# Comparing the experimental and calculated UV/vis spectra for ethene

I am trying to compute UV/Vis absorption spectrum for Ethene using Gaussian 09.

I created the ethene molecule in GaussView 5, and cleaned it. Then I optimized the molecule and checked if I got the minimum energy conformation with the following:

# freq=noraman cphf=noread b3lyp/6-31g(d) geom=connectivity formcheck
integral=grid=ultrafine scf=maxcycle=1000


Next I performed the energy calculation as follows:

# td b3lyp/6-31g(d) geom=connectivity


As a result I got a single peak with the maximum at 134 nm (see picture below) which seems to be way off from what I googled around on the Internet, which is like 173 nm or 180 nm.

Can anyone please help me figure out if I have done it correctly and whether I am way off the experimental data?

In short, there are two obvious problems with the setup OP uses for TD-DFT calculations:

1. B3LYP functional is not a good choice for TD-DFT.
2. 6-31G(d) basis is usually too small.

At M06-2X/Def2-TZVP level I get a maximum at ~160 nm, which, taking the accuracy of the TD-DFT approximations into account, is close enough to the experimental value.

• Thank you @Wildcat. I tried to redo the calculation according to your suggestion. I just took the molecule optimized at b3lyp/6-31g(d) and calculated the energy as follows: # td M062X/Def2TZVP geom=connectivity. I got the maximum 158.53 nm, so close to what you kindly reported. I wonder however if it's OK what I did in terms of optimizing the geometry at a different level than the one used to do the TD calculation for UV/Vis spectra? Looks like it works here. Do you think I do not need to reoptimize all of my molecules then? – Ricardo Moreno Sep 15 '16 at 1:14
• B3LYP/6-31G* might be a bad choice for a lot of calculations but it is not to be doomed a priori. We calculate a lot with it and reach acceptable accuracy. It always depends on the molecule that you are investigating. M06-2X for example does not give acceptable excitation energies for my complexes. Not even with triple zeta bs while B3LYP/6-31G* is way better for us. – pH13 - Yet another Philipp Sep 15 '16 at 8:00
• B3LYP/6-31G* might occasionally spit out some good numbers for excitation energies, right, but I would not trust this level of theory anyway since even when it works fine, it is very likely just the result of a fortunate cancellation of errors. – Wildcat Sep 15 '16 at 9:01
• @RicardoMoreno, B3LYP/6-31G* geometry of ethene should be good enough, so that there is no need for reoptimization. – Wildcat Sep 15 '16 at 9:03
• @pentavalentcarbon, why do you say that "M06-2X is not meant to be used for excitation energies"? It is one of the best hybrids according to benchmarks (10.1002/qua.24438). – Wildcat Oct 1 '16 at 22:56

For smaller molecules like ethene, the webbook by NIST is a good source of experimental data. Search results for ethene in particular here yield both a figure of a vacuum UV spectrum, indicating an absorption maximum centred around 160-165 nm with $\log \epsilon$ of about 4.2, as well with a primary literature reference (Platt, J.R.; Price, W.C., J. Chem. Phys., 1949, 17, 466).
Of course, other databases like Scifinder/Chemical Abstracts by the American Chemical Society may indidicate more recent data. A specialized compilation, more suitable for ethene in particular, is the MPI-Mainz UV/VIS Spectral Atlas of Gaseous Molecules of Atmospheric Interest here, with an entry about ethene.

Side note: NIST database equally offers access to other thermophysical data (like Vibrational and/or electronic energy levels) potentially of interest for you, too.

Addendum: With the searchable Computational Chemistry Comparison and Benchmark DataBase, NIST equally hosts numerous results of calculations of energies and structures for small molecules. This that may serve as a valuable reference, comparing the methods with each other, as well against experimentally determined data.

• Dear @Buttonwood, thank you so much for your guidance and the awesome links! By the way, do you think that the # td M062X/Def2TZVP level as suggested by Wildcat (and it seems to be working fine for ethene) will be good enough for UV/Vis computation for larger molecules, let's say 20-25 heavy atoms like carbon, and only a few oxygens or nitrogens around? – Ricardo Moreno Sep 15 '16 at 11:52
• @Ricardo Moreno You are wellcome. Yet: My practice in computational chemistry is too limited to provide you sound advice about the method / basis set to be deployed other than too look out how similar questions were solved by others in the field. Drawing a structure, (pre)optimising here and then with a force field & PM3 as a starting point / comparision e. g. for powder diffraction differs on what your question adresses and (in terms of computational cost) is at least a league below b3lyp and other hybrid functionals. – Buttonwood Sep 15 '16 at 14:46
• @RicardoMoreno Take a tour d'horizon in CCBDB just discovered. (Ethene is present, too.) – Buttonwood Sep 16 '16 at 17:11