Frequency Analysis Output

=== Harmonic Frequencies ===
 Mode   Frequency (cm⁻¹)   Reduced Mass (amu)   IR Intensity (km/mol)
 ----   ----------------   -------------------   --------------------
    1        1645.82               1.0823              45.23
    2        3825.39               1.0321               2.10
    3        3942.56               1.0456              18.67

Zero-Point Energy:            0.05895 Hartree
Thermal Correction (E):       0.06123 Hartree
Thermal Correction (H):       0.06217 Hartree
Thermal Correction (G):       0.04188 Hartree
Entropy:                      0.04432 Hartree/K

Fields

Field	Description
Mode	Normal mode index
Frequency (cm⁻¹)	Harmonic vibrational frequency
Reduced Mass (amu)	Effective mass for the normal mode
IR Intensity (km/mol)	Infrared absorption intensity

Thermochemistry

Quantity	Description
Zero-Point Energy	½ Σ hνᵢ (all real modes)
Thermal Correction (E)	Vibrational + rotational + translational energy correction
Thermal Correction (H)	E + RT
Thermal Correction (G)	H - TS
Entropy	S_trans + S_rot + S_vib

Frequency Scaling

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

Imaginary Frequencies

Imaginary frequencies are printed as negative values:

 Frequencies (cm⁻¹):  -1247.3   1652.1   3825.4

A single imaginary frequency indicates a transition state. Multiple imaginary frequencies indicate a higher-order saddle point.

Symmetry Number

The symmetry number σ is auto-detected from point group:

Point Group	σ
C₁	1
Cₙ	n
Dₙ	2n
T_d	12
O_h	24
C∞ᵥ	1
D∞ₕ	2