Also in physconst, one can do math in #define statements, so should we define only the fundamental ones, then compute the derived ones in terms of those to avoid errors? Ignore the documentation complication for now.

Another upvote for the new version. I think it is important to at some point make the constants derive from one another (it increases that odds that floating point equalities like 2*pc_pi==pc_twopi actually work), but I also see it as a low priority TODO.

While we are on the topic of units and stuff, I also would like to bring to people’s attention C++11 SI-Prefixes and suggest that we start using built-in language constructs for such matters (when C-side). And if we really want to go nuts C++11 literals (“units”) a simple application to radians/degrees, but I will admit that this does add to the interface.

I think wrapping units in brackets is a good idea. I would say that it is easier to write scripts that extract both energies and units from the output files if there are fewer special characters and no spaces (e.g. [kcal/molK] instead of [kcal/mol K] or [kcal mol^-1 K^-1]). I usually prefer [au] for Hartrees, but [Ha]/[mHa] is probably best since SAPT uses milliHartrees. Using [Eh] seems ambiguous to me since E with a subscript is often used for a component of the total energy. For instance, if you label data as “Energy (Eh)”, it could look like either a unit or a type of energy.

If you need people to help with the formatting updates, I would volunteer some of my time.

keeps same quantity with multiple units on same line to avoid reprinting blocks w/diff units

tries to be clear on how all these numbers interrelate

Notes:

we don’t calculate Cp, but gamess does, so potentially possible

everyone uses different terminology, here’s a few to choose from if you’d like to comment

<< ZPE >>
Zero-point correction to Energy
Electronic Energy at 0 [K]
Sum of electronic and zero point energies
<< U >>
Thermal energy
Thermal correction to Energy
Internal energy
Sum of electronic and thermal energies
Electronic Energy at 298.15 [K]
<< H >>
thermal correction to Enthalpy
Sum of electronic and thermal Enthalpies
Enthalpy at 298.15 [K]
<< G >>
thermal correction to Gibbs Free Energy
Sum of electronic and thermal Free Energies
Free Enthalpy at 298.15 [K]

next post will have samples from other programs for comparison

so what comments/approval/disapproval do you have for the below?

==> Components <==
Entropy, S
Electronic S 0.000 [cal/(mol K)] 0.000 [J/(mol K)] 0.00000000 [mEh/K] (multiplicity = 1)
Translational S 38.979 [cal/(mol K)] 163.089 [J/(mol K)] 0.06211698 [mEh]K] (mol. weight = 16.0400)
Rotational S 22.945 [cal/(mol K)] 96.003 [J/(mol K)] 0.03656518 [mEh/K] (rotational # = 12)
Vibrational S 4.460 [cal/(mol K)] 18.661 [J/(mol K)] 0.00710746 [mEh/K]
Total S 66.385 [cal/(mol K)] 277.753 [J/(mol K)] 0.10579120 [mEh/K]
Constant volume heat capacity, Cv
Electronic Cv 0.000 [cal/(mol K)] 0.000 [J/(mol K)] 0.00000000 [mEh/K]
Translational Cv 2.981 [cal/(mol K)] 12.472 [J/(mol K)] 0.00475052 [mEh/K]
Rotational Cv 2.981 [cal/(mol K)] 12.472 [J/(mol K)] 0.00475052 [mEh/K]
Vibrational Cv 11.351 [cal/(mol K)] 47.494 [J/(mol K)] 0.01808897 [mEh/K]
Total Cv 17.313 [cal/(mol K)] 72.437 [J/(mol K)] 0.02759002 [mEh/K]
Constant pressure heat capacity, Cp
Electronic Cp 0.000 [cal/(mol K)] 0.000 [J/(mol K)] 0.00000000 [mEh/K]
Translational Cp
Rotational Cp 2.981 [cal/(mol K)] 12.472 [J/(mol K)] 0.00475052 [mEh/K]
Vibrational Cp 11.351 [cal/(mol K)] 47.494 [J/(mol K)] 0.01808897 [mEh/K]
Total Cp
==> Energy Analysis <==
Raw electronic energy, E0
Total E0, Electronic energy at well bottom at 0 [K] -229.41921654 [Eh]
Zero-point energy, ZPE = Sum_i nu_i / 2
Electronic ZPE 0.000 [kcal/mol] 0.000 [kJ/mol] 0.00000000 [Eh]
Translational ZPE 0.000 [kcal/mol] 0.000 [kJ/mol] 0.00000000 [Eh]
Rotational ZPE 0.000 [kcal/mol] 0.000 [kJ/mol] 0.00000000 [Eh]
Vibrational ZPE 63.053 [kcal/mol] 263.813 [kJ/mol] 0.10048094 [Eh] 22053.013 [cm^-1]
Correction ZPE 63.053 [kcal/mol] 263.813 [kJ/mol] 0.10048094 [Eh] 22053.013 [cm^-1]
Total ZPE, Electronic energy at 0 [K] -229.31873560 [Eh]
Thermal Energy, E (includes ZPE)
Electronic E 0.000 [kcal/mol] 0.000 [kJ/mol] 0.00000000 [Eh]
Translational E 0.889 [kcal/mol] 3.718 [kJ/mol] 0.00141671 [Eh]
Rotational E 0.889 [kcal/mol] 3.718 [kJ/mol] 0.00141671 [Eh]
Vibrational E 64.046 [kcal/mol] 267.970 [kJ/mol] 0.10206380 [Eh]
Correction E 65.824 [kcal/mol] 275.407 [kJ/mol] 0.10489696 [Eh]
Total E, Electronic energy at 298.15 [K] -229.31431957 [Eh]
Enthalpy, H = E + k_b * T
Electronic H 0.000 [kcal/mol] 0.000 [kJ/mol] 0.00000000 [Eh]
Translational H 0.889 [kcal/mol] 3.718 [kJ/mol] 0.00141671 [Eh]
Rotational H 0.889 [kcal/mol] 3.718 [kJ/mol] 0.00141671 [Eh]
Vibrational H 64.639 [kcal/mol] 270.448 [kJ/mol] 0.10300799 [Eh]
Correction H 66.416 [kcal/mol] 277.8860 [kJ/mol] 0.10584115 [Eh]
Total H, Enthalpy at 298.15 [K] -229.31337538 [Eh]
Gibbs free energy, G = H - T * S
Electronic G 0.000 [kcal/mol] 0.000 [kJ/mol] 0.00000000 [Eh]
Translational G -10.733 [kcal/mol] -44.905 [kJ/mol] -0.01710346 [Eh]
Rotational G -5.952 [kcal/mol] -24.903 [kJ/mol] -0.00948520 [Eh]
Vibrational G 63.308 [kcal/mol] 264.882 [kJ/mol] 0.10088809 [Eh]
Correction G 46.624 [kcal/mol] 195.074 [kJ/mol] 0.07429966 [Eh]
Total G, Free enthalpy at 298.15 [K] -229.34491687 [Eh]

