Simple thermodynamic calculations with MOLTRAN.
The simplest kind of thermodynamic (TD) calculations which can be performed with MOLTRAN is a calculation in the Rigid-Rotor-Harmonic-Oscillator (RRHO) approximation. MOLTRAN can calculate electronic, translational, rotational, vibrational, and total contributions to the molecular partition function Z, and, using them, obtain the internal energy, enthalpy, entropy, Helmholtz and Gibbs free energies in the state of ideal gas for various temperatures and pressures. As input data, MOLTRAN uses the results of molecular calculations performed with a quantum chemical (QC) programs, e.g. with GAMESS or GaussianXX. As a whole, this kind of calculations is analogous to that which can be performed by these programs itself. The only advantage of MOLTRAN is that it does it faster and easier, without any additional QC runs, and with fast variation of temperature and pressure conditions, atomic masses, symmetry numbers and other parameters. In many cases, it also gives much more detailed reports with many important details omitted in the GAMESS and Gaussian outputs.
The TD calculations can be performed by MOLTRAN within any regular work session. Thus, to perform the sample TD calculations, download the sample file Moltran-Sample1.txt , and run the command (it is proposed that MOLTRAN is already installed at your system):
moltran Moltran-Sample1.txt
After the graphical window is appeared, just click “q” to quit or, otherwise choose “File”->“CalcTD and Quit”. Do not the window cross at the right window corner — it will close the program without TD calculations. You can use also other ways to perform the calculations — see MOLTRAN Manual for further details.
After the execution is finished, the output file Moltran-Sample1.out will be created. Open it and inspect the results. At the beginning of output file, the logo and some system information are located
*******************************************************
* MOLTRAN v.2.5 *
* (build number 686) *
* A program for molecular visualization, *
* normal modes animation, *
* and thermochemical properties evaluation. *
* *
* Originally written by Stanislav Ignatov *
* Theoretical Chemistry Group *
* N.I.Lobachevsky State University of Nizhny Novgorod *
* ignatov@ichem.unn.runnet.ru *
* http://ichem.unn.runnet.ru/tcg *
* Nizhny Novgorod, Russia, 1999-2004 *
*******************************************************
Input file :Moltran-Sample1.txt
Output file :Moltran-Sample1.log
TD specifications file :none
Current directory :D:\Projects\WinMoltran\Source\WebPage\
Moltran home directory :C:\Program Files\Moltran\
Configuration file :C:\Program Files\Moltran\MolTran.cfg
Fragment database :C:\Program Files\Moltran\Moltran.fdb
Input file format : Gaussian 98 detected
After the execution is finished, the output file Moltran-Sample1.out will be created. Open it and inspect the results. At the beginning of output file, the logo and some system information are located
Step = 0
Standard orientation:
---------------------------------------------------------------------
Center Atomic Atomic Coordinates (Angstroms)
Number Number Type X Y Z
---------------------------------------------------------------------
1 14 0 0.002622 0.007912 0.000022
2 9 0 -0.592291 1.462130 -0.005416
3 9 0 -0.541297 -0.759036 1.267762
4 9 0 -0.536589 -0.766946 -1.264925
5 8 0 1.605810 0.139262 0.002452
6 1 0 2.148396 -0.650188 0.003285
---------------------------------------------------------------------
Step = 1
Standard orientation:
---------------------------------------------------------------------
Center Atomic Atomic Coordinates (Angstroms)
Number Number Type X Y Z
---------------------------------------------------------------------
1 14 0 0.002596 0.007960 0.000019
2 9 0 -0.593620 1.464034 -0.005418
3 9 0 -0.541932 -0.760297 1.269788
4 9 0 -0.537243 -0.768207 -1.266948
5 8 0 1.607746 0.139399 0.002452
6 1 0 2.156846 -0.646406 0.003321
---------------------------------------------------------------------…etc. (4 more coordinate sets)…
Step = 6
Standard orientation:
---------------------------------------------------------------------
Center Atomic Atomic Coordinates (Angstroms)
Number Number Type X Y Z
---------------------------------------------------------------------
1 14 0 0.003045 0.007644 0.000019
2 9 0 -0.586240 1.467400 -0.005417
3 9 0 -0.546203 -0.757879 1.270605
4 9 0 -0.541588 -0.765800 -1.267765
5 8 0 1.608317 0.131687 0.002445
6 1 0 2.157117 -0.654006 0.003357
---------------------------------------------------------------------After the coordinates are read-in, MOLTAN is looking for the energies and gradients. MOLTRAN analyzes them and choose the “base” optimization cycle, i.e. cycle which will be used as a ground state of molecule for the further TD calculations. Usually, this level is that one with the lowest value of electronic energy. Sometimes, however, the procedure can fail. Thus, it is useful to check the program decision manually. In the current example, the program chooses the 6-th optimization cycle as a “base” one and will use its coordinates in the further work.
