Quantum Mechanics / Extremely Localized Molecular Orbital Embedding Strategy for Excited-States. 1. Coupling to Time-Dependent Density Functional Theory

Abstract

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.

Quantum Mechanics / Extremely Localized Molecular Orbital Embedding Strategy for Excited-States. 2. Coupling to the Equation-of-Motion Coupled Cluster Method

“…Extremely localized molecular orbitals are transferred to the ELMO region from the constructed libraries 56 or from tailor-made model molecules by exploiting the rotation/transfer strategy proposed by Philipp and Friesner 49,61 in the context of QM/MM approaches that use strictly localized bond orbitals (SLBOs) to describe the frontier between the QM and MM subsystems. For more details about theory, transfer and libraries of ELMOs, we refer the readers to the papers on the construction of the ELMO databanks 49,50,56 or to the Supporting Information of our related work about the TDDFT/ELMO approach 62 .…”

“…is the embedded EOM-CCSD/ELMO excitation energy before the TDDFT correction (including only the approximate ground state polarization), 𝜔 63376 is the traditional TDDFT excitation energy on the full system, and 𝜔 63376/-5/. is the embedded TDDFT excitation energy obtained through the recently developed TDDFT/ELMO strategy 62 . Of course, from the computational perspective, this option is convenient only if the cost of the full TDDFT computation is small compared to the one associated with the corresponding full EOM-CCSD calculation.…”