### http://www.msg.ameslab.gov/tutorials/nh3.hess.log.pdf
-------------------------------
THERMOCHEMISTRY AT T= 298.15 K
-------------------------------
USING IDEAL GAS, RIGID ROTOR, HARMONIC NORMAL MODE APPROXIMATIONS.
P= 1.01325E+05 PASCAL.
ALL FREQUENCIES ARE SCALED BY 1.00000
THE MOMENTS OF INERTIA ARE (IN AMU*BOHR**2)
6.38706 6.38706 9.55178
THE ROTATIONAL SYMMETRY NUMBER IS 3.0
THE ROTATIONAL CONSTANTS ARE (IN GHZ)
282.30345 282.30345 188.76982
THE HARMONIC ZERO POINT ENERGY IS (SCALED BY 1.000)
.040127 HARTREE/MOLECULE 8806.922200 CM**-1/MOLECULE
25.180279 KCAL/MOL 105.354289 KJ/MOL
Q LN Q
ELEC. 1.00000E+00 .000000
TRANS. 2.76149E+06 14.831281
ROT. 7.44840E+01 4.310585
VIB. 1.00119E+00 .001190
TOT. 2.05932E+08 19.143056
E H G CV CP S
KJ/MOL KJ/MOL KJ/MOL J/MOL-K J/MOL-K J/MOL-K
ELEC. .000 .000 .000 .000 .000 .000
TRANS. 3.718 6.197 -36.766 12.472 20.786 144.099
ROT. 3.718 3.718 -10.686 12.472 12.472 48.312
VIB. 105.375 105.375 105.351 .500 .500 .080
TOTAL 112.812 115.291 57.900 25.443 33.757 192.491
E H G CV CP S
KCAL/MOL KCAL/MOL KCAL/MOL CAL/MOL-K CAL/MOL-K CAL/MOL-K
ELEC. .000 .000 .000 .000 .000 .000
TRANS. .889 1.481 -8.787 2.981 4.968 34.441
ROT. .889 .889 -2.554 2.981 2.981 11.547
VIB. 25.185 25.185 25.180 .119 .119 .019
TOTAL 26.963 27.555 13.838 6.081 8.068 46.006
......END OF NORMAL COORDINATE ANALYSIS......
STEP CPU TIME = .15 TOTAL CPU TIME = 3.0 ( .0 MIN)
TOTAL WALL CLOCK TIME= 3.0 SECONDS, CPU