************ READING FROM INPUT FILE IS FINISHED ************
Coordinate sets found: 6 Energies and gradients at each cycles:
Step Energy GMax Grms
---------------------------------------------------------------------
0 -665.2665743600 0.002604 0.001286
1 -665.2666060070 0.000697 0.000318
2 -665.2666082900 0.000257 0.000080
3 -665.2666081260 0.000242 0.000114
4 -665.2666084800 0.000090 0.000031
5 0.0000000000 999999.000000 0.000000
6 -665.2666084800 0.000090 0.000031
Lowest Energy: Step 4 Energy = -665.26660848
Lowest GMax : Step 4 GMax = 0.000090
Lowest GRms : Step 5 GRms = 0.000000For the chosen base level, the coordinates and atomic masses are printed out, together with intermolecular distances.
Final coordinates (A) and atomic masses (AMU), for cycle: 6
------------------------------------------------------------------------------
Si1 14 0.003045 0.007644 0.000019 27.976930
F2 9 -0.586240 1.467400 -0.005417 18.998400
F3 9 -0.546203 -0.757879 1.270605 18.998400
F4 9 -0.541588 -0.765800 -1.267765 18.998400
O5 8 1.608317 0.131687 0.002445 15.994910
H6 1 2.157117 -0.654006 0.003357 1.007830
------------------------------------------------------------------------------
Mass center, mol.mass: -0.037459 0.005804 -0.000058 101.974865
Distance matrix (A):
1 Si1 2 F2 3 F3 4 F4 5 O5
--------------------------------------------------------------------
1 Si1 0.000000
2 F2 1.574222 0.000000
3 F3 1.581799 2.565483 0.000000
4 F4 1.581808 2.565677 2.538387 0.000000
5 O5 1.610059 2.569099 2.653585 2.653490 0.000000
6 H6 2.253401 3.467917 2.987415 2.985173 0.958382
6 H6
--------------------------------------------------------------------
6 H6 0.000000
After that, the chosen coordinates are reduced to principal axes and principal moments of inertia and the corresponding rotational constants are printed out (in different units) together with the principal axes themselves and the molecular coordinates reduced to the principal axes.
Principal moments of inertia and rotational constants:
---------------------------------------------------------------
Ia,Ib,Ic, a.u. : 454.809198 450.940484 441.017549
Ia,Ib,Ic, amu*A^2: 127.359546 126.276195 123.497491
A, B, C, a.u. : 0.002199 0.002218 0.002267
A, B, C, GHz : 3.968126 4.002169 4.092218
Principal axes : 1 2 3
X 0.006686 -0.704364 0.709807
Y -0.004524 0.709794 0.704394
Z 0.999967 0.007920 -0.001559
Molecular coordinates in principal axes (A)
---------------------------------------------------------------
Si1 14 0.000340 -0.027222 0.030046
F2 9 -0.015640 1.423933 0.640019
F3 9 1.270675 -0.173652 -0.901025
F4 9 -1.267545 -0.202630 -0.899371
O5 8 0.012937 -1.069854 1.256851
H6 1 0.021072 -2.014083 1.092954
---------------------------------------------------------------Then, the symmetry properties of the molecule are studied and the summary of molecular parameters are printed out. It shows the symmetry group, the approximate symmetry group, and the rotational symmetry number corresponding to the current (exact) symmetry group. In the current example, the approximate symmetry of SiF3OH molecule is Cs whereas the exact group is only C1 due to the small distortions of the atom positions resulted from the non-precise molecular optimization performed with Gaussian.
Rotational Symmetry : Asymmetric Top
Symmetry Index : 40000000
Symmetry Group : C1 (will be used in further analysis)
Approximate Symmetry : Cs
Rotational Symmetry Number: 1Below, the summary of molecular parameters are printed out showing the data found in the input file. By default, temperature and pressure for further TD calculations are ser to the standard conditions. These conditions can be set to other values using command string options /TT and /PP or with menu commands “Calculations”->“Thermodynamics”: options “Temperature” and “Pressure”. Using the command-string options, you can also set other values of symmetry numbers, scaling factors and other calculation parameters (see program manual for further details).
