Calculation of absolute molecular entropies and heat capacities made simple

We propose a fully-automated composite scheme for the accurate and numerically stable calculation of molecular entropies by efficiently combining density-functional theory (DFT), semi-empirical methods (SQM), and force-field (FF) approximations. The scheme is systematically expandable and can be integrated seamlessly with continuum-solvation models. Anharmonic effects are included through the modified rigid-rotor-harmonic-oscillator (msRRHO) approximation and the Gibbs–Shannon formula for extensive conformer ensembles (CEs), which are generated by a metadynamics search algorithm and are extrapolated to completeness. For the first time, variations of the ro-vibrational entropy over the CE are consistently accounted-for through a Boltzmann-population average. Extensive tests of the protocol with the two standard DFT approaches B97-3c and B3LYP-D3 reveal an unprecedented accuracy with mean deviations <1 cal mol⁻¹ K⁻¹ (about <1–2%) for the total gas phase molecular entropy of medium-sized molecules. Even for the hardship case of extremely flexible linear alkanes (C₁₄H₃₀–C₁₆H₃₄), errors are only about 3 cal mol⁻¹ K⁻¹. Comprehensive tests indicate a relatively strong variation of the conformational entropy on the underlying level of theory for typical drug molecules, inferring the complex potential energy surfaces as the main source of error. Furthermore, we show some application examples for the calculation of free energy differences in typical chemical reactions.

A novel scheme for the automated calculation of the conformational entropy together with a modified thermostatistical treatment provides entropies with unprecedented accuracy even for large, complicated molecules.     

Low-temperature heat capacities and standard molar enthalpy of formation of the complex

Low-temperature heat capacities of a solid complex Zn(Val)SO₄·H₂O(s) were measured by a precision automated adiabatic calorimeter over the temperature range between 78 and 373 K. The initial dehydration temperature of the coordination compound was determined to be, T _D=327.05 K, by analysis of the heat-capacity curve. The experimental values of molar heat capacities were fitted to a polynomial equation of heat capacities (C _p,m) with the reduced temperatures (x), [x=f (T)], by least square method. The polynomial fitted values of the molar heat capacities and fundamental thermodynamic functions of the complex relative to the standard reference temperature 298.15 K were given with the interval of 5 K. Enthalpies of dissolution of the [ZnSO₄·7H₂O(s)+Val(s)] (Δ_sol H _m,l ⁰) and the Zn(Val)SO₄·H₂O(s) (Δ_sol H _m,2 ⁰) in 100.00 mL of 2 mol dm^–3 HCl(aq) at T=298.15 K were determined to be, Δ_sol H _m,l ⁰=(94.588±0.025) kJ mol^–1 and Δ_sol H _m,2 ⁰=–(46.118±0.055) kJ mol^–1, by means of a homemade isoperibol solution–reaction calorimeter. The standard molar enthalpy of formation of the compound was determined as: Δ_f H _m ⁰ (Zn(Val)SO₄·H₂O(s), 298.15 K)=–(1850.97±1.92) kJ mol^–1, from the enthalpies of dissolution and other auxiliary thermodynamic data through a Hess thermochemical cycle. Furthermore, the reliability of the Hess thermochemical cycle was verified by comparing UV/Vis spectra and the refractive indexes of solution A (from dissolution of the [ZnSO₄·7H₂O(s)+Val(s)] mixture in 2 mol dm^–3 hydrochloric acid) and solution A’ (from dissolution of the complex Zn(Val)SO₄·H₂O(s) in 2 mol dm^–3 hydrochloric acid).     

