Thermodynamic Properties of Species Calculation with Khimera
Thermodynamic properties of individual substances are required for any analysis of multielemental multiphase physico-chemical systems. As a rule most of them are retrieved from existing databases. In some cases the data for a substances you need are not available or out-of-date in these databases and should be calculated.
Types of species for which the calculation of thermodynamic properties can be done by Khimera
Statistical mechanics approach is used to calculate partition functions over electronic, vibrational and rotational energy levels for mono, di, and polyatomic gases. The calculations for condensed phases are based on low temperature thermodynamic functions (at some selected temperatures, standard entropy and enthalpy at room temperature) and equations for heat capacity temperature dependence, temperatures and enthalpies of phase transitions.
Example: intermediate data preparation for the ground electronic state of AlH
The realization of direct summation technique requires constructing full set of vibrational-rotational levels for all electronic states taking into account for partition functions calculations. Experimental data as a rule refer to low-lying vibrational and rotational levels. Dissociation energy value and constructing Limiting Curve of Dissociation (LCD) allows extrapolate experimental data to describe all bound and quasibound states.
The result of calculations of the rotational levels for selected vibrational quantum number is presented in the picture. It should be noted that only four vibrational levels of the ground state of AlH molecule are investigated in spectroscopic studies.
- Full set of vibrational and rotational levels is constructed for the ground electronic state of AlH molecule.
Example: general case of internal rotation in polyatomic molecules
The usual approximation with one term potential:
V(f)=V0/2[1+cos(nf)]
is not applicable for the general case of internal rotation (IR) with complicated potential. The case of torsional potential for relatively simple methyl n-propyl ether is shown on the picture. The potential was obtained from quantum chemical calculation and is fully unsymmetrical. The most general form of periodic function containing cosine and sine terms should approximate it. The results are presented in the picture. The direct summation over calculated torsional levels using such potential give reliable result of IR contribution calculation into thermal functions.
- Potential function of internal rotation and torsional energy levels for methyl n-propyl ether (CH3 – O – CH2CH2CH3).
Example: thermodynamic properties and geometry of FeF3
As a result of thermal functions calculation and selection of enthalpy of formation the full thermodynamic properties table can be calculated. The table consists of thermal functions in a wide temperature range, equilibrium constant for a given reaction (for example, dissociation), basic thermochemical quantities (the enthalpy of formation at 0 K and room temperature, the enthalpy of a given reaction), and equations approximating reduced Gibbs energy function in the same temperature range. It should be noted that the approximation is carried out by several conjugated piecewise functions. The heat capacity values in the points of conjugation and its first temperature derivatives are equal for conjugated functions.
Thermodynamic properties table for FeF3(g)
-----------------------------------P=1 atm---------------------------------
IRON TRIFLUORIDE FeF3(g)
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FeF3=Fe+3F ΔкH(0)= 1383.438 kJ/mol
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T(K) : Cp : Φ : S : H(T)-H(0) : lgK
(J/(K.mol) kJ/mol
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100 49.414 208.324 247.919 3.959 -708.7343
200 59.630 238.319 285.548 9.446 -345.9280
298.15 67.274 258.226 310.864 15.694 -226.2024
300 67.393 258.552 311.280 15.819 -224.6962
5700 83.075 465.758 546.243 458.765 6.3363
5800 83.077 467.158 547.688 467.072 6.5638
5900 83.080 468.536 549.109 475.381 6.7840
6000 83.082 469.890 550.505 483.689 6.9970
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M = 112.84220
ΔfH(0) = -739.957 kJ/mol
ΔfH(298.15) = -742.006 kJ/mol
Snucl = 20.256 J/(K.mol)
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T= 298- 1500K, X=T/10000 :
Φ = 4.688608E+02 + 6.786536E+01*ln(X) - 3.604143E-03*X + 8.173496E-01*X+ 1.590141E+02*X - 4.055775E+02*X + 5.362902E+02*X J/(K.mol)
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T= 1500- 6000K, X=T/10000 :
Φ = 5.097200E+02 + 8.307927E+01*ln(X) - 1.070131E-02*X + 1.542127E+00*X+1.627659E-01*X - 1.008190E-01*X + 3.264821E-02*X J/(K.mol)
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