Excitation and Emission (Fluorescence) from First Excited State (n→π*) of Acetaldehyde in Solution

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 how to calculate excitation and emission energies in the solution phase. There are 7 steps in total for emission calculations but steps 1-5 are sufficient for computing excitation energies. This tutorial assumes familiarity with GaussView and with Gaussian input and output files. Master the basic Gaussian tutorial before running this one. It is a good idea to do the gas phase version of this tutorial first.

Step 1: Ground state geometry optimization and frequency calculation including PCM equilibrium solvation. Use Gaussview to build acetaldehyde and set up the Gaussian input.^[1] Here is a sample file:

%nprocshared=1

%mem=3800MB

%chk=01-ac

# opt freq=noraman b3lyp/6-31+g(d,p) SCRF=(Solvent=Ethanol)

Acetaldehyde ground state

0 1

 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 all positive frequencies so it is a minimum on the PES. The electronic energy is: SCF Done: E(RB3LYP) = -153.851763013 A.U. after        1 cycles.

Review the MO’s so you can characterize the HOMO and LUMO.

Step 2: Vertical excitation with linear response - non-equilibrium solvation. A single-point TD-DFT calculation on ground state geometry defaults to non-equilibrium solvation. The results are used to identify which state or states are of interest and their ordering. These results give a reasonable description of the solvation of the excited state, but not quite as good as that from a state-specific solvation calculation. In this case, we will see that the n->π* state is the first singlet excited state. In later steps, we will use the state-specific method to produce a better description of the vertical excitation step.

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.

%nprocshared=1

%mem=3800MB

%oldchk=01-ac

%chk=02-ac

# B3LYP/6-31+G(d,p) TD=(nstates=6) Geom=Check Guess=Read SCRF=(Solvent=Ethanol)

Acetaldehyde: linear response vertical excited states

0 1

Geom=Check requests the starting geometry and Guess=Read requests the initial orbital data from the chk. %oldchk=01-ac means that the chk from step 1 will be the starting point for this step. TD=(nstates=6) requests the 6 lowest singlet excited states. http://www.gaussian.com/g_tech/g_ur/k_td.htm shows how to look for triplets or other variations. The end of the input file is the charge and multiplicity (the 0 1 line) because the geometry information is being read from the chk file. [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 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 so 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  4.3768 eV  283.27 nm  f=0.0000  <S**2>=0.000.This is the ground state to first excited state linear-response absorption. 12 -> 13             0.70587 shows the MO numbers. Visualize the MO’s with Gaussview to characterize this further.

Step 3: State-specific solvation of the vertical excitation. This requires two joined parts: first a single point calculation uses the Step 1 chk as input and NonEq=write stores the ground state non-equilibrium solvation data into 03-ac.chk. Second, the actual state-specific calculation is done using NonEq=read to get  the non-equilibrium solvation data from 03-ac.chk. The part 2 TD calculation writes more data to 03-ac.chk.  

%mem=23GB

%nprocshared=6

%oldchk=01-ac

%chk=03-ac

# B3LYP/6-31+G(d,p) SCRF=(Solvent=Ethanol,Read) Geom=Check Guess=Read

Acetaldehyde: saving the solvent reaction field from the ground state

0 1

NonEq=write

--link1--

%mem=23GB

%nprocshared=6

%chk=03-ac

# B3LYP/6-31+G(d,p) TD(NStates=6,Root=1) Geom=Check Guess=Read

  SCRF=(Solvent=Ethanol,ExternalIteration,Read)

Acetaldehyde: read non-eq solvation from ground state and

compute energy of the first excited with the state-specific method

0 1

NonEq=read

The keyword Root=1 specifies that the first excited state is the state of interest. You can change the root number to your desired state. We use more processors and memory since this is a larger calculation. The mem/proc ratio is based on the physical hardware of the MGCF server (6 procs are requested and the MGCF server has just approximately 3.8GB/proc so 3.8x6 is about 23GB). Ask us for help before you adjust these.

