Excimer Energies

Anisole-Water and Anisole-Ammonia Complexes in Ground and Excited (S1) States: A Multiconfigurational Symmetry-Adapted Perturbation Theory (SAPT) Study

Binary complexes of anisole have long been considered paradigm systems for studying microsolvation in both the ground and electronically excited states. We report a symmetry-adapted perturbation theory (SAPT) analysis of intermolecular interactions in anisole-water and anisole-ammonia complexes within the framework of the multireference SAPT(CAS) method. Upon the S1 ← S0 electronic transition, the hydrogen bond in the anisole-water dimer is weakened, which SAPT(CAS) shows to be determined by changes in the electrostatic energy. As a result, the water complex becomes less stable in the relaxed S1 state despite decreased Pauli repulsion. Stronger binding of the anisole-ammonia complex following electronic excitation is more nuanced and results from counteracting shifts in the repulsive (exchange) and attractive (electrostatic, induction and dispersion) forces. In particular, we show that the formation of additional binding N-H···π contacts in the relaxed S1 geometry is possible due to reduced Pauli repulsion in the excited state. The SAPT(CAS) interaction energies have been validated against the coupled cluster (CC) results and experimentally determined shifts of the S1 ← S0 anisole band. While for the hydrogen-bonded anisole-water dimer SAPT(CAS) and CC shifts are in excellent agreement, for ammonia SAPT(CAS) is only qualitatively correct.

Structure of Multi-State Correlation in Electronic Systems

Beyond the Hohenberg-Kohn density functional theory for the ground state, it has been established that the Hamiltonian matrix for a finite number (N) of lowest eigenstates is a matrix density functional. Its fundamental variable─the matrix density D(r)─can be represented by, or mapped to, a set of auxiliary, multiconfigurational wave functions expressed as a linear combination of no more than N2 determinant configurations. The latter defines a minimal active space (MAS), which naturally leads to the introduction of the correlation matrix functional, responsible for the electronic correlation effects outside the MAS. In this study, we report a set of rigorous conditions in the Hamiltonian matrix functional, derived by enforcing the symmetry of a Hilbert subspace, namely the subspace invariance property. We further establish a fundamental theorem on the correlation matrix functional. That is, given the correlation functional for a single state in the N-dimensional subspace, all elements of the correlation matrix functional for the entire subspace are uniquely determined. These findings reveal the intricate structure of electronic correlation within the Hilbert subspace of lowest eigenstates and suggest a promising direction for efficient simulation of excited states.

Size Isn't Everything: Geometric Tuning in Polycyclic Aromatic Hydrocarbons and Its Implications for Carbon Nanodots

Recent developments in light-emitting carbon nanodots and molecular organic semiconductors have seen renewed interest in the properties of polycyclic aromatic hydrocarbons (PAHs) as a family. The networks of delocalized π electrons in sp2-hybridized carbon grant PAHs light-emissive properties right across the visible spectrum. However, the mechanistic understanding of their emission energy has been limited due to the ground state-focused methods of determination. This computational chemistry work, therefore, seeks to validate existing rules and elucidate new features and characteristics of PAHs that influence their emissions. Predictions based on (time-dependent) density functional theory account for the full 3-dimensional electronic structure of ground and excited states and reveal that twisting and near-degeneracies strongly influence emission spectra and may therefore be used to tune the color of PAHs and, hence, carbon nanodots. We particularly note that the influence of twisting goes beyond torsional destabilization of the ground-state and geometric relaxation of the excited state, with a third contribution associated with the electric transition dipole. Symmetries and peri-condensation may also have an effect, but this could not be statistically confirmed. In pursuing this goal, we demonstrate that with minimal changes to molecular size, the entire visible spectrum may be spanned by geometric modification alone; we have also provided a first estimate of emission energy for 35 molecules currently lacking published emission spectra as well as clear guidelines for when more sophisticated computational techniques are required to predict the properties of PAHs accurately.

Analysis of Site Energies and Excitonic Couplings: The Role of Symmetry and Polarization

An excitonic coupling model is developed based on an equation-of-motion coupled cluster combined with the fragment molecular orbital method. The effects of polarization and excitonic coupