$TDDFT group
                     (relevant if TDDFT chosen in $CONTRL)
 
   This group generates molecular excitation energies by
time-dependent density functional theory computations (or
time-dependent Hartree-Fock, also known as the Random Phase
Approximation).  The functional used for the excited states
is necessarily the same one that is used for the reference
state, specified by DFTTYP in $CONTRL.
 
   For conventional TD-DFT (TDDFT=EXCITE in $CONTRL), the
orbitals are optimized for RHF or UHF type reference
states.  Analytic nuclear gradients are available for
singlet excited states, while the energy of excited states
of other multiplicities can be computed.  Two-photon
absorption cross-sections may be predicted for singlet
excited states.  Ground state hyperpolarizabilities may be
computed with the TDDFT module.
 
   For spin-flip TD-DFT (TDDFT=SPNFLP in $CONTRL), the
calculation obtains orbitals for a reference state of
either UHF or ROHF type, with MULT in $CONTRL determining
the Ms quantum number of the reference.  The reference
state's Ms is set equal to the S value implied by $CONTRL's
MULT=2S+1.  The SF-TD-DFT then uses only determinants with
Ms=S-1, due to the flip of one alpha spin into a beta spin.
This means that target states (which are spin contaminated)
will have multiplicities around the range S-1 to S, only.
It is quite possible for some of the target states to have
a lower energy than the reference!!!  Nuclear gradients and
properties are available.
 
   See just below for "limitations" below regarding the two
different TD-DFT types.
 
   TD-DFT is a single excitation theory.  All of the
caveats listed in the $CIS input group about states with
double excitation character, need for Rydberg basis sets,
greatly different topology of excited state surfaces, and
so on apply here as well.  Please read the introduction to
the $CIS input group!  If you use very large or very small
Gaussian exponents, you may need to increase the number of
radial grid points (the program prints advice in such
cases).
 
   TDHF, TDDFT, and CIS are related in the following way:
          -- Tamm/Dancoff approximation -->
        |     TDHF                   CIS
   DFT  |
        V     TDDFT               TDDFT/TDA
 
Here TDHF means absorption of photons, to produce excited
states (TDHF is called RPA in the physics community).  This
meaning of TDHF should not be confused with the photon
scattering processes computed by RUNTYP=TDHF or TDHFX,
which generate polarizabilities.  Note, in particular, that
CITYP=CIS is equivalent to using TDDFT=EXCITE DFTTYP=NONE
TAMMD=.TRUE., provided the former is run with no frozen
cores.  Solvent effects for CIS calculations are therefore
available via the TDDFT codes.
 
   Excited state properties are calculated using the TDDFT
excited state electronic density only during gradient runs,
or by setting TDPRP below.
 
   The TD-DFT codes excite all electrons, that is, there is
no frozen core concept.  Please see the 4th chapter of this
manual for more information on both types of TD-DFT.
 
            "limitations" for TDDFT=EXCITE:
 
   Permissible values for DFTTYP are shown below.  These
include "NONE" which uses TDHF (i.e. the Random Phase
Approximation), noting that extra states may need to be
solved for in order to be sure of getting the first few
states correctly.  If nuclear gradients are needed, you may
choose any of the following functionals:
   NONE
   SVWN, SOP, SLYP, OLYP,
   BVWN, BOP, BLYP (and their LC=.TRUE. versions)
   B3LYP, CAMB3LYP, B3LYPV1R, PBE, PBE0
   CAMQTP00, CAMQTP01
For evaluation of just the excitation energies, you may use
many more functionals, notably including the metaGGAs in
the last three lines:
   NONE
   SVWN, SVWN1RPA, SPZ81, SP86, SOP, SLYP,
   BVWN, BVWN1RPA, BPZ81, BP86, BOP, BLYP, OLYP,
   B3LYP, CAMB3LYP, B3LYPV1R, B3PW91, X3LYP,
   PW91, PBE, PBE0,
   APF,
   VS98, PKZB,
   M05, M05-2X, M06, M06-HF, M06-L, M06-2X, M08-HX, M08-SO,
   MN12-L, MN12-SX, MN15, MN15-L,
   TPSS, TPSSm, TPSSh, and revTPSS
 
   The LC flag in $DFT automatically carries over to TDDFT
runs.  The LC option may be used with the "B" functionals,
and (like the similar range-separated CAMB3LYP) is useful
in obtaining better descriptions for charge-transfer
excitations or Rydberg excitation energies than are the
conventional exchange correlation functionals (whether pure
or hybrid).  The LC flag is also available for excited
state gradient computation.
 
