34.4 Vibrational Frequencies (FREQUENCIES)

FREQUENCIES,method,SYMM=flag,START=rec.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.

The accuracy of the hessian is determined by method.

method=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.

method=CENTRAL

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

method=NUMERICAL

differentiate the energy twice, using central differences.

method=FORWARD

use forward differences/low quality force constants.

The symmetry of the molecular wavefunction can be switched on and off independently from the symmetry defined in the geometry specification. Giving SYMM=AUTO the program uses the symmetry of the molecular wavefunction in each step of a numerical frequency calculation. With SYMM=NO no symmetry is used in calculating the molecular wavefunction (default). Note that the SYMM option is independent from the use of symmetry unique cartesian displacements in numerical frequency calculations (COORD option, see below).

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.

By default the vibrational frequencies, normal modes and IR Intensities of regular vibrations (i.e. no imaginary frequencies or frequencies belonging to translations or rotations) are printed out. But it is possible to give out more informations by giving one or more of the following print options:

PRINT,FORCE

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.

PRINT,IMAG

print imaginary vibrational frequencies and their normal modes. Imaginary frequencies appear at transition states. The normal mode of an imaginary frequency represents the transition vector of that state.

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 translation 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 using finite differences.

If a numerical hessian is computed by differentiation of the energy or the gradients, molecular symmetry is used to compute only the symmetry unique cartesian displacements, sparing redundant gradient and/or energy calculations. However it is possible (though usually not reasonable) to compute the displacements of all 3N cartesian coordinates using the COORD,3N command.

It is also possible to calculate the thermodynamical properties of the molecule. Since MOLPRO can only handle Abelian point groups it is necessary to give the point group of the molecule in the input file:

THERMO,SYM=pointgroup

pointgroup has to be the Schoenflies Symbol (e.g. C3v for ammonia; linear molecules have to be C*v or D*h respectively). If no point group card is given, rotational degeneracy will be set to 1, eventually causing deviations in the rotational entropy. If no other input card is given the zero-point vibrational energy and the enthalpy $H(t)-H(0)$ [kJ/mol], heat capacity $C_v$ [J/mol K] and entropy $S$ [J/mol K] are calculated for standard Temperature and Pressure ($T=298.150$ [K], $p=1$ [atm]).

Subcommands of THERMO are

[PRINT,THERMO] additional information (such as atomic masses, partition functions and thermodynamical function in calories) is printed to the output. [SCALE,factor] in calculating the thermodynamical properties use vibrational frequencies scaled with factor, in order to take account of systematic errors of the wavefunction (e.g. using SCF wavefunctions factor=0.89 is reasonable).

TEMP,tmin,tmax,tstep

calculate the thermodynamical properties at different temperatures, starting with tmin [K] up to tmax [K] in steps of tstep [K].

PRESSURE,p

calculate the thermodynamical properties at a given pressure of p [atm].

The FREQUENCIES program sets the variable zpe containing the zero-point-energy of the harmonic vibrations in atomic units. If the THERMO option is used, the variables htotal and gtotal, containing the enthalpy and the free enthalpy of the system in atomic units, are also set.