Can you clarify your question? Is your question about how to calculate hyperpolarizability or is it about what does the values mean?
I have calculated the first hyperpolarizability of different derivatives of azatricyclo-8-ene-3,5-dione and I got different values. I want to compare these values on the basis of their structure. I want to know how the hyperpolarizability of a compound changes by adding groups like CH3, benezene ring etc. in the parent structure.
Again, not sure exactly what molecule(s) you are talking about, but changes in the hyperpolarizability are difficult to predict or to explain. Sebastien is correct, it seems to depend to some extent on the HOMO-LUMO gap, and the molecule cannot have a center of symmetry. My students have done a lot of calculations of beta with a wide array of substituents (on the central molecular structure that we are interested in) and with a large number of basis sets, levels of theory, etc. It's a sticky problem - there doesn't seem to be an obvious correlation with electronegativity, electron-withdrawing ability, group polarizability, etc. (Of course, the known molecules with large beta have a motif of an electron-donating group + a long conjugated pi system + an electron-donating group (think of p-nitroaniline, for example, or 4'-nitro-4-N,N-dimethylaminoazobenzene), so if you can build in that motif, you will be on the right track. Adding methyls, etc.probably won't have any effect - phenyl, probably yes (extending the conjugation length). Give us more details, and good luck with this.
P.S. Is this related to your di-(4-formylphenyl)anthracenes?
Dear Allen Clabo,
My question is related with the following derivatives.
(i) 1,7,8,9-Tetrachloro-4-(4-bromo-butyl)-10,10-dimethoxy-4-aza-tricyclo[5.2.1.02,6] dec-8-ene-3,5-dione. [beta value is 1.53×10-30 esu (b3lyp/cc-pVDZ)
(ii) 1,7,8,9-tetrachloro-10,10-dimethoxy-4-[3-(4-phenylpiperazin-1-yl)propyl]-4-azatricyclo[5.2.1.02,6]dec-8-ene-3,5-dione [ beta value is 4.49×10-30 esu (b3lyp/sdd)]
(ii) 1,7,8,9-tetrachloro-10,10-dimethoxy-4-{3-[4-(3-methoxyphenyl)piperazin-1-yl]propyl}-4-azatricyclo[5.2.1.02,6]dec-8-ene-3,5-dione.[beta value is 1.38×10-30 esu (b3lyp/6-31G ]
Looks like interesting molecules - I'd be surprised if you get beta much bigger than 1 (which is not very significant) since you don't have an extensively conjugated molecule - (we are fighting the same battle since our core structure is aromatic but not highly conjugated) - I look forward to seeing what you learn.
Good morning Renjith Raveendran Pillai and all researchgate group;
You can see the gap between HOMO and LUMO, if the gap is decreased so the hyperpolarizability Beta is increase. you can introduce a donor and acceptor group in the side of your molecule, and you see the effect.
Then, gather all those informations and it's done! Renjith Raveendran Pillai