Summary of excited state methods

This is not a "how to" section, as the actual calculations 
will be carried out by means described elsewhere in this 
chapter.  Instead, a summary of methods that can treat 
excited states is given.

The simplest possibility is SCFTYP.  For example, a closed 
shell molecule's first triplet state can always be treated 
by SCFTYP=ROHF MULT=3.  Assuming there is some symmetry 
present, the GVB program may be able to do excited singlets 
variationally, provided they are of a different space 
symmetry than the ground state.  The MCSCF program gives a 
general entree into excited states, since upper roots of a 
Hamiltonian are always variational: see for example NSTATE 
and WSTATE and IROOT in $DET.  Of course, 2nd order 
perturbation theory can include correlation energy into 
these SCF level calculations.  Note in particular the 
usefulness of quasi-degenerate multireference perturbation 
theory when electronic states have similar energies.

CI calculations also give a simple entree into excitated 
states.  There are a variety of programs, selected by CITYP 
in $CONTRL.  Note in particular CITYP=CIS, programmed for 
closed shell ground states, with gradient capability for 
singlet excited states, and for the calculation of triplet 
state energies.  The other CI programs can generate very 
flexible wavefunctions for the evaluation of the excitation 
energy, and property values.  Note that the GUGA program 
will do nuclear gradients provided the reference is RHF.

The TD-DFT method treats singly excited states, including 
correlation effects, and is a popular alternative to CIS.  
The program allows for excitation energies from a UHF 
reference, but is much more powerful for RHF references: 
nuclear gradients and/or properties may be computed.  Use 
of a "long range corrected" or "range separated" functional 
(the two terms are synonymous) is often thought to be 
important when treating charge transfer or Rydberg states: 
see the LC=.TRUE. flag or CAMB3LYP.  Spin-flip TDDFT allows 
the users to select as the reference state something more 
appropriate to the orbital optimization stage.  See $TDDFT 
for details.

Equation of Motion (EOM) coupled cluster can give accurate 
estimates of excitation energies.  There are no gradients, 
and properties exist only for the EOM-CCSD level, but 
triples corrections to the energy are available.  See 
$EOMINP for more details.

Most of the runs will predict oscillator strengths, or 
Einstein coefficients, or similar data regarding the 
electronic transition moments.  Full prediction of UV-vis 
spectra is not possible without Franck-Condon information.

Excited states frequently come close together, and 
crossings between them are of great interest.

See RUNTYP=TRANSITION for spin-orbit coupling, which is 
responsible for InterSystem Crossing (ISC) between states 
of different spin multiplicity.  See RUNTYP=NACME for the 
computation of the non-adiabatic coupling matrix elements 
that cause Internal Conversion (IC) between states of the 
same spin multiplicity.  Alternatively, diabatic potential 
surfaces may be generated at the MCSCF or MCQDPT levels: 
see DIABAT in the $MCSCF group.

It is possible to search for the lowest energy on the 
crossing seam between two surfaces.  In case those surfaces 
have different spins, or different space symmetries (or 
both), see RUNTYP=MEX.  When the surfaces have the same 
symmetry, see RUNTYP=CONINT for location of conical 
intersections.

Solvent effects (EFP and/or PCM) can easily be incorporated 
when using SCFTYP to generate the states, and nuclear 
gradients are available.  It is now possible to assess 
solvent effects on TD-DFT excitation energies from closed 
shell references, using either EFP or PCM.

Excited states often possess Rydberg character, so diffuse 
functions in the basis set are likely to be important.