Calculating Raman intensities is by no means a trivial task, and because of the computational cost of such calculations (as there does not exist any program which avoids the numerical differentiation of the polarizability with respect to nuclear distortions), there are few theoretical investigations of basis set requirements and correlation effects on calculated Raman intensities.
DALTON is the only quantum chemical program package capable of calculating the Raman intensities at the frequency of the incident laser beam. DALTON also has the same possibilities as other common quantum chemical software packages to calculate static Raman intensities (that is, where the frequency dependence of the polarizability has been neglected). The Raman intensities calculated are the ones obtained within the Placzek approximation [21] , and the implementation is described in Ref. [22].
The Raman intensity is the differentiated frequency-dependent polarizability with respect to nuclear displacements. As it is a third derivative depending on the nuclear positions through the basis set, numerical differentiation of the polarizability with respect to nuclear coordinates is necessary.
The input looks very similar to the input needed for the calculation
of Raman optical activity described
in Section 
**DALTON INPUT
.WALK
.MAX IT
31
*WALK
.NUMERI
**WAVE FUNCTIONS
.HF
*HF INPUT
.THRESH
1.0D-8
**START
.RAMAN
.ABALNR
*ABALNR
.THRLNR
1.0D-7
.FREQUE
2
0.0 0.09321471
**PROPERTIES
.RAMAN
.ABALNR
*ABALNR
.THRLNR
1.0D-7
.FREQUE
2
0.0 0.09321471
**FINAL
.RAMAN
.ABALNR
.VIBANA
*RESPONSE
.THRESH
1.0D-6
*ABALNR
.THRLNR
1.0D-7
.FREQUE
2
0.0 0.09321471
*VIBANA
.PRINT
1
1 1 1 2 3
*END OF INPUT
The keyword .ABALNR in the general input module indicates that a frequency dependent linear response calculation is to be done, in this case the calculation of the frequency-dependent polarizability as specified by the .ALFA keyword in the *ABALNR input module. The keyword .RAMAN indicates that we are only interested in the Raman intensities and depolarization ratios . Note that these parameters are also obtainable by using the keyword .VROA . In this calculation we calculate the Raman intensities for two frequencies, the static case and a frequency of the incident light corresponding to a laser of wavelength 488.8 nm. Note, however, that Raman intensities corresponding to zero frequency cannot be calculated with the .POLARI keyword, even though static polarizabilities may be obtained using this keyword.
Due to the numerical differentiation
that is done, the threshold for
the iterative solution of the response equations are by default
10 
, in order to get Raman intensities that are numerically
stable to one decimal digit.
In the *WALK input module we have specified that the walk is a numerical differentiation in the *WALK input module. This will automatically turn off the calculation of the geometric Hessian , putting limitations on what kind of properties that may be calculated at the same time as Raman intensities. Because the Hessian is not calculated, there will not be any prediction of the energy at the new point.
It should also be noted that in a numerical differentiation the program will step plus and minus one displacement unit along each Cartesian coordinate of all nuclei, as well as calculating the property at the reference geometry. Thus, for a molecule with N atoms the properties will need to be calculated in a total of 2*3*N + 1 points, which for a 5 atom molecule will amount to 31 points. The default maximum number of steps in DALTON is 20. Thus one often need to change the maximum number of allowed iterations by adding the keyword .MAX IT in the **DALTON input module.
The default step length in the numerical
differentiation is 
a.u., and this step length may be adjusted by the keyword
.DISPLA
in the *WALK
input module. The steps are taken
in the Cartesian directions and
not along normal modes. This enables us to study the Raman intensities
of a large number of isotopically substituted molecules at once. This
is done in the **FINAL
input section, where we
have requested one isotopically substituted species in addition to the
isotopic species containing the most abundant isotope of each element.
It should be evident that the calculation of Raman intensities is a task for connoisseurs. However, the fact that DALTON can calculate Raman intensities at the frequency of the incident light, puts DALTON\ in a special position among ab initio programs, as these only can at most calculate Raman intensities based on static polarizabilities.
Concerning basis sets requirement for Raman intensities, there is yet much work to be done. In the only study presented of Raman Optical Activity using London atomic orbitals, it is argued in favor of the aug-cc-pVDZ basis set supplied with the basis set library. However, in order to get Hartree-Fock limit quality of the vibrational frequencies as well, a basis set of at least aug-cc-pVTZ seems to be necessary. Whether these observations will also apply to the Raman intensities is not known.