Low-temperature heat capacities and standard molar enthalpy of formation of aspirin

Molar heat capacities (C _p,m) of aspirin were precisely measured with a small sample precision automated adiabatic calorimeter over the temperature range from 78 to 383 K. No phase transition was observed in this temperature region. The polynomial function of C _p,m vs. T was established in the light of the low-temperature heat capacity measurements and least square fitting method. The corresponding function is as follows: for 78 K≤T≤383 K, C _p,m/J mol^-1 K^-1=19.086X ⁴+15.951X ³-5.2548X ²+90.192X+176.65, [X=(T-230.50/152.5)]. The thermodynamic functions on the base of the reference temperature of 298.15 K, {ΔH _T -ΔH _298.15} and {S _T-S _298.15}, were derived. Combustion energy of aspirin (Δ_c U _m) was determined by static bomb combustion calorimeter. Enthalpy of combustion (Δ_c H ^o _m) and enthalpy of formation (Δ_f H ^o _m) were derived through Δ_c U _m as - (3945.26±2.63) kJ mol^-1 and - (736.41±1.30) kJ mol^-1, respectively. This revised version was published online in July 2006 with corrections to the Cover Date.     

The enthalpies and entropies of dilution of alkali halides and tetraalkylammonium halides in N-methylacetamide

The enthalpies of dilution of some alkali and tetraalkylammonium halides have been measured in N-methylacetamide at 35°C. The results approach the Debye-Hückel limiting law at low concentrations. Excess free energies and entropies were calculated from the present results and previous freezing point measurements. The excess enthalpies of the alkali halides in N-methylacetamide are in the same range as the excess enthalpies in water. The effect of changing anions is quite small in N-methylacetamide. The cation order is Li⁺?Na⁺>Cs⁺>K⁺. The excess enthalpies of the tetraalkylammonium halides in N-methylacetamide are very different from the excess enthalpies in water, confirming the conclusion that in water the large excess enthalpies are due to hydrophobic bonding and that in N-methylacetamide this effect is not present.     

Thermodynamics of liquids: standard molar entropies and heat capacities of common solvents from 2PT molecular dynamics

We validate here the Two-Phase Thermodynamics (2PT) method for calculating the standard molar entropies and heat capacities of common liquids. In 2PT, the thermodynamics of the system is related to the total density of states (DoS), obtained from the Fourier Transform of the velocity autocorrelation function. For liquids this DoS is partitioned into a diffusional component modeled as diffusion of a hard sphere gas plus a solid component for which the DoS(υ) → 0 as υ→ 0 as for a Debye solid. Thermodynamic observables are obtained by integrating the DoS with the appropriate weighting functions. In the 2PT method, two parameters are extracted from the DoS self-consistently to describe diffusional contributions: the fraction of diffusional modes, f, and DoS(0). This allows 2PT to be applied consistently and without re-parameterization to simulations of arbitrary liquids. We find that the absolute entropy of the liquid can be determined accurately from a single short MD trajectory (20 ps) after the system is equilibrated, making it orders of magnitude more efficient than commonly used perturbation and umbrella sampling methods. Here, we present the predicted standard molar entropies for fifteen common solvents evaluated from molecular dynamics simulations using the AMBER, GAFF, OPLS AA/L and Dreiding II forcefields. Overall, we find that all forcefields lead to good agreement with experimental and previous theoretical values for the entropy and very good agreement in the heat capacities. These results validate 2PT as a robust and efficient method for evaluating the thermodynamics of liquid phase systems. Indeed 2PT might provide a practical scheme to improve the intermolecular terms in forcefields by comparing directly to thermodynamic properties.     

On the enthalpies and entropies of formation of solid nickel—zinc alloys

The enthalpies of formation of solid nickel—zinc alloys have been measured at 355 K using an isoperibol calorimeter and the technique of tin-solution calorimetry, and values have been obtained for the nickel-rich α-solid solutions and for the β₁, γ, γ₁ and δ intermediate phases. Exothermic values have been observed throughout and these have been compared with the results obtained in previous free energy studies and with those suggested by the empirical model of Miedema. The existing free energy data have been re-assessed at 900 K and the results combined with the present calorimetric enthalpies to derive entropies of formation. The possible contributions to the entropies of the phases are discussed and their Debye temperatures are estimated.     

The low-temperature heat capacity of alkali and alkaline-earth metal uranoborates

The results of heat capacity measurements for several crystalline uranoborates over the temperature range 0–340 K were discussed and analyzed. Low-temperature heat capacities (T < 50 K) were considered using the Debye theory of the heat capacity of solids and its multifractal generalization. The fractal dimensions of compounds were calculated and the heterodynamic characteristics of their structures determined.     

