Energy transfer from a photoexcited donor molecule to a nearby ground-state acceptor molecule is a process of fundamental interest in many fields of science, including polymer photophysics, surface photochemistry, photochemical synthesis and molecular device engineering. It is usually known as electronic energy transfer (EET) or resonance energy transfer (RET). The fundamental theoretical treatment was presented by Förster in 1948 [Forster48], and it EET analysis computes the excitation energy transfer rate between molecules (or parts of molecules) from the overlap of the fluorescence spectrum of the donor molecule/fragment with the absorption spectum of the acceptor molecule/fragment. However, not all energy transfers are described well by this treatment. Accordingly, there have been many extensions to Förster’s theory, beginning with Dexter [Dexter53]. In recent years, a variety of new models have built upon these foundations; see [Scholes03] for a review.

In Gaussian 16, the EET analysis is a quantum mechanical model for EET based on a DFT description of the wavefunction, incorporating a time-dependent variational approach [Curutchet05, Russo07]. EET is available in the gas phase and in solution. Indeed, Förster’s original theory recognizes the importance of solvent effects. The implementation in solution in Gaussian 16 is the formulation of Iozzi, Mennucci, Tomasi and Cammi [Iozzi04], a model that differs from its predecessors (e.g., [Hsu01]) in that it incorporates solvent effects by adding the appropriate operators to the Hamiltonian and the linear response equations; in this way, solvation is present in all steps of the quantum mechanical calculation [Cammi99b, Cammi00, Caricato04, Caricato05]. The solvation cavity for this model is the same for other employments of IEFPCM [Cances97, Mennucci97a, Cances98a] (rather than a simplistic sphere or multipolar expansion).

The EET keyword performs an excitation energy transfer calculation using the results of the CIS/TDA/TD-DFT calculation or of an EOM-CCSD calculation. This type of calculation uses the same setup of Guess(Fragment=…) but it can also process ONIOM-like link-atom input information to cap the fragments. An excited-state calculation is performed on each fragment, and all the coupling among all the resulting states are computed. Solvent effects can be introduced using PCM and a single cavity, or a fragment-pair cavity can be used to evaluated the solvent-mediated coupling.

#### Fragment=N

Set up N fragments.

#### FullSystemCavity

Use the PCM cavity for the whole system when evaluating the EET coupling. This is the default.

#### FragmentCavity

Set up a PCM cavity for each pair of fragments when evaluating the EET coupling.

#### NonEqSolv

Force the use of non-equilibrium solvation for the solvent-mediated term of the coupling.

#### EqSolv

Force the use of equilibrium solvation for the solvent-mediated term of the coupling.

The default choice of equilibrium vs non-equilibrium is such that the EET is consistent with what has been done in L913/L914.

The following simple input file performs an EET calculation on formaldehyde dimer, treating each molecule as a separate fragment. This job models the EET for a single excited state.

# td(nstates=1) b3lyp/6-31G(d) eet(fragment=2)
EET in gas phase (Closed shell fragments done as closed shell)
Full : H2CO ... H2CO
Frag 1: H2CO
Frag 2: H2CO
0 1 0 1 0 1
C(fragment=1) 0.000000 -0.542500 0.000000
O(fragment=1) 0.000000 0.677500 0.000000
H(fragment=1) 0.000000 -1.082500 0.935307
H(fragment=1) 0.000000 -1.082500 -0.935307
C(fragment=2) 2.000000 -0.542500 0.000000
O(fragment=2) 2.000000 0.677500 0.000000
H(fragment=2) 2.000000 -1.082500 0.935307
H(fragment=2) 2.000000 -1.082500 -0.935307

Here is the key part of the EET output:

===============================================================================
Electronic Coupling for Excitation Energy Tranfer
===============================================================================
Separate basis set information will be generated for each pair of fragments.
Using analytical method for overlap contributions to EET.
The minimum distance is a measure of how far the electron moves.
Frag= 2 1 min distance between atoms 5 1 = 2.000 Angs (sum of Rcov= 1.520)
excluding hydrogens 5 1 = 2.000 Angs (sum of Rcov= 1.520)
Frag= 2 State= 1 (w= 3.9574 eV) Frag= 1 State= 1 (w= 3.9574 eV) Value of ω for these two fragments & states.
delta-w = 0.000000000 eV Energy difference between the two states.
Coulomb = -0.035983294 eV
Exact-exchange = 0.014046399 eV
Exchange-correlation = 0.006375024 eV
w-avg*Overlap = -0.000357708 eV (w-avg= 3.9574 eV, Ovlp=-0.903895D-04)
Total coupling = -0.015919579 eV Parameter used to compute the rate of EET.

This output will be repeated for each interaction requested by the calculation.