I am attempting to use ADF to calculate frequency-dependent
hyperpolarizabilities. Upon the advice of the ADF manual, I have read
some "introductory" papers, and quickly realized that, amidst the
complicated landscape of nomenclature and notation, perhaps replicating
someone else's results would be a nice initial step.

Therefore, I have performed a Response calculation of CO2, following the
same computational details of van Gisbergen et al., J. Chem. Phys., 109,
10657 (1998). The output is, to me, somewhat cryptic, and I cannot figure
out the manipulations required to transform the ADF output into the
numbers in Table IV of the aforementioned paper.

In my input file, the key lines are:

EFIELD 0 0 0.001

Response
Allcomponents
Hyperpol 0.0656
Dynahyp
End

To simulate an electric field along the z-axis of D(inf)h CO2, and to
calculate hyperpolarizabilities at a laser frequency of 694.3 nm (0.0656
au). In the output, there are eight sections of hyperpolarizability data:

(1) The STATIC hyperpolarizability tensor beta, followed by Non-zero
components

(2) The SHG hyperpolarizability tensor beta, followed by Non-zero
components

(3) The EOPE hyperpolarizability tensor beta, followed by Non-zero
components

(4) The OR hyperpolarizability tensor beta, followed by Non-zero
components

(5) - (8) are (1) - (4) repeated, except with output consisting of single
values for quantities labelled beta_z, mu_z, beta_bar, and beta-vec
(and beta_Kerr for the EOPE section).

My questions are:

[A]: What manipulations of Sections (1) through (8) above give the correct
gamma (z z z z) values of Table IV? It seems that the value beta_z of
Section 5 above divided by the electric field strength of 0.001 au might
be right, in that it gives me (to two significant figures) Stan's values
for BLYP and LB94, but I get 2000 for LDA instead of 1900.

[B]: How do I manipulate the data of Sections (1) through (8) to get gamma
(x x x x) and gamma (x x z z)? For the former, my first inclination would
be to change the EFIELD line in my input file to: EFIELD 0.001 0 0, and
then manipulate the beta (x x x) values, but no such values are reported.
Do I use the beta (z z z) values with the EFIELD line which sets up a
field polarized along the x-axis?

[C]: What about getting gamma (||), which is also known as <gamma> (z z z
z)? I know Equation 3 explains its derivation, but I must confess
bafflement about the meaning of the indices i and j.

[D]: What do I have to do to obtain the value EOKE? I believe it has
something to do with Equation 9.20 from Stan van Gisbergen's thesis
(available from the SCM website), but said equation is utterly inscrutable
to me (no offense, Stan -- it's my ignorance, not your writing :). It
seems I have to manipulate the EOPE values, but I'm not sure how. Also,
does the reported value beta_Kerr get used at all?

[E]: Finally, is there a difference between the Electro-Optical Kerr
Effect (EOKE) terminology used in ADF and the Optical Kerr Effect (OKE)
designation I've seen elsewhere? How do these (or does this, if they're
one and the same) correspond to the phenomena termed "dc Kerr effect" and
"ac Kerr effect" by Shelton and Rice in their review (Chem. Rev., 94, 3
(1994))?

I apologize in advance for the neophyte (and time-consuming) questions.

Thank you,
Michael Drummond

Postdoctoral Research Associate
Computational Chemical Sciences Group
Computer Science and Mathematics Division
Oak Ridge National Laboratory
Received on 2005-04-11 20:36:02