Linear-Response Time-Dependent Embedded Mean-Field Theory

Abstract

We present a time-dependent (TD) linear-response description of excited electronic states within the framework of embedded mean-field theory (EMFT). TD-EMFT allows for subsystems to be described at different mean-field levels of theory, enabling straightforward treatment of excited-states and transition properties. We provide benchmark demonstrations of TD-EMFT for both local and non-local excitations in organic molecules, as well as applications to chlorophyll a, solvatochromic shifts of a dye in solution, and sulfur K-edge X-ray absorption spectroscopy (XAS). It is found that mixed-basis implementations of TD-EMFT lead to substantial errors in terms of transition properties; however, as previously found for ground-state EMFT, these errors are largely eliminated with the use of Fock-matrix corrections. These results indicate that TD-EMFT is a promising method for the efficient, multi-level description of excitedstate electronic structure and dynamics in complex systems.

Imaging covalent bond formation by H atom scattering from graphene

“…Embedded mean-field theory (EMFT) (17)(18)(19) provides energies and forces from first-principles for parameterization of the REBO potential. EMFT is an electronic structure embedding approach that allows a subset of a system to be described using a relatively more accurate but expensive mean-field theory (such as DFT with a hybrid functional and large basis set), while the remainder of the system is described using a lower accuracy and cheaper mean-field level (such as DFT with a LDA functional and a small basis set).…”

“…Unlike the ONIOM method (37), EMFT does not require specification of the number of electrons per subsystem, nor does it require specification of the spin-state of the subsystem; only the total number of electrons and the total spin-state of the system is specified. The method is accurate and efficient over a wide range of systems and chemical applications, including those that involve subsystem partitioning across conjugated bonding networks (17)(18)(19).…”

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

“…However, more interestingly, TDDFT has been also interfaced with fully quantum mechanical embedding methods, such as the density matrix [26][27][28][29] and density functional embedding approaches [30][31][32][33][34][35][36][37][38][39][40][41][42] . In the former case, TDDFT has been coupled with the Embedded Mean Field Theory (EMFT) 28 , as suggested by Manby and Miller, who proposed the so-called Linear-Response Time-Dependent EMFT (LR-TD-EMFT) 43 , or by Parkhill and coworkers, who actually exploited the blockorthogonalized version of EMFT and extended it to Real-Time Time-Dependent Density Functional Theory (RT-TDDFT) 44 . A larger number of developments have been actually proposed in the case of density functional embedding strategies.…”

“…and the remaining part through frozen extremely localized molecular orbitals [59][60][61] (ELMOs) that are exported from suitable databanks [62][63][64] or tailor-made model molecules. In fact, being orbitals strictly localized on small molecular subunits (e.g., atoms, bonds or functional groups), ELMOs are reliably transferable from a molecule to another [62][63][64][65][66][67][68][69] As already stated above, here the focus will be on the TDDFT/ELMO technique, which underwent most of the validation tests that were conceived to assess performances and capabilities of the LR-TD-EMFT method 43 and of the absolutely localized PBE strategy for excited-states 54 . We wanted to prove that the new approach is able i) to describe local excited-states in large systems also when the partition between the QM and ELMO subunits occurs across covalent bonds, ii) to eliminate the typical spurious low-lying charge-transfer states of TDDFT, iii) to provide accurate results when sufficiently large parts of biological systems are considered as chemically active regions in the calculations.…”

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

“…However, more interestingly, TDDFT has been also interfaced with fully quantum mechanical embedding methods, such as the density matrix [26][27][28][29] and density functional embedding approaches [30][31][32][33][34][35][36][37][38][39][40][41][42] . In the former case, TDDFT has been coupled with the Embedded Mean Field Theory (EMFT) 28 , as suggested by Manby and Miller, who proposed the so-called Linear-Response Time-Dependent EMFT (LR-TD-EMFT) 43 , or by Parkhill and coworkers, who actually exploited the blockorthogonalized version of EMFT and extended it to Real-Time Time-Dependent Density Functional Theory (RT-TDDFT) 44 . A larger number of developments have been actually proposed in the case of density functional embedding strategies.…”