCaF2 + CaC2 + C(diamond), Pt The reversible emf of this cell is directly related by the Nernst equation to the Gibbs free energy change for the conversion of diamond to graphite. The difference in the chemical potential of carbon in the two crystal structures varies linearly with temperature in the range 940 to 1260 K ?C(diamond) ? ?C(graphite) = 1100 + 4.64T (±50) J mol?1 On the average, the values given by the equation are 320 J mol?1 less positive than the currently accepted ones based on calorimetric studies. The difference is primarily in the enthalpy term.

Absolute Entropy and Energy of Carbon Dioxide Using the Two-Phase Thermodynamic Model

The two-phase thermodynamic (2PT) model is used to determine the absolute entropy and energy of carbon dioxide over a wide range of conditions from molecular dynamics trajectories. The 2PT method determines the thermodynamic properties by applying the proper statistical mechanical partition function to the normal modes of a fluid. The vibrational density of state (DoS), obtained from the Fourier transform of the velocity autocorrelation function, converges quickly, allowing the free energy, entropy, and other thermodynamic properties to be determined from short 20-ps MD trajectories. The anharmonic effects in the vibrations are accounted for by the broadening of the normal modes into bands from sampling the velocities over the trajectory. The low frequency diffusive modes, which lead to finite DoS at zero frequency, are accounted for by considering the DoS as a superposition of gas-phase and solid-phase components (two phases). The analytical decomposition of the DoS allows for an evaluation of properties contributed by different types of molecular motions. We show that this 2PT analysis leads to accurate predictions of entropy and energy of CO2 over a wide range of conditions (from the triple point to the critical point of both the vapor and the liquid phases along the saturation line). This allows the equation of state of CO2 to be determined, which is limited only by the accuracy of the force field. We also validated that the 2PT entropy agrees with that determined from thermodynamic integration, but 2PT requires only a fraction of the time. A complication for CO2 is that its equilibrium configuration is linear, which would have only two rotational modes, but during the dynamics it is never exactly linear, so that there is a third mode from rotational about the axis. In this work, we show how to treat such linear molecules in the 2PT framework.

Gibbs free energies of formation of indium (III) oxide and sulphate

Emf measurements on the galvanic cell Pt, Ta, In + In,O, / Tho,-Y,03 / Cu + C+O, Pt were used to obtain the standard free energy of formation of 1%03fr om 600 to 900°C. Differential thermal analysis was used to detect the decomposition of In2(S0,), under controlled SO2 + O2 + Ar mixtures in thqtemperature range 640-8wC. X-ray diffraction analysis indicated that the decomposition product was 1%03 without an oxywlphate intermediate. The following equations were obtained for the variation of the standard free-energy change(Jlmole) with temperature:

Gibbs’ free energies of formation of Cu2Ln2O5 (Ln = Tb, Dy, Er, Yb) compounds

The standard Gibbs' free energies of formation of compounds of type Cu2L%05 (Ln = Tb,Dy,Er,Yb) were measured using the solid state cell in the temperature range of 970 to 1323 K For formation of Cu2L?O5 compounds from their binary component oxides according to the reaction 2 CUO (s) + L%03 (s) -, Cu,,L%05 (s),the Gibbs' free energy changes can be represented by the following equations:AGO = 13 080 - 13.70 'I" (+80) J mol-' (Ln = Tb)AGq = 11 480 - 13.51 T (260) J mol-I (Ln = Dy)AGO = 10 750 - 13.99 T (260) J mol-I (Ln = Er)AGO = 9 920 - 13.90 T (260) J mol-' (Ln = Yb) Since formation of the compounds is endothermic, the compounds become thermodynamically unstable with respect to their component oxides below 955 K for Cu2Tb205, 850 K for Cu2Dy205, 768 K for Cu2Er205 and 714 K for Cu2Yb2OS When the oxygen partial pressure over Cu2L%05 is lowered, they decompose according to the scheme, 2 CU,L%O, (s) -r 2 L%03 (s) +2 cu20 (s) + 02(g)The equilibrium chemical potentials of oxygen corresponding to the dissociation reactions are computed from the emf data and auxiliary information on Cu20 and CuO. The computed decomposition temperatures at an oxygen partial pressure of 5.0 x ld Pa are compared with those obtained directly from combined thermogravimetric (TGA) and differential thermal analyses (DTA).The free energy, enthalpy and entropy of formation of Cu2Ln205 compounds show systematic variation with the ionic radius of the trivalent lanthanide ion. The trends obtained in this study are compared with information available in the literature. The staZbility of Cu2Ln205 compounds increases with the decrease in ionic radii of the ~ n ion~. +

