Towards an understanding of the heat capacity of liquids. A simple two-state model for molecular association

A model for the temperature dependence of the isobaric heat capacity of associated pure liquids C(p,m)(o)(T) is proposed. Taking the ideal gas as a reference state, the residual heat capacity is divided into nonspecific C(p) (res,ns) and associational C(p) (res,ass) contributions. Statistical mechanics is used to obtain C(p)(res,ass) by means of a two-state model. All the experimentally observed C(p,m)(o)(T) types of curves in the literature are qualitatively described from the combination of the ideal gas heat capacity C(p)(id)(T) and C(p)(res,ass)(T). The existence of C(p,m)(o)(T) curves with a maximum is predicted and experimentally observed, for the first time, through the measurement of C(p,m)(o)(T) for highly sterically hindered alcohols. A detailed quantitative analysis of C(p,m)(o)(T) for several series of substances (n-alkanes, linear and branched alcohols, and thiols) is made. All the basic features of C(p,m)(o)(T) at atmospheric and high pressures are successfully described, the model parameters being physically meaningful. In particular, the molecular association energies and the C(p)(res,ns) values from the proposed model are found to be in agreement with those obtained through quantum mechanical ab initio calculations and the Flory model, respectively. It is concluded that C(p,m)(o)(T) is governed by the association energy between molecules, their self-association capability and molecular size.     

Structures and conformations of trifluoromethanesulfonic anhydride, (CF3SO2)2O, and bis(trifluoromethylsulfonyl)difluoromethane, (CF3SO2)2CF2

The geometric structures and conformational properties of trifluoromethanesulfonic anhydride, (CF₃SO₂)₂O, and bis(trifluoromethylsulfonyl)difluoromethane, (CF₃SO₂)₂CF₂ have been studied by gas electron diffraction (GED) and ab initio calculations (HF/3–21G*). The calculations predict for both systems two stable conformers with C₂ symmetry and one with C₁ symmetry. In both compounds structures with C₂ symmetry and dihedral angles SOSC ≈ 100° ((CF₃SO₂)₂O) and SCSC≈ 150° ((CF₃SO₂)₂CF₂ are lowest in energy. According to the GED analyses the dominant conformer of (CF₃SO₂)₂O₂ possesses C₂ symmetry with SOSC dihedral angles of 99.1(14)°. The presence of up to 30% of the two other conformers cannot be excluded; for (CF₃SO₂)₂CF₂ only one conformer with C₂ symmetry and SCSC dihedral angles of 143(2)° is observed. A complete set of geometric parameters is given.     

Structures and conformations of trifluoromethanesulfonic anhydride, (CF3SO2)2O, and bis(trifluoromethylsulfonyl)difluoromethane, (CF3SO2)2CF2

The geometric structures and conformational properties of trifluoromethanesulfonic anhydride, (CF₃SO₂)₂O, and bis(trifluoromethylsulfonyl)difluoromethane, (CF₃SO₂)₂CF₂ have been studied by gas electron diffraction (GED) and ab initio calculations (HF/3–21G*). The calculations predict for both systems two stable conformers with C₂ symmetry and one with C₁ symmetry. In both compounds structures with C₂ symmetry and dihedral angles SOSC ≈ 100° ((CF₃SO₂)₂O) and SCSC ≈ 150° ((CF₃SO₂)₂CF₂) are lowest in energy. According to the GED analyses the dominant conformer of (CF₃SO₂)₂O possesses C₂ symmetry with SOSC dihedral angles of 99.1(14)°. The presence of up to 30% of the two other conformers cannot be excluded; for (CF₃SO₂)₂CF₂ only one conformer with C₂ symmetry and SCSC dihedral angles of 143(2)° is observed. A complete set of geometric parameters is given.     