Save/close 03-ac.com and submit it using the terminal command: run_gaussian 03-ac.com

03-ac.out shows the energy of first excited state at the ground state optimized geometry from the non-equilibrium solvation state-specific calculation: After PCM corrections, the energy is  -153.687684759 a.u. Subtract this energy from the ground state energy (from step 1) to get the ground state to first excited state absorption with the state-specific solvation. The wavelength for this is 285.32nm.

Notes on step 3: For excited state calculations in solution, there is a distinction between equilibrium and non-equilibrium calculations. The solvent responds in two different ways to changes in the state of the solute: it polarizes its electron distribution, which is a very rapid process, and the solvent molecules reorient themselves (e.g., by a rotation), a much slower process. An equilibrium calculation is where the solvent had time to fully respond to the solute (in both ways), e.g., a geometry optimization (a process that takes place on the same time scale as molecular motion in the solvent). A non-equilibrium calculation is appropriate for processes which are too rapid for the solvent to have time to fully respond, e.g. a vertical electronic excitation.

Equilibrium solvation is the default for CIS and TD-DFT excited state geometry optimizations. Non-equilibrium is the default for CIS and TD-DFT energies using the default PCM procedure, and equilibrium is the default for the external iteration approach (SCRF=ExternalIteration). See the examples for the method for computing non-equilibrium external iteration calculations.

The same checkpoint name is use for both parts of Step 3 because part 2 uses solvation information from part 1. Step 3 could be broken into two different com files where the chk file from the first com is used as an %oldchk for the second com. This is only necessary if you get an “error reading the pcm file”.

Step 4: Relaxation of the excited state geometry. Next, we perform a TD-DFT geometry optimization, with equilibrium, linear response solvation, to find the minimum energy point on the excited state potential energy surface. Since this is a TD-DFT optimization, the program defaults to equilibrium solvation. As is typical of such cases, the molecule has a plane of symmetry in the ground state but the symmetry is broken in the excited state, so the ground state geometry is perturbed slightly to break symmetry at the start of the optimization. We retrieve the geometry and other data from the chk from Step 2:

%mem=23GB

%nprocshared=6

%oldchk=02-ac

%chk=04-ac

# B3LYP/6-31+G(d,p) TD=(Read,NStates=6,Root=1) SCRF=(Solvent=Ethanol)

  Geom=Modify Guess=Read Opt=ReadFC

Acetaldehyde: excited state opt, Geom=Modify breaks first excited state symmetry

0 1

7 4 1 2 10.0

5 4 1 3 -50.0

We 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 may not 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 with 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. Read the step 2 output into Gaussview, label the atoms and measure a few dihedrals to make good choices. In our example, atoms 7, 4, 1, 2 had a dihedral of 0 so we changed it by 10 degrees.  5, 4, 1, 3 was -58 so we changed it to -50.0.]

Save/close 04-ac.com and submit it using the terminal command: run_gaussian 04-ac.com

04-ac.out shows: Excited State 1: Singlet-A 3.2080 eV  386.49 nm  f=0.0013  <S**2>=0.000

. . . . Total Energy, E(TD-HF/TD-KS) =  -153.705918686

The wavelength for this is 386.49nm.

Step 5: Vibrational frequency calculation of the excited state optimized geometry. We verify that the step4 geometry is a minimum. The results could also be used as part of a Franck-Condon calculation (see below).

%mem=23GB

%nprocshared=6

%oldchk=04-ac

%chk=05-ac

# B3LYP/6-31+G(d,p) TD=(Read,NStates=6,Root=1) Freq

  SCRF=(Solvent=Ethanol) Geom=Check Guess=Read

Acetaldehyde excited state freq

0 1

Use gedit to make a file called 05-ac.com  with the above 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 4.

This is a frequency calculation on the optimized geometry from step 4 so you must include the Freq=noraman keyword.^[2] Again, you may need to adjust the basis set, functional, etc when doing calculations on other molecules. Make sure %chk matches the name of the current calculation and %oldchk matches the prior step.

Save/close 05-ac.com and submit it using the terminal command: run_gaussian 05-ac.com

Review 05-ac.out to verify all frequencies are positive and thus at a minimum on the excited state PES.

