Orientational melting and reorientational motion in a cubane molecular crystal: a molecular simulation study

Detailed molecular simulations are carried out to investigate the effect of temperature on orientational order in cubane molecular crystal. We report a transition from an orientationally ordered to an orientationally disordered plastic crystalline phase in the temperature range 425-450 K. This is similar to the experimentally reported transition at 395 K. The nature of this transition is first order and is associated with a 4.8% increase in unit cell volume that is comparable to the experimentally reported unit cell volume change of 5.4% (Phys. Rev. Lett. 1997, 78, 4938). An orientational order parameter, eta(T), has been defined in terms of average angle of libration of a molecular 3-fold axis and the orientational melting has been characterized by using eta(T). The orientational melting is associated with an anomaly in specific heat at constant pressure (C(P)) and compressibility (kappa). The enthalpy of transition and entropy of transition associated with this orientational melting are 20.8 J mol(-1) and 0.046 J mol(-1) K(-1), respectively. The structure of crystalline as well as plastic crystalline phases is characterized by using various radial distribution functions and orientational distribution functions. The coefficient of thermal expansion of the plastic crystalline phase is more than twice that of the crystalline phase.     

The thermodynamic properties of polytetrafluoroethylene

Polytetrafluoroethylenes of different crystallinity were analyzed between 220 and 700 K by differential scanning calorimetry. A new computer coupling of the standard DSC is described. The measured heat capacity data were combined with all literature data into a recommended set of thermodynamic properties for the crystalline polymer and a preliminary set for the amorphous polymer (heat capacity, enthalpy, entropy, and Gibbs energy; range 0–700 K). The crystal heat capacities have been linked to the vibrational spectrum with a θ₃ of 54 K, and θ₁ of 250 K, and a full set of group vibrations. C_v to C_p conversion was possible with a Nernst–Lindemann constant of A = 1.6 × 10^?3 mol K/J. The glass transition was identified as a broad transition between 160 and 240 K with a ΔC_p of 9.4 J/K mol. The room-temperature transitions at 292 and 303 K have a combined heat of transition of 850 J/mol and an entropy of transition of 2.90 J/K mol. The equilibrium melting temperature is 605 K with transition enthalpy and entropy of 4.10 kj/mol and 6.78 J/K mol, respectively. The high-temperature crystal from is shown to be a condis crystal (conformationally disordered), and for the samples discussed, the crystallinity model holds.     

The rotation and the phase transition in solid C60

The interaction between C60's in solid C60 has been calculated by (exp-6-1) potential, and the cause and the controlled factor of the high rapid rotations of C60 's were discussed. In order to describe the disordered degree of C60 rotation, an equivalent M is introduced. The phase transitions at the ~260 K and at the ~90 K are studied from the viewpoint of C60 rotation. The potential barriers of the ordered rotation below the ~260 K and the disordered rotation above the ~260 K have been given, and the effect of the external pressure on the temperature of phase transition has also been given.     

A calorimetric study on the low temperature dynamics of doped ice V and its reversible phase transition to hydrogen ordered ice XIII

Doped ice V samples made from solutions containing 0.01 M HCl (DCl), HF (DF), or KOH (KOD) in H(2)O (D(2)O) were slow-cooled from 250 to 77 K at 0.5 GPa. The effect of the dopant on the hydrogen disorder --> order transition and formation of hydrogen ordered ice XIII was studied by differential scanning calorimetry (DSC) with samples recovered at 77 K. DSC scans of acid-doped samples are consistent with a reversible ice XIII <--> ice V phase transition at ambient pressure, showing an endothermic peak on heating due to the hydrogen ordered ice XIII --> disordered ice V phase transition, and an exothermic peak on subsequent cooling due to the ice V --> ice XIII phase transition. The equilibrium temperature (T(o)) for the ice V <--> ice XIII phase transition is 112 K for both HCl doped H(2)O and DCl doped D(2)O. From the maximal enthalpy change of 250 J mol(-1) on the ice XIII --> ice V phase transition and T(o) of 112 K, the change in configurational entropy for the ice XIII --> ice V transition is calculated as 2.23 J mol(-1) K(-1) which is 66% of the Pauling entropy. For HCl, the most effective dopant, the influence of HCl concentration on the formation of ice XIII was determined: on decreasing the concentration of HCl from 0.01 to 0.001 M, its effectiveness is only slightly lowered. However, further HCl decrease to 0.0001 M drastically lowered its effectiveness. HF (DF) doping is less effective in inducing formation of ice XIII than HCl (DCl) doping. On heating at a rate of 5 K min(-1), kinetic unfreezing starts in pure ice V at approximately 132 K, whereas in acid doped ice XIII it starts at about 105 K due to acceleration of reorientation of water molecules. KOH doping does not lead to formation of hydrogen ordered ice XIII, a result which is consistent with our powder neutron diffraction study (C. G. Salzmann, P. G. Radaelli, A. Hallbrucker, E. Mayer, J. L. Finney, Science, 2006, 311, 1758). We further conjecture whether or not ice XIII has a stable region in the water/ice phase diagram, and on a metastable triple point where ice XIII, ice V and ice II are in equilibrium.     

Efficient calculation of α- and β-nitrogen free energies and coexistence conditions via overlap sampling with targeted perturbation

A recently introduced solid-phase free-energy calculation method that is based upon overlap sampling with targeted free-energy perturbation is further developed and extended to systems with orientational degrees of freedom. Specifically we calculate the absolute free energy of the linear-molecular nitrogen model of Etter et al., examining both the low-temperature low-pressure α-N(2) structure and the orientationally disordered β-N(2) phase. In each perturbation (for the α-N(2) phase) to determine the free-energy difference between systems at adjacent temperatures, harmonic coordinate scaling is applied to both the translational and rotational degrees of freedom in the nitrogen molecule to increase the phase-space overlap of the two perturbing systems and consequently, improve the free-energy difference results. For the plastic β-N(2) phase, a novel method that requires several perturbation paths is introduced to calculate its absolute free energy. Through these methods, the absolute free energies for both the α-N(2) and β-N(2) phase can be accurately and precisely determined. We find again that the anharmonic contribution to the free energy has weak dependence on system size. The transition properties for the α-N(2) and β-N(2) phase are also investigated. The α-β phase transition for the model at atmospheric pressure (0.1 MPa) is found to occur at 40.35 ± 0.01 K with volumetric and entropy changes of 0.44 ± 0.01 cm(3)/mol and 1.99 ± 0.01 cal/mol.K respectively.     

Phonons and thermodynamics of unmixed and disordered Li0.6FePO4

The lithium-storage material Li(0.6)FePO(4) was studied by inelastic neutron scattering and differential scanning calorimetry. Li(0.6)FePO(4) undergoes a transformation from a two-phase mixture (heterosite and triphylite) to a disordered solid-solution at 200 degrees C. Phonon densities of states (DOS) obtained from the inelastic neutron scattering were similar for the two-phase sample measured at 180 degrees C and the disordered sample measured at 220 degrees C. The vibrational entropy of transformation is 1.8 +/-0.9 J/(K mol), which is smaller than the configurational entropy difference of approximately 3.1 J/(K mol). The measured enthalpy of the disordering transition was estimated as 2.5 kJ/mol. The phonon data show a small change in lattice dynamics upon disordering.     

