This method keyword requests an excited state calculation using the time-dependent Hartree-Fock or DFT method [Bauernschmitt96a, Casida98, Stratmann98, VanCaillie99, VanCaillie00, Furche02, Scalmani06]; analytic gradients [Furche02, Scalmani06] and frequencies [Liu11, Liu11a, WilliamsYoung17p] are available in Gaussian 16. For a review of using TD-DFT to predict excited state properties, see [Adamo13, Laurent13].

Time-dependent DFT calculations can employ the Tamm-Dancoff approximation, via the TDA keyword. TD-DFTB calculations can also be performed [Trani11].

Note that the normalization criteria used is <X+Y|X-Y>=1.

Electronic circular dichroism (ECD) analysis is also performed during these calculations [Helgaker91, Bak93, Bak95, Olsen95, Hansen99, Autschbach02]

### General Options

#### Singlets

Solve only for singlet excited states. Only effective for closed-shell systems, for which it is the default.

#### Triplets

Solve only for triplet excited states. Only effective for closed-shell systems.

#### 50-50

Solve for half triplet and half singlet states. Only effective for closed-shell systems.

#### Root=N

Specifies the “state of interest”. The default is the first excited state (N=1).

#### NStates=M

Solve for M states (the default is 3). If 50-50 is requested, NStates gives the number of each type of state for which to solve (i.e., the default is 3 singlets and 3 triplets).

The keyword Read may also be specified as the parameter to the NStates option. In this case, the number of states to compute is read from the input stream. This features is typically used in EET calculations.

#### Add=N

Read converged states off the checkpoint file and solve for an additional N states. This option implies Read as well.

#### Read

Reads initial guesses for the states off the checkpoint file. Note that, unlike for SCF, an initial guess for one basis set cannot be used for a different one.

#### Restart

This option restarts a TD calculation after the last completed geometry. A failed frequency job may be restarted from its checkpoint file by simply repeating the route section of the original job, adding the Restart option to the keyword/option. No other input is required.

#### EqSolv

Whether to perform equilibrium or non-equilibrium PCM solvation. NonEqSolv is the default except for excited state optimizations and when the excited state density is requested (e.g., with Density=Current or All).

#### IVOGuess

Force use of IVO guess. This is the default for TD Hartree-Fock. NoIVOGuess forces the use of canonical single excitations for guess, and it is the default for TD-DFT. The HFIVOGuess option forces the use of Hartree-Fock IVOs for the guess, even for TD-DFT.

#### SOS

Do sum-over states polarizabilities, etc. By default, all excited states are solved for. A list of frequencies at which to do the sums is read in. Zero frequency is always done and need not be in the list.

#### NonAdiabaticCoupling

Requests that the ground-to-excited-state non-adiabatic coupling be computed [Send10]. NAC is a synonym for this option. NoNonAdiabaticCoupling and NoNAC suppress this behavior. The default is NoNAC when computing energies or energies+gradients because the extra cost is non-trivial. The default is NAC during frequency calculations where the extra cost is negligible.

#### Conver=N

Sets the convergence calculations to 10^{–N} on the energy and 10^{-(N-2)} on the wavefunction. The default is N=4 for single points and N=6 for gradients.

### Energy Range Options

An energy range can be specified for CIS and TD excitation energies using the following options to CIS, TD and TDA.

#### GOccSt=N

Generate initial guesses using only active occupied orbitals N and higher.

#### GOccEnd=N

Generate initial guesses: if N>0, use only the first N active occupied orbitals; if N<0, do not use the highest |N| occupieds.

#### GDEMin=N

Generate guesses having estimated excitation energies ≥ N/1000 eV.

#### DEMin=N

Converge only states having excitation energy ≥ N/1000 eV; if N=-2, read threshold from input; if N<-2, set the threshold to |N|/1000 Hartrees.

#### IFact=N

Specify factor by which the number of states updated during initial iterations is increased. The default for IFact is Max(4,g) where g is the order of the Abelian point group.

#### WhenReduce=M

Reduce to the desired number of states after iteration M. The default for WhenReduce is 1 for TD and 2 for TDA. Larger values may be needed if there are many states in the range of interest.

Here is the key part of the output from a TD excited states calculation:

Excitation energies and oscillator strengths:
Excited State 1: Singlet-A2 4.0147 eV 308.83 nm f=0.0000 <S**2>=0.000
8 -> 9 0.70701
This state for optimization and/or second-order correction.
Copying the excited state density for this state as the 1-particle RhoCI density.
Excited State 2: Singlet-B1 9.1612 eV 135.34 nm f=0.0017 <S**2>=0.000
6 -> 9 0.70617
Excited State 3: Singlet-B2 9.5662 eV 129.61 nm f=0.1563 <S**2>=0.000
8 -> 10 0.70616

The results on each state are summarized, including the spin and spatial symmetry, the excitation energy, the oscillator strength, the S^{2}, and (on the second line for each state) the largest coefficients in the CI expansion.

The ECD results appear slightly earlier in the output as follows:

1/2[<0|r|b>*<b|rxdel|0> + (<0|rxdel|b>*<b|r|0>)*]
Rotatory Strengths (R) in cgs (10**-40 erg-esu-cm/Gauss)
state XX YY ZZ R(length) R(au)
1 0.0000 0.0000 0.0000 0.0000 0.0000
2 0.0000 0.0000 0.0000 0.0000 0.0000
3 0.0000 0.0000 0.0000 0.0000 0.0000
1/2[<0|del|b>*<b|r|0> + (<0|r|b>*<b|del|0>)*] (Au)
state X Y Z Dip. S. Osc.(frdel)
1 0.0000 0.0000 0.0000 0.0000 0.0000
2 -0.0050 0.0000 0.0000 0.0050 0.0033
3 0.0000 -0.2099 0.0000 0.2099 0.1399