Heat capacities of the tungsten oxides WO3, W20O58, W18O49 and WO2

The heat capacities of the tungsten oxides WO₃, W₂₀O₅₈, W₁₈O₄₉ and WO₂ have been measured over the temperature range 340–999 K using differential scanning calorimetry. The lower oxides were prepared by controlled reduction of WO₃ in H₂/H₂O gas atmospheres. Previous calorimetric work on WO₃ is confirmed in the temperature range 340–800 K, however, significant increases in heat capacity were observed in the range 800–999 K prior to the orthorhombic—tetragonal phase transition. W₂₀O₅₈ is shown to behave similarly to WO₃. A high temperture phase change is evident, however, this appears to be complete by 970–990 K. The measured values of heat capacity for W₁₈O₄₉ are in close agreement with estimated data for W₁₈O₄₉. There is no evidence of any phase transitions for this oxide in the temperature range studied. The heat capacity data for WO₂ confirm previous drop calorimetry measurements and give no evidence of any phase changes for WO₂ in the temperature range 340–990 K.     

A Classical and Quantum Chemical Analysis of Gaseous Heat Capacity

Physical chemistry is considered to be a scientifically abstract and mathematically intensive course in the undergraduate chemistry curriculum. To most students, the physical chemistry course involves a semester that deals with macroscopic properties and another that deals with microscopic evaluations of chemical systems. They often fail to see the importance of statistical mechanics in making the connection between the content of the two semesters. In this paper, we propose a computational exercise that complements a simple physical chemistry experiment that can be used to understand the chemical basis of a macroscopic property such as the heat capacity of gases using microscopic (classical and quantum) mechanics. Students are given the opportunity to use (1) computational chemistry software to calculate the contributions of translational, rotational, and vibrational motion to the energy of molecules; (2) a graphing program to study the linear and nonlinear dependence of energy on temperature; (3) classical, quantum, and statistical mechanical theory to verify experimental data; (4) regression analysis to approximate the heat capacity constant of simple gases from energy calculations.     

Thermal analysis via molecular dynamics simulation

Thermal analysis by classical molecular dynamics simulations is discussed on hand of heat capacity of crystals of 9600 atoms. The differences between quantum mechanical and classical mechanical calculations are shown. Anharmonicity is proven to be an important factor. Finally, it is found that defects contribute to an increase in heat capacity before melting. The energy of conformational gauche defects within the crystal is only about 10% due to internal rotation. The other energy must be generated by cooperative strain. The conclusion is that the next generation of faster computers may permit wider use of molecular dynamics simulations in support of the interpretation of thermal analysis.Dedicated to Professor Bernhard Wunderlich on the occasion of his 65th birthday     

Infrared and ab initio studies of hydrogen bonding and proton transfer in the complexes formed by pyrazoles

The results of experimental studies and quantum mechanical calculations of vibrational spectra and structure of hydrogen bonded complexes formed by pyrazole (P) and 3,5-dimethylpyrazole (DMP) are presented. IR spectra of pyrazoles in solutions, gas phase, and solid state have been investigated in wide range of concentrations and temperatures. It has been found that in the gas phase both P and DMP reveal the equilibrium between monomers, dimers, and trimers. In solutions the equilibrium between monomers and trimers dominates, no bands, which can be attributed to dimers were detected. DMP retains the trimer structure in solid state, while in the case of pyrazole P, formation of the crystal provides another type of association. Geometrical and spectral characteristics of dimers and trimers, obtained by ab initio calculations, are presented and compared with experimental data.

IR spectra of solutions containing P and DMP with a number of acids (acetic and trifluoroacetic acids, pentachlorophenol, HBr) have been studied in parallel with ab initio calculations. It has been found that pentachlorophenol forms with pyrazoles complexes with one strong hydrogen bond O–HN, while NH pyrazole group remains unbonded. With carboxylic acids DMP forms 1:1 cyclic complexes with two hydrogen bonds. In the case of acetic acid, the complex in CH₂Cl₂ solution reveals molecular structure with OHN and C=OHN bonds, in accordance with results of the calculations. For trifluoroacetic acid, the calculations predict the molecular structure to be energetically more stable in the case of the isolated binary complex (in gas phase), while the experimental spectrum of CH₂Cl₂ solution gives an evidence of the proton transfer with formation of the cyclic ionic pair with two NH⁺O⁻ bonds. The agreement with experimental results can be improved by taking into account the influence of environment in the framework of Onsager or Tomasi models. The shape of proton potential function of the complexes and medium effect on its parameters, resulted from experimental data and calculations, are discussed. It has been found that the number of potential minima and their relative depth depend strongly on the method of calculations and the basic set. Under excess of trifluoroacetic acid, the formation of 2:1 acid–DMP complex has been detected. Spectral characteristics and results of calculations point to the cyclic structure of this complex, which includes homoconjugated bis-trifluoroacetate anion and DMPH⁺ cation. With HBr both studied pyrazoles were found to form ionic complexes including one or two pyrazole molecules per one acid molecule and correspondingly monocation or homoconjugated cation BHB⁺.     