Molar heat capacities and standard molar enthalpy of formation of pyrimethanil butanedioic salt

A noval anilino-pyrimidine fungicide, pyrimethanil butanedioic salt (C₂₈H₃₂N₆O₄), was synthesized by a chemical reaction of pyrimethanil and butanedioic acid. The low-temperature heat capacities of the compound were measured with an adiabatic calorimeter from 80 to 380 K. The thermodynamic function data relative to 298.15 K were calculated based on the heat capacity fitted curve. The thermal stability of the compound was investigated by TG and DSC. The TG curve shows that pyrimethanil butanedioic salt starts to sublimate at 455.1 K and totally changes into vapor when the temperature reaches 542.5 K with the maximal speed of weight loss at 536.8 K. The melting point, the molar enthalpy (Δ_fus H _m), and entropy (Δ_fus S _m) of fusion were determined from its DSC curves. The constant-volume energy of combustion (Δ_c U _m) of pyrimethanil butanedioic salt was measured by an isoperibol oxygen-bomb combustion calorimeter at T = (298.15 ± 0.001) K. From the Hess thermochemical cycle, the standard molar enthalpy of formation was derived and determined to be Δ_f H _m ^o (pyrimethanil butanedioic salt)=?285.4 ± 5.5 kJ mol^?1.     

ViscosityB-coefficients,structural entropies and heat capacities,and the effects of ions on the structure of water

The water-structural contributions to the entropies and heat capacities of hydration of over 120 ions and the viscosity B-coefficients of nearly 80 aqueous ions are tabulated and correlated. B-coefficients for many more ions are predicted from this relationship and from their dependence on ionic size and charge. The structural entropies determine a unique scale of water structure making and breaking by the ions.     

The standard molar enthalpy of formation,molar heat capacities,and thermal stability of anhydrous caffeine

The constant-volume energy of combustion of crystalline anhydrous caffeine (C₈H₁₀N₄O₂) in α (lower temperature steady) crystal form was measured by a bomb combustion calorimeter, the standard molar enthalpy of combustion of caffeine at T = 298.15 K was determined to be −(4255.08 ± 4.30) kJ · mol⁻¹, and the standard molar enthalpy of formation was derived as −(322.15 ± 4.80) kJ · mol⁻¹. The heat capacity of caffeine in the same crystal form was measured in the temperature range from (80 to 387) K by an adiabatic calorimeter. No phase transition or thermal anomaly was observed in the above temperature range. The thermal behavior of the compound was further examined by thermogravimetry (TG), differential thermal analysis (DTA) over the range from (300 to 700) K and by differential scanning calorimetry (DSC) over the range from (300 to 540) K, respectively. From the above thermal analysis a (solid–solid) and a (solid–liquid) phase transition of the compound were found at T = (413.39 and 509.00) K, respectively; and the corresponding molar enthalpies of these transitions were determined to be (3.43 ± 0.02) kJ · mol⁻¹for the (solid–solid) transition, and (19.86 ± 0.03) kJ · mol⁻¹ for the (solid–liquid) transition, respectively.     

Molar heat capacities and standard molar enthalpy of formation of 2-amino-5-methylpyridine

The heat capacities (C _p,m) of 2-amino-5-methylpyridine (AMP) were measured by a precision automated adiabatic calorimeter over the temperature range from 80 to 398 K. A solid-liquid phase transition was found in the range from 336 to 351 K with the peak heat capacity at 350.426 K. The melting temperature (T _m), the molar enthalpy (Δ_fus H _m⁰), and the molar entropy (Δ_fus S _m⁰) of fusion were determined to be 350.431±0.018 K, 18.108 kJ mol⁻¹ and 51.676 J K⁻¹ mol⁻¹, respectively. The mole fraction purity of the sample used was determined to be 0.99734 through the Van’t Hoff equation. The thermodynamic functions (H _T-H _298.15 and S _T-S _298.15) were calculated. The molar energy of combustion and the standard molar enthalpy of combustion were determined, ΔU _c(C₆H₈N₂,cr)= −3500.15±1.51 kJ mol⁻¹ and Δ_c H _m⁰ (C₆H₈N₂,cr)= −3502.64±1.51 kJ mol⁻¹, by means of a precision oxygen-bomb combustion calorimeter at T=298.15 K. The standard molar enthalpy of formation of the crystalline compound was derived, Δ_r H _m⁰ (C₆H₈N₂,cr)= −1.74±0.57 kJ mol⁻¹.     

