Frequencies and Thermochemical Corrections

TeraChem computes the Hessian (force-constant) matrix by finite differences of analytic gradients, which yields the vibrational frequencies of a molecule. Request this with run frequencies. The output contains a thermochemical analysis at the requested temperature (300 K by default; change it with thermo_temp).

run             frequencies
method          rhf
basis           lanl2dz_ecp
coordinates     coord.xyz
charge          0
spinmult        1
thermo_temp     298.15
end

Use thermo_temp, not T0

The thermochemistry temperature is set with thermo_temp. (T0 is the initial MD temperature and has no effect on a frequency calculation.)

Restart behavior

If a frequency calculation is interrupted it can be restarted from the checkpoint stored in scr/Hessian.restart. The restart is automatic: when you request a frequency calculation, TeraChem looks for scr/Hessian.restart, and if it is found and corresponds to the same number and types of atoms, the calculation resumes where it left off.

The final Hessian is stored in scr/Hessian.bin. If this file exists when a frequency calculation is requested, TeraChem simply reads the Hessian and carries out the normal-mode analysis without recomputing it — a quick way to repeat the thermochemical analysis at a different temperature.

Finite-difference and analysis keywords

Keyword	Default	Description
`thermo_temp`	`300.0`	Temperature (K) for the vibrational/thermochemical analysis.
`nderivpoints`	`3`	Number of points in the numerical derivative of the gradient (`3`, `5`, or `7`).
`displacement`	`0.005`	Finite-difference displacement (bohr).
`maxgradnorm`	`0.001`	If the largest gradient component exceeds this at the input geometry, the run aborts (the geometry is not a stationary point).
`mincheck`	`true`	Whether to verify that the input geometry is a minimum.

Thermochemical corrections

The analysis is performed at the specified temperature and a pressure of 1 atm, and free-energy corrections are computed. The corrections are:

a) non-thermal correction — zero-point energy (ZPE);
b) thermal corrections — vibrational, rotational, and translational energies;
c) enthalpic correction;
d) entropic correction.

The internal energy \(U\) is

\[U = E_{\text{elec}} + \text{ZPE} + E_{\text{vib}} + E_{\text{rot}} + E_{\text{trans}} \, ,\]

where \(E_{\text{elec}}\), \(E_{\text{vib}}\), \(E_{\text{rot}}\), and \(E_{\text{trans}}\) are the electronic, vibrational, rotational, and translational energies. \(E_{\text{rot}}\) and \(E_{\text{trans}}\) use the number of rotational and translational degrees of freedom \(f\): \(f = 2\) for the rotational degrees of freedom of a linear molecule, otherwise \(f = 3\); for translation \(f = 3\) for all systems.

\[E_{\text{rot}} = \frac{f}{2} k_b T \, , \qquad E_{\text{trans}} = \frac{3}{2} k_b T \, .\]

The enthalpy \(H\) is

\[H = U + k_b T \, .\]

The entropic corrections are multiplied by temperature to carry units of energy:

\[T S_{\text{total}} = T S_{\text{elec}} + T S_{\text{vib}} + T S_{\text{rot}} + T S_{\text{trans}} \, ,\]

where \(S_{\text{elec}}\), \(S_{\text{vib}}\), \(S_{\text{rot}}\), and \(S_{\text{trans}}\) are the electronic, vibrational, rotational, and translational entropies. The rotational entropy is

\[S_{\text{rot}} = R \left[ \ln\!\left(\frac{8 \pi^{2}}{\sigma}\right) + \frac{3}{2} \ln\!\left(\frac{2 \pi k_b T}{h^{2}}\right) + \frac{1}{2} \ln (I_A I_B I_C) + \frac{3}{2} \right] \, ,\]

where \(I_A\), \(I_B\), \(I_C\) are the principal moments of inertia and \(\sigma\) is the symmetry number. The translational entropy is

\[S_{\text{trans}} = R \left[ \frac{3}{2} \ln\!\left(\frac{2 \pi m k_b T}{h^{2}}\right) + \ln (V) + \frac{5}{2} \right] \, ,\]

where \(V\) is the volume of the system.

The Gibbs free energy is

\[G = H - T S_{\text{total}} = U + k_b T - \left( T S_{\text{elec}} + T S_{\text{vib}} + T S_{\text{rot}} + T S_{\text{trans}} \right) \, ,\]

and the free-energy correction to the electronic energy is

\[G - E_{\text{elec}} = \text{ZPE} + E_{\text{vib}} + E_{\text{rot}} + E_{\text{trans}} + k_b T - T S_{\text{elec}} - T S_{\text{vib}} - T S_{\text{rot}} - T S_{\text{trans}} \, .\]