Shifts in the π → π^∗ excitation energy of the cis-7-hydroxyquinoline chromophore induced by hydrogen bonding with small molecules, obtained with the frozen-density embedding theory (FDET), are compared with the results of the high-level equation-of-motion coupled-cluster (EOMCC) calculations with singles, doubles, and noniterative triples, which provide the reference ab initio data, the supermolecular time-dependent density functional theory (TDDFT) calculations, and the available experimental data. It is demonstrated that the spectral shifts resulting from the FDET calculations employing nonrelaxed environment densities and their EOMCC counterparts are in excellent agreement with one another, whereas the analogous shifts obtained with the supermolecular TDDFT approach do not agree with the EOMCC reference data. Among the discussed issues are the effects of higher-order correlations on the excitation energies and complexation-induced excitation energy shifts resulting from the EOMCC calculations, and the choice of the approximants that represent the nonadditive kinetic energy contributions to the embedding potential of FDET.

In embedding methods such as those labeled commonly as QM/MM, the embedding operator is frequently approximated by the electrostatic potential generated by nuclei and electrons in the environment. Such approximation is especially useful in studies of the potential energy surface of embedded species. The effect on energy of neglecting the non-Coulombic component of the embedding operator is corrected a posteriori. The present work investigates applicability of such approximation in evaluation of electronic excitation energy, the accuracy of which depends directly on that of the embedding potential. For several model systems involving cis-7-hydroxiquinoline hydrogen-bonded to small molecules, we demonstrate that such truncation of the embedding operator leads to numerically unstable results upon increasing the size of the atomic basis sets. Approximating the non-Coulombic component of the embedding potential using the expression derived in Frozen-Density Embedding Theory ([Wesolowski and Warshel, J. Phys. Chem.1993, 97, 8050] and subsequent works) by means of even a simple bifunctional dependent on the electron density of the chromophore and its hydrogen-bonded environment, restores the numerical stability of the excitation energies that reach a physically meaningful limit for large basis sets.

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.

The importance of the nonelectrostatic component of the embedding potential is investigated by comparing the complexation induced shifts of the iso-g obtained in embedding calculations to its supermolecular counterparts. The analyses are made in view of such multilevel simulations, for which supermolecular strategy is either impractical or impossible, such as the planned simulations for the whole enzyme ferredoxin oxidoreductase. For the biliverdin radical surrounded by a few amino acids, it is shown that the embedding potential comprising only Coulomb terms fails to reproduce even qualitatively the shifts evaluated from supermolecular calculations. The nonelectrostatic component of the exact embedding potential is a bifunctional of two electron densities [Wesolowski and Warshel, J. Phys. Chem. 1993, 97, 8050; Wesolowski, Phys. Rev. A 2008, 77, 012504]. Therefore we analyze in detail both the quality of the approximant for the bifunctional and the importance of the choice of the electron densities at which it is evaluated in practical calculations.

Laser resonant two-photon ionization UV spectra provide clear evidence that the effect of increasing the length of the hydrogen-bonded chain consisting of molecules such as NH₃, H₂O, or CH₃OH on the Ï€ → Ï€* excitations of cis-7-hydroxyquinoline (cis-7HQ) is strongly cooperative [Thut; et al. J. Phys. Chem. A 2008, 112, 5566.] A theoretical analysis of the experimental data is provided to identify the origin of this cooperativity for four chains. The computational method to determine the changes of the electronic structure of a molecule due to interactions with its environment uses the nonempirical expression for the embedding potential [Wesolowski; WarshelJ. Phys. Chem. 1993, 97, 8050.] It is concluded that the electronic coupling between the molecules at the ends of the chain, which are hydrogen-bonded to cis-7HQ, plays a crucial role in this cooperativity.