Thermodynamic calculations taking into account the internal rotations.
2. Manual procedure using the TD option file (.tdi)
Because automatic procedure has the restrictions in the setting of the additional calculation parameters, the manual mode of the TD calculations can be used. For this purpose a TD options file with extension .tdi should be created. The tdi-file is a regular ASCII file and can be created using any ASCII file editor.
Using the previous example — SiF3OH molecule (file Moltran-Sample1) — create the file Moltran-Sample1.tdi containing two lines:
T=298.15 P=101325. ZeroModes=(1,2,3,4,5,6) RotNum=1 Vibr=3 Axes=(1,5) Group=(5,6) GenCoord V0=2.5 Rot=3
Here, the command Vibr=3 means that the vibration mode 3 will be considered as an internal rotation. Option Axes=(1,5) means that the rotation axis is the Si-O direction (atoms 1 and 5), and the rotating group is atoms 5 and 6 (Group=(5,6)). Note, that Group=(1,2,3,4) will give the same results. V0=2.5 means that the rotation barrier height is 2.5 kJ/mol. Rot=3 for the given vibration mode means that the rotation has the 3-fold barrier and the corresponding rotation symmetry number (3) for this mode should be set. Command GenCoord is not necessary and tells MOLTRAN generate the input files (in GAMESS format) for calculation of the rotation potential point-by-point. T= and P= options set the temperature and pressure, and ZeroModes defines the normal modes corresponding to translations and rotatitions of molecule as whole. Other options which can be found in tdi-file are explained in the MOLTRAN manual.
Please note that it is frequently convenient to determine values of Axis, Group, and V0 options on the basis of ARIR results from the previous MOLTRAN run (see TD calculations using ARIR).
After the .tdi-file is created, run the command:
moltran Moltran-Sample1.txt /0
or just start MOLTRAN, set input and tdi-file names and run TD calculations using menu items “Command”->“Thermodynamics”->“OK”. Close the program.
Inspect the output file (Moltran-Sample1.log). Skipping the beginning of file find the data marked with a header:
*** Contributions of internal rotations ***
The calculation of internal rotation contributions starts here. At first, MOLTRAN prints out the molecular parameters used in the further analysis:
*** Internal rotation No. 1 (replacing the vibration mode 7)
Masses (amu) and moments of inertia (amu*bohr^2) of rotating groups:
Group 1: M1= 17.00274 I1= 2.22532
Group 2: M2= 84.97213 I2= 443.24832
Reduced I=I1*I2/(I1+I2) = 2.21421
Pitzer's estimator I0 = 2.20962
Pitzer's estimator I = 2.20962
Rotation axes:
Point 1: Center of mass of Group1. Coords: 3.100751 0.160845 0.004723
Point 2: Center of mass of Group2. Coords: -0.705404 -0.019023 -0.001077
The rotation barrier height is estimated on the basis of maximum value of potential curve. Because the obtained barrier height is lower than 1.4RT at the given temperature, the conclusion is made that this rotation is free:
Rotation barrier height for n-fold potential V=V0/2*[1-Cos(n*x)] (n=1):
V0 = 2.4783 kJ/mol
0.5923 kcal/mol
0.9997 RT (T= 298.15K) => Free rotation (V0<1.4RT)
Because of GenCoord option MOLTRAN generates the coordinates corresponding the point of rotation and print the coordinates for all the probed points:
Unique point : 1
Internal rotation: 1 Rotation angle: 0.0
------------------------------------------------------------
Si1 14 0.003045 0.007644 0.000019
F2 9 -0.586240 1.467400 -0.005417
F3 9 -0.546203 -0.757879 1.270605
F4 9 -0.541588 -0.765800 -1.267765
O5 8 1.608317 0.131687 0.002445
H6 1 2.157117 -0.654006 0.003357
------------------------------------------------------------
Please note that several input files with these coordinates will be created in the working directory ready for calculation of energy by quantum chemical method.
