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 exam 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). The proposed TDDFT/ELMO strategy has been subjected to a series of preliminary tests that were already considered for the validations of other embedding TDDFT methods. The obtained results show that the novel technique allows the accurate description of local excitations in large systems by only including a relatively small group of atoms in the region treated at fully quantum chemical level. Furthermore, it was observed that, even using functionals that do not take into account long-range corrections, the method enables to avoid the presence of artificial low-lying charge-transfer states that may affect traditional TDDFT calculations. Finally, through the application to a reduced model of the Green Fluorescent Protein, it was proved that the TDDFT/ELMO approach can be also successfully exploited to investigate local electronic transitions in large systems and that the accuracy of the results can be improved by including a sufficient number of fragments/residues that are chemically crucial in the quantum mechanical region. 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 methods for excited-states, from the simplest ΔSCF techniques to the most advanced and computationally expensive multi-references methods.
Predicting excited states from ground state wavefunction by supervised quantum machine learning