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.