High-precision quantum thermochemistry on nonquasiharmonic potentials: converged path-integral free energies and a systematically convergent family of generalized Pitzer-Gwinn approximations

Accurate quantum mechanical (QM) vibrational-rotational partition functions for HOOD, D(2)O(2), H(18)OOH, H(2)(18)O(2), D(18)OOH, and H(18)OOD are determined using a realistic potential energy surface for temperatures ranging from 300 to 2400 K by using the TT-FPI-ESPE path-integral Monte Carlo method. These data, together with our prior results for H(2)O(2), provide benchmarks for testing approximate methods of estimating isotope effects for systems with torsional motions. Harmonic approximations yield poor accuracy for these systems, and although the well-known Pitzer-Gwinn (PG) approximation provides better results for absolute partition functions, it yields the same results as the harmonic approximation for isotope effects because these are intrinsically quantal phenomena. We present QM generalizations of the PG approximation that can provide high accuracy for both isotope effects and absolute partition functions. These approximations can be systematically improved until they approach the accurate result and converge rapidly. These methods can also be used to obtain affordable estimates of zero-point energies from accurate partition functions-even those at relatively high temperatures.     

Statistical thermodynamics of polymer crystallization

A survey was made on the recent development of the mean-field lattice theory of polymer solutions to predict the properties of equilibrium melting points of bulk polymers. The interaction parameters were identified for several real polymers.     

Statistical thermodynamics of polymer crystal and melt

A crystalline-state theory recently developed by Midha and Nanda is commented on and applied to the isobars of polyethylene, poly(vinylidene fluoride), and poly(chlorotrifluoroethylene) at atmospheric pressure, and to an isotherm of polyethylene. Satisfactory agreement with experiment results. This includes the volume change at the melting point T_m and the volume difference ΔV between crystal and melt below T_m, when crystal and the earlier liquid-state theory are combined. A similar agreement is noted with respect to the results at high pressure. The scaling parameters obtained indicate the approximate role of melt temperature and volume as reducing quantities. An inverse proportionality between T_m and α_l, the expansivity of the melt at T_m, derived much earlier for low-molecular-weight solids, is recovered with an identical numerical coefficient. The thermodynamic functions of polyethylene are investigated in both phases. For this purpose contributions of internal harmonic modes are considered within the framework of the equivalent s-mer model. One or, at most, two average frequencies are adequate to represent the temperature dependence of the excess free energy and entropy over the value at absolute zero, when the external contributions are included for the crystal. A similar representation of the hard modes can be adopted for the melt. However, the free energy of segmental disorientation computed either from a constant entropy for the s-mer or a rotational isomeric state model for the isolated chain does not appear to be an adequate representation over a sufficient temperature range. An additional temperature-dependent term in the entropy and free energy is introduced and tentatively attributed to a volume- and temperature-dependent short-range ordering. Good agreement with experiment, including the entropy and temperature of fusion, ensues.     

Statistical thermodynamics of single-chain single crystals

A simple statistical mechanical theory is developed assuming a chain-folded crystal. Taking account of the side-surface energy of the single-chain single crystal, the partition function and the free energy are calculated. Also, the expressions for equilibrium thickness l_e and melting temperature T_{m, e} of the single-chain single crystal are obtained, and they are similar to that given by a thermodynamic analysis of the single-chain single crystal. It is shown that l_e depends on temperature and on the molar mass of the single-chain single crystal, while T_{m, e} depends on the molar mass. Furthermore, it is found that the side-surface and the fold-surface free energies γ and γ_e can be explained on a molecular basis.     

