Multistate Energy Decomposition Analysis of Molecular Excited States

Abstract

A multistate energy decomposition analysis (MS-EDA) method is described to dissect the energy components in molecular complexes in excited states. In MS-EDA, the total binding energy of an excimer or an exciplex is partitioned into a ground-state term, called local interaction energy, and excited-state contributions that include exciton excitation energy, superexchange stabilization, and orbital and configuration-state delocalization. An important feature of MS-EDA is that key intermediate states associated with different energy terms can be variationally optimized, providing quantitative insights into widely used physical concepts such as exciton delocalization and superexchange charge-transfer effects in excited states. By introducing structure-weighted adiabatic excitation energy as the minimum photoexcitation energy needed to produce an excited-state complex, the binding energy of an exciplex and excimer can be defined. On the basis of the nature of intermolecular forces through MS-EDA analysis, it was found that molecular complexes in the excited states can be classified into three main categories, including (1) encounter excited-state complex, (2) charge-transfer exciplex, and (3) intimate excimer or exciplex. The illustrative examples in this Perspective highlight the interplay of local excitation polarization, exciton resonance, and superexchange effects in molecular excited states. It is hoped that MS-EDA can be a useful tool for understanding photochemical and photobiological processes.

Nonorthogonal Multireference Wave Function Description of Triplet–Triplet Energy Transfer Couplings

“…However, the diabats break spatial symmetry, and so the signs correspond to restoration of the spatial symmetry in the adiabatic picture, in which one adiabat corresponds to the in-phase interaction and the other adiabat corresponds to the out-of-phase interaction, where the signs are dependent on the overlap of the diabats, which are given in the Supporting Information. Although the previous discussion of kinetics was based on the Fermi golden rule in a time-independent formalism, the lowest adiabatic state includes a significant component of a CT character, which illustrates that in reality that there may not be two distinct TEnT mechanisms, but rather the CT acts as resonance states to stabilize the TEnT pathway. , …”

“…The large orbital expansion combined with nonorthogonality presents a substantial computational challenge and is most suited to deployment on highly parallel leadership class computing facilities. Similarly, block-localized molecular orbitals permit strict localization of orbitals to fragments, so defining diabatic states, which can be used to extract direct and CT coupling terms using a multistate energy decomposition analysis. , …”

“…Although the previous discussion of kinetics was based on the Fermi golden rule in a time-independent formalism, the lowest adiabatic state includes a significant component of a CT character, which illustrates that in reality that there may not be two distinct TEnT mechanisms, but rather the CT acts as resonance states to stabilize the TEnT pathway. 53,54 To understand the role of geometry on TEnT rates, the same analysis as described above was performed at different monomer distances up to 5.0 Å (Table 1 and Figure 4). As is expected, due to the symmetry of the ethylene dimer system, diabatic coupling elements between D*A and hole and electron transfer diabats are very similar.…”

Leveling the Mountain Range of Excited-State Benchmarking through Multistate Density Functional Theory

“…Then, we illustrate the MSDFT-NOSI method against the best theoretical estimates from the work of Loos et al, making use of two popular density functional approximations developed for the KS-DFT, namely, the Minnesota M06-2X and the hybrid PBE0 models. – We also compare the performance of TDDFT that works well for many compounds . It is hoped that the present assessment, along with the previous evaluations of organic compounds and exciplex complexes against TDDFT, , of local valence and charge transfer excitations against EOM-CCSDT, and of core-level excitations of open-shell species shall stimulate further developments of multistate models in density functional theory and design of transition density functional approximations for excited states.…”

“…The multistate density functional theory (MSDFT) offers opportunities to develop novel density functional approximations beyond the realm of traditional KS-DFT and to treat both the ground state and excited states on an equal footing . By introducing a minimal active space (MAS) according to Theorem 3 of Lu and Gao, – we have the original benefits of DFT with a balanced treatment of computational efficiency and accuracy in light of increased complexity of multiple states. In this article, we present the results from a nonorthogonal state interaction (NOSI) method in the framework of MSDFT. , The findings are compared with the TBE of WFT on a list of benchmark molecules that has been established previously …”