Phase equilibria in the system NiO-CaO-SiO2 and Gibbs energy of formation of CaNiSi2O6

Phase relations in the pseudoternary system NiO-CaO-SiO2 at 1373 K are established. The coexisting phases are identified by X-ray diffraction and energy-dispersive X-ray analysis of equilibrated samples. There is only one quaternary oxide CaNiSi2O6 with clinopyroxene structure. The Gibbs energy of formation of CaNiSi2O6 is measured using a solid state galvanic cell incorporating stabilized zirconia as the solid electrolyte in the temperature range of 1000 to 1400 K:Pt, Ni + SiO2 + CaSiO3 + CaNiSi2O6 \ (Y2O3)ZrO2 \ Ni + NiO, Pt From the electromotive force (emf) of the cell, the Gibbs energy of formation of CaNiSi2O6 from NiO, SiO2, and CaSiO3 is obtained. To derive the Gibbs energy of formation of the quaternary oxide from component binary oxides, the free energy of formation of CaSiO, is determined separately using a solid state cell based on single crystal CaF2 as the electrolyte: Pt, O-2, CaO + CaF2 \ CaF2 \ CaSiO3 + SiO2 + CaF2, O-2, Pt The results can be expressed by the following equations: NiO (r.s) + CaO (r.s) + 2SiO(2) (qz) --> CaNiSi2O6 (pyr) Delta G degrees = -115,700 + 10.63T (+/-100) J mol(-1) CaO (r.s) + SiO2 (qz) --> CaSiO3 (wol) Delta G degrees = -90,030 -0.61T (+/-60) J mol(-1).

System Ho-Rh-O: Phase Equilibria, Chemical Potentials and Gibbs Energy of Formation of HoRhO3

The thermodynamic properties of the HoRhO3 were determined in the temperature range from 900 to 1300 K by using a solid-state electrochemical cell incorporating calcia-stabilized zirconia as the electrolyte. The standard Gibbs free energy of formation of orthorhombic perovskite HoRhO3, from Ho2O3 with C-rare earth structure and Rh2O3 with orthorhombic structure, can be expressed by the equation; Delta G(f)degrees((ox)) (+/- 78)/(J/mol) = -50535 + 3.85(T/K) Using the thermodynamic data of HoRhO3 and auxiliary data for binary oxides from the literature, the phase relations in the Ho-Rh-O system were computed at 1273 K. Thermodynamic data for intermetallic phases in the binary Ho-Rh were estimated from experimental enthalpy of formation for three compositions from the literature and Miedema's model, consistent with the phase diagram. The oxygen potential-composition diagram and three-dimensional chemical potential diagram at 1273 K, and temperature-composition diagrams at constant oxygen partial pressures were computed for the system Ho-Rh-O. The decomposition temperature of HoRhO3 is 1717(+/- 2) K in pure O-2 and 1610(+/- 2) K in air at a total pressure p(o) = 0.1 MPa.

Electrochemical Determination of Gibbs Energy of Formation of LaCrO3 Using a Composition-Graded Bielectrolyte

Presented are new measurements of the standard Gibbs free energy of formation of rhombohedral LaCrO3 from component oxides La2O3 and Cr2O3 in the temperature range from 875 to 1175K, using a bielectrolyte solid-state cell incorporating single crystal CaF2 and composition-graded solid electrolyte (LaF3)(y)(CaF2)(1-y) (y=0-0.32). The results can be represented analytically as Delta G(f(ox))(o) (+/- 2270)/Jmol(-1)=-72329+4.932 (T/K). The measurements were undertaken to resolve serious discrepancies in the data reported in the literature. A critical analysis of previous electrochemical measurements indicates several deficiencies that have been rectified in this study. The enthalpy of formation obtained in this study is consistent with calorimetric data. The standard enthalpy of formation of orthorhombic LaCrO3 from elements at 298.15K computed from the results of this study is Delta H-f(298.15)(o)/kJmol(-1)=-1536.2 (+/- 7). The standard entropy of orthorhombic LaCrO3 at 298.15K is estimated as 99.0 (+/- 4.5)J(molK)(-1).