5.17. Absorption and Fluorescence Bandshapes using ORCA_ASA¶
Please also consider using the more recent ORCA_ESD, described in Section Excited State Dynamics, to compute bandshapes.
Bandshape calculations are nontrivial but can be achieved with ORCA using the procedures described in section Simulation and Fit of Vibronic Structure in Electronic Spectra, Resonance Raman Excitation Profiles and Spectra with the orca_asa Program. Starting from version 2.80, analytical TD-DFT gradients are available, which make these calculations quite fast and applicable without expert knowledge to larger molecules.
Note
Functionals with somewhat more HF exchange produce better results and are not as prone to “ghost states” as GGA functionals unfortunately are!
Calculations can be greatly sped up by the RI or RIJCOSX approximations!
Analytic gradients for the (D) correction and hence for double-hybrid functionals are NOT available.
In a nutshell, let us look into the H\(_{2}\)CO molecule. First we
generate some Hessian (e.g. BP86/SV(P)). Then we run the job that makes
the input for the orca_asa program. For example, let us calculate the
five lowest excited states:
! aug-cc-pVDZ BHandHLYP TightSCF NMGrad
%tddft nroots 5 end
# this is ASA-specific input
%rr states 1,2,3,4,5
HessName "Test-ASA-H2CO-freq.hess"
ASAInput True
end
*int 0 1
C 0 0 0 0 0 0
O 1 0 0 1.2 0 0
H 1 2 0 1.1 120 0
H 1 2 3 1.1 120 180
*
The ORCA run will produce a file Test-ASA-H2CO.asa.inp that is an
input file for the program that generates various spectra. It is an
ASCII file that is very similar in appearance to an ORCA input file:
#
# ASA input
#
%sim model IMDHO
method Heller
AbsRange 25000.0, 100000.0
NAbsPoints 1024
FlRange 25000.0, 100000.0
NFlPoints 1024
RRPRange 5000.0, 100000.0
NRRPPoints 1024
RRSRange 0.0, 4000.0
NRRSPoints 4000
# Excitation energies (cm**-1) for which rR spectra will
# be calculated. Here we choose all allowed transitions
# and the position of the 0-0 band
RRSE 58960, 66884, 66602
# full width half maximum of Raman bands in rR spectra
# (cm**-1):
RRS_FWHM 10.0
AbsScaleMode Ext
FlScaleMode Rel
# RamanOrder=1 means only fundamentals. For 2 combination
# bands and first overtones are also considered, for 3
# one has second overtones etc.
RamanOrder 1
# E0 means the adiabatic excitation energy
# EV would mean the vertical one. sprints vertical
# excitations in the TD-DFT output but for the input into
# the ASA program the adiabatic excitation energies are
# estimated. A rigorous calculation would of course in-
# volve excited state geometry optimization
EnInput E0
CAR 0.800
end
# These are the calculated electronic states and transition moments
# Note that this is in the Franck-Condon approximation and thus
# the transition moments have been calculated vertically
$el_states
5
1 32200.79 100.00 0.00 -0.0000 0.0000 -0.0000
2 58960.05 100.00 0.00 0.0000 -0.4219 0.0000
3 66884.30 100.00 0.00 -0.0000 0.4405 0.0000
4 66602.64 100.00 0.00 -0.5217 -0.0000 0.0000
5 72245.42 100.00 0.00 0.0000 0.0000 0.0000
# These are the calculated vibrational frequencies for the totally
# symmetric modes. These are the only ones that contribute. They
# correspond to x, H-C-H bending, C=O stretching and C-H stretching
# respectively
$vib_freq_gs
3
1 1462.948534
2 1759.538581
3 2812.815170
# These are the calculated dimensional displacements for all
# electronic states along all of the totally symmetric modes.
$sdnc
3 5
1 2 3 4 5
1 -0.326244 0.241082 -0.132239 0.559635 0.292190
2 -1.356209 0.529823 0.438703 0.416161 0.602301
3 -0.183845 0.418242 0.267520 0.278880 0.231340
After setting NAbsPoints variable and spectral ranges in this file
to the desired values, we invoke orca_asa as:
orca_asa Test-ASA-H2CO.asa.inp
This produces the following output:
******************
* O R C A A S A *
******************
--- A program for analysis of electronic spectra ---
Reading file: Test-ASA-H2CO.asa.inp ... done
**************************************************************
* GENERAL CHARACTERISTICS OF ELECTRONIC SPECTRA *
**************************************************************
--------------------------------------------------------------------------------
State E0 EV fosc Stokes shift Effective Stokes shift
(cm**-1) (cm**-1) (cm**-1) (cm**-1)
--------------------------------------------------------------------------------
1: 30457.24 32200.79 0.000000 0.00 0.00
2: 58424.56 58960.05 0.031879 0.00 0.00
3: 66601.54 66884.30 0.039422 0.00 0.00
4: 66111.80 66602.64 0.055063 0.00 0.00
5: 71788.55 72245.42 0.000000 0.00 0.00
--------------------------------------------------------------------------------------------------
BROADENING PARAMETETRS (cm**-1)
--------------------------------------------------------------------------------------------------
Intrinsic Effective
State -------------------------- --------------------------------------------------------
Sigma FWHM
Gamma Sigma FWHM --------------------------- ---------------------------
0K 77K 298.15K 0K 77K 298.15K
--------------------------------------------------------------------------------------------------
1: 100.00 0.00 200.00 0.00 0.00 0.00 200.00 200.00 200.00
2: 100.00 0.00 200.00 0.00 0.00 0.00 200.00 200.00 200.00
3: 100.00 0.00 200.00 0.00 0.00 0.00 200.00 200.00 200.00
4: 100.00 0.00 200.00 0.00 0.00 0.00 200.00 200.00 200.00
5: 100.00 0.00 200.00 0.00 0.00 0.00 200.00 200.00 200.00
Calculating absorption spectrum ...