Then, the rotation barrier and free-rotation partition functions are printed:
Rotation barrier height for n-fold potential V=V0/2*[1-Cos(n*x)] (n=3):
V0 = 2.5000 kJ/mol
0.5975 kcal/mol
1.0085 RT (T= 298.15K) => Free rotation (V0<1.4RT)
Free-rotation function: 1/Qf = 6.130750E-01 Qf = 1.631122E+00
Free-rotation (Pitzer): 1/Qf = 6.137101E-01 Qf = 1.629434E+00
Now, the thermodynamic contribution is estimated using three different approximations: harmonic oscillator, free rotator, and Pitzer-Gwinn model. The most comprehensive is the last column (obtained on the basis of Pitzer-Gwinn’s numeric tables for comprehensive estimator of inertia moments). The results are printed for several separate vibrations (if any) and for total contribution of all the internal rotations.
Thermodynamic functions for internal rotation 1 (vibration mode 7)
Harmonic Free Rotator Pitzer-Gwinn tables
Ocsillator I(*) I(**) I(*) I(**)
C, J/K/mol= 8.110 4.157 4.157 4.672 4.672
U, kJ/mol = 2.541 1.239 1.239 1.259 1.259
H, kJ/mol = 2.541 1.239 1.239 1.259 1.259
S, J/K/mol= 13.428 8.225 8.217 7.892 7.883
G, kJ/mol = -1.463 -1.213 -1.210 -1.094 -1.092
U+ZPE,kJ/mol = 3.219 1.918 1.918 1.938 1.937
H+ZPE,kJ/mol = 3.219 1.918 1.918 1.938 1.937
G+ZPE,kJ/mol = -0.785 -0.534 -0.532 -0.415 -0.413
I(*) - reduced moments of inertia are calculated by formula 1/I=1/Ia+1/Ib
I(**) - reduced moments of inertia are calculated by Pitzer-Gwinn formulas
Note: I(*)=I(**) for symmetric rotors.
Then, the total values of thermodynamic functions of the molecule are printed together with total energy values corrected for the total (electr+trans+rota+vibr+int.rot.) thermodynamic contributions.
Total values of thermodynamic functions (T= 298.15 K, P= 101325.00 Pa)
taking into account 1 internal rotations (in different approximations)
----------------------------------------------------------------------------------------------------------------------
Harmonic Free Rotator Pitzer-Gwinn tables
Ocsillator I(*) I(**) I(*) I(**)
----------------------------------------------------------------------------------------------------------------------
Cv, J/K/mol= 77.176 73.223 73.223 73.738 73.737
Cp, J/K/mol= 85.490 81.537 81.537 82.053 82.052
U, kJ/mol = 76.986 75.007 75.007 75.705 75.704
H, kJ/mol = 79.465 77.486 77.486 78.184 78.183
S, J/K/mol= 318.525 313.322 313.314 312.989 312.980
G, kJ/mol = -15.503 -15.931 -15.929 -15.134 -15.132
----------------------------------------------------------------------------------------------------------------------
I(*) - reduced moments of inertia are calculated by formula 1/I=1/Ia+1/Ib
I(**) - reduced moments of inertia are calculated by Pitzer-Gwinn formulas
Note: Internal rotation contributions to U, H, G include U0=H0=ZPE
in HO and PG models (U0=H0=0 in FR model)
*** Total energy corrected by TD functions (including internal rotations) ****
Minimum electronic-nuclear energy was taken from the input file at step: 4
Minimum Etot: -665.26660848 (Please check the program decision manually!)
Harmonic Free Rotator Pitzer-Gwinn tables
Ocsillator I(*) I(**) I(*) I(**)
E -665.26660848 -665.26660848 -665.26660848 -665.26660848 -665.26660848
E+ZPE -665.24329545 -665.24329545 -665.24329545 -665.24329545 -665.24329545
E+U -665.23728531 -665.23803928 -665.23803928 -665.23777341 -665.23777352
E+H -665.23634110 -665.23709507 -665.23709507 -665.23682920 -665.23682931
E+G -665.27251350 -665.27267658 -665.27267561 -665.27237283 -665.27237201
The values here are the results of total energy corrected by the contributions of internal rotation calculated at the current temperature and pressure ( program defaults: T=298.15K, P=101325Pa).
The file is finished with the thermodynamic functions calculated at different temperatures. As before, the temperature range can be set manually (default 0–500 K). Now, the internal rotation contributions are included. The WARNING’s are just a result of numerical errors during the interpolation of Pitzer-Gwinn tables for low temperatures for the light molecules (the tables are given for the values of the rotation partition function Qf large enough and their extrapolation to zero is frequently unrobust). In this case, just ignore the values with warnings. These values can be incorrect and should not be used. However, they have no effect on the remaining values.