Contact mechanics of nanometer-scale molecular contacts: correlation between adhesion, friction, and hydrogen bond thermodynamics

Using a scanning force microscope, adhesion forces have been measured between carboxylic acid terminated self-assembled monolayers in different nonpolar solvents or in two-component liquid mixtures consisting of a polar solvent (ethyl acetate or acetone) in heptane. The adhesion forces measured in pure acetone and ethyl acetate were small (0.24 nN) but increased logarithmically as the concentration of the polar solvent decreased to reach a maximum value (2.77 nN), equal to that measured in pure heptane, and for lower concentrations of polar solvent, the adhesion force remained constant. This behavior is identical to that observed for association constants measured for the formation of 1:1 H-bonded complexes between dilute solutes in solvent mixtures. The transition between the solvent-dependent and -independent regimes occurs at a polar solvent concentration corresponding to 1/K(S), where K(S) is the equilibrium constant for solvation of a carboxylic acid by the polar solvent in heptane. A simple model, in which the solvation of the carboxylic acid groups may be estimated by considering the concentration and polarity of functional groups in the liquid, accurately predicts values of K(S) that were found to correlate very well with the observed solvent-dependence of the adhesion force. Friction-load relationships were measured using friction-force microscopy. In pure acetone and ethyl acetate, a linear friction-load relationship was observed, in agreement with Amontons' law. However, as the concentration of polar solvent was reduced, a nonlinear relationship was observed and the friction-load relationship was found to fit the Derjaguin-Müller-Toporov (DMT) model for single asperity contacts. For pure heptane and a range of other nonpolar liquids with identical dielectric constants, the friction-load relationship was described by DMT mechanics. Exceptionally, for perfluorodecalin, Johnson-Kendall-Roberts mechanics was observed. These observations may be rationalized by treating the friction force as the sum of load-dependent and shear contributions. Under conditions of low adhesion, where the carboxylic acid surface is solvated by polar solvent molecules, the shear term is negligible and the sliding interaction is dominated by load-dependent friction. As the degree of solvation of the carboxylic acid groups decreases and the adhesion force increases, the shear friction contribution increases, dominating the interaction for media in which the adhesion force is greater than ca. 0.6 nN.     

Vibrational spectrum, ab initio calculations, conformational equilibria and torsional modes of 1,3-dichloropropane

Ab initio calculations are reported for three of four possible conformers of 1,3-dichloropropane. The fourth conformer, with Cs symmetry, has a predicted enthalpy difference of more than 1500 cm(-1) from the most stable conformer from each calculation regardless of the basis set used, so there is little chance of observing it. Thus, there is no evidence in the infrared or Raman spectrum of the presence of a fourth conformer. The order of stability given by the ab initio calculations is C2(GG)>C1(AG)>C2v(AA)>Cs(GG'), where A indicates the anti form for one of the CH2Cl groups and G indicates the gauche conformation for the other CH2Cl group relative to the plane of the carbon atoms. Almost every band observed can be confidently assigned to one or another of the conformers. Many observed bands proved to be of a composite nature, with several nearly coincident vibrations of different conformers contributing to the band contour. Nonetheless, a complete assignment of fundamentals is possible for the most stable C2 conformer, and 5 of the fundamentals of the C2v conformer and 13 those of the C1 conformer can be confidently assigned.     

Statistical thermodynamics of 1-butanol, 2-methyl-1-propanol, and butanal

The purpose of the present investigation is to calculate partition functions and thermodynamic quantities, viz., entropy, enthalpy, heat capacity, and Gibbs free energies, for 1-butanol, 2-methyl-1-propanol, and butanal in the vapor phase. We employed the multi-structural (MS) anharmonicity method and electronic structure calculations including both explicitly correlated coupled cluster theory and density functional theory. The calculations are performed using all structures for each molecule and employing both the local harmonic approximation (MS-LH) and the inclusion of torsional anharmonicity (MS-T). The results obtained from the MS-T calculations are in excellent agreement with experimental data taken from the Thermodynamics Research Center data series and the CRC Handbook of Chemistry and Physics, where available. They are also compared with Benson's empirical group additivity values, where available; in most cases, the present results are more accurate than the group additivity values. In other cases, where experimental data (but not group additivity values) are available, we also obtain good agreement with experiment. This validates the accuracy of the electronic structure calculations when combined with the MS-T method for estimating the thermodynamic properties of systems with multiple torsions, and it increases our confidence in the predictions made with this method for molecules and temperatures where experimental or empirical data are not available.     

