Thermochemistry fields in ORCA

[schneiderfelipe]

Hi,

The following thermochemical values are written by ORCA when one requests a frequency calculation (this issue was inspired by #625, that discusses similar matters in Gaussian):

• [x] Temperature
• [x] Pressure
• [ ] Electronic energy
  • [X] SCF energies
  • [ ] CC energies (#806, #840)
  • [ ] Dispersion corrections (#418, #660, #664, #806)
  • [ ] Geometrical counterpoise (gCP) corrections (#806)
• [ ] Zero-point correction
• [ ] Thermal correction to (electronic) energy
• [ ] Thermal enthalpy correction (?)
• [ ] Thermal correction to Gibbs Free Energy (?)

(Above are only the terms that I believe are non-trivial to calculate from the others.)

The electronic energy is simply the "final single point energy", i.e., the SCF energy plus corrections (coupled-cluster corrections, dispersion, gCP, etc.). I tried to separate the relevant corrections and reference some related issues/PRs.

The thermal correction to the (electronic) energy is actually shown in the logfile as the three separate contributions (vibrational, rotational and translational). Do we need them separately? I'm assuming no and including only the sum in the list above (this would apply as to why not parse vibrational, rotational and translational entropies too). (As a side note, the total thermal energy in the logfile includes ZPE. Should we separate ZPE?)

So, in the end, all that I believe to be needed is marked in the following with a *:

U = E(el)* + E(ZPE)* + E(vib+rot+trans)*  [or = E(el)* + E(ZPE+vib+rot+trans)*]
G = U + kB T - T*S(el+vib+rot+trans)*

As such, cclib:

• doesn't parse all corrections of E(el) (#418, #660, #664, #806, #840),
• doesn't parse E(ZPE) and E(vib+rot+trans), or a combined E(ZPE+vib+rot+trans) at all, and
• parses S(el+vib+rot+trans) but in a non-standard way (#663).

---

The thermal enthalpy correction has a (?) in the list since it is easily reproduced. Compare the result below with the example logfile section below.

from scipy.constants import R, kilo, calorie, physical_constants, N_A
hartree = physical_constants["Hartree energy"][0]
temperature = 298.15

R * temperature / (hartree * N_A)  # 0.0009441848676268876 Eh
R * temperature / (kilo * calorie)  # 0.5924849497028442 kcal/mol

A similar comment holds for the thermal correction to Gibbs free energy. (Observe that entropies in ORCA are given multiplied by temperature, giving units of energy, see #663).

---

Below are pieces of a typical thermochemistry section (from this logfile) for reference:

--------------------------
THERMOCHEMISTRY AT 298.15K
--------------------------

Temperature         ... 298.15 K
Pressure            ... 1.00 atm
Total Mass          ... 2.02 AMU
The molecule is recognized as being linear

...

------------
INNER ENERGY
------------

...

Summary of contributions to the inner energy U:
Electronic energy                ...     -1.17581168 Eh
Zero point energy                ...      0.00988644 Eh       6.20 kcal/mol
Thermal vibrational correction   ...      0.00000000 Eh       0.00 kcal/mol
Thermal rotational correction    ...      0.00094418 Eh       0.59 kcal/mol
Thermal translational correction ...      0.00141627 Eh       0.89 kcal/mol
-----------------------------------------------------------------------
Total thermal energy                     -1.16356479 Eh


Summary of corrections to the electronic energy:
(perhaps to be used in another calculation)
Total thermal correction                  0.00236045 Eh       1.48 kcal/mol
Non-thermal (ZPE) correction              0.00988644 Eh       6.20 kcal/mol
-----------------------------------------------------------------------
Total correction                          0.01224689 Eh       7.69 kcal/mol


--------
ENTHALPY
--------

...
Total free energy                 ...     -1.16356479 Eh
Thermal Enthalpy correction       ...      0.00094421 Eh       0.59 kcal/mol
-----------------------------------------------------------------------
Total Enthalpy                    ...     -1.16262058 Eh

...

-------
ENTROPY
-------

...

Electronic entropy                ...      0.00000000 Eh      0.00 kcal/mol
Vibrational entropy               ...     -0.00000000 Eh     -0.00 kcal/mol
Rotational entropy                ...      0.00146684 Eh      0.92 kcal/mol
Translational entropy             ...      0.01334204 Eh      8.37 kcal/mol
-----------------------------------------------------------------------
Final entropy term                ...      0.01480888 Eh      9.29 kcal/mol

...

-------------------
GIBBS FREE ENERGY
-------------------

The Gibbs free energy is G = H - T*S

Total enthalpy                    ...     -1.16262058 Eh
Total entropy correction          ...     -0.01480888 Eh     -9.29 kcal/mol
-----------------------------------------------------------------------
Final Gibbs free energy         ...     -1.17742946 Eh

...