Excitation and Emission (Fluorescence) from First Excited State (n→π*) of Acetaldehyde in Gas Phase
MGCF - College of Chemistry, University of California, Berkeley
This tutorial is adapted from: http://www.gaussian.com/g_tech/g_ur/k_scrf.htm and shows the steps to determine excitation and emission energies in the gas phase. There is a separate tutorial for solvent effects. This tutorial assumes familiarity with GaussView and with Gaussian input and output files. Master the basic Gaussian tutorial before running this one. You will also need some command line and gedit skills.
Step 1: Ground state geometry optimization and frequency calculation. Use Gaussview to build acetaldehyde and set up the Gaussian calculation. Here is a sample input file:
# opt freq=noraman b3lyp/6-31+g(d,p)
Acetaldehyde ground state
C 0.32808400 0.10498688 0.00000000
O 1.54562805 0.09882658 0.15445244
H -0.25463557 -0.82847589 -0.14899911
C -0.49311213 1.40776733 0.00000000
H -0.25659697 1.97846327 -0.87365137
H -1.53671310 1.17155339 0.00000013
H -0.25659741 1.97846359 0.87365128
Submit it to the MGCF server. Review of 01-ac.out shows frequencies are all positive so it is a minimum on the PES. The electronic energy is: SCF Done: E(RB3LYP) = -153.845188788 A.U. after 1 cycles.
Review the MO’s so you can characterize the HOMO and LUMO.
Step 2: Vertical excitation with linear response. The next step is a vertical excitation calculation at the ground state geometry. This is a single-point TD-DFT calculation of the absorption energy of the initial excitation to the lowest excited states. This will be used to identify which excited states are of interest. We will solve for singlets only but http://www.gaussian.com/g_tech/g_ur/k_td.htm shows the syntax for triplets and other variations. In this case, we will see that the n -> π* state is the first singlet excited state.
The best way to set up the next few steps is using the command line (terminal) and gedit.
Use gedit to make a file called 02-ac.com with the following contents. [Add several blank lines at the end of the com file, after the 0 1 line.] Put this file in the same folder as the files from step 1.
# B3LYP/6-31+G(d,p) TD=(nstates=6) Geom=Check Guess=Read
Acetaldehyde: linear response vertical excited states
%oldchk=01-ac means that the optimized geometry and orbital data from step 1 so will be the starting point for the 02-ac calculation. Geom=Check and Guess=Read tell Gaussian to obtain the starting geometry (Geom=Check) and initial orbital data (Guess=Read) from the chk data. TD=(nstates=6) calculates the 6 lowest singlet excited states. The end of the input file is the charge and multiplicity (the 0 1 line) because the geometry is read from the chk. [When using this tutorial as a guide for calculations on your own molecules, make sure %chk matches the name of the current calculation and %oldchk matches the name of the prior calculation. The functional and basis set information may need to be changed for other molecules but should be consistent throughout all of these steps. If you need custom basis sets or pseudopotentials, add the information to the end of the com file. The memory and processors are MGCF defaults and can be changed. Larger calculation require more resources. Ask for help till you understand these variables. ]
Save/close 02-ac.com and submit the calculation using the terminal command: run_gaussian 02-ac.com
Review of 02-ac.out shows: Excited State 1: Singlet-A 4.2846 eV 289.37 nm f=0.0000 <S**2>=0.000
and also shows the MO numbers. You can visualize the MO’s with Gaussview to characterize this further.
Step 3: Optimization of the excited state geometry. Next, we do a TD-DFT geometry optimization to find the minimum energy point on the excited state potential energy surface. The molecule has a plane of symmetry in the ground state but the symmetry is broken in the excited state, so we slightly perturb the ground state geometry to break symmetry at the start of this optimization.
Use gedit to make a file called 03-ac.com with the following contents. [Add several blank lines at the end of the file, after the 5 4 1 3 -50.0 line.] Put this file in the same folder as the files from step 2.
# Opt B3LYP/6-31+G(d,p) TD=(Read,NStates=6,Root=1) Geom=Modify Guess=Read
Acetaldehyde: excited state opt. Modify geometry to break Cs symmetry since first excited state is A"
7 4 1 2 10.0
5 4 1 3 -50.0
Here we use more processors and memory since this is a larger calculation. The mem/proc ratio is selected based on the physical hardware of the MGCF server (6 procs are requested and the MGCF server has 3.8GB/proc so 3.8x6 is about 23GB). Ask us for help before you adjust these.
