Frequency, IR Intensity, and Thermochemistry Output
If you calculate vibrational frequencies, any SCF calculations during the run use the RMS density change convergence criterion described in SCF Settings instead of the usual energy convergence criterion. Therefore, these SCF calculations often proceed for several more iterations than single point energy calculations do.
To compute the Hessian for vibrational frequencies, Jaguar calculates the second derivatives either analytically or numerically as the derivatives of the analytical first derivatives, depending on the type of calculation (see Vibrational Frequencies and Related Properties from Jaguar Calculations for details). Whenever numerical second derivatives are computed after an SCF calculation—whether for frequency output, for an initial Hessian, or for updating during geometry optimization—the programs nude, onee, hfig, grid, rwr, scf, der1a, rwr, and der1b run, setting up and performing SCF calculations and evaluating analytic gradients at 6Natom perturbed geometries (unless the number of perturbed geometries needed is reduced by the use of molecular symmetry). After the calculations at the perturbed geometry, Jaguar performs one final calculation at the unperturbed geometry. (The Jaguar programs run may vary slightly for non-HF calculations, as described earlier in this section.) After the data from all perturbed geometries is collected, the program nude prints the numerical first derivatives in a force table similar to the usual geometry optimization force table described earlier in this section. The output then lists the matrix indices of the most asymmetrical Hessian element before symmetrization. (The symmetrized numerical Hessian is not printed in the output, but can be found in the restart file, which is discussed in Restarting Jaguar Jobs and Using Previous Results.)
For either analytic or numerical frequency calculations, the output from the program freq contains the actual frequencies and normal modes from the computed Hessian, or from the last available Hessian (generally the initial Hessian guess) if you used the Use available Hessian choice to request vibrational frequencies. The output from the program freq first lists the harmonic frequencies in cm−1 and their symmetries (if symmetry is on for the job), then the normal modes. The system’s thermochemical properties, the constant volume heat capacity (Cv), entropy (S), enthalpy (H), internal energy (U), Gibbs free energy, and logarithm of the partition function (ln Q) are then listed for the specified pressure and temperatures, as well as at 0 K. Here is an example of this output from a vibrational frequency calculation on FOOF:
start of program freq
harmonic frequencies in cm**-1, reduced masses in amu,
force constants in mDyne/A, and
normal modes in cartesian coordinates:
IR intensities in km/mol
frequencies 208.85 555.11 707.73 1135.28 1145.49 1162.53
symmetries A A B B A A
intensities 0.48 0.22 9.07 66.55 34.46 0.43
reduc. mass 5.84 4.35 4.66 4.39 4.47 7.14
force const 0.15 0.79 1.37 3.33 3.46 5.69
f1 X 0.04113 0.08347 0.06928 0.00885 -0.00551 -0.00792
f1 Y 0.11637 0.05538 0.05480 -0.07045 0.06790 0.02561
f1 Z -0.06710 0.04044 0.02627 -0.07517 0.07145 0.02804
o1 X 0.01465 -0.03712 -0.08228 -0.01051 -0.03085 0.16720
o1 Y -0.03534 0.11710 -0.06509 0.08368 -0.10738 0.02016
o1 Z 0.07971 -0.04803 0.10082 0.10699 -0.08487 -0.03330
o2 X -0.01465 0.03712 -0.08228 -0.01051 0.03085 -0.16720
o2 Y 0.03534 -0.11710 -0.06509 0.08368 0.10737 -0.02016
o2 Z 0.07971 -0.04803 -0.10082 -0.10699 -0.08487 -0.03330
f2 X -0.04113 -0.08347 0.06928 0.00885 0.00551 0.00792
f2 Y -0.11637 -0.05538 0.05480 -0.07045 -0.06790 -0.02561
f2 Z -0.06710 0.04044 -0.02627 0.07517 0.07145 0.02804
Thermochemical properties at 1.0000 atm
rotational symmetry number: 2
rotational temperatures (K): 1.122334 0.289429 0.255263
vibrational temperatures:
mode: 1 2 3 4 5 6
temp. (K): 300.48 798.68 1018.26 1633.42 1648.10 1672.61
Thermodynamic properties calculated assuming an ideal gas
In the table below, the units for temperature
are kelvins, the units for U, H, and G are
kcal/mol and the units for Cv and S are cal/(mol K)
The zero point energy (ZPE): 7.026 kcal/mol
is not included in U, H, or G in the table below
T = 298.15 K
U Cv S H G ln(Q)
--------- --------- --------- --------- --------- ---------
trans. 0.889 2.981 38.654 1.481 -10.044 16.95158
rot. 0.889 2.981 22.198 0.889 -5.730 9.67056
vib. 0.568 4.495 3.038 0.568 -0.338 0.57052
elec. 0.000 0.000 0.000 0.000 0.000 0.00000
total 2.345 10.457 63.891 2.938 -16.111 27.19266
Total internal energy, Utot (SCFE + ZPE + U): -348.207340 hartrees
Total enthalpy, Htot (Utot + pV): -348.206396 hartrees
Total Gibbs free energy, Gtot (Htot - T*S): -348.236753 hartrees
end of program freq
If infrared intensities were calculated, several additional programs are run after the first run of the program scf. These programs compute the derivatives of the dipole moment, which are needed to calculate the IR intensities. The IR intensities are listed in the frequencies table. If Raman activities were calculated, both the scattering activities (Raman Act.) and intensities (Raman Int.) are listed in the frequencies table also.
For introductory information on thermodynamic quantities, see https://cccbdb.nist.gov/thermox.asp.