$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                           
   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:                                        
   SVWN, SOP, SLYP, OLYP,                                                       
   BVWN, BOP, BLYP (and their LC=.TRUE. versions)                               
   B3LYP, CAMB3LYP, B3LYPV1R, PBE, PBE0                                         
For evaluation of just the excitation energies, you may use                     
many more functionals, notably including the metaGGAs in                        
the last three lines:                                                           
   SVWN, SVWN1, SPZ81, SP86, SOP, SLYP,                                         
   BVWN, BVWN1, BPZ81, BP86, BOP, BLYP, OLYP,                                   
   B3LYP, CAMB3LYP, B3LYPV1R, B3PW91, X3LYP,                                    
   PW91, PBE, PBE0,                                                             
   VS98, PKZB,                                                                  
   M05, M05-2X, M06, M06-HF, M06-L, M06-2X, M08-HX, M08-SO                      
   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.                                       
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                                
         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.                              
NLEB   = number of angular points in the Lebedev grid.                          
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".                                    
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                          
NTRIAL = the number of initial expansion vectors used.                          
         (default is the larger of 5 and NSTATE).                               

generated on 7/7/2017