The enthalpies and heat capacities of hydration of ammonium and tetraalkylammonium bromides

The heat effects of solution of ammonium, tetraethylammonium, and tetrabutylammonium bromides in water were measured over the temperature range 277.15-328.15 K. The standard enthalpies of solution were calculated in the second approximation of the Debye-Hückel theory. The results were compared with the literature data on the enthalpies of solution of tetrabutylammonium and tetrapentylammonium bromides. The applicability of various equations suggested to describe the temperature dependences of enthalpy characteristics was analyzed. Heat capacity changes caused by the hydration of the salts and the temperature dependences of the entropies of hydration were calculated and discussed.     

The carvoxime system: IV. heat capacities and enthalpies of melting of dl-carvoxime, l-carvoxime and standard n-heptane

Heat capacities between 160 and 385 K and enthalpies of melting of dl-carvoxime and l-carvoxime were determined by adiabatic calorimetry. The performance of the apparatus was checked on standard n-heptane. The enthalpy of melting values are dl-carvoxime, 22.70 ± 0.06; l-carvoxime, 17.02 ± 0.02; n-heptane, 14.059 ± 0.010 kJ mol⁻¹.     

Heat capacities and entropies of linear,aliphatic polyesters

New measurements of the heat capacity in the melt of poly(trimethylene succinate) (PTMS), poly(trimethylene adipate) (PTMA), and poly(hexamethylene sebacate) (PHMS) from 310 to 400 K are presented. Based on these data and literature data on eight other molten polylactones and poly(ethylene sebacate) (PES), an addition scheme is developed for linear, aliphatic polyesters that leads to the equation: which represents the ATHAS-recommended melt heat capacities for all linear polyesters. Combining previously discussed solid heat capacities, derived from an approximate frequency spectrum, with the new liquid heat capacities, the various thermodynamic functions (enthalpy, entropy, and Gibbs function) could be derived using the ATHAS computation scheme. The average value of residual entropy at zero kelvin of 5.3 ± 1.8 J/(K mol) per mobile bead for glassy linear polysters was found to be somewhat higher than for many other polymers in the data bank, but closer to that observed for linear, aliphatic polyamides. The phase transitions of PTMS, PTMA, and PHMS are also analyzed using the quantitative baselines available from the heat capacity study.     

The standard enthalpies of formation of alkoxy-NNO-azoxy compounds

The standard enthalpies of combustion Δ_c H ^o and formation Δ_f H ^o of seven alkoxy-NNO-azoxy compounds containing the-N⁺(O^?)=NO-characteristic group were determined by combustion in a calorimetric bomb in the atmosphere of oxygen. The contribution of this group to the Δ_f H ^o enthalpies of the substances studied was calculated. The Δ_f H ^o enthalpies found by the method of group contributions were in satisfactory agreement with experimental data.     

Investigation on enthalpies of combustion and heat capacities for 2-aminomethylpyridine derivatives

Journal of Thermal Analysis and Calorimetry - The molar energies of combustion $$\left( {\Delta_{\text{c}} U_{\text{m}} } \right)$$ for 2-aminomethylpyridine (AMP), tert-butyl...     

Excess heat capacities and excess molar enthalpies of the mixtures containing tetrahydropyran,piperidine and cyclic alkanones

Journal of Thermal Analysis and Calorimetry - In the present study, molar heat capacities, $$\left( {C_{\text{P}}^{{}} } \right)_{123}$$ , at T/K&nbsp;=&nbsp;293.15–308.15&nbsp;K...