Alkyl group as entropy reservoir in an MMX chain complex, Pt2(n-PenCS2)4I

Heat capacity of halogen-bridged one-dimensional binuclear metal complex (so-called MMX chain) having four n-pentyl groups, Pt2(n-PenCS2)4I, was measured by adiabatic calorimetry. A first-order phase transition was observed at 207.4 K when measurement was made after cooling from room temperature. The enthalpy and entropy of transition were determined to be 10.19 kJ mol(-1) and 49.1 J K(-1) mol(-1), respectively. A monotropic phase transition was observed at 324 K on heating, and the entropy of transition was essentially null. The sample once heated above 324 K never returned to the initial phase at room temperature and underwent a higher-order phase transition at 173 K and a first-order phase transition at 220.5 K. The enthalpy and entropy of the first-order phase transition were estimated to be 11.6 kJ mol(-1) and 52.4 J K(-1) mol(-1), respectively. The magnitude of the entropy gain at the phase transition from the initial room-temperature phase to the high-temperature phase at 324 K shows that in Pt2(n-PenCS2)4I a large amount of entropy reserved in alkyl chain is transferred to dithiocarboxylato groups upon the phase transition, as in the cases of Pt2(n-PrCS2)4I and Pt2(n-BuCS2)4I.     

Calculation of the stability of nonperiodic solids using classical force fields and the method of increments: N2o as an example

Combining classical force fields for the Hartree–Fock (HF) part and the method of increments for post‐HF contributions, we calculate the cohesive energy of the ordered and randomly disordered nitrous oxide (N₂O) solid. At 0 K, ordered N₂O is most favorable with a cohesive energy of ?27.7 kJ/mol. At temperatures above 60 K, more disordered structures become compatible and a phase transition to completely disordered N₂O is predicted. Comparison with experiment in literature suggests that experimentally prepared N₂O crystals are mainly disordered due to a prohibitively high activation energy of ordering processes. © 2015 Wiley Periodicals, Inc.     

Understanding thermodynamic properties at the molecular level: multiple temperature charge density study of ribitol and xylitol

X-ray diffraction data of high quality measured to high resolution on crystals of the two pentitol epimers ribitol (centric) and xylitol (acentric) at 101, 141, and 181 K and data on the two compounds previously recorded at 122 K have formed the basis for multipole refinements with the VALRAY system. Our analysis showed that it is possible to obtain a reliable crystal electron density for an acentric compound (xylitol) from X-ray diffraction data and that the thermal motion can be deconvoluted from the static density in this temperature range. The Bader-type topological analysis of the static electron densities revealed virtually identical intramolecular interactions as well as very similar hydrogen bond interactions of ribitol and xylitol; the only minor differences are found in the weaker intermolecular interactions. The high-level periodic DFT calculations are in accordance with the thermodynamic measurements that show that the two pentitols have identical sublimation energies. A rigid body normal coordinate analysis was performed on the atomic displacement parameters obtained at the four different temperatures. The translational and librational mean square deviations derived through this analysis were used in a quantum statistical approach to derive frequencies of the corresponding harmonic oscillators. The analysis showed a consistent vibrational model for all temperatures. The frequencies were subsequently used to calculate crystal entropies assuming an Einstein-type behavior. These calculations show that the crystal entropy of ribitol is 8 J K(-1) mol(-1) higher than the crystal entropy of xylitol, confirming that it is a difference in the entropy of the two compounds that causes the difference in their free energy. Our results presented in this Article show the potential to use X-ray diffraction data to obtain physicochemical properties of crystals.     

C60晶体在有序相的分子取向结构

以C60晶体中分子两种取向排列形成的双能级系统为基础,通过探讨C60晶体在有序相的热力学性质,得到了38o和98o两种取向排列的分子在晶体中均匀分布的结构稳定性结论.根据已报道的C60晶体在有序相两端点温度85 K 和260 K取向分布的实验结果,将较高的分子取向(38o)能级的概率转化成分数值1/6和3/8,得到了有序相两种取向分子在两温度端点的分布规律.当概率的分数值为1/4和1/3时,C60晶体将具有较大的结构稳定性和较小的介电损耗及内耗值,对应的温度分别为122.6和194.3 K.因而解释了介电实验结果出现异常的现象是由38o取向分子均匀分布的"规则-无规-规则"变化所造成的.     