We also break the symmetry of the ground state geometry by including new dihedral information at the end of the input file and using the keyword Geom=Modify. [You probably don’t need Geom=Modify and new dihedral information for calculations on lower symmetry molecules. However, if molecules are symmetric or you otherwise want to explore excited states of alternate conformations, then pick suitable geometry modifications. Don’t just copy these. Even for acetaldehyde, if you build the step 1 input geometry differently than ours, the 4 atom numbers and dihedral adjustments above could be nonsense. Open the step 2 output in Gaussview, label the atoms and measure a few dihedrals to make good choices. In our example, atoms 7, 4, 1, 2 had a dihedral=0 so we changed it by 10 degrees. 5, 4, 1, 3 was -58 so we changed it to -50.0.] Root=1 specifies that the first excited state is the state of interest but this can be changed to explore other states.
This is an optimization so include the opt keyword. Make sure the basis set, functional, etc match those used in step 2. Make sure %chk matches the name of the current calculation and %oldchk matches the prior step.
Save/close 03-ac.com and submit it using the terminal command: run_gaussian 03-ac.com
Review of 03-ac.out shows: Excited State 1: Singlet-A 3.0791 eV 402.67 nm f=0.0009 <S**2>=0.000
. . . . . Total Energy, E(TD-HF/TD-KS) = -153.704134683
Subtract this energy from the ground state energy (step 1) to get the ground state to first excited state absorption at 402.67 nm.?????
Step 4: Vibrational frequencies of the excited state structure. Now we run a frequency calculation to verify that the geometry located in step 3 is a minimum. The results could also be used as part of a Franck-Condon calculation if desired (see below). This is a numerical frequency calculation.
Use gedit to make a file called 04-ac.com with the following contents. [Add several blank lines at the end of the file, after the 0 1 line.] Put this file in the same folder as the files from step 3.
# Freq=noraman B3LYP/6-31+G(d,p) TD=(Read,NStates=6,Root=1) Geom=Check Guess=Read
Acetaldehyde excited state freq
This is a frequency calculation on the optimized geometry from step 3 so you must include Freq=noraman. Make sure the basis set, functional, etc match those used in step 3. Make sure %chk matches the name of the current calculation and %oldchk matches the prior step.
Save/close 04-ac.com and submit it using the terminal command: run_gaussian 04-ac.com
Review 04-ac.out to verify all frequencies are positive and thus that the structure is at a minimum on the excited state PES.
Optional - Band Shape Calculation: To calculate the band shape, first calculate the frequency at the ground state and the excited state. Then run a Franck-Condon calculation. Here is a sample input:
%chk=01-ac -chk from step 1
#P B3LYP/6-31+G(d,p) Freq=saveNM geom=check
Acetaldehyde ground state freq
%chk=04-ac -chk from step 4
#p B3lyp/6-31+G(d,p) freq=savenm geom=check
excited state freq
%chk=01-ac -chk from step 1
#P freq=(fc,Readfcht,vibrot,readfc,emission) geom=check nosymm -This is an emission example. For absorption, omit emission from the freq keyword.
calc of fc spectra
SPECRES=8 NORELI00 SPECMIN=5200. SPECMAX=100000.
04-ac.chk -chk from step 4, but note lack of % is deliberate
Red text are comments that should be omitted in the input file. SPEC keywords can be adjusted to match the region where emission and absorption occurs. Check the accompanying for minimum and maximum value.
For an Electronic Spectroscopy primer:
For more on the FC calculation:
To understand the A” symmetry, see https://en.wikipedia.org/wiki/List_of_character_tables_for_chemically_important_3D_point_groups
If there is an imaginary frequency, rerun the optimization with the keyword opt=vtight. This should eliminate the imaginary frequency. Check for the presence of negative frequencies by opening the output in Gaussview, then use the menu Results > Vibrations. If present, the negative frequency is reported first.
If the frequency calculation is taking > 2 days, qdel the job and resubmit with the Iop(10/7=7) keyword.