Vibrational spectrum, ab initio calculation, conformational equilibria and torsional modes of 1,3-dibromopropane

The infrared and Raman spectrum of 1,3-dibromopropane is reported in the crystalline, liquid and gaseous states. These measurements are compared to the results of ab initio calculations carried out using the 6-31+g* Gaussian basis set for a restricted Hartree-Fock computation. The calculation was repeated using second order Moeller-Ploesset perturbation theory to accommodate electron correlation using the 6-31 g* basis set. The three most stable conformers are GG (C2), AG (C1) and AA (C2v), where A and G stand for anti and gauche orientations of the bromomethyl group relative to the plane of the carbon atoms. The point group symmetry of each structure is given in parentheses. The fourth conformer, G'G (Cs) is of such high energy that it is not observed experimentally in isotropic media in either the infrared or Raman spectrum. In the crystalline state, comparison of the infrared and Raman spectrum with that calculated for the C2 conformer shows that only the GG (C2) conformer survives, and the doublet structure of many of the bands in the spectrum indicates at least two molecules per unit cell. The ab initio calculations predict and the temperature dependence of the Raman spectrum of the liquid confirms that the stability order is C2相似文献   

二元及三元离子交换体系的统计热力学

本文用统计热力学方法对二元及三元离子交换体系进行了研究,得到了修正选择系数与交换剂组成关系的理论表达式,并得到二元交换体系的交换剂组分活度系数与组成的关系式,即Kielland公式。     

Statistical thermodynamics and dielectric properties of dipole-quadrupole hard-sphere fluid

Within a hindered rotation model, approximate analytical expressions have been obtained for thermodynamic functions and the Kirkwood factor of the model polar fluid of dipole-quadrupole hard spheres in the nearest neighbor approximation. A peculiarity of the considered system from the viewpoint of the hindered rotation model is the ability to generate a three-dimensional grid of quadrupole-bonded molecules, as indicated by the behavior of quadrupole hard-sphere fluid at large values of the quadrupole moment.     

Statistical thermodynamics of ABA block copolymers. II

A microstructural model for the phase-separated states of ABA triblock copolymers is proposed. It postulates the simultaneous existence of three phases: pure A, pure B, and a mixed region. Incorporation of the mixed region distinguishes this treatment from all other theories and is responsible for considerable flexibility in the model without increased numbers of parameters. Calculations of free energy changes required to establish specific microstructures permit the prediction of a favored one from among five possibilities: discrete spheres of A (or B), discrete cylinders of A (or B), and lamellae.     

Statistical thermodynamics of the isomerization reaction between n-heptane and isoheptane

We have employed electronic structure calculations and the recently proposed multi-structural (MS) anharmonicity method to calculate partition functions and thermodynamic quantities, in particular entropy and heat capacity, for n-heptane and isoheptane. We included all structures, of which there are 59 for n-heptane and 37 for isoheptane, and we carried out the calculations both in the local harmonic approximation and by including torsional (T) anharmonicity. In addition, ΔS°, ΔH, and ΔG° for the isomerization reaction between these two species were also calculated. It is found that all calculated thermodynamic quantities based on the MS-T approximation in the temperature range from 298 K to 1500 K agree well with experimental data from the American Petroleum Institute (API) tables or Thermodynamics Research Center (TRC) data series and with values obtained from Benson's empirical parameters fit to experiment. This demonstrates not only the high accuracy of the electronic structure calculations but also that the MS-T method can be used to include both multiple-structure anharmonicity and torsional anharmonicity in the calculation of thermodynamic properties for complex molecules that contain many torsions. It also gives us confidence that we can apply the MS-T statistical thermodynamic method to obtain thermodynamic properties (i) over a broader temperature range than that for which data are available in the API tables, TRC data series, or from empirical estimation and (ii) to the many molecules for which experimental data are not available at any temperature.     

Symmetry analysis of periodicity and internal torsional conformers around a single bond

A simple formula to predict the number of equivalent conformations upon internal rotation around a single bond is derived. If the separate parts A and B, of a single bonded molecule A-B, possess N_a and N_b symmetry planes that contain the single bond, the number of symmetrical conformations is found to be Z = N_aN_b/J, where J is the number of these planes which are common. The energy potential for internal rotation then has a period of 2π/Z. Unsymmetrical conformations are infinite in number, but are shown to occur in infinite sets, each set with 2N_aN_b/J equivalent conformations. Extension to three-center molecules is also made.     