   Limits specific to the references for TDDFT=EXCITE are:
 
   For SCFTYP=RHF, excitation energies can be found for
singlet or triplet coupled excited states.  For singlet
excited states only, analytic gradients and properties can
be found, for either full TD-DFT or in the Tamm/Dancoff
approximation.  For RHF references, solvent effects can be
included by EFP1 or PCM (or both together), for both TD-DFT
excitation energies and their nuclear gradients.  DFTB
(possibly combined with PCM) may be chosen as well, and
analytic gradients for singlet and triplet are available.
 
   For SCFTYP=UHF, excited states with the same spin
projection as the ground state are found.  MULT in $CONTRL
governs the number of alpha and beta electrons, hence
Ms=(MULT-1)/2 is the only good quantum number for either
the ground or excited states.  Since U-TDDFT is a single
excitation theory, excited states with (S) values near Ms
and near Ms+1 will appear in the calculation.  There are no
properties other than the excitation energy, nor gradients,
nor solvent effects, at present.
 
            "limitations" for TDDFT=SPNFLP:
 
   Spin-flip TDDFT is programmed in the "collinear
approximation" which means only the HF exchange term
carries a large impact on the excitation energies.  Pure
DFT functionals may be used, but normally hybrids with
large HF exchange fractions are used.  The LC option for
range-separation hybrids cannot be used, which also removes
CAMB3LYP.  Finally, no meta-GGA may be used.  Note that
spin-flip TD-DFT in the Tamm/Dancoff approximation using
DFTTYP=NONE is equivalent to spin-flip CIS.
 
   MULT below is ignored, as the Ms of target states is
fixed solely by MULT in $CONTRL.  The spin-flip code
operates only in the Tamm/Dancoff approximation, so TAMMD
below is automatically .TRUE.  Nuclear gradients and/or
excited state properties are available only in the gas
phase.  Solvation effects are available for both energy and
gradient calculations, for EFP1, C-PCM, or both.
 
 
                         ---------
 
NSTATE = Number of states to be found (excluding the
         reference state).  The default is 1 more state.
 
IROOT  = State used for geometry optimization and property
         evaluation. (default=1)
         TDDFT=EXCITE counts the reference as 0, and this
         should be the lowest state.  Hence IROOT=1 means
         the 1st excited state, just as you might guess.
         TDDFT=SPNFLP labels the reference state as 0, but
         this might not be the lowest state overall.  The
         meaning of IROOT=1 is the lowest state, omitting
         the reference state from consideration.  Hence
         IROOT=1 might specify the ground state!
 
MULT   = Multiplicity (1 or 3) of the singly excited
         states.  This keyword applies only when the
         reference is a closed shell.  (default is 1)
         This parameter is ignored when TDDFT=SPNFLP.
 
TDPRP  = a flag to request property computation for the
         state IROOT.  Properties can only be obtained when
         the nuclear gradient is computable, see gradient
         restrictions noted in the introduction to this
         group.  Properties require significant extra
         computer time, compared to the excitation energy
         alone, so the default is .FALSE.  Properties are
         always evaluated during nuclear gradient runs,
         when they are a free by-product.
 
TRNSD  = a flag that requests the use of the transition density
         in property computations. The transition density is
         taken for the transition between the ground state
         and the state IROOT. All nuclear contributions to
         properties are set to zero when using the transition
         density. By default this flag is set to .FALSE.
         TRNSD=.TRUE. also requires TDPRP=.TRUE.
 
