Thermochemistry

Harmonic frequency analysis computes:

Zero-Point Energy

$ZPE = \frac{1}{2} i \sum h ν_{i}$

Thermal Corrections (at temperature $T$ )

Component	Model
Vibrational	RRHO for all real modes ( $f > 0$ )
Rotational	Classical rigid rotor with symmetry number $σ$
Translational	Sackur–Tetrode equation

Entropy

$S = S_{trans} + S_{rot} + S_{vib}$

Gibbs Free Energy

$G = H - TS$

Symmetry Number

The symmetry number $σ$ is automatically determined from the detected point group:

Point Group	$σ$
$C_{1}$	1
$C_{n}$	$n$
$D_{n}$	$2 n$
$T_{d}$	12
$O_{h}$	24
$C_{\infty v}$	1
$D_{\infty h}$	2

Frequency Scaling

Use the Scale keyword in the FREQ section to apply a scaling factor to frequencies for ZPE and thermal corrections (e.g., Scale 0.9854 for B3LYP/6-31G*).

Usage

FREQ
  Hessian     analytical
  Temperature 298.15
  Pressure    1.0
  Scale       1.0
  SymmetryNumber 1  # auto-detected if not specified
  ...
END

Linear Molecule Detection

Linear molecule detection is automatic. The Molecule struct provides:

atomic_mass — atomic masses
total_mass — total molecular mass
center_of_mass — center of mass
inertia_tensor — moment of inertia tensor
is_linear — linear molecule detection

Rotational entropy uses the rigid rotor formula with principal moments from Molecule::inertia_tensor().

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