Statistical thermodynamics of fluids with both dipole and quadrupole moments

New Gibbs ensemble simulation data for a polar fluid modeled by a square-well potential plus dipole-dipole, dipole-quadrupole, and quadrupole-quadrupole interactions are presented. This simulation data is used in order to assess the applicability of the multipolar square-well perturbation theory [A. L. Benavides, Y. Guevara, and F. del Ri?o, Physica A 202, 420 (1994)] to systems where more than one term in the multipole expansion is relevant. It is found that this theory is able to reproduce qualitatively well the vapor-liquid phase diagram for different multipolar moment strengths, corresponding to typical values of real molecules, except in the critical region. Hence, this theory is used to model the behavior of substances with multiple chemical bonds such as carbon monoxide and nitrous oxide and we found that with a suitable choice of the values of the intermolecular parameters, the vapor-liquid equilibrium of these species is adequately estimated.     

Incoherent inelastic neutron scattering studies of the torsional modes of hexachloroethane

From incoherent inelastic neutron scattering studies of solid C₂Cl₆ the in- and out-of-phase torsions about the C-C axis are assigned at 56 and 95 cm^?1, respectively. Using a model for the potential barriers in the solid the torsional frequency in the gas has been calculated to be 76.7 cm^?1 and the internal barrier to be 67.8 kJ mol^?1.     

Databases for transition element bonding: metal-metal bond energies and bond lengths and their use to test hybrid, hybrid meta, and meta density functionals and generalized gradient approximations

We propose a data set of bond lengths for 8 selected transition metal dimers (Ag(2), Cr(2), Cu(2), CuAg, Mo(2), Ni(2), V(2), and Zr(2)) and another data set containing their atomization energies and the atomization energy of ZrV, and we use these for testing density functional theory. The molecules chosen for the test sets were selected on the basis of the expected reliability of the data and their ability to constitute a diverse and representative set of transition element bond types while the data sets are kept small enough to allow for efficient testing of a large number of computational methods against a very reliable subset of experimental data. In this paper we test 42 different functionals: 2 local spin density approximation (LSDA) functionals, 12 generalized gradient approximation (GGA) methods, 13 hybrid GGAs, 7 meta GGA methods, and 8 hybrid meta GGAs. We find that GGA density functionals are more accurate for the atomization energies of pure transition metal systems than are their meta, hybrid, or hybrid meta analogues. We find that the errors for atomization energies and bond lengths are not as large if we limit ourselves to dimers with small amounts of multireference character. We also demonstrate the effects of increasing the fraction of Hartree-Fock exchange in multireference systems by computing the potential energy curve for Cr(2) and Mo(2) with several functionals. We also find that BLYP is the most accurate functional for bond energies and is reasonably accurate for bond lengths. The methods that work well for transition metal bonds are found to be quite different from those that work well for organic and other main group chemistry.     

Statistical thermodynamics evaluation of polymer–polymer miscibility

The Simha and Somcynsky (S–S) statistical thermodynamics theory was used to compute the solubility parameters as a function of temperature and pressure [δ = δ(T, P)], for a series of polymer melts. The characteristic scaling parameters required for this task, P*, T*, and V*, were extracted from the pressure–temperature–volume (PVT) data. To determine the potential polymer–polymer miscibility, the dependence of δ versus T (at ambient pressure) was computed for 17 polymers. Close proximity of the δ versus T curves for four miscible polymer pairs: PPE/PS, PS/PVME, and PC/PMMA signaled the usefulness of this approach. It is noteworthy, that the tabulated solubility parameters (derived from the solution data under ambient conditions) propounded the immiscibility of the PVC/PVAc pair. The computed values of δ also suggested miscibility for polymer pairs of unknown miscibility, namely PPE/PVC, PPE/PVAc, and PET/PSF. In recognizing the limitations of the solubility parameter approach (the omission of several thermodynamic contributions), these preliminary results are auspicious because they indicate a new route for estimating the miscibility of any polymeric material at a given temperature and pressure. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2909–2915, 2004