****** PARAMETERS IN EFFECT *******
Temperature, K, set to : 298.15
Pressure, Pa, set to : 101325.00
Rotation number set to : 1
Internal rotations found: 0
Coordinate sets found : 7
Frequencies found : 18
Num. of imaginary freqs : 0
Frequencies scaled by : 1.0000
Number of atoms : 6
Molecular mass : 101.9749
Symmetry group : C1
Stoichiometry : H 1
O 1
F 3
Si 1
***********************************At this point, the interactive work with MOLTRAN graphical interface is finished and the program prints the parameters of last view (i.e. rotation matrix of molecular coordinate system (MCS) relatively to the laboratory one (LCS)), view angles (the Euler angles for rotation MCS to LCS), shift lengths MCS relatively to MCS, the zooming factor, and view command summarizing all these options. The view command is a string written in the input format of MOLTRAN suitable for putting to the command string of further MOLTRAN runs. Thus, running MOLTRAN with this command will produce the same view at the screen as it was obtained last time. Moreover, the coordinates of molecule is printed both in MCS and LCS.
************ INTERACTIVE WORK IS FINISHED ************
Last view parameters:
Rotation matrix: 1.00000 0.00000 0.00000
: 0.00000 1.00000 0.00000
: 0.00000 0.00000 1.00000
View Angles : 0.0 0.0 0.0 (Discrep: 0.000000)
ShiftX,Y, Zoom : 0.00000 0.00000 1.00000
View command :/v0.0:0.0:0.0:0.00:0.00:1.00
Last view coordinates and bonds in a molecular (moving) frame, (A):
-------------------------------------------------------------------------------
Si1 14 0.003045 0.007644 0.000019 2 3 4 5 0 0 0 0 0 0 0 0 0 0 0 0
F2 9 -0.586240 1.467400 -0.005417 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
F3 9 -0.546203 -0.757879 1.270605 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
F4 9 -0.541588 -0.765800 -1.267765 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
O5 8 1.608317 0.131687 0.002445 1 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0
H6 1 2.157117 -0.654006 0.003357 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-------------------------------------------------------------------------------
Last view coordinates and bonds in a laboratory (fixed) frame, (A):
-------------------------------------------------------------------------------
Si1 14 0.003045 0.007644 0.000019 2 3 4 5 0 0 0 0 0 0 0 0 0 0 0 0
F2 9 -0.586240 1.467400 -0.005417 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
F3 9 -0.546203 -0.757879 1.270605 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
F4 9 -0.541588 -0.765800 -1.267765 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
O5 8 1.608317 0.131687 0.002445 1 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0
H6 1 2.157117 -0.654006 0.003357 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-------------------------------------------------------------------------------
Then, the results of TD calculations are printed out. The program gives again the key options used in the calculation — T, P, rotational symmetry number and molecular mass.
******************** THERMOCHEMICAL PROPERTIES EVALUATION ********************
Molecular geometry corresponds to the last coordinate set - Step No. 6
Temperature : 298.15 K
Pressure : 101325.00 Pa
Rot. number : 1
Molecular mass: 101.97 amuThe electronic contribution is calculated using the value of molecular multiplicity found in the input file. Check this value. If you will find it is wrong, you can override it using the /mult command string option (see manual for details). The electronic contributions to partition function (called here Q) is given, together with contributions to heat capacity (Cp and Cv), internal energy (U), enthalpy (H), entropy (S) and the Gibbs free energy (G).
