Hi everybody,

I am getting seriously confused trying to understand the output of the
TDDFT "Response" calculations in BAND. For example, let's take the the
output of the silicon example (in examples/band directory). Could
somebody explain to me, what is the definition of the "Chi_jj"
tensor, which is printed in the course of the TDDFT calculation?

This cannot be the electric susceptibility tensor, as it does not
match the dielectric function, printed later in the calculation:

   eps(omega) = 1 + 4 pi chi(omega)

eps(0.042) = 16.1 (which seems about right for silicon)
chi_jj(0.042) = -9.99

The only other quantity denoted by the chi_jj symbol, which I can see
in Fred Koostra's thesis is the current-current response kernel -
however, this is not a material property. Looking at the code in
"caldec.d", it appears that the relationship between eps and chi_jj
is given by:

                     4 pi chi_jj(omega) - chi_jj(0)
   eps(omega) = 1 + ----- -------------------------
                      V omega**2

Comparing to eq. (4.62) in Fred's thesis, I assume that the "chi_jj"
value printed in the code is, in fact, the integral of the paramagnetic
current density over the Wigner-Seitz cell. Is this interpretation
correct?

The second puzzle is that for 1D linear chains, the program will
instead calculate (in calpol.d) and print the X,X component of the
quantity:

                     chi_jj(omega) - chi_jj(0)
   alpha(omega) = - ---------------------------
                            omega**2

> From eqs. 9.21-9.22 of the thesis, this appears to be the longitudinal
polarizability of a single unit cell, in Bohr**3. Is this interpretation
correct? Why other components of the electric susceptibility tensor are
discarded in this case?

Serguei

---
Dr. Serguei Patchkovskii
Tel: +1-(613)-990-0945
Fax: +1-(613)-947-2838
E-mail: Serguei.Patchkovskii_at_nrc.ca
Coordinator of Modelling Software
Theory and Computation Group
Steacie Institute for Molecular Sciences
National Research Council Canada
Room 2011, 100 Sussex Drive
Ottawa, Ontario
K1A 0R6 Canada