Absorption / Emission Spectra in the Harmonic approximation

It is possible to generate full absorption and emission spectra in the harmonic approximation using a combination of Vcham and Quantics. This is an approximation that works well for states that have little vibronic coupling to other states. The procedure uses quantum chemistry calculations of the Hessian for each state of interest at the Franck-Condon (FC) point. Vcham is then used to provide the potentials as harmonic surfaces expanded around the FC point in the ground-state normal modes. This Hamiltonian is then used in Quantics calculations, using a vertical excitation (or de-excitation) to calculate the absorption (or emission) spectrum.

Below the steps are described, using NH₃ as an example. The file names in italics should be changed to appropriate names. Steps 4-6 using quantics are started from a template file generated by Vchfit. You will need to edit this and check convergence of basis set and as usual for a quantics simulation. The length of propagation and time step for output determines the resolution of the resulting spectra and should be changed appropriately.

Step 1. Quantum Chemistry.

Obtain the frequencies and normal modes at the FC point for each state. For example, using Gaussian, 3 calculations are required for NH₃. At the chosen level of theory,

1. Optimise ground-state geometry (obtain FC point).
2. Calculate ground-state frequencies at FC (GS harmonic PES).
3. Calculate frequencies for the excited state(s) at FC (excited-state harmonic PES).

For example the S0 and S1 frequencies for NH₃ at the HF / CIS level are in nh3_freq.log and nh3_freq_s1.log respectively. NB, if using Gaussian the keyword freq=hpmodes must be used to write the normal modes to high precision in the log file.

Step 2. Set up data for fitting PES.

Run the VCTRANS program to convert the information in the Quantum chemistry output files to be read by VCHFIT which will set up the operator for quantics. Write the input file trans.inp and type

  vctrans  trans

to create the file trans.info For example, see nh3_trans.inp and nh3_trans.info

Step 3. Create the Operator file.

Run the VCHFIT program to read the .info file set up in step 2 and create the operator file and template input file for Quantics. Write the input file vchfit.inp and type

  vchfit  vchfit

to create the files fit.op and fit.qinp. For this you will need the keywords quantics_op and quantics_inp. You need to specify a diab2_mod calculation For example, see nh3_fit.inp, nh3_fit.op and nh3_fit.qinp

VCHFIT also creates a .vcham file with the parameters for the Taylor expansion of the PES.

Step 4. Absorption Spectrum Run a Quantics calculation with the GS vibrational wavefunction started in the excited state. Copy the template input file fit.qinp to name_abs.inp. You will need to change the name directory specified to name_abs. Run the calculation

  quantics -mnd  name_abs

You can now go in to the directory name_abs and plot the spectrum from the autocorrelation file using autospec, look at the potential surfaces using showsys etc. as usual. The input file to calculate the NH₃ absorption spectrum for the model is in nh3_abs.inp. The Quantics files are in nh3_abs.

Step 5. Create vibrational wavefunction in S1 Copy the file name.inp to name_rlx.inp. Edit the file to perform a relaxtion calculation in the excited state to create the ground-state vibrational wavefunction in the excited electronic state.

Change the name directory to the new one.
change propagation to relaxation
run the calculation
```
quantics -mnd name_rlx
```

The input file to calculate the NH₃ excited state wavefunction is in nh3_rlx.inp. The Quantics files from the simulation are in nh3_rlx.

Step 6. Emission Spectrum Finally, calculate the emission spectrum. This involves a vertical downwards transition of the excited-state wavefunction created in step 4 and subsequent propagation. To do this, copy name_rlx.inp to name_emi.inp and edit it

Change the name directory to the new one.
change relaxation back to propagation
change the INIT_WF-SECTION to read the initial wavepacket from the relaxation calculation and place it in the greoun state.
```
INIT_WF-SECTION
read-inwf
file = name_rlx
SPF 2 -> 1,2
A 2 -> 1
end-read-inwf
end-init_wf-section
```
run the calculation
```
quantics -mnd name_emi
```
Go in to the directory name_emi and plot the spectrum from the autocorrelation file using autospec.

The input file to calculate the NH₃ emission spectrum is in nh3_emi.inp. The Quantics files from the simulation are in nh3_emi.