*** Electronic contribution ***
Spin multiplicity of molecule = 1
Qelec = 1.00000E+00 ln(Qelec)= 0.00000 lg(Qelec)= 0.00000
CVelec= 0.000 J/K/mol 0.000 cal/K/mol 0.00000000 Hartree/K
CPelec= 0.000 J/K/mol 0.000 cal/K/mol 0.00000000 Hartree/K
Uelec = 0.000 kJ/mol 0.000 kcal/mol 0.00000000 Hartree
Helec = 0.000 kJ/mol 0.000 kcal/mol 0.00000000 Hartree
Selec = 0.000 J/K/mol 0.000 cal/K/mol 0.00000000 Hartree/K
Gelec = 0.000 kJ/mol 0.000 kcal/mol 0.00000000 HartreeFor rotational contribution, the principal moments are printed again, and the decision are made on the kind of molecule (here, asymmetric non-linear top). The rotational contributions are then calculated and printed out:
*** Translational contribution ***
Qtran = 4.04757E+07 ln(Qtran)= 17.51621 lg(Qtran)= 7.60719
CVtran= 12.472 J/K/mol 2.981 cal/K/mol 0.00000475 Hartree/K
CPtran= 20.786 J/K/mol 4.968 cal/K/mol 0.00000792 Hartree/K
Utran = 3.718 kJ/mol 0.889 kcal/mol 0.00141631 Hartree
Htran = 6.197 kJ/mol 1.481 kcal/mol 0.00236052 Hartree
Stran = 166.424 J/K/mol 39.776 cal/K/mol 0.00006339 Hartree/K
Gtran = -43.422 kJ/mol -10.378 kcal/mol -0.01653896 Hartree For rotational contribution, the principal moments are printed again, and the decision are made on the kind of molecule (here, asymmetric non-linear top). The rotational contributions are then calculated and printed out:
*** Rotational contribution ***
Principal moments of inertia, a.u.
454.8091983
450.9404840
441.0175495
Asymmetric top
Non-linear molecule
Qrot = 1.07659E+05 ln(Qrot)= 11.58672 lg(Qrot)= 5.03205
CVrot= 12.472 J/K/mol 2.981 cal/K/mol 0.00000475 Hartree/K
CProt= 12.472 J/K/mol 2.981 cal/K/mol 0.00000475 Hartree/K
Urot = 3.718 kJ/mol 0.889 kcal/mol 0.00141631 Hartree
Hrot = 3.718 kJ/mol 0.889 kcal/mol 0.00141631 Hartree
Srot = 108.809 J/K/mol 26.006 cal/K/mol 0.00004144 Hartree/K
Grot = -28.723 kJ/mol -6.865 kcal/mol -0.01094028 Hartree For the calculation of the total vibrational contribution, the vibrational frequencies found in the input file are printed, together with IR intensities, scaled values of frequency, and reduced mass.
It should be noted that calculation of reduced mass after on the basis of GAMESS output file requires the additional file containing the molecular hessian (also provided by GAMESS). By default, reduced masses calculated on the basis of GAMESS output produces the wrong values (all reduced masses are set to 1.0).
Farther in the table, “Used in TD” flag shows whether the current vibration contributes to the TD functions. By default, six initial frequencies are considered as translations and rotations and will not be taken into account. However, user can override this decision using the .tdi-file with additional options for TD calculations described in the Manual.
For each frequency, MOLTRAN gives the contributions of the corresponding vibration to entropy, ZPE of given mode, enthalpy (H-H0), enthalpy including ZPE (Hvib), Gibbs free energy (including ZPE), heat capacity (Cvib), and the contributions to the total partition function (Q). At the bottom of table, the sum of contributions for all the vibrations taken into account are given.
*** Vibrational contribution ***
Scaling factor for frequencies: 1.0000
No. Frequency Intensity Scaled Reduced Used Theta Svib ZPE (H-H0) Hvib Gvib Cvib Qvib
cm-1 km/mol Freq Mass inTD? K J/K/mol kJ/mol kJ/mol kJ/mol kJ/mol J/K/mol
----------------------------------------------------------------------------------------------------------------------
1 0.000 0.000 0.000 0.00 0 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00000E+00
2 0.000 0.000 0.000 0.00 0 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00000E+00
3 0.000 0.000 0.000 0.00 0 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00000E+00
4 0.000 0.000 0.000 0.00 0 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00000E+00
5 0.000 0.000 0.000 0.00 0 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00000E+00
6 0.000 0.000 0.000 0.00 0 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.00000E+00
7 113.424 102.367 113.424 1.19 1 163.191 13.428 0.678 1.862 2.541 -1.463 8.110 2.37239E+00
8 262.689 1.702 262.689 11.45 1 377.950 6.878 1.571 1.231 2.802 0.752 7.285 1.39177E+00
9 276.356 18.597 276.356 6.46 1 397.614 6.511 1.653 1.183 2.836 0.895 7.184 1.35782E+00
10 360.778 40.805 360.778 7.63 1 519.078 4.681 2.158 0.918 3.076 1.680 6.498 1.21263E+00
11 373.713 43.731 373.713 18.24 1 537.690 4.454 2.235 0.882 3.117 1.789 6.385 1.19722E+00
12 382.993 51.468 382.993 17.31 1 551.041 4.298 2.291 0.857 3.147 1.866 6.303 1.18697E+00
13 762.595 6.608 762.595 9.98 1 1097.203 1.004 4.561 0.236 4.797 4.498 2.989 1.02587E+00
14 814.258 175.792 814.258 1.42 1 1171.535 0.820 4.870 0.195 5.066 4.821 2.626 1.02005E+00
15 960.531 231.101 960.531 22.61 1 1381.988 0.459 5.745 0.113 5.858 5.721 1.768 1.00980E+00
16 989.905 264.957 989.905 19.73 1 1424.251 0.408 5.921 0.101 6.022 5.900 1.625 1.00849E+00
17 1026.792 186.919 1026.792 6.05 1 1477.323 0.351 6.142 0.087 6.229 6.124 1.459 1.00710E+00
18 3908.961 138.588 3908.961 1.07 1 5624.117 0.000 23.381 0.000 23.381 23.381 0.000 1.00000E+00
----------------------------------------------------------------------------------------------------------------------
Total for 12 vibrations 43.292 61.207 7.664 68.871 55.963 52.232 8.29156E+00
Now, the total (electronic+translational+rotational+vibrational) contributions to the TD functions are printed.
