Quantum Mechanics/Extremely Localized Molecular Orbital Embedding Strategy for Excited States: Coupling to Time-Dependent Density Functional Theory and Equation-of-Motion Coupled Cluster

The
QM/ELMO (quantum mechanics/extremely
localized molecular orbital) method is a recently
developed embedding technique in which the most important region of
the system under examination is treated at fully quantum mechanical
level, while the rest is described by means of transferred and frozen
extremely localized molecular orbitals. In this paper, we propose
the first application of the QM/ELMO approach to the investigation
of excited states, and, in particular, we present the coupling of
the QM/ELMO philosophy with Time-Dependent Density Functional Theory
(TDDFT) and Equation-of-Motion Coupled Cluster with single and double
substitutions (EOM-CCSD). The proposed TDDFT/ELMO and EOM-CCSD/ELMO
strategies underwent a series of preliminary tests that were already
considered for the validation of other embedding methods for excited
states. The obtained results showed that the novel techniques allow
the accurate description of localized excitations in large systems
by only including a relatively small number of atoms in the region
treated at fully quantum chemical level. Furthermore, for TDDFT/ELMO,
it was also observed that (i) the method enables to avoid the presence
of artificial low-lying charge-transfer states that may affect traditional
TDDFT calculations, even using functionals that do not take into account
long-range corrections, and (ii) the novel approach can be also successfully
exploited to investigate local electronic transitions in quite large
systems (e.g., reduced model of the Green Fluorescent Protein), and
the accuracy of the results can be improved by including a sufficient
number of chemically crucial fragments/residues in the quantum mechanical
region. Finally, concerning EOM-CCSD/ELMO, it was also seen that,
despite the quite crude approximation of an embedding potential given
by frozen extremely localized molecular orbitals, the new strategy
is able to satisfactorily account for the effects of the environment.
This work paves the way to further extensions of the QM/ELMO philosophy
for the study of local excitations in extended systems, suggesting
the coupling of the QM/ELMO approach with other quantum chemical strategies
for excited states, from the simplest ΔSCF techniques to the
most advanced and computationally expensive multireferences methods.