多原子反应体系的高精度拟合势能面

本文介绍了近几年来我们组构建多原子反应体系的高精度拟合势能面的进展。我们基于神经网络(NN)方法,成功构建了多原子气相分子体系和气相分子在金属表面解离的一系列势能面。这些势能面的拟合精度相当高,并且经过了严格的量子动力学测试,能广泛应用到动力学研究中。我们还提出了一种新的置换不变势能面的拟合方法,即基本不变量神经网络方法(FI-NN)。基本不变量的使用极大地减少了神经网络输入层多项式的个数,有效提高了势能面的计算速度。     

Benchmark calculations of proton affinities and gas-phase basicities of molecules important in the study of biological phosphoryl transfer

Benchmark calculations of proton affinities and gas-phase basicities of molecules most relevant to biological phosphoryl transfer reactions are presented and compared with available experimental results. The accuracy of proton affinity and gas-phase basicity results obtained from several multi-level model chemistries (CBS-QB3, G3B3, and G3MP2B3) and density-functional quantum models (PBE0, B1B95, and B3LYP) are assessed and compared. From these data, a set of empirical bond enthalpy, entropy, and free energy corrections are introduced that considerably improve the accuracy and predictive capability of the methods. These corrections are applied to the prediction of proton affinity and gas-phase basicity values of important biological phosphates and phosphoranes for which experimental data does not currently exist. Comparison is made with results from semiempirical quantum models that are commonly employed in hybrid quantum mechanical/molecular mechanical simulations. Data suggest that the design of improved semiempirical quantum models with increased accuracy for relative proton affinity values is necessary to obtain quantitative accuracy for phosphoryl transfer reactions in solution, enzymes, and ribozymes.     

Development of a force field for zeolitic imidazolate framework-8 with structural flexibility

A force field is developed for zeolitic imidazolate framework-8 (ZIF-8) with structural flexibility by combining quantum chemical calculations and classical Amber force field. The predicted crystalline properties of ZIF-8 (lattice constants, bond lengths, angles, dihedrals, and x-ray diffraction patterns) agree well with experimental results. A structural transition from crystalline to amorphous as found in experiment is observed. The mechanical properties of ZIF-8 are also described fairly well by the force field, particularly the Young's modulus predicted matches perfectly with measured value. Furthermore, the heat capacity of ZIF-8 as a typical thermophysical property is predicted and close to experimental data available for other metal-organic frameworks. It is revealed the structural flexibility of ZIF-8 exerts a significant effect on gas diffusion. In rigid ZIF-8, no diffusive behavior is observed for CH(4) within the simulation time scale of current study. With the structural flexibility, however, the predicted diffusivities of CH(4) and CO(2) are close to reported data in the literature. The density distributions and free energy profiles of CH(4) and CO(2) in the pore of ZIF-8 are estimated to analyze the mechanism of gas diffusion.     

Thermodynamic functions for methylhalosilanes

Thermodynamic functions (heat capacity, enthalpy, entropy and free energy) are calculated for methylhalosilanes, dimethylhalosilanes, and dimethyldihalosilanes in the ideal gas state from 298.16 to 1200 K at 1 atm pressure. Statistical thermodynamic methods have been used in the calculations, with functions corrected for internal rotation by the method of Pitzer. Agreement with other literature data, where available, is satisfactory.     