TPA    = a flag requesting two-photon absorption cross-
         sections.  These are computed for each of the
         NSTATE excited states, after first evaluating
         their excitation energies.  The TPA calculation is
         only available for closed shell references, only
         for singlet excited states (MULT=1), and may not
         be used with the Tamm/Dancoff approximation.
         Solvent effects may be treated by EFP.
 
 
TAMMD    is a flag selecting the Tamm/Dancoff approximation
         be used.  This may be used with closed shell
         excitation energies or gradients, or open shell
         excitation energies.  Default = .FALSE.
         This parameter is ignored by TDDFT=SPNFLP, which
         is only coded in the Tamm/Dancoff approximation.
 
 
NONEQ    is a flag controlling PCM's solvent behavior:
         .TRUE. splits the dielectric constant into a bulk
         value (EPS in $PCM) and a fast component (EPSINF),
         see Cossi and Barone, 2001.  The idea is that
         NONEQ=.t. is appropriate for vertical excitations,
         and .f. for adiabatic.  (the default is .TRUE.)
         This keyword is ignored by TDDFT=SPNFLP.
 
      * * * ground state polarizability calculation * * *
          (use TDDFT=HPOL option in $CONTRL)
These two frequency dependent polarizability calculations
may be requested in the same run (more efficient).  These
properties are available only for closed shell references,
require the default MULT=1 value in this input group, and
may not be used with the Tamm/Dancoff approximation.
Solvent effects may be treated by EFP.
 
ALPHA  = requests the polarizability.       Default=.FALSE.
         If BETA is not chosen, give just one PFREQ.
 
BETA   = requests the hyperpolarizability.  Default=.FALSE.
         Two values are required for PFREQ.
 
PFREQ  = an array of one or two input frequencies, omega1
         and omega2, to yield the polarizability
                 alpha(omega1;omega1)  [if BETA=.F.]
                 alpha(omega2;omega2)  [if BETA=.T.]
                 alpha(omega3;omega3)  [if BETA=.T.]
         and/or to yield the hyperpolarizability
                 beta(omega3;omega1,omega2).
         The output photon frequency is determined from
         omega3=-(omega1+omega2).  Useful special cases
            second harmonic generation   beta(-2W;W,W),
            electro-optic Pockels effect beta(-W;W,0), and
            optical rectification        beta(0;W,-W)
         are among the possibilities.
         The default is the static polarizability and/or
         static hyperpolarizability: PFREQ(1)=0.0,0.0
         PFREQ is given in atomic units: PFREQ=45.56/lamda,
         for wavelength lambda in nm.
 
 
               * * * Grid Selection * * *
 
The grid type and point density used in $TDDFT may be
chosen independently of the values in $DFT.  Excitation
energies accurate to 0.01 eV may be obtained with grids
that are much sparser than those needed for the ground
state, and this is reflected in the defaults.  Prior to
April 2008, the default grid was NRAD=24 NTHE=8 NPHI=16.
 
NRAD   = number of radial grid points in Euler-Maclaurin
         quadrature, used in calculations of the second or
         third derivatives of density functionals.
         (default=48)
 
NLEB   = number of angular points in the Lebedev grid.
         (default=110)
 
NTHE   = number of theta grid points if a polar coordinate
         grid is used.
 
NPHI   = number of phi grid points if a polar coordinate
         grid is used.  NPHI should be twice NTHE.
 
SG1    = flag selecting "standard grid one".
         (default=.FALSE.)
 
See both $DFT and REFS.DOC for more information on grids.
The "army grade" standard for $TDDFT is NRAD=96 combined
with either NLEB=302 or NTHE=12/NPHI=24.
 
 
      the remaining parameters are technical in nature:
 
CNVTOL = convergence tolerance in the iterative TD-DFT
         step.  (default=1.0E-7)
 
MAXVEC = the maximum number of expansion vectors used by
         the solver's iterations, per state (default=50).
         The total size of the expansion space will be
         NSTATE*MAXVEC.
 
NTRIAL = the number of initial expansion vectors used.
         (default is the larger of 5 and NSTATE).
 
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