Gaussian M-062x/6-31+g (d,p) Calculation of Standard Enthalpy, Entropy and Heat Capacity of Some Fluorinated Alcohol’s and Its Radicals at Different Temperatures

Thermochemical properties of fluorinated alcohols are needed for understanding their stability and reactions in the environment and in thermal process. Structures and thermochemical properties of these species were determined by the Gaussian M-062x/6-31+g (d,p) calculation. Contributions of entropy, S°298, and heat capacities, Cp(T) due to vibration, translation, and external rotation of the molecules were calculated based on the vibration frequencies and structures obtained from the M-062x/6-31+g (d,p) density functional method. Potential barriers are calculated using M-062x/6-31+g (d,p) density functional method and are used to calculate rotor contributions to entropy and heat capacity using integration over energy levels of rotational potential. Enthalpies of formation for 19 fluorinated ethanol and some radicals were calculated with a popular ab initio and density functional theory methods: the Gaussian M-062x/6-31+g (d,p) via several series of isodesmic reactions. The recommended ideal gas phase ∆Hf298° (kcal mol) values calculated in this study are the following: -101.74 ± 0.72 for CH2FCH2OH; -113.51 ±1.39 for CH3CHFOH; -50.66 ± 0.75 for C•HFCH2OH; -56.05±0.62 for CH2FCH•OH; 45.00±1.31 for CH2FCH2O•; -59.61±1.20 for CH2•CHFOH; -67.99± 1.29 for CH3CF•OH; -58.76±1.20 for CH3CHFO•; 154.12±1.72 for CH2FCHFOH; -155.26±1.67 for CF2HCH2OH; -174.53±1.54 for CH3CF2OH; -104.07 ± 1.45 for CH2FC•FOH; -105.63±1.74 for C•HFCFHOH; -99.08±1.57 for CH2FCHFO•; -102.34±1.74 for CHF2C•HOH; -102.23±1.57 for C•F2CH2OH; -98.86±1.57 for CHF2CH2O•; -119.41±1.74 for CH2•CF2OH; -110.56±1.62 for CH3CF2O•. Entropies (S298° in cal mol K) were estimated using the M-062x/6-31+g (d,p) computed frequencies and geometries. Rotational barriers were determined and hindered internal rotational contributions for S298 °1500°, and Cp(T) were calculated using the rigid rotor harmonic oscillator approximation, with direct integration over energy levels of the intramolecular rotation potential energy curves.


Introduction
Fluorinated hydrocarbons used as refrigerants, in polymers, heat exchange fluids, and as solvents. They are present in the atmosphere, lithosphere, and hydrosphere. Because of their less adverse effects on the stratospheric ozone layer, they are used in place of greenhouse gases. [1] Fluorinated hydrocarbons exist as compounds ranging from pure to oxidized intermediates resulting from oxidation in the environment. In order to study their reactivity in biological systems, lifetimes, and in the environment, it's critical to understand the chemical and thermodynamic properties of fluorocarbons and their breakdown intermediates.
The thermochemistry of fluorinated alcohols with one carbon atom were studied in the past and are in the literature [2]. In 2016 Hang Wang studied thermodynamic properties of fluorinated methanol using CBS-QB3, M06, M06-2X, WB97X, W1U, B3LYP, CBS-APNO and G4 Calculations. Small standard deviation suggests good error cancellation of Heat Capacity of Some Fluorinated Alcohol's and Its Radicals at Different Temperatures work reactions and accuracy. M06-2x/6-31+g (d,p) calculation have small values for standard deviations, it is an accurate method to calculate Enthalpy of fluorinated alcohols, it shows the second smallest standard deviation after CBS-QB3 method of calculation Halogenated compounds are highly stable, have low reactivity and are valued chemicals in industry [3]. Due to its widespread use and their persistence in the environment, they are of concern to the environment. In order to understand the oxidation and reduction reactions involving such molecules, their thermochemical properties must be studied. [3]

Computational Method
Composite calculations and series of Isodesmic Reactions are used to calculate enthalpy of formation of fluorinated ethanols. All calculations are performed using the Gaussian 16 program. The DFT method M06-2x is used to initially analyze optimized structures, frequencies, thermo energies and internal rotors of the molecules studied. It's a Global-hybrid meta-GGA density functional approximation, GGA, generalized gradient approximation, in which the density functional depends on the up and down spin densities and their reduced gradient, meta GGA, in which the functional also depends on the up and down spin kinetic energy densities, hybrid GGA, a combination of GGA with Hartree-Fock exchange, hybrid meta GGA, a combination of meta GGA with Hartree-Fock exchange [21]. All reported values are for standard state of 298 K and 1 atm. We continue the calculation of fluorinated alcohols in this study with this method, because the M-062x/6-31+g (d,p) level of calculation have been applied to fluoro hydrocarbons [4] with small reported standard deviations values.