Molecular density of states from estimated vapor phase heat capacities

Heat capacity data between 298 and 1500K are used to derive a reduced set of apparent vibrational frequencies that can be used for estimation of molecular density of states, ρ(E). Estimates for a number of molecule and radical species, using a reduced set of three frequencies with noninteger degeneracies, are shown to compare favorably to direct count methods, which require specification of the complete frequency set. Use of the reduced set of three frequencies leads to significant improvement in calculations of ρ(E)/Q as compared to similar calculations which use only a single geometric- or arithmetic-mean frequency approximation. Since vapor phase heat capacity data of molecules and radicals can be estimated accurately by a group additivity formalism, this approach provides a method to estimate ρ(E) for use in calculations of pressure effects in unimolecular and chemical activation reaction systems. The accuracy of the ρ(E)/Q distributions obtained from heat capacity data makes this a viable method for those cases where the complete frequency distribution is not known. It is especially valuable for those cases where contributions to ρ(E) from internal rotors or low frequency vibrations such as inversions are not well known. This approach is useful for quantum RRK or inverse Laplace transform calculations of k(E) since no assignment of transition state properties is necessary. The reduced frequency set can also be combined with ΔH_f(298) and S(298) to provide a compact data set to describe thermodynamic properties at any temperature. © 1997 John Wiley & Sons, Inc.     

Non-Born-Oppenheimer molecular dynamics of Na...FH photodissociation

The accuracy of non-Born-Oppenheimer (electronically nonadiabatic) semiclassical trajectory methods for simulations of "deep quantum" systems is reevaluated in light of recent quantum mechanical calculations of the photodissociation of the Na...FH van der Waals complex. In contrast to the conclusion arrived at in an earlier study, semiclassical trajectory methods are shown to be qualitatively accurate for this system, thus further validating their use for systems with large electronic energy gaps. Product branching in semiclassical surface hopping and decay-of-mixing calculations is affected by a region of coupling where the excited state is energetically forbidden. Frustrated hops in this region may be attributed to a failure of the treatment of decoherence, and a stochastic model for decoherence is introduced into the surface hopping method and is shown to improve the agreement with the quantum mechanical results. A modification of the decay-of-mixing method resulting in faster decoherence in this region is shown to give similarly improved results.     

Quantum chemical study on the coordination environment of the catalytic zinc ion in matrix metalloproteinases

X-ray analyses of matrix metalloproteinases (MMPs) have shown that the catalytic zinc ion (Zn1) can bind to one to three water molecules in addition to three conserved histidine residues. To estimate the relative stability of the possible Zn1 coordination structures in the active site of the MMPs, we carry out computational analyses on the coordination environment of the Zn1 ion in the gelatinase A enzyme (or matrix metalloproteinase 2; MMP-2). Four-, five-, and six-coordinated complexes representative of the Zn1 site are fully characterized by means of quantum mechanical (QM) methodologies. On one hand, B3LYP/LACVP* minimizations of various cluster models of the MMP-2 active site show that the trigonal bipyramidal geometry is energetically favored in the gas phase and that continuum solvent effects stabilize preferentially the tetrahedral complexes. On the other hand, B3LYP/OPLS-AA hybrid QM/molecular mechanical calculations in the solvated catalytic domain of the MMP-2 enzyme complemented with electrostatic Poisson-Boltzmann calculations show that the mature enzyme presents most likely a Zn1 ion coordinated by three histidine residues and two water molecules, while the active site glutamic acid is negatively charged. In consonance with X-ray diffraction data, other possible Zn1 configurations, a six-coordinated structure with Zn1-water as well as four- and five-coordinated complexes with a Zn1-bound hydroxide, are predicted to be very close in energy.     

A low-parametric state equation for calculating the thermodynamic properties of substances in liquid and gaseous state

Using methods and approaches developed by the authors, a new low-parametric state equation for describing the thermal properties of normal substances is obtained that allows us to describe the thermal properties of gases, liquids, and fluids over a range of densities from the ideal gas state to the triple point, except for a critical region, with a high degree of accuracy close to that of an experiment. The caloric properties and speed of sound are calculated for argon, nitrogen, and carbon dioxide without using any caloric data except for the enthalpy of an ideal gas. It is established that the calculated values of enthalpy, heat capacity, the speed of speed of sound, etc., are in good agreement with the experimental (reliably tabulated) data.     

