Vibrational Raman Optical Activity (VROA)

The calculation of vibrational Raman intensities and vibrational 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 set-up 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 [42]. 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 9.4 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. [42]. We thus need to do a geometry walk of the 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
*WALK
.NUMERI
**WAVE FUNCTIONS
.HF
*HF INPUT
.THRESH
1.0D-8
**START
.VROA
*ABALNR
.THRESH
1.0D-7
.FREQUE
     2
0.0 0.09321471
**EACH STEP
.VROA
*ABALNR
.THRESH
1.0D-7
.FREQUE
     2
0.0 0.09321471
**PROPERTIES
.VROA
.VIBANA
*ABALNR
.THRESH
1.0D-7
.FREQUE
     2
0.0 0.09321471
*RESPONSE
.THRESH
1.0D-6
*VIBANA
.PRINT
 2
.ISOTOP
 1 5
 1 1 1 2 3
**END OF DALTON INPUT

This is the complete input for a calculation of VROA on the CFHDT molecule. In addition to the keyword .VROA in the different ABACUS input modules, we still need to tell the program that frequencies of the laser field are to be read in the *ABALNR section.

The only isotopic substitution of this molecule that shows vibrational optical activity is the one containing one hydrogen, one deuterium and one tritium nucleus. If we want the center-of-mass to be the gauge origin for the VROA calculation not employing London atomic orbitals, this have to be reflected in the specification of the isotopic constitution of the molecule, see Chapter 23. 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. 9.4. Note that because of the numerical differentiation the response equations need to be converged rather tightly (1.0$\cdot$10$^{-7}$). 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. By default the program will for numerical differentiation calculations reset the maximum number of iterations to 6$N$+1. However, it is also possible to set the number of iterations explicitly in the general input module using the keyword .MAX IT described in Section 21.1.

The default step length in the numerical integration is 10$^{-4}$ 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 **PROPERTIES input module, but as only one isotopic substituted species show optical activity, we have only requested a vibrational analysis for this species.

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

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

Concerning basis sets requirement for Raman Optical Activity, a thorough investigation of the basis set requirements for the circular intensity differences (CIDs) in VROA was presented by Zuber and Hug [88]. They also presented a close-to-minimal basis set that yields high-quality CIDs. The force fields do, however, have to be determined using larger basis (aug-cc-pVTZ) and including electron correlation for a reliable prediction of VROA spectra.