Isodesmic and Isogyric Reaction
The enthalpy of formation of mono and di fluorinated ethanol's and its radicals has been calculated using Gaussian M-062x/6-31+g (d,p) method of calculation. In order to calculate the enthalpy of formation of fluorinated ethanols using this method, we use the calculated enthalpies of formation in work reactions along with reference species. The number of each type of bond must be conserved in the isodesmic reactions in order to cancel any systematic error in the molecular orbital calculations using this method. Calculations of enthalpies of formation is allowed to accuracies close to experimental values by the careful choice of the isodesmic reactions [5]. Taking 1fluoroethanol as an example, two isodesmic reactions (Table 2) are selected to determine the ∆Hf298 of the target molecule, 1-fluoroethanol. Since the ∆Hf298 values of all species but 1-fluoroethanol in 1− 2 (Table 2) are known, the ∆Hf298 of the target species 1-fluoroethanol, is obtained from this data and the calculated ∆Hrxn, 298. ∆Hf298 calculated using two different reference molecules are within ±. 2 Kcal mol -1 .

Results and Discussion
Optimized Structures

Standard Enthalpy Values
Enthalpies of formation were determined from isodesmic work reactions from M-062x/6-31+g (d,p) method of calculation. The standard enthalpy of formation for the reference species along with their uncertainties, which are used the isodesmic work reactions, table 4, are listed in table 1 in kcal mol −1 . The standard deviation was calculated [14] for all Enthalpies of formation values for all 19 fluorinated ethanol and are included in table 4. Details of the method of standard deviation [14] and example calculation(s) are shown in the *Supporting Information table provided. Hartrees, kcal mole -1 *SD Standard Deviation kcal mol -1 Errors reported avg of sum of uncertainties in rxn's reference species

Entropy and Heat Capacity Values
Internal rotor contributions to calculated entropy and heat capacity at 298-1500K were determined using the molecular mass of each molecule, number of optical isomers, symmetry of the molecule, electron degeneracy, moment of inertia, and vibrational frequencies values (table 5). The vibrational frequencies for the calculation of heat capacity and entropy at the M-062x/6-31+g (d,p) level of calculation was scaled by a factor of 0.97. The moment of inertia values is shown in the Supporting Information Table provided. To calculate the contributions of external rotor, vibration and transition to the calculated entropy and heat capacity, the "SMCPS" program is used. It employs the rigid-rotor harmonic oscillator approximation using moment of inertia from optimized structure and frequencies. The "Rotator' program by Lay et al. is used to calculate internal rotor contributions from the corresponding internal rotor torsion frequencies. In this paper, a torsional potential curve presenting a ten-parameter Fourier series function is used to calculate the contribution of internal rotor. Parameters and detailed functions are shown in the Supporting Information Table provided. Rotor [15][16][17][18] program is used to calculate thermodynamic functions from hindered rotations with arbitrary potentials.
Calculation of the Hamiltonian matrix of the internal rotor, and subsequent calculation of energy levels by direct diagonalization of the matrix are employed by this technique. Rotational barriers versus dihedral angle is presented as a potential curve. In this paper, the calculated torsional potential at discrete torsional angles V(Φ)= a 0 + Σ a i cos (iΦ) + Σ b j cos (jΦ) i,j= 1-10 (1) The coefficients ai and bj are calculated to present the maxima and minima of the torsional potentials with a possibility to shift from the extreme angular positions.
Calculations of heat capacity and standard entropy based on benchmark database and the computational chemistry comparison for the M-062x/6-31+g (d,p) calculation method, the vibrational frequencies were scaled by a factor of 0.987 [19]. Potential Energy profiles for mono and di fluorinated ethanol and their related radicals are listed in the Supporting Information Table provided., the solid lines are the fit of Fourier series expansion, rotator contribution for barriers below 7 kcal mol -1 were added to the SMCPS calculated entropy and heat capacity. Energies are in kcal mol -1 . Table 6.

Conclusions
Thermodynamic properties of 19 mono and di-fluoro ethanols and their related radicals are calculated using the ab initio and Global-hybrid meta-GGA density function methods. Isodesmic work reactions are employed for cancellation of calculation errors. Multiple work reactions are utilized to calculate standard enthalpy of formation at the Gaussian M06-2X calculation level. Optimized geometries and frequencies are used to determine entropy and heat capacity with M06-2x/6-31+g (d,p) level of calculation. Intermolecular torsion potential curves at the M-06-2x/6-31+g (d,p) level of calculation are used to calculate hindered internal rotation contributions to heat capacity and entropy with a correction to the calculated heat capacity and entropy. The Thermochemical properties: Entropy, Heat Capacities at (298 -1500K), Standard Enthalpy of formation (298K), and the C-

Supporting Information
Supporting information is available, Cartesian Coordinates; Z-matrixes, vibration frequencies, moments of inertia, the method of standard deviation, Optimized Geometries, and C-C and C-O internal rotors potential energy profile for target fluorinated ethanol and their related radicals are included.