Step 6: Emission (part 1). This step does state-specific equilibrium solvation of the excited state at its equilibrium geometry, writing out the solvation data for the next step via the PCM NonEq=write input.

%mem=23GB

%nprocshared=6

%oldchk=05-ac

%chk=06-ac

# B3LYP/6-31+G(d,p) TD=(Read,NStates=6,Root=1)  Geom=Check Guess=Read

  SCRF=(Solvent=Ethanol,ExternalIteration,Read)

Acetaldehyde emission state-specific solvation at first excited state opt geom

0 1

NonEq=write

Save/close 06-ac.com and submit it using the terminal command: run_gaussian 06-ac.com

Review 06-ac.out to see the energy of first excited state at its optimized geometry from the equilibrium solvation state-specific calculation: After PCM corrections,the energy is -153.707148803 a.u.

The wavelength for this is 402.86 nm.

Step 7: Emission to final ground state (part 2). Finally, we compute the ground state energy with non-equibrium solvation, at the excited state geometry and with the static solvation from the excited state.

%mem=23GB

%nprocshared=6

%oldchk=06-ac

%chk=07-ac

# B3LYP/6-31+G(d,p) SCRF=(Solvent=Ethanol,Read) Geom=Check Guess=Read

Acetaldehyde: ground state non-equilibrium at excited state geometry.

0 1

NonEq=read

Save/close 07-ac.com and submit it using the terminal command: run_gaussian 07-ac.com

Review 07-ac.out to see the energy of first excited state at its optimized geometry from the equilibrium solvation state-specific calculation:

SCF Done:  E(RB3LYP) =  -153.822044519         A.U. after   10 cycles

The difference between the energies from steps 6 and 7 gives the vertical emission energy. In this case, the first excited state to ground state emission, including the state-specific solvation correction, is at 396.55 nm.  Based on -153.822044519 - -153.707148803 = 0.1149 hatrees; then converted to nm using:

https://www2.chemistry.msu.edu/faculty/reusch/virttxtjml/cnvcalc.htm

Steps 1, 2, and 4 would be sufficient to compute the excitation and emission energies in the gas-phase (along with step 5 to confirm the nature of stationary point). They are not sufficient when solvent effects are included because the energies computed in step 4 correspond to the ground state solvent reaction field, while the emission takes place in the reaction field created in response to the excited state charge distribution. This is what is accounted for properly in steps 6 and 7.

For an Electronic Spectroscopy primer:

http://chemwiki.ucdavis.edu/Physical_Chemistry/Spectroscopy/Electronic_Spectroscopy/Electronic_Spectroscopy

For a TDDFT review:

 http://pubs.rsc.org/en/Content/ArticleLanding/2013/CS/c2cs35394f#!divAbstract

To calculate band shape in the gas phase, run a calculation with Freq=(ReadFC,FC,Emission), giving the checkpoint file from step 1 as the main checkpoint file for the job, and providing the name of the checkpoint file from step 5 in the input stream to specify the other state. For the solvated band shape, one must do Freq=(ReadFC,FC,Emission,ReadFCHT) using the checkpoint files for steps 1 and 5, but also providing the state-specific emission energy in the input section for the Franck-Condon calculation.

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:

%nprocshared=6

%mem=23GB

%chk=01-ac                        -chk from step 1

#P B3LYP/6-31+G(d,p) Freq=saveNM geom=check

Acetaldehyde ground state freq

0 1

--link1--

%nprocshared=6

%mem=23GB

%chk=05-ac                        -chk from step 5

#p B3lyp/6-31+G(d,p) freq=savenm geom=check

excited state freq

0 1

--link1--

%chk=01-ac             -chk from step 1

%nprocshared=6

%mem=23GB

#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

0,1

SPECMIN=5200. SPECMAX=100000.

05-ac.chk              -chk from step 5, 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 more on the FC calculation:

http://dreamslab.sns.it/pdf/vibronic_spectra_G09-A02.pdf

To understand the A” symmetry, see https://en.wikipedia.org/wiki/List_of_character_tables_for_chemically_important_3D_point_groups