What are qualities in parenthesis in the Gamma tensor?

esmuigors

Dear developers and others.

I am a bit confused about the output of the second hyperpolarizability calculation:

*******************************************************************************
 SECOND HYPERPOLARIZABILITY (GAMMA) TENSOR
  COMPONENT      GAMMA
 *******************************************************************************

     XXXX    1.0077E+04 (   1.0077E+04)
     XXXY    4.1650E-13 (   1.9458E-08)
     XXXZ    5.9072E-13 (   2.5339E-08)
     XXYY    3.9702E+03 (   3.9702E+03)
     XXYZ   -1.0917E+03 (  -1.0917E+03)
     XXZZ    3.2158E+03 (   3.2158E+03)
     XYYY    7.0166E-13 (   1.4903E-07)
     XYYZ    5.2035E-14 (   2.4139E-08)
     XYZZ    1.9596E-13 (   1.3356E-08)
     XZZZ    6.7898E-13 (  -7.7814E-09)
     YYYY    7.2247E+03 (   7.2247E+03)
     YYYZ   -4.5162E+02 (  -4.5162E+02)
     YYZZ    3.0331E+03 (   3.0331E+03)
     YZZZ   -1.5476E+01 (  -1.5476E+01)
     ZZZZ    1.1089E+04 (   1.1089E+04)

What are the quantities in parentheses? Are these a result of some rotation? If so, then why only the minor components change? Which ones are the real ones I should use?

Thank You in advance.

aerba

Hi,

I understand your confusion as this is not clearly explained anywhere in the output. The values within parentheses are those obtained as such from the CPHF/KS calculation. The values outside the parentheses are those obtained with an a posteriori symmetrization.

In your case above, the large components are not affected by the symmetrization, which only helps "cleaning" the vanishing components (i.e. they become cleaner "zeros").

Hope this clarifies things a little,

esmuigors

Thank You very much, prof. Erba! That did clarify the matter!

esmuigors

To clarify better, does the symmetrization correspond to the frequency symmetry (which determines the equal components, e.g., xxyy = xyxy = xyyx, etc. for the static case?
Or is this about the geometrical symmetry (and possible reorientation of the molecule to have the dipole moment along an axis)?

esmuigors

Dear prof. Erba,

Have You got any time to look into the source maybe?
Quite interestingly, I have recently noticed that in some other QC code values for the components change a lot (by up to 60%) from run to run, except for the dipole orientation (when the molecular dipole is aligned with z axis). Is (or could be) the reorientation You are referring to connected with this? Seems like something similar to the struggle fir gauge invariance in NMR calculations...