$TDHFX group     (relevant for SCF=RHF if RUNTYP=TDHFX)
 
    This group permits the analytical determination of
static and/or frequency dependent polarizabilities and
hyperpolarizabilities (alpha, beta, and gamma), as well as
their first- and second-order geometrical derivatives (of
alpha and beta).  This permits the prediction of dynamic
(nonresonant) Raman and hyper-Raman spectra, yielding both
intensities and depolarizations.  The method is only
available for closed shell systems (RHF).
 
   For other polarizability options, see $FFCALC and $TDHF.
For ordinary Raman spectra, see $RAMAN.
 
   You must not use point group symmetry in this kind of
calculation (except to enter the molecule's structure), so
provide NOSYM=1.  Since the derivative level is quite high,
it is a good idea to converge the SCF problem crisply,
CONV=1.0D-6.  These options are not forced by the RUNTYP,
so please use explicit input.
 
   The $TDHFX group acts as a script.  Each keyword must be
on a separate line, terminated by a $END.  The available
keywords are gathered into 3 sets.  Those belonging to the
first set must appear before the second set, which must
appear before the third set.
 
Set 1:
 
Here is a list of keywords that specifies the number of
parameters (electric fields and geometrical distortions)
that will be taken into account in the computations.
 
ALLDIRS = compute the responses for all the electric field
          directions (x,y,z).
 
DIR idir = compute the responses for one electric field
           specific direction:
           x(idir=1), y(idir=2) and z(idir=3).
 
USE_C   = do the computation in Cartesian coordinates.
 
USE_Q   = do the computation in normal coordinates.
 
The default is ALLDIRS and USE_C.
 
Set 2:
 
The following two keywords must be specified before any
computation that requires vibrational frequencies or normal
modes of vibration:
 
FREQ  = compute the normal modes and the harmonic
        vibrational frequencies.  Do a HESSIAN job.
 
FREQ2 = same as FREQ but store the second derivative of
        the monoelectronic Hamiltonian.  Required if you
        want to determine geometrical second-order
        derivatives of properties.
 
Set 3:
 
The following keywords are related to the generalized
iterative method to solve TDHF mixed derivative equations.
They can be inserted anywhere in the $TDHFX group and
change the behavior of the generalized iterative method for
any of the following tasks that might be requested.
 
DIIS = Use the DIIS method. This is the default method.
 
NOACCEL = Do not use any accelerating method.
 
ITERMAX imax = Specify the maximum number of iterations to
               obtain the converged solution.  Default=100.
 
CONV threshold = the threshold convergence criterion for
                 the U response matrices.  Default=1E-5.
 
Below are the keywords to select a particular computation.
The xx_NI version will call a non-iterative procedure.
 
The laser energy (w) must be given in Hartree.  Divide by
219,474.6 to convert a frequency in wavenumbers (cm-1) to a
photon energy in Hartree.  Wavelength (in nm) is 45.56/w,
when w is in Hartree.  Static polarizabilities may be
obtained from w=0.0.
 
MU = compute the dipole moment.
 
ALPHA w =
    compute the dynamic polarizability:
          alpha(-w;w).
 
BETA w1 w2 / BETA_NI w1 w2 =
    compute the dynamic first hyperpolarizability:
          beta(-w1-w2;w1,w2).
 
GAMMA w1 w2 w3 / GAMMA_NI w1 w2 w3 =
    compute the dynamic second hyperpolarizability:
          gamma(-w1-w2-w3;w1,w2,w3).
 
POCKELS w / POCKELS_NI w =
     compute electro-optic Pockels effect: beta(-w;w,0).
 
OR w / OR_NI w =
     optical rectification: beta(0;w,-w).
 
SHG w / SHG_NI w =
     second harmonic generation: beta(-2w;w,w).
 
KERR w / KERR_NI w =
     DC Kerr effect: gamma(-w;w,0,0).
 
ESHG w / ESHG_NI w =
     electric field induced 2nd harm gen: gamma(-2w;w,w,0).
 
THG w / THG_NI w =
     third harmonic generation: gamma(-3w;w,w,w).
 
DFWM w / DFWM_NI w =
     degenerate four wave mixing gamma(-w;w,-w,w).
 
See the review
    D.P.Shelton, J.E.Rice  Chem.Rev. 94, 3-29(1994)
for more information on the quantities just above.  The
next options are nuclear derivatives of some of the above.
 
DMDX_NI =
     compute the dipole derivative matrix,
     the geometrical first derivative of MU.
 
DADX w / DADX_NI w =
     compute the polarizability derivative matrix, the
     geometrical first-order derivative of alpha(-w;w).
 
DBDX w1 w2 / DBDX_NI w1 w2 =
     compute the geometrical first-order derivative
     of beta(-w1-w2;w1,w2).
 
D2MDX2_NI =
     compute geometrical second derivatives of MU
 
D2ADX2_NI w =
     compute geometrical second derivatives of alpha(-w;w).
 
D2BDX2_NI w1 w2 =
     geometrical second derivatives of beta(-w1-w2;w1,w2).
 
The next two keywords automatically select paths through
the package generating the required intermediates (both
polarizabilities and their nuclear derivatives) to form
spectra.  The most efficient path through the program will
be selected automatically.
 
RAMAN w = Summarize the Raman responses in a table, and if
          necessary, compute the geometrical first-order
          derivatives of alpha(-w;w).
 
HRAMAN w = Summarize the hyper-Raman responses in a table,
           and if necessary, compute the geometrical first-
           order derivatives of beta(-2w;w,w).
 
The following keywords permit the deletion of disk files
associated with the set of frequencies w1,w2,...
 
FREE w1
FREE w1 w2
FREE w1 w2 w3
 
Below is an example of a TDHFX group:
 
$TDHFX
  ALLDIRS
  USE_Q
  FREQ
  DIIS
  ITERMAX 100
  CONV 0.1E-7
  HRAMAN 0.02
  FREE 0.02
  FREE 0.02 0.02
  HRAMAN 0.03
$END
 
References:
"Time Dependent Hartree-Fock schemes for analytic
evaluation of the Raman intensities"
O.Quinet, B.Champagne  J.Chem.Phys. 115, 6293-6299(2001).
 
"Analytical TDHF second derivatives of dynamic electronic
polarizability with respect to nuclear coordinates.
Application to the dynamic ZPVA correction."
O.Quinet, B.Champagne, B.Kirtman
J.Comput.Chem. 22, 1920-1932(2001).
 
"Analytical time-dependent Hartree-Fock schemes for the
evaluation of the hyper-Raman intensities"
O.Quinet, B.Champagne  J.Chem.Phys. 117, 2481-2488(2002).
errata: JCP 118, 5692(2003)
 
"Analytical time-dependent Hartree-Fock evaluation of the
dynamically zero-point averaged (ZPVA) first
hyperpolarizability"
O.Quinet, B.Kirtman, B.Champagne
J.Chem.Phys. 118, 505-513(2003).
 
Computer quirks:
 
1. This package uses file numbers 201, 202, ... but some
compilers (chiefly g77) may not support unit numbers above
99.  The remedy is to use a different computer or compiler.
 
2. If you experience trouble running this package under
AIX, degrade the optimization of subroutine JDDFCK in
hss2b.src, by placing this line
    @PROCESS OPT(2)
immediately before JDDFCK, recompile hss2b, and relink.
 
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