What does the output of freeH mean?

[Dempsey]

Dear Users,

Could you please clarify what some of the values are in the freeH output, there's no information on this in the manual. The value "chem. pot." is consistent with H - TS so I think this is my Gibbs free energy, could you please confirm this? If so, what exactly is this "energy" value? I'm not familiar with the equation given here.

freeh.out:

Code: [Select]

           zero point vibrational energy
           -----------------------------
           zpe=   252.3     kJ/mol

   T        p       ln(qtrans) ln(qrot) ln(qvib) chem.pot.   energy    entropy
  (K)      (MPa)                                 (kJ/mol)   (kJ/mol) (kJ/mol/K)

 298.15   0.1000000      17.43    12.00    11.71    150.32    288.52   0.47182

   T        P              Cv            Cp       enthalpy
  (K)     (MPa)        (kJ/mol-K)    (kJ/mol-K)   (kJ/mol)
 298.15   0.1000000     0.1783006     0.1866149    291.00

 ******************************************************
 | qtrans=(m*k*T/(2*pi))^1.5*v h/(2*pi)=1a.u.(omitted)|
 |   m=mol. mass in a.u. v=vol. per mol. of ideal gas |
 | qvib=product(i) 1/(1-exp(-e(i)/kT)                 |
 |   e(i)=frequency of i-th vibrational mode          |
 | qrot=((2*pi*kT)^3*A*B*C)^0.5/(sigma*pi)            |
 |   A,B,C=moments of inertia in a.u.                 |
 | qrot=2*pi*kT*A/(sigma*pi) for lin. mol.            |
 | chem.pot.=ZPE-RT*ln(qtrans*qrot*qvib)              |
 |   ZPE=zero point vibrational energy                |
 | energy=ZPE+3RT                                     |
 |  +sum(i) e(i)*(1+exp(-e(i)/kT))/2*(1-exp(-e(i)/kT) |
 |       =3/2RT for atoms etc.                        |
 | enthalpy=energy+RT                                 |
 | entropy=(energy+RT-chem.pot.)/T                    |
 | const.vol.Heat Capacity : Cv=d(energy)/dT          |
 | const.press.Heat Capacity : Cp=d(enthalpy)/dT      |
 | These formulas are applicable only if              |
 | * rotation can be treated classically              |
 | * the molecule forms an ideal gas/solution         |
 | * the harmonic approximation to vibrational        |
 |   modes is not grossly misleading                  |
 | Electronic (SCF or MP2) energies still have        |
 | to be added to obtain "absolute potentials"        |
 | for chemical equilibrium constants.                |
 ******************************************************

Thanks,
Dempsey

[Arnim]

Hello,

indeed, chem. pot. is the Gibbs free energy.

What is defined as energy can also be called the contributions to internal thermal energy.

Best regards
Arnim

[Dempsey]

Dear Arnim,

Thanks for confirming.

Best,
Dempsey

[ym21d@fsu.edu]

I'm confused because from what I've seen, the value of chem. pot. is always a positive number. I thought that the Gibbs free energy would be negative in value.

Any help would be appreciated.

[uwe]

Hi,

freeh computes the thermal part of the Gibbs free energy only, the contribution which stems from the vibrational frequencies as well as the rotational and translational degrees of freedom. The electronic part (DFT energies) and, if needed, the free energy of solvation, needs to be added.

I find this paper very helpful: https://arxiv.org/pdf/1610.07370

[ym21d@fsu.edu]

Thank you. That is so helpful.

[ym21d@fsu.edu]

I'm a bit confused because this article discusses the Gibbs free energy of a reaction, but right now I want to calculate the Gibbs free energy of a single molecule. Is the information in the article still relevant for that?

Thank you.

[uwe]

Hi,

what is the meaning of an absolute energy of a single molecule? Absolute energies have no meaning in themselves, because they always refer to an arbitrarily defined reference (for example, energy is set to zero for non-interacting particles). Therefore, physically meaningful applications always refer to relative energy values only.

However, if you refer to the same reference, you can also use absolute values - in computational chemistry the standard enthalpy of formation is usually used. Also called the heat of formation. See for example  https://doi.org/10.1002/jcc.22918 and references therein.