Molpro

FREQUENCIES * CALCULATION OF THERMODYNAMICAL PROPERTIES
Temperature 298.150 [K] Pressure 1.00000 [atm]
Atom 1: C Mass 12.01100
Atom 2: H Mass 1.00794
Atom 3: H Mass 1.00794
Atom 4: H Mass 1.00794
Atom 5: H Mass 1.00794
Molecular Mass: 16.04276 [a.u.]
Moments of Inertia 11.25587 11.25587 11.25587 [a.u.]
Point Group C2V Order of principal axis 2
Rotational Symmetry factor 2.0
Rotational Temperatures 7.69484 7.69484 7.69484 [K]
Rotational Constants 160.33541 160.33541 160.33541 [GHz]
Vibrational Temperatures [K] 2187.11 2187.11 2187.11 2502.98 2502.98
4584.72 4718.87 4718.87 4718.87
Zero-Point vibrational Energy 126.001 [kJ/Mol]
30.115 [kcal/Mol]
Electronic Energy at 0 [K]: -39.976878 [H]
Electronic Energy + Zero-Point correction: -39.928886 [H]
Electronic Energy at 298.150 [K]: -39.926037 [H]
Enthalpy H at 298.150 [K]: -39.925093 [H]
Free Enthalpy G at 298.150 [K]: -39.947873 [H]
Partition Function Z log10(Z) ln(Z)
Electronic 0.100000D+01 0.000000 0.000000
Translation 0.252574D+07 6.402389 14.742046
Rotation 0.213746D+03 2.329898 5.364787
Vibration 0.100241D+01 0.001046 0.002409
Total 0.541169D+09 8.733333 20.106833
H(T)-H(0) Cv S
[kJ/Mol] [J/Mol K] [J/Mol K]
Electronic 0.000 0.000 0.000
Translation 3.718 12.472 143.359
Rotation 3.718 12.472 57.077
Vibration 0.045 1.142 0.171
Volume (RT) 2.479 0.000 0.000
Total 9.961 26.086 200.608
Thermal energies including ZPE:
H(T)-E(0) 135.962 kJ/Mol
U(T)-E(0) 133.483 kJ/Mol
H(T)-H(0) Cv S
[kcal/Mol] [cal/Mol K] [cal/Mol K]
Electronic 0.000 0.000 0.000
Translation 0.889 2.981 34.264
Rotation 0.889 2.981 13.642
Vibration 0.011 0.273 0.041
Volume (RT) 0.592 0.000 0.000
Total 2.381 6.235 47.946
Thermal energies including ZPE:
H(T)-E(0) 32.496 kcal/Mol
U(T)-E(0) 31.903 kcal/Mol

NW-Chem

### example from http://institute.loni.org/NWChem2012/documents/mp2-session.pdf
Temperature = 298.15K
Zero-Point correction to Energy = 63.088 kcal/mol ( 0.100537 au)
Thermal correction to Energy = 65.855 kcal/mol ( 0.104947 au)
Thermal correction to Enthalpy = 66.447 kcal/mol ( 0.105891 au)
Total Entropy = 64.162 cal/mol-K
- Translational = 38.962 cal/mol-K (mol. weight = 78.0469)
- Rotational = 20.753 cal/mol-K (symmetry # = 12)
- Vibrational = 4.448 cal/mol-K
Cv (constant volume heat capacity) = 17.280 cal/mol-K
- Translational = 2.979 cal/mol-K
- Rotational = 2.979 cal/mol-K
- Vibrational = 11.321 cal/mol-K

Q-Chem

STANDARD THERMODYNAMIC QUANTITIES AT 298.15 K AND 1.00 ATM
This Molecule has 0 Imaginary Frequencies
Zero point vibrational energy: 30.118 kcal/mol
Atom 1 Element C Has Mass 12.00000
Atom 2 Element H Has Mass 1.00783
Atom 3 Element H Has Mass 1.00783
Atom 4 Element H Has Mass 1.00783
Atom 5 Element H Has Mass 1.00783
Molecular Mass: 16.031320 amu
Principal axes and moments of inertia in amu*Bohr^2:
1 2 3
Eigenvalues -- 11.25464 11.25464 11.25464
X 1.00000 0.00000 0.00000
Y 0.00000 1.00000 0.00000
Z 0.00000 0.00000 1.00000
Rotational Symmetry Number is 1
The Molecule is a Spherical Top
Translational Enthalpy: 0.889 kcal/mol
Rotational Enthalpy: 0.889 kcal/mol
Vibrational Enthalpy: 30.129 kcal/mol
gas constant (RT): 0.592 kcal/mol
Translational Entropy: 34.261 cal/mol.K
Rotational Entropy: 15.019 cal/mol.K
Vibrational Entropy: 0.041 cal/mol.K
Total Enthalpy: 32.498 kcal/mol
Total Entropy: 49.321 cal/mol.K