44 VIBRATIONAL FREQUENCIES (FREQUENCIES)

FREQUENCIES,method,SYMM=flag,START=rec.ifil,DUMP=dumprec.ifil;

Calculate harmonic vibrational frequencies and normal modes. To get reasonable results it is necessary to do a geometry optimization before using the frequency calculation. This option uses a hessian matrix calculated numerically from $3N$ cartesian coordinates. Z-Matrix coordinates will be destroyed on this entry. The hessian is calculated analytically or numerically by finite differences from the input coordinates. In numerical differentiation, if analytic gradients are available, these are differentiated once to build the hessian, otherwise the energy is differentiated twice. Using numerical differentiation the dipole derivatives and the IR intensities are also calculated. Note that numerical hessians cannot be computed when dummy atoms holding basis functions are present.

The accuracy of the hessian is determined by method, which can be one of the following :

ANALYTICAL

use analytical second derivatives of the energy. At present, analytical second derivatives are only possible for closed shell Hartree-Fock (HF) and MCSCF wavefunctions without symmetry. It is not yet possible to calculate IR-intensities analytically. Note that, due to technical reasons, the analytical MCSCF second derivatives have to be computed in the MCSCF-program using e.g. multi; cpmcscf,hess (see MULTI) before they can be used in FREQUENCIES. If analytical MCSCF second derivatives are available, FREQUENCIES will use them by default.

CENTRAL

use central differences/high quality force constants (default).

NUMERICAL

differentiate the energy twice, using central differences.

FORWARD

use forward differences/low quality force constants.

During the numerical calculation of the hessian, the symmetry of the molecule may be lowered. Giving SYMM=AUTO the program uses the maximum possible symmetry of the molecular wavefunction in each energy/gradient calculation, and this option therefore minimizes the computational effort. With SYMM=NO no symmetry is used during the frequency calculation (default). For single reference calculations like HF, MP2, CCSD, RCCSD the AUTO option can be safely used and is recommended. However, it should be noted that SYMM=AUTO cannot be used for MRCI calculations, since the MRCI energy is slighly different with and without symmetry (this is due to first-order interacting space restrictions and can be avoided using REF cards, see secion 21.2.6). Furthermore, certain input, which depends on orbital occupations or symmetry labels, cannot be used in frequency calculations with symmetry: for instance, the use of RESTRICT, SELECT, REF, PROJECT, LOCAL, state-averaged MCSCF will lead on an error unless the calculation is performed in $C_1$ symmetry (NOSYM option in the geometry input).

If the energy second derivatives of a given wavefunction have been calculated numerically or analytically in a previous FREQUENCIES run, the frequency calculation can be restarted from a given frequencies-record irec on file ifil using the command FREQUENCIES,START=irec.ifil; If no irec.ifil is given, information is recovered from the latest FREQUENCIES calculation. By default frequency information is saved in record 5300 on file 2. After completion of the frequency calculation, the normal modes and frequencies are dumped to record 5400 on file 2. This default record can be changed using the DUMP option. The normal modes stored in this record can be visualized using MOLDEN (see PUT command, section 12.4). By default, imaginary and low frequency modes are not stored. By specifying DUMPALL rather than DUMP all modes are written out.

By default, all computed frequencies (including low and imaginary ones) are printed. The following options can be used to modify the print level

PRINT,HESSIAN

print the force constant matrix (hessian) i.e. the second derivative matrix of the energy and the mass weighted hessian matrix.

PRINT,LOW

print low vibrational frequencies (i.e. the 5 or 6 frequencies belonging to rotations and translations) and their normal modes (default; PRINT,LOW=-1 suppresses the print).

PRINT,IMAG

print imaginary vibrational frequencies and their normal modes (default; PRINT,IMAG=-1 suppresses the print). Imaginary frequencies appear at transition states. The normal mode of an imaginary frequency represents the transition vector of that state.

The threshold for low vibrations (default 150 cm$^{-1}$ can be changed using

THRESH, LOW=value

where value is the threshold in cm$^{-1}$.

Other subcommands of FREQUENCIES are:

STEP,rstep

determines the step size of the numerical differentiation of the energy. Default step size rstep=0.001 [bohr].

NOPROJECT

don't project translations and rotations out of the hessian.

SAVE,irec.ifil

Save information of numerical frequency calculation to record irec. By default frequencies are saved on record 5300.2.

START,irec.ifil

Restart numerical frequency calculation from record irec on file ifil (usually the .wfu-file 2).

VARIABLE,variable

Name of a variable for which the hessian is computed

COORD=UNIQUE

Use symmetry-unique displacements in the numerical calculation of the hessian (default).

COORD=3N

Don't use symmetry-unique displacements (not recommended). using finite differences.