*** Total for ELEC+TRANS+ROT+VIBR contributions ***
Qtot = 3.61310E+13 ln(Qtot)= 31.21817 lg(Qtot)= 13.55788
CVtot= 77.176 J/K/mol 18.445 cal/K/mol 0.00002940 Hartree/K
CPtot= 85.490 J/K/mol 20.433 cal/K/mol 0.00003256 Hartree/K
ZPEtot 61.207 kJ/mol 14.629 kcal/mol 0.02331303 Hartree
Utot = 76.308 kJ/mol 18.238 kcal/mol 0.02906476 Hartree
Htot = 78.787 kJ/mol 18.830 kcal/mol 0.03000897 Hartree
Stot = 318.525 J/K/mol 76.129 cal/K/mol 0.00012132 Hartree/K
Gtot = -16.182 kJ/mol -3.868 kcal/mol -0.00616343 Hartree The values above are “absolute TD values”, i.e. values of TD functions counted off from the total (electronic+numclear) energy of molecule. In order to calculate the real values of TD functions for i.e. chemical reactions, these values should be summed with the molecular energy obtained by quantum chemical method.
Below, MOLTRAN gives the corrected values of molecular total energy (found in the input file as described above). Because the base (minimum) energy found in the file can be determined incorrectly (e.g. when finishing cycles of the input file were corrupted), it is strongly recommended to check the program decision manually.
The bottom values give the energy of molecule corrected to ZPE, U, H, and G. They can be used in calculations of thermodynamics of reactions with participation of the given molecule
*** Total energy corrected by TD functions ****
Minimum electronic-nuclear energy was taken from the input file at step: 4
Minimum Etot: -665.26660848 (Please check the program decision manually!)
Etot = -665.26660848
Etot+ZPEtot = -665.24329545
Etot+Utot = -665.23754372
Etot+Htot = -665.23659951
Etot+Gtot = -665.27277191Finally, the condenced table of TD functions are given, calculated for wide range of temperatures. By default, T ranges from 10 K to 500 K. However, the required range and step size can be set using the command-string options /thermo, usnig the .tdi-file options, or directly from the menu “Calculations”->Thermodynamics” of MOLTRAN graphical interface.