Structure prediction, disorder and dynamics in a DMSO solvate of carbamazepine

We have applied crystal structure prediction methods to understand and predict the formation of a DMSO solvate of the anti-convulsant drug carbamazepine (CBZ), in which the DMSO molecules are disordered. Crystal structure prediction calculations on the 1:1 CBZ:DMSO solvate revealed the generation of two similar low energy structures which differ only in the orientation of the DMSO molecules. Analysis of crystal energy landscapes generated at 0 K suggests the possibility of solvent disorder. A combined computational and experimental study of the changes in the orientation of the DMSO within the crystal structure revealed that the nature of the disorder changes with temperature. At low temperature, the DMSO disorder is static whilst at high temperature the DMSO configurations can interconvert by a 180° rotation of the DMSO molecules within the lattice. This 180° rotation of the DMSO molecules drives a phase change from a high temperature dynamically disordered phase to a low temperature phase with static disorder. Crystallisation of a DMSO solvate of the related molecule epoxycarbamazepine resulted in a different degree of DMSO disorder in the crystal structure, despite the similarity of the carbamazepine and epoxycarbamazepine molecules. We believe consideration of disorder and its contribution to entropy and crystal free energies at temperature other than 0 K is fundamental for the accuracy of future energy rankings in crystal structure prediction calculations of similar solvated structures.     

Prediction of a phase transition to a hydrogen bond ordered form of ice VI

Ice VI is a hydrogen bond disordered crystal over its known region of stability. In this work, we predict that ice VI will transform into a hydrogen bond ordered phase near 108 K, and have identified the likely low-temperature phase as ferroelectric (space group Cc) with an antiferroelectric structure (space group P2(1)2(1)2(1)) close by in energy. Electronic density functional theory calculations provide input to our calculations, which are extended to cells large enough for statistical simulations by using graph invariants. A significant decrease in the configurational entropy is predicted as hydrogen bonds exhibit partial order above the transition, provided that the hydrogen bonds can equilibrate on an experimental time scale. Conversely, partial disorder is predicted at temperatures below the transition. Although some evidence for ordering of ice VI has been observed in experiments, a low-temperature proton ordered phase has not been identified experimentally.     

Decomposition reaction rate of BCl3-C3H6(propene)-H2 in the gas phase

The decomposition reaction rate in the BCl(3)-C(3)H(6)-H(2) gas phase reaction system in preparing boron carbides was investigated based on the most favorable reaction pathways proposed by Jiang et al. [Theor. Chem. Accs. 2010, 127, 519] and Yang et al. [J. Theor. Comput. Chem. 2012, 11, 53]. The rate constants of all the elementary reactions were evaluated with the variational transition state theory. The vibrational frequencies for the stationary points as well as the selected points along the minimum energy paths (MEPs) were calculated with density functional theory at the B3PW91/6-311G(d,p) level and the energies were refined with the accurate model chemistry method G3(MP2). For the elementary reaction associated with a transition state, the MEP was obtained with the intrinsic reaction coordinates, while for the elementary reaction without transition state, the relaxed potential energy surface scan was employed to obtain the MEP. The rate constants were calculated for temperatures within 200-2000 K and fitted into three-parameter Arrhenius expressions. The reaction rates were investigated by using the COMSOL software to solve numerically the coupled differential rate equations. The results show that the reactions are, consistent with the experiments, appropriate at 1100-1500 K with the reaction time of 30 s for 1100 K, 1.5 s for 1200 K, 0.12 s for 1300 K, 0.011 s for 1400 K, or 0.001 s for 1500 K, for propene being almost completely consumed. The completely dissociated species, boron carbides C(3)B, C(2)B, and CB, have very low concentrations, and C(3)B is the main product at higher temperatures, while C(2)B is the main product at lower temperatures. For the reaction time 1 s, all these concentrations approach into a nearly constant. The maximum value (in mol/m(3)) is for the highest temperature 1500 K with the orders of -13, -17, and -23 for C(3)B, C(2)B, and CB, respectively. It was also found that the logarithm of the overall reaction rate and reciprocal temperature have an excellent linear relationship within 700-2000 K with a correlation coefficient of 0.99996. This corresponds to an apparent activation energy 337.0 kJ/mol, which is comparable with the energy barrier 362.6 kJ/mol of the rate control reaction at 0 K but is higher than either of the experiments 208.7 kJ/mol or the Gibbs free energy barrier 226.2 kJ/mol at 1200 K.     

