I am new to TDDFT calculations. I am facing problem in the interpretation of .log file. I have run TDDFT of one of the conformers of Phenylalanine to get "rotatory strength (R)" value. Following is the result which I couldn't interpret:
* + *
Rotatory Strengths (R) in cgs (10**-40 erg-esu-cm/Gauss)
state XX YY ZZ R(velocity) E-M Angle
1 0.5672 -18.1242 19.3397 0.5942 89.50
2 1.1961 -4.7002 -5.6729 -3.0590 121.18
3 11.1825 4.7169 12.7308 9.5434 38.33
1/2[* + (*)*]
Rotatory Strengths (R) in cgs (10**-40 erg-esu-cm/Gauss)
state XX YY ZZ R(length)
1 2.0778 31.2853 -19.3186 4.6815
2 -11.5976 -3.1967 2.5528 -4.0805
3 8.8754 15.8155 2.0687 8.9198
1/2[* + (*)*] (Au)
state X Y Z Dip. S. Osc.(frdel)
1 -0.0090 -0.0006 -0.0004 0.0100 0.0067
2 -0.0003 0.0000 -0.0001 0.0004 0.0003
3 -0.0018 -0.0031 0.0000 0.0049 0.0033
What is the magnitude and sign of the R value? What is R(length) and R(velocity)? How can I correlate this data with circular dichroism (CD)?
As for interpreting the results you have included, the best explanation I have ever seen of this type of calculation is Chemical Physics Letters 246 (1995) 1-8 (Pedersen and Hansen). Using them as a guide, I would interpret the columns in your question as the rotary strength tensor (the XYZ and XXYYZZ columns), which has two different measures of the magnitude (length and velocity, with the difference explained in some detail in Pedersen and Hansen). My understanding of their paper indicates that the velocity form is superior. E-M Angle is probably the angle between the electric and magnetic dipole transition moments; rotary strength is their scalar product. frdel is the associated oscilator strength; I am not sure what Dip. S. is, but it might be the dipole strength (a measure of the transition dipole moment?).
The connection between this information (which is limited to the three lowest excitations, as you probably noticed) is complicated, but if you have access to GaussView, it will compute the spectrum for you, making certain assumptions which you can generally control. To improve the match to experiment, you may want to consider the sum-over-states option in TD or computing explicit vibronic coupling to improve the simulation of the band shapes of the various transitions. This latter approach (which is computationally expensive) is described in the excellent tutorial review by Adamo and Jacquemin: Chem. Soc. Rev., (2013), 42, 845.
I hope my answer will be of at least a little help to you.
R is the value under R(velocity) and R(length), they correspond to velocity representation and length representation of rotatory strength, respectively. At complete basis set limitation, they are identical, while for finite-sized basis set, they differ with each other. You can use either of them to plot ECD spectrum, commonly R(velocity) is used since it is origin-independent.
ECD spectrum can be simulated by Gauss broadenin using calculated transition energies and rotatory strengths. For more detail about the underlying mechanism, please consult Section 3.13 of Multiwfn manual (http://sobereva.com/multiwfn). This program can easily plot ECD spectrum based on Gaussian TDDFT output file, see Section 4.11.3 of its manual for example.
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