Vibrational Raman Optical Activity (VROA)

 

The calculation of vibrational Raman intensities and Raman optical activity (VROA)    is one of the more computationally expensive properties that can be evaluated with DALTON .

Due to the time spent in the numerical differentiation , we have chosen to calculate ROA both with and without London atomic orbitals  in the same calculation, because the time used in the setup of the right-hand sides differentiated with respect to the external magnetic field is negligible compared to the time used in the solution of the time-dependent response equations [22]. Because of this, all relevant Raman properties (intensities and depolarization ratios)   is also calculated at the same time as ROA.

A very central part in the evaluation of Raman Optical Activity is the evaluation the electric dipole-electric dipole, the electric dipole-magnetic dipole, and the electric dipole-electric quadrupole polarizabilities, and we refer to Section  for a more detailed description of the input for such calculations.

When calculating Raman intensities  and ROA   we need to do a numerical differentiation  of the electric dipole-electric dipole, the electric dipole-magnetic dipole, and the electric dipole-electric quadrupole polarizabilities along the normal modes  of the molecule. The procedure is described in Ref. [22]. Thus we need to do a geometry walk of type numerical differentiation. In each geometry we need to evaluate the electric dipole-electric dipole, the electric dipole-magnetic dipole, and the electric dipole-electric quadrupole polarizabilities. This may be achieved by the following input:

**DALTON INPUT
.WALK
.MAX IT
 31
*WALK
.NUMERI
**WAVE FUNCTIONS
.HF
*HF INPUT
.THRESHOLD
1.0D-8
**START
.VROA
.ABALNR
.ISOTOP
    5
 1 1 1 2 3
*ABALNR
.THRLNR
1.0D-7
.FREQUE
     2
0.0 0.09321471
**PROPERTIES
.VROA
.ABALNR
.ISOTOP
    5
 1 1 1 2 3
*ABALNR
.THRLNR
1.0D-7
.FREQUE
     2
0.0 0.09321471
**FINAL
.VROA
.ABALNR
.VIBANA
.ISOTOP
    5
 1 1 1 2 3
*ABALNR
.THRLNR
1.0D-7
.FREQUE
     2
0.0 0.09321471
*RESPONSE
.THRESHOLD
1.0D-6
*VIBANA
.PRINT
 2
.ISOTOP
    1
 1 1 1 2 3
*END OF INPUT

This is the complete input for a calculation of VROA   on the CFHDT molecule . Although the keyword .VROA   is added in the different ABACUS  input modules, we still need to tell the program that frequencies are to be read in the *ABALNR   section by also adding the keyword .ABALNR   in the general input module.

The only isotopic substitution of this molecule that shows vibrational optical activity is the one containing one hydrogen, one deuterium and one tritium nucleus. This is reflected in the keyword .ISOTOP  , as we want the center-of-mass  to be the gauge origin  for the VROA calculation not employing London atomic orbitals. We note that a user specified gauge origin can be supplied with the keyword .GAUGEO   in the ABACUS  input modules. The gauge origin can also be chosen as the origin of the Cartesian Coordinate system (0,0,0) by using the keyword .NOCMC  . Note that neither of these options will affect the results obtained with London orbitals.

The input in the *ABALNR   input section should be self-explanatory from the discussion of the frequency dependent polarizability  in Sec. . Note that because of the numerical differentiation  the response equations need to be converged rather tightly (1.0 10 ). Remember also that this will require you to converge your wave function   more tightly than is the default.

The numerical differentiation  is invoked through the keyword .NUMERI   in the *WALK   submodule. Note that this will automatically turn off the calculation of the molecular Hessian , putting limitations on what properties may be calculated during a ROA calculation. Because of this there will not be any prediction of the energy at the new point.

It should also be noted that the program in a numerical differentiation will step plus and minus one displacement along each Cartesian coordinate of all nuclei, as well as calculating the property in the reference geometry. Thus, for a molecule with N atoms the properties will 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 of the program is 20. Thus one often also need to change the maximum number of allowed iterations by for instance adding the appropriate number of iterations in the general input module using the keyword .MAX IT   described in Section .

The default step length in the numerical integration is 10 a.u., and this step length may be adjusted by the keyword .DISPLA   in the *WALK   module. The steps are taken in the Cartesian directions  and not along normal modes . This enables us to study a large number of isotopically substituted  molecules at once, as the London orbital   results for ROA does not depend on the choice of gauge origin. This is done in the **FINAL   input module, but as only one isotopic substituted species show optical activity, we have only requested a vibrational analysis for one species.

We note, that just as for Vibrational Circular Dichroism, a different force field may be used in the estimation of the VROA intensity paramaters. Indeed, a number of force fields can be used to estimate the VROA paramaters obtained with a given basis set through the input:

**DALTON INPUT
.WALK
.MAX IT
 31
.ITERATION
 31
*WALK
.NUMERI
**FINAL
.VROA
.ABALNR
.VIBANA
.ISOTOP
    5
 1 1 1 2 3
*ABALNR
.THRLNR
1.0D-7
.FREQUE
     2
0.0 0.09321471
*RESPONSE
.THRESHOLD
1.0D-6
*VIBANA
.HESFIL
.PRINT
 2
.ISOTOP
    1
 1 1 1 2 3
*END OF INPUT

by copying different DALTON.HES files to the scratch directory, which in turn is read through the keyword .HESFIL  . By choosing the start iteration to be 31 through the keyword .ITERAT  , we tell the program that the walk has finished (for CHFDT with 31 points that need to be calculated). However, this requires that all information is available in the DALTON.WLK file.

Thus, it is evident that the calculation of Vibrational Raman Optical Activity   is indeed a task for connoisseurs. However, the use of London orbitals as well as frequency dependent properties, makes DALTON the currently most accurate way of calculating Raman optical activity.

Concerning basis sets requirement for Raman Optical Activity, 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. However, this is far to large to use in a calculation of ROA of a naturally optical active molecule. Further work is thus needed.