# Harmonic vibrational frequencies (FREQUENCIES)

FREQUENCIES,options, [forces:frequencies]

Calculate harmonic vibrational frequencies and normal modes. For the calculation of anharmonic vibrational frequencies see sections POTENTIAL ENERGY SURFACES (SURF) to vibration correlation programs. The hessian is calculated analytically or numerically by finite differences in 3N cartesian coordinates (Z-Matrix coordinates will be destroyed on entry). If analytic gradients are available these are differentiated once to build the hessian, otherwise the energy is differentiated twice. If for the wavefunction method dipole moments are available, 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. To get reasonable results it is necessary to do a geometry optimization before using the frequency calculation.

The FREQUENCIES command must be given after the energy calculation to which it refers or after OPTG. If the command for the energy calculation (e.g. HF, KS, MP2, etc.) is in a procedure, the OPTG and FREQUENCIES commands must also be in the procedure. Furthermore, no procedures without an energy calculation must directly precede FREQUENCIES or OPTG.

The following options are available:

• 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 have been computed using multi; cpmcscf,hess, 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 (only effective if gradients are available).
• SYMM=AUTO|NO 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, the AUTO option cannot be used for multireference methods (MCSCF/MRCI/ACPF/AQCC/RS2). If given, the option is disabled in these cases. For these methods frequency calculations are only possible without symmetry. Symmetry is turned off atomatically if the state symmetry is 1. Note that this may fail if there are lower states in other symmetries. Use of RESTRICT, SELECT, REF, PROJECT, LOCAL, state-averaged MCSCF will lead on errors unless the calculation is performed in $C_1$ symmetry In such cases the whole calculation must be done without symmetry.
• AUTO Same as SYMM=AUTO, see above.
• NOAUTO|NOSYM Same as SYMM=NO, see above.
• HESSREC|SAVE=record Save hessian to record. By default the hessian is saved on record 5300.2.
• FREQREC=record Save frequencies and normal modes to record (default 5400.2) This information is used, e.g., by the VSCF/VCI program.
• TASKREC=record Save task information in numerical hessian calculation to the given record. This information is required for a restart of a numerical hessian calculation. By default, the information is saved on record 5500.2.
• READH Read hessian from default hessian record.
• READH|START=record Use hessian from previously saved on record. If the hessian has been computed for the current method and geometry already, it is used by default.
• READF Read frequencies and normal modes from default record.
• READF=record Read hessian from previously saved on record..
• RESTART Attempt to restart a previous numerical frequency/hessian calculation using default task record.
• RESTART=record Attempt to restart a previous numerical frequency/hessian calculation using task record record.
• LOW=value Threshold for printing low frequencies in cm$^{-1}$. If this option is given, frequencies below the given value are not printed. By default, all frequencies are printed.
• STEP=value Determines the step size of the numerical differentiation of the energy or the gradient. The default step size is 0.01 a.u.
• MAXTASK=value Stop the calculation if the number of tasks is exceeded (the calculation can be restarted later).
• MAXCPU=value Stop the calculation if the given CPU-time (in sec) exceeded (the calculation can be restarted later).
• NEW Recompute hessian, even if a hessian is already available.
• PROJECT Project rotations and translations out of the hessian (default).
• NOPROJECT Don’t project rotations and translations out of the hessian.
• PRINT=value Print option. If value is greater or equal to zero, the hessian and other information is printed (default $-1$).
• DEBUG Print Debug information, same as PRINT=1.
• SCALE=value Scaling factor for frequencies. The scaled frequencies are used to compute the ZPE and thermodynamic properties.

For compatibility with older MOLPRO versions many of the options can also be set using directives, as described in the following sections.

PRINT,options

This directive can be used to control the output:

The following options can be given:

• HESSIAN Print the force constant matrix (hessian) i.e. the second derivative matrix of the energy and the mass weighted hessian matrix.
• LOW Print low vibrational frequencies (i.e. the 5 or 6 frequencies belonging to rotations and translations) and their normal modes (default; LOW=-1 suppresses the print).
• LOW=value Threshold for printing low vibrations in cm$^{-1}$ (default 150). If a value $>0$ is given, frequencies below this value are not printed.

SAVE,options

The following options can be given:

• hessian=record Save hessian to record (same effect as option HESSREC). By default the hessian is saved on record 5300.2.
• FREQ=record Save frequencies and normal modes to record (same effect as option FREQREC). By default the frequencies are saved on record 5400.2.
• TASK=record Save task information for possible restart of hessian calculation to record (same effect as option TASKREC). By default the frequencies are saved on record 5500.2.

START,options

The following options can be given:

• HESSIAN=record Read hessian from record record (same effect as option READHESS).
• TASK=record Read task information from record record and restart numerical hessian calculation (same effect as option RESTART).

COORD,type

type can be one of the following:

• UNIQUE Use symmetry-unique displacements in the numerical calculation of the hessian (default).
• 3N Don’t use symmetry-unique displacements (not recommended).

[STEP,rstep]

determines the step size of the numerical differentiation of the energy or the gradient. The default step size is rstep=0.01 a.u.

VARIABLE,name; [freq:var]

Defines a variable name which holds the energy value to be used for computing the hessian using finite differences. By default, this is ENERGY(1) as set by the most recent program. For other other variables which can be used see section optimizing energy variables (VARIABLE). Note that numerical hessians cannot be computed when dummy atoms holding basis functions are present.

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],[TEMP=value], [PRESS=value], [TMIN=value, TMAX=value, TSTEP=value]

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 is given, the point group is determined automatically, but only Abelian groups (D2H and subgroups) are recognized. If the molecule has higher symmetry this may eventually cause deviations in the rotational entropy.

The temperature (in K), pressure (in atm) or a range of temperatures (in K) can be given as options.

If no temperature or pressure is specified 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]).

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.

examples/form_freq.inp
***,formaldehyde freqency calculation

basis=vdz
gthresh,energy=1.d-8

geomtyp=xyz
symmetry,nosym
geometry={
4
FORMALDEHYDE
C          0.0000000000        0.0000000000       -0.5265526741
O          0.0000000000        0.0000000000        0.6555124750
H          0.0000000000       -0.9325664988       -1.1133424527
H          0.0000000000        0.9325664988       -1.1133424527
}

hf;accu,14
optg;coord,3n;

{frequencies,analytic
thermo,sym=c2v
print,thermo}

mp2
optg;coord,3n
{frequencies
thermo,sym=c2v
print,thermo}
examples/pf5_freq.inp
***, Phosphorous-pentafluoride Vibrational Frequencies
basis=3-21G

geomtyp=xyz        ! use cartesian coordinates xmol style
symmetry,nosym     ! don't use symmetry
geometry={         ! geometry input
6
PF5
P        0.00000        0.00000        0.00000
F        0.00000        1.11100       -1.12400
F        0.00000       -1.52800       -0.40100
F        0.00000        0.41700        1.52500
F       -1.60400        0.00000        0.00000
F        1.60400        0.00000        0.00000}

rhf
optg              ! optimize geometry

frequencies       ! calculate vibrational frequencies
print,low         ! print frequencies+modes of zero frequencies
thermo,sym=d3h    ! calculate thermodynamical properties
temp,200,400,50   ! temperature range 200 - 400 [K]
---
examples/h2o_freqdft.inp
include procedures
geometry={O;                 !Z-matrix for water
H1,O,R;
H2,O,R,H1,THETA}
R=0.96 Ang                   !start bond distance
Theta=104                    !start bond angle
basis=6-31g**                !Pople basis set
\$functional=b3lyp            !define fucntional (optional, b3lyp is default)
freqdft                      !run frequency calculation
examples/diboran_freq.inp
***, Diboran Z-Matrix
basis=sto-3g
r1=0.9023299 ang
r2=0.9722889 ang
r3=1.1540618 ang
a1=118.723 degree

geometry={
Q1
B1,Q1,r1
H1,Q1,r2,B1,90
B2,Q1,r1,H1,90,B1,180
H2,Q1,r2,B1,90,H1,180
H3,B1,r3,Q1,a1,H1,90
H4,B1,r3,Q1,a1,H1,-90
H5,B2,r3,Q1,a1,H1,90
H6,B2,r3,Q1,a1,H1,-90}

hf
print,thermo}