Hello Everyone,
I have a question regarding the determination of thermodynamic quantities using the internal program freeh. I was trying to use frequency dependent scaling factors and wanted to recalculate thermodynamic properties by using the frequencies from my aoforce calculations.
I used the equations given in the output of the freeh calculation.
However, I was only able to recalculate:
qvib = product(i) 1/(1-exp(-e(i)/kT) and
chem.pot. = ZPE-RT*ln(qtrans*qrot*qvib) and
the ZPE itself.
Unfortunately I could not get the same results for the internal energy E:
energy=ZPE + 3RT + sum(i) e(i)*(1+exp(-e(i)/kT))/2*(1-exp(-e(i)/kT)
Frequencies:
mode symmetry wave number intensity selection rules
cm**(-1) km/mol
1 0.00 0.0000000 - -
2 0.00 0.0000000 - -
3 0.00 0.0000000 - -
4 0.00 0.0000000 - -
5 0.00 0.0000000 - -
6 0.00 0.0000000 - -
7 a 76.29 0.4158000 YES YES
8 a 430.57 4.6595700 YES YES
9 a 545.01 29.8828900 YES YES
10 a 590.45 35.8843700 YES YES
11 a 661.64 ********** YES YES
12 a 856.86 4.4155700 YES YES
13 a 1000.43 81.9322100 YES YES
14 a 1070.80 7.6460300 YES YES
15 a 1203.96 ********** YES YES
16 a 1337.60 32.6408900 YES YES
17 a 1411.57 50.2645300 YES YES
18 a 1474.99 15.7249400 YES YES
19 a 1478.70 10.8687900 YES YES
20 a 1820.67 ********** YES YES
21 a 3051.63 1.5803000 YES YES
22 a 3112.18 4.2956400 YES YES
23 a 3161.39 4.9184500 YES YES
24 a 3736.08 55.9035900 YES
My calculations:
ei = waveNumber(mode_i)*c*h; % [1/cm --> J]
E = ZPE + 3*R*T + sum(ei.*(1+exp(-ei./(k*T)))/2.*(1-exp(-ei./(k*T)))); % calculation of E
When I tried to compare the equation above with those from Turbomole theory I somehow could not see the connection of both equations.
(
http://hincklab.uthscsa.edu/html/soft_packs/msi_docs/insight980/turbo/2_Theory.html - equation 44)
Can anyone help? I tried several ways as well via the helmholtz energy E = -kT (d(A/T)/dT). Maybe these are all due to wrong calculations but I checked the code several times.
But maybe one of you can find a general problem in my approach.
Thanks for your help!
Hannes