Thermodynamics at various temperatures (w/o internal rotations):
Temperature CV CP U H S G Q ln(Q)
K J/K/mol J/K/mol kJ/mol kJ/mol J/K/mol kJ/mol
-------------------------------------------------------------------------------------------------
10.000 24.944 33.258 61.456 61.539 162.323 59.916 5.51448E+06 15.52289
20.000 25.102 33.416 61.706 61.872 185.397 58.165 8.82568E+07 18.29576
30.000 26.028 34.342 61.961 62.211 199.094 56.238 4.48622E+08 19.92169
40.000 27.470 35.785 62.228 62.561 209.165 54.194 1.43618E+09 21.08525
50.000 29.103 37.418 62.511 62.927 217.322 52.061 3.58697E+09 22.00057
60.000 30.948 39.262 62.811 63.310 224.303 49.852 7.67820E+09 22.76165
70.000 33.057 41.371 63.131 63.713 230.511 47.577 1.48037E+10 23.41814
80.000 35.404 43.719 63.473 64.138 236.186 45.243 2.64785E+10 23.99960
90.000 37.909 46.223 63.840 64.588 241.479 42.855 4.47787E+10 24.52500
100.000 40.478 48.792 64.232 65.063 246.482 40.415 7.25225E+10 25.00716
110.000 43.035 51.349 64.649 65.564 251.253 37.926 1.13498E+11 25.45505
120.000 45.529 53.843 65.092 66.090 255.828 35.390 1.72748E+11 25.87510
130.000 47.931 56.245 65.559 66.640 260.233 32.810 2.56927E+11 26.27206
140.000 50.229 58.544 66.050 67.214 264.486 30.186 3.74735E+11 26.64948
150.000 52.424 60.739 66.564 67.811 268.601 27.521 5.37463E+11 27.01013
160.000 54.522 62.837 67.098 68.429 272.588 24.815 7.59656E+11 27.35613
170.000 56.533 64.847 67.654 69.067 276.458 22.069 1.05993E+12 27.68922
180.000 58.465 66.779 68.229 69.725 280.220 19.286 1.46195E+12 28.01079
190.000 60.327 68.641 68.823 70.403 283.881 16.465 1.99568E+12 28.32201
200.000 62.127 70.441 69.435 71.098 287.448 13.609 2.69879E+12 28.62382
210.000 63.870 72.185 70.065 71.811 290.927 10.717 3.61847E+12 28.91707
220.000 65.561 73.876 70.712 72.542 294.324 7.790 4.81356E+12 29.20246
230.000 67.203 75.517 71.376 73.289 297.644 4.830 6.35706E+12 29.48059
240.000 68.797 77.111 72.056 74.052 300.892 1.838 8.33925E+12 29.75199
250.000 70.345 78.660 72.752 74.831 304.072 -1.187 1.08713E+13 30.01715
260.000 71.849 80.163 73.463 75.625 307.186 -4.244 1.40897E+13 30.27646
270.000 73.307 81.622 74.189 76.434 310.239 -7.331 1.81611E+13 30.53030
280.000 74.721 83.036 74.929 77.257 313.233 -10.448 2.32889E+13 30.77900
290.000 76.091 84.406 75.683 78.094 316.171 -13.595 2.97200E+13 31.02284
300.000 77.418 85.732 76.451 78.945 319.055 -16.771 3.77535E+13 31.26210
310.000 78.701 87.015 77.231 79.809 321.887 -19.976 4.77504E+13 31.49701
320.000 79.940 88.255 78.025 80.685 324.669 -23.209 6.01454E+13 31.72779
330.000 81.138 89.452 78.830 81.574 327.404 -26.469 7.54605E+13 31.95463
340.000 82.293 90.608 79.647 82.474 330.091 -29.757 9.43204E+13 32.17772
350.000 83.408 91.722 80.476 83.386 332.734 -33.071 1.17472E+14 32.39722
360.000 84.482 92.796 81.315 84.308 335.333 -36.411 1.45803E+14 32.61328
370.000 85.516 93.831 82.165 85.242 337.890 -39.778 1.80371E+14 32.82604
380.000 86.513 94.827 83.025 86.185 340.405 -43.169 2.22429E+14 33.03563
390.000 87.472 95.786 83.895 87.138 342.881 -46.586 2.73457E+14 33.24217
400.000 88.395 96.709 84.775 88.101 345.318 -50.027 3.35204E+14 33.44576
410.000 89.282 97.597 85.663 89.072 347.717 -53.492 4.09729E+14 33.64652
420.000 90.136 98.451 86.560 90.052 350.079 -56.981 4.99452E+14 33.84453
430.000 90.958 99.272 87.466 91.041 352.405 -60.493 6.07208E+14 34.03989
440.000 91.748 100.062 88.379 92.038 354.697 -64.029 7.36318E+14 34.23268
450.000 92.507 100.822 89.301 93.042 356.954 -67.587 8.90660E+14 34.42298
460.000 93.238 101.552 90.229 94.054 359.178 -71.168 1.07476E+15 34.61087
470.000 93.940 102.254 91.165 95.073 361.369 -74.771 1.29386E+15 34.79641
480.000 94.616 102.930 92.108 96.099 363.529 -78.395 1.55409E+15 34.97967
490.000 95.266 103.580 93.057 97.132 365.658 -82.041 1.86253E+15 35.16071
500.000 95.891 104.206 94.013 98.171 367.757 -85.708 2.22738E+15 35.33960
-------------------------------------------------------------------------------------------------