There exist a broad class of weakly interacting molecular complexes which give
rise to interesting excited-state properties that are potentially very
different from those of a single chromophore. The “TDDFT for molecular
interactions" or TDDFT(MI) method is designed for efficient excited-state
calculations in such cases in (potentially large) systems composed of
weakly-interacting but electronically-coupled
monomers.^{577, 371} Such systems include molecular
aggregates, chromophores in explicit solvent, and even proteins, for which the
traditional TDDFT method become prohibitively expensive. TDDFT(MI) starts from
a ground-state SCF MI calculation, and the use of ALMOs is central to its
efficiency. In addition, the excitations are confined within monomer units and
the explicit charge-transfer excitations are ignored, significantly reduced the
two-electron integrals cost. The method works by coupling together excitations
computed individually on different molecular fragments, and the number of
excited states per fragment can be increased (at very low cost) in order to
increase the variational flexibility of this exciton-type basis. Thus,
despite the localized nature of the basis states, TDDFT(MI) is capable of
describing collective excitations that are delocalized over multiple monomer
units, as for example in the case of organic semiconductors. In general,
TDDFT(MI) reproduces full super-system TDDFT excitation energies to within
$\sim $0.2 eV, but with an order or magnitude reduction in total CPU
time.^{577} Formally, the cost of the method scales as $\mathcal{O}({N}_{\mathrm{fragment}}^{2}{N}_{\mathrm{roots}}^{2}{N}_{\mathrm{sub}\text{-}\mathrm{AO}}^{x})$ where ${N}_{\mathrm{fragment}}$ is the number of monomers, ${N}_{\mathrm{roots}}$ is the number of excited
states per monomer, and ${N}_{\mathrm{sub}\text{-}\mathrm{AO}}$ is the number of AOs on a dimer
subsystem. The exponent $x$ (with $2\le x\le 4$) reflects the cost of forming
the Fock-like matrices of a traditional TDDFT calculation.

An especially promising application of the TDDFT(MI) method is to study
excitation energies of a single chromophore in solution using a large number of
explicit, quantum-mechanical solvent molecules. In such cases, the excitations
are localized on the single chromophore and we can introduce a local excitation
approximation (LEA) to TDDFT(MI) in which all of the Coulomb and exchange
couplings between the solvent molecules and the chromophore are
neglected.^{578} Following the ground-state SCF(MI) calculation, the
cost of the TDDFT part of the calculation becomes essentially the same as the
cost of a TDDFT calculation on the gas-phase chromophore. In addition, this
approach avoids the appearance of, and mixing with, spurious
charge-transfer-to-solvent states,^{578, 371} of the sort
that are known to arise in TDDFT calculations with explicit
solvent.^{516, 408} Three versions of LEA-TDDFT(MI), named
LEA0, LEA-Q and LEAc, have been implemented in Q-Chem.^{578} In the
LEA0 method, ALMOs from the ground state SCF(MI) calculation are used to
perform the TDDFT calculation. In LEAc, a sub-block of the TDDFT(MI) working
equation localized on chromophore is extracted to calculate the excitation
energies. Finally, LEA-Q is almost the same as LEAc except for some
transformations to eliminate the overlap matrices. These approaches have been
applied to converge solvatochromatic shifts for several aqueous
chromophores.^{578}

In addition to the normal TDDFT job controls variables described in Section 7.3.3, there are several others to request TDDFT(MI). Note that only single-point energies (not gradients) are available for this method.

TDDFT_MI

Perform an TDDFT(MI) calculation

TYPE:

LOGICAL

DEFAULT:

FALSE

OPTIONS:

FALSE
Do not perform an TDDFT(MI) calculation
TRUE
Perform an TDDFT(MI) calculation

RECOMMENDATION:

False

MI_ACTIVE_FRAGMENT

Sets the active fragment

TYPE:

INTEGER

DEFAULT:

NO DEFAULT

OPTIONS:

$n$
Specify the fragment on which the TDDFT calculation is to be performed, for LEA-TDDFT(MI).

RECOMMENDATION:

None

MI_LEA

Controls the LEA-TDDFT(MI) methods

TYPE:

INTEGER

DEFAULT:

NO DEFAULT

OPTIONS:

0
The LEA0 method
1
The LEA-Q method
2
The LEAc method

RECOMMENDATION:

1