Gas phase chemical equilibrium in dinitrogen trioxide and dinitrogen tetroxide

The ideal gas chemical thermodynamic properties for NO, NO₂, N₂O₃, and N₂O₄ for the temperature range 50 to 5000 K were evaluated by the statistical thermodynamic method using the most recent molecular parameters. In the calculations for NO and NO₂, the effects of anharmonicity and vibration—rotation interaction were included. The contributions due to centrifugal distortion were also included for NO₂. For evaluation of the thermodynamic properties for N₂O₃ and N₂O₄ molecules, the rigid-rotor and harmonic-oscillator model were adopted. A free internal rotation was assumed for N₂O₃ and an internal rotation barrier height (V₂) of 1.58 kcal mol⁻¹ was derived for N₂O₄. The thermodynamic properties due to hindered internal rotation were clculated using a partition function formed by summation of internal rotation energy levels. The thermodynamic properties for two equilibrium mixtures: NO₂---N₂O₄ and N₂O₃---NO---NO₂---N₂O₄ were also calculated. The effects of temperature and pressure on heat capacities and compositions of these two mixtures are illustrated graphically and the calculated heat capacities and equilibrim constants are in good agreement with available experimental values.     

Charge distributions in polyatomic ions

The determination of charge distributions in polyatomic ions through both energetic and quantum mechanical (CNDO/2) methods is discussed. Results from both methods are shown to be in good agreement.The author is grateful to Dr. R. Grinter of the University of East Anglia for assistance with the quantum mechanical calculations.     

Bimolecular reaction rates from ring polymer molecular dynamics: application to H + CH4 → H2 + CH3

In a recent paper, we have developed an efficient implementation of the ring polymer molecular dynamics (RPMD) method for calculating bimolecular chemical reaction rates in the gas phase, and illustrated it with applications to some benchmark atom-diatom reactions. In this paper, we show that the same methodology can readily be used to treat more complex polyatomic reactions in their full dimensionality, such as the hydrogen abstraction reaction from methane, H + CH(4) → H(2) + CH(3). The present calculations were carried out using a modified and recalibrated version of the Jordan-Gilbert potential energy surface. The thermal rate coefficients obtained between 200 and 2000 K are presented and compared with previous results for the same potential energy surface. Throughout the temperature range that is available for comparison, the RPMD approximation gives better agreement with accurate quantum mechanical (multiconfigurational time-dependent Hartree) calculations than do either the centroid density version of quantum transition state theory (QTST) or the quantum instanton (QI) model. The RPMD rate coefficients are within a factor of 2 of the exact quantum mechanical rate coefficients at temperatures in the deep tunneling regime. These results indicate that our previous assessment of the accuracy of the RPMD approximation for atom-diatom reactions remains valid for more complex polyatomic reactions. They also suggest that the sensitivity of the QTST and QI rate coefficients to the choice of the transition state dividing surface becomes more of an issue as the dimensionality of the reaction increases.     

Wave packet dynamics of photon- and electron-stimulated desorption of ammonia from surfaces

Time-dependent quantum mechanical calculations have been carried out for the photon- and electron-stimulated desorption of ammonia from metal or semiconductor surfaces. The desorption is facilitated by a short-lived complex which excites the N---H₃ inversion mode. The desorption yield and its isotope effect have been obtained from a wave packet on two-dimensional empirical potential energy surfaces. The translational and vibrational distributions of the desorbed ammonia are also calculated. The desorption mechanism includes both direct and predesorption, but the latter predominates. It is shown that the quantum desorption dynamics is much more complex than the simple MGR model.     

Temperature measurement from scattering spectra of clusters: theoretical treatment

Scattering spectra from X-ray, electron or neutron diffraction experiments are sufficient to describe the phase behaviour of noble gas clusters and to determine their temperature. Using classical Monte Carlo simulations combined with optimized data analysis and Path Integral Monte Carlo calculations as “idealized experiments” we obtain scattering spectra of Ar- and Ne-clusters. Starting from the classical and quantum mechanical hypervirial theorems we devise a method to estimate the temperature and the caloric curves (which describe the phase behaviour of the noble gas clusters) directly from these scattering spectra using an interatomic potential function as input. As applications we studied for Ar-clusters the effect of different model potentials on the temperature estimate thus contributing to the intricate question of what experimentally is the temperature of an isolated cluster. For Ne-clusters we investigate the differences between classical and quantum mechanical treatment.