Embedding vs Supermolecular Strategies in Evaluating the Hydrogen-Bonding-Induced Shifts of Excitation Energies

Abstract

Shifts in the excitation energy of the organic chromophore, cis-7-hydroxyquinoline (cis-7HQ), corresponding to the π→π* transition in cis-7HQ and induced by the complexation with a variety of small hydrogen-bonded molecules, obtained with the frozen-density embedding theory (FDET), are compared with the results of the supermolecular equation-of-motion coupled-cluster (EOMCC) calculations with singles, doubles, and non-iterative triples, which provide the reference theoretical data, the supermolecular time-dependent density functional theory (TDDFT) calculations, and experiment. Unlike in the supermolecular EOMCC and TDDFT cases, where each complexation-induced spectral shift is evaluated by performing two separate calculations, one for the complex and another one for the isolated chromophore, the FDET shifts are evaluated as the differences of the excitation energies determined for the same many-electron system, representing the chromophore fragment with two different effective potentials. By considering eight complexes of cis-7HQ with up to three small hydrogen-bonded molecules, it is shown that the spectral shifts resulting from the FDET calculations employing non-relaxed environment densities and their EOMCC reference counterparts are in excellent agreement with one another, whereas the analogous shifts obtained with the supermolecular TDDFT method do not agree with the EOMCC reference data. The average absolute deviation between the complexation-induced shifts, which can be as large, in absolute value, as about 2000 cm-1, obtained using the non-relaxed FDET and supermolecular EOMCC approaches that represent two entirely different computational strategies, is only about 100 cm-1, i.e., on the same order as the accuracy of the EOMCC calculations. This should be contrasted with the supermolecular TDDFT calculations, which produce the excitation energy shifts that differ from those resulting from the reference EOMCC calculations by about 700 cm-1 on average. Among the discussed issues are the choice of the electronic density defining the environment with which the chromophore interacts, which is one of the key components of FDET considerations, the basis set dependence of the FDET, supermolecular TDDFT, and EOMCC results, the usefulness of the monomer vs supermolecular basis expansions in FDET considerations, and the role of approximations that are used to define the exchange-correlation potentials in FDET and supermolecular TDDFT calculations

Communication: Existence of the doubly excited state that mediates the photoionization of azulene

“…We note that doubly excited states at energies as low as 4.95 eV have been detected by the magnetic circular dichroism experiments on azulene derivatives. 21 By computing a large number of singlet excited states (for the lowest 10 states found, see Table I) at the high level of the equation-of-motion coupled-cluster (EOMCC) theory 22 capable of capturing the singly and doubly excited states, abbreviated as δ-CR-EOMCC(2,3), 23 we have confirmed the existence of the postulated doubly excited state. The number of electronic states we had to converge had to be much larger than in the case of the earlier complete-active-space self-consistent-field (CASSCF) and multi-reference perturbation theory CASPT2 calculations of the low-lying excitations in azulene dominated by one-electron transitions.…”

“…Our δ-CR-EOMCC(2,3) calculations were performed using the 6-31G(d) and cc-pVDZ basis sets, which were the largest basis sets we could accommodate when calculating so many excited states of azulene at such a high EOMCC level. The initial δ-CR-EOMCC(2,3)/6-31G(d) calculations were performed at the ground-state geometry optimized at the MP2/6-31G(d) level with GAMESS, 33 where our δ-CR-EOMCC(2,3) and other EOMCC routines 23,26,29,30 are incorporated. The final δ-CR-EOMCC(2,3)/cc-pVDZ calculations were performed at the improved ground-state geometry obtained using the numerical CR-CC(2,3)/cc-pVDZ gradients, consistent with the δ-CR-EOMCC(2,3)/cc-pVDZ description of excited states.…”

The behavior of active diffusiophoretic suspensions: An accelerated Laplacian dynamics study

“…But we do note the great promise of density embedding methods, of which there are various flavors. [47][48][49][50][51][52][53] However, we will not cover embedding methods further in this perspective, except to note that density embedding not only can serve as a way to speed up DFT calculations, but also it can serve as a new way to combine WFT with DFT, which is an approach that has great promise but is not fully covered in this article.…”

Embedding potentials for excited states of embedded species

“…10 It has been shown to be a powerful tool in modeling the effect of environment on local excitations in embedded chromophores. [10][11][12] References 13 and 14 provide comprehensive recent reviews. The FDET/LR-TDDFT framework can be seen as introduction of an additional approximation, namely, Neglect of the Dynamic Response of the Environment in the LR-TDDFT generalization of the ground-state subsystem DFT formulation 5 to excited states.…”