The maximum number of grid points ... 5840
Time for absorption ... 9.569 sec (= 0.159 min)
Writing file: Test-ASA-H2CO.asa.abs.dat ... done
Writing file: Test-ASA-H2CO.asa.abs.as.dat ... done
Generating vibrational states up to the 1-th(st) order ... done
Total number of vibrational states ... 3
Calculating rR profiles for all vibrational states up to the 1-th order
State 1 ...
The maximum number of grid points ... 6820
Resonance Raman profile is done
State 2 ...
The maximum number of grid points ... 6820
Resonance Raman profile is done
State 3 ...
The maximum number of grid points ... 6820
Resonance Raman profile is done
Writing file: Test-ASA-H2CO.asa.o1.dat... done
Writing file: Test-ASA-H2CO.asa.o1.info... done
Calculating rR spectra involving vibrational states up to the 1-th(st) order
State 1 ... done
State 2 ... done
State 3 ... done
Writing file: Test-ASA-H2CO.asa.o1.rrs.58960.dat ... done
Writing file: Test-ASA-H2CO.asa.o1.rrs.58960.stk ... done
Writing file: Test-ASA-H2CO.asa.o1.rrs.66884.dat ... done
Writing file: Test-ASA-H2CO.asa.o1.rrs.66884.stk ... done
Writing file: Test-ASA-H2CO.asa.o1.rrs.66602.dat ... done
Writing file: Test-ASA-H2CO.asa.o1.rrs.66602.stk ... done
Writing file: Test-ASA-H2CO.asa.o1.rrs.as.58960.dat ... done
Writing file: Test-ASA-H2CO.asa.o1.rrs.as.58960.stk ... done
Writing file: Test-ASA-H2CO.asa.o1.rrs.as.66884.dat ... done
Writing file: Test-ASA-H2CO.asa.o1.rrs.as.66884.stk ... done
Writing file: Test-ASA-H2CO.asa.o1.rrs.as.66602.dat ... done
Writing file: Test-ASA-H2CO.asa.o1.rrs.as.66602.stk ... done
Writing file: Test-ASA-H2CO.asa.o1.rrs.all.xyz.dat ... done
TOTAL RUN TIME: 0 days 0 hours 1 minutes 17 seconds 850 msec
The computed vibrationally resolved absorption spectrum is plotted as shown in Figure Fig. 5.50.
Fig. 5.50 The computed vibrationally resolved absorption spectrum of the H\(_{2}\)CO molecule¶
The computed fluorescence spectrum of the lowest energy peak is plotted as shown in Figure Fig. 5.51. This peak corresponds to S2. Although it is not realistic, it is sufficient for illustrative purposes.
Fig. 5.51 The computed fluorescence spectrum of the lowest energy peak of the H\(_{2}\)CO molecule¶
The computed Resonance Raman (rR) excitation profiles of the three totally symmetric vibrational modes are plotted as shown in Figure Fig. 5.52.
Fig. 5.52 The computed Resonance Raman excitation profiles of the three totally symmetric vibrational modes of the H\(_{2}\)CO molecule¶
As might be expected, the dominant enhancement occurs under the main peaks for the C\(=\)O stretching vibration. Higher energy excitations particularly enhance the C-H vibrations. The computed rR spectra at the vertical excitation energies are provided in Figure Fig. 5.53.
Fig. 5.53 The computed Resonance Raman spectra at the vertical excitation energies of the H\(_{2}\)CO molecule¶
In this toy example, the dominant mode is the C\(=\)O stretching, and the spectra look similar for all excitation wavelengths. However, electronically excited states are mostly of different natures, yielding drastically different rR spectra. Thus, rR spectra serve as powerful fingerprints of the electronic excitation being studied. This is also true even if the vibrational structure of the absorption band is not resolved, which is usually the case for large molecules.
The orca_asa program is much more powerful than described in this section.
Please refer to section Simulation and Fit of Vibronic Structure in Electronic Spectra, Resonance Raman Excitation Profiles and Spectra with the orca_asa Program for a full description of its
features. The orca_asa program can also be interfaced to other electronic
structure codes that deliver excited state gradients and can be used to fit
experimental data. It is thus a tool for experimentalists and theoreticians
at the same time!