Molecular dynamics and residual entropy in the soft crystal, SmE phase, of 4-butyl-4'-isothiocyano-1,1'-biphenyl

Molecular dynamics and resulting disorder in the soft crystal, smectic E (SmE) phase, were studied in detail for the title compound, 4-butyl-4'-isothiocyano-1,1'-biphenyl (4TCB), by (1)H NMR spectroscopy and adiabatic calorimetry. The ordered crystal phase of 4TCB was realized for the first time under ambient pressure after long two-step annealing and used as the reference state in the analysis of the experimental results. Four motional modes were identified in the SmE phase through the analysis of the (1)H NMR T(1). The residual entropy was determined as ca. 6 J K(-1) mol(-1). This magnitude implies that most of the disorder in the SmE phase at high temperatures is removed on cooling except for the head-to-tail disorder of the rod-shaped 4TCB molecule. Standard thermodynamic functions are tabulated below 375 K.     

Determination of fluid--solid transitions in model protein solutions using the histogram reweighting method and expanded ensemble simulations

Protein crystallization conditions are usually identified by empirical screening methods because of the complexity of the process, such as the existence of nonequilibrium phases and the different crystal forms that may result from changes in solution conditions. Here the crystallization of a model protein is studied using computer simulation. The model consists of spheres that have both an isotropic interaction of short range and anisotropic interactions between patch-antipatch pairs. The free energy of a protein crystal is calculated using expanded ensemble simulations of the Einstein crystal, and NpT-Monte Carlo simulations with histogram reweighting are used to determine the fluid-solid coexistence. The histogram reweighting method is also used to trace out the complete coexistence curve, including multiple crystal phases, with varying reduced temperature, which corresponds to changing solution conditions. At a patch-antipatch interaction strength five times that of the isotropic interaction, the protein molecules form a stable simple cubic structure near room temperature, whereas an orientationally disordered face-centered-cubic structure is favored at higher temperatures. The anisotropic attractions also lead to a weak first-order transition between orientationally disordered and ordered face-centered-cubic structures at low temperature, although this transition is metastable. A complete phase diagram, including a fluid phase, three solid phases, and two triple points, is found for the six-patch protein model. A 12-patch protein model, consistent with the face-centered-cubic structure, leads to greater thermodynamic stability of the ordered phase. Metastable liquid-liquid phase equilibria for isotropic models with varying attraction tails are also predicted from Gibbs ensemble simulations.     

Predicting aqueous free energies of solvation as functions of temperature

This work introduces a model, solvation model 6 with temperature dependence (SM6T), to predict the temperature dependence of aqueous free energies of solvation for compounds containing H, C, and O in the range 273-373 K. In particular, we extend solvation model 6 (SM6), which was previously developed (Kelly, C. P.; Cramer, C. J.; Truhlar, D. G. J. Chem. Theory Comput. 2005, 1, 1133) for predicting aqueous free energies of solvation at 298 K, to predict the variation of the free energy of solvation relative to 298 K. Also, we describe the database of experimental aqueous free energies of solvation for compounds containing H, C, and O that was used to parametrize and test the new model. SM6T partitions the temperature dependence of the free energy of solvation into two components: the temperature dependence of the bulk electrostatic contribution to the free energy of solvation, which is computed using the generalized Born equation, and the temperature dependence of first-solvation-shell effects which is modeled using a parametrized solvent-exposed surface-area-dependent term. We found that SM6T predicts the temperature dependence of aqueous free energies of solvation with a mean unsigned error of 0.08 kcal/mol over our entire database, whereas using the experimental value at 298 K produces a mean unsigned error of 0.53 kcal/mol.     

A reexamination of the ice III/IX hydrogen bond ordering phase transition

Ice III is a hydrogen bond disordered crystal which when cooled 1 K / min or faster transforms to an antiferroelectric hydrogen bond ordered structure, ice IX. Throughout its region of stability, experiments indicate that the H bonds in ice III are, in fact, partially ordered, i.e., some proton arrangements are preferred. In addition, there has been evidence that the structure of ice IX retains some residual disorder after the transition. Diffraction experiments and calorimetry apparently conflict with regard to the degree of ordering at the ice III/IX transition. Mean field statistical mechanical theories have been used to link partial occupations from diffraction data with thermodynamics. In this work, we investigate the ice III/IX proton ordering phase transition using electronic density functional theory calculations for small unit cells, extended to simulate the phase transition in a large unit cell using graph invariants. In agreement with experiment, we observe partial ordering over a wide range of temperatures as ice III transforms to partially disordered ice IX, near 126 K, which becomes fully ordered at lower temperatures. We compare our results from full statistical mechanical simulations with mean field models, finding small errors for the low-temperature ice IX phase and much larger errors for the high-temperature ice III phase. The failure of mean field theories may explain the apparent conflict between diffraction experiments and calorimetry.     

Ab initio crystal structure predictions for flexible hydrogen‐bonded molecules. Part III. Effect of lattice vibrations

In crystal structure predictions possible structures are usually ranked according to static energy. Here, this criterion has been replaced by the free energy at any temperature. The effects of harmonic lattice vibrations were found by standard lattice‐dynamical calculations, including a rough estimate of the effects of thermal expansion. The procedure was tested on glycol and glycerol, for which accurate static energies had been obtained previously (Part II of this series). It was found that entropy and zero‐point energy give the largest contribution to free energy differences between hypothetical crystal structures, adding up to about 3 kJ/mol for the structures with lowest energy. The temperature‐dependent contribution to the energy and the effects of thermal expansion showed less variation among the structures. The overall accuracy in relative energies was estimated to be a few kJ/mol. The experimental crystal structure for glycol corresponded to the global free energy minimum, whereas for glycerol it ranked second at 1 kJ/mol. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 816–826, 2001     

Calorimetric study of correlated disordering in [Hdamel]2[Cu(II)(tdpd)2] x 2 THF crystal

The heat capacity of [Hdamel]2[Cu(II)(tdpd)2] x 2 THF was measured from 6 to 250 K by adiabatic calorimetry. There are four heat anomalies around 150 K associated with disordering in the orientation of the uncoordinated THF molecules and in the conformation of the out-of-plane allyl groups of [Hdamel](+) units. The total entropy of transition was determined to be 19.8 J K(-1) mol(-1), less than the 4R ln 2 (R = gas constant) expected from the crystal structure at room temperature. The smallness of the total entropy change on phase transitions proves the presence of the strong motional correlation between the adjacent allyl groups. The calorimetric conclusion agreed with the crystal structure at 200 K re-examined in this study.     

Preparation and phase behavior of poly(4‐trimethylsilylstyrene)‐block‐polyisoprene

Three poly(4‐trimethylsilylstyrene)‐block‐polyisoprenes (TIs), the molecular weights of which were 82,000, 152,000 and 291,000 (TI‐82K, TI‐152K, and TI‐291K), were synthesized by sequential anionic polymerizations. The component polymers were a miscible pair that presented a lower critical solution temperature phase diagram if blended. The TI phase behavior was investigated with transmission electron microscopy. The order–disorder transition could be observed at a temperature between 200 °C (the ordered state) and 150 °C (the disordered state) for the block copolymer TI‐152K. The block copolymer TI‐82K presented the disordered state at 200 °C, whereas TI‐291K was in the ordered state at 150 °C. With the Flory–Huggins interaction parameter between poly(4‐trimethylsilylstyrene) and polyisoprene, which was evaluated by small‐angle neutron scattering for the block copolymers, the TI phase behavior could be reasonably explained by mean‐field theory. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 1214–1219, 2005