Vibrational averaged properties

The change in the geometry accounts for part of the contribution to a vibrationally averaged property, namely that due to the anharmonicity of the potential [101]. Although this term is important, we need to include also the contribution from the averaging of the molecular property over the harmonic oscillator wave function in order to get an accurate estimate of the vibrational corrections to the molecular property.

At the effective geometry, this contribution to for instance the nuclear shielding constants can be obtained from the following input

**DALTON INPUT
.WALK
*WALK
.VIBAVE
.DISPLACEMENT
0.05
.TEMPERATURES
 1
 300.0
**WAVE FUNCTIONS
.HF
*SCF INPUT
.THRESH
 1.0D-10
**START
.SHIELD
*LINRES
.THRESH
 1.0D-6
*RESPONS
.THRESH
 1.0D-5
**EACH STEP
.SHIELD
*LINRES
.THRESH
 1.0D-6
*RESPONS
.THRESH
 1.0D-5
**END OF DALTON INPUT

This input will calculate the harmonic contribution to the (ro)vibrational average to the nuclear shielding constants at 300K for $^{17}$ODH. It is important to realize that since each isotopic species for each temperature will have its own unique (ro)vibrationally averaged geometry, we will have to calculate the harmonic contribution for each temperature and each isotopic species separately. The isotopic constitution is specified in the MOLECULE.INP file as described in Chapter 23.

We note that we may reuse the property derivatives from a different geometry for calculating the harmonic contribution to the vibrational correction at the given geometry by using the keyword .REUSE in the *WALK module. A new force field is calculated, but the property derivatives are assumed to remain unchanged. The approximation has been tested and been shown to account, through the change in the effective geometry for different temperatures, for a very large fraction of the temperature effects on molecular properties [16].

This calculation will always be done in normal coordinates, and the recommended step length is 0.05 [15]. As for the calculation of (ro)vibrationally averaged geometries in normal coordinates, the calculation requires the determination of one analytical Hessian in order to determine the harmonic force field.

The default maximum number of iterations is 20. However, DALTON will automatically reset the maximum number of iterations to 6$K$+1 in case of vibrational averaging calculations. The maximum number of iterations can also be set explicitly by using the keyword .MAX IT in the **DALTON INPUT module.