$TDHF group    (relevant for SCFTYP=RHF if RUNTYP=TDHF)
 
    This group permits the analytic calculation of various
static and/or frequency dependent polarizabilities, with an
emphasis on important NLO properties such as second and
third harmonic generation.  The method is programmed only
for closed shell wavefunctions, at the semi-empirical or ab
initio level.  Ab initio calculations may be direct SCF, or
parallel, if desired, except INIG=2.
 
    For a more general numerical approach to the static
properties, see $FFCALC.  For additional closed shell
dynamic polarizabilities and spectra, see $TDHFX.  To
compute the hyperpolarizability for closed shell DFT, or to
use fully general frequency combinations, see TDDFT=HPOL.
There is a summary of all possible different types of
polarizability computations in the 4th manual chapter.
 
 
NFREQ  = Number of frequencies to be used. (default=1)
 
FREQ   = An array of energy values in atomic units.  For
         example: if NFREQ=3 then FREQ(1)=0.0,0.1,0.25.
         By default, only the static polarizabilities are
         computed.  (default is freq(1)=0.0)
 
    The conversion factor from wavenumbers to Hartree
    is to divide by 219,474.6.  To convert a wavelength
    to Hartree, compute FREQ=45.56/lamda, lambda in nm.
 
MAXITA = Maximum number of iterations for an alpha
         computation. (default=100)
 
MAXITU = Maximum number of iterations in the second order
         correction calculation.  This applies to iterative
         beta values and all gammas. (default=100)
 
DIIS   = use the DIIS extrapolation using residual induced
         Fock matrix (default=.TRUE.).
 
MAXDII = the maximum number of Fock matrices to be used in
         DIIS extrapolation (default=50).
 
ATOL   = Tolerance for convergence of first-order results.
         (default=1.0d-05)
 
BTOL   = Tolerance for convergence of second-order results.
         (default=1.0d-05)
 
RETDHF = a flag to choose starting points for iterative
         calculations from best previous results.
         (default=.true.)
 
 
* * * the following NLO properties are available  * * *
 
    Note: alpha polarizabilities are always calculated.
 
INIB   = 0 turns off all beta computation (default)
       = 1 calculates only noniterative beta
       = 2 calculate iterative and noniterative beta
           The next flags allow further BETA tuning
 
BSHG   = Calculate beta for second harmonic generation.
 
BEOPE  = Calculate beta for electrooptic Pockels effect.
 
BOR    = Calculate beta for optical rectification.
 
INIG   = 0 turns off all gamma computation (default)
       = 1 calculates only noniterative gamma
       = 2 calculate iterative and noniterative gamma
           The next flags allow further GAMMA tuning
 
GTHG   = Calculate gamma for third harmonic generation.
 
GEFISH = Calculate gamma for electric-field induced
         second harmonic generation.
 
GIDRI  = Calculate gamma for intensity dependent
         refractive index.
 
GOKE   = Calculate gamma for optical Kerr effect.
 
    These will be computed only if a nonzero energy (FREQ)
is requested.  The default for each flag is .TRUE., and
they may be turned off individually by setting some .FALSE.
Note however that the program determines the best way to
calculate them.  For example, if you wish to have the SHG
results but no gamma results are needed, the SHG beta will
be computed in a non-iterative way from alpha(w) and
alpha(2w).  However if you request the computation of the
THG gamma, the second order U(w,w) results are needed and
an iterative SHG calculation will be performed whether you
request it or not, as it is a required intermediate.
 
Only the following combinations make sense:
     INIB   INIG giving FREQ(1)=0.0,0.1     e.g. w=0.1
       0      0       static alpha,       a(w)
       1      0       static alpha,beta   a(w),a(2w)
                      noniterative b(OR), b(EOPE), b(SHG)
       2      0       static alpha,beta   a(w),a(2w)
                      noniterative b(OR), b(EOPE), b(SHG)
                         iterative b(OR), b(EOPE), b(SHG)
       2      1       static alpha,beta,gamma  a(w),a(2w)
                         iterative b(OR), b(EOPE), b(SHG)
                      noniterative g(THG), g(EFISH),
                                   g(IDRI), g(OKE)
       2      2       static alpha,beta,gamma  a(w),a(2w)
                         iterative b(OR), b(EOPE), b(SHG)
                      noniterative g(THG), g(EFISH),
                                   g(IDRI), g(OKE)
                         iterative static gamma, g(OKE),
                                   g(THG), g(EFISH),
                                   g(IDRI), g(DC-OR)
 
This is a quirky program:
 
1. INIG=2 only runs in serial, and only runs with AO
integrals stored on disk.
2. ISPHER=1 may not be chosen.
3. INIB=1 and INIB=2 print the same components for OR, OPE,
SHG, but different totals from the whole tensor.  It is not
clear which is correct.
4. units are not well specified on the output!
 
References:
 
for static polarizabilities,
G.J.B.Hurst, M.Dupuis, E.Clementi
   J.Chem.Phys.  89, 385-395(1988)
 
for dynamic polarizabilities,
S.P.Karna, M.Dupuis  J.Comput.Chem.  12, 487-504 (1991).
P.Korambath, H.A.Kurtz, in "Nonlinear Optical Materials",
ACS Symposium Series 628, S.P.Karna and A.T.Yeates, Eds.
pp 133-144, Washington DC, 1996.
 
Review: D.P.Shelton, J.E.Rice, Chem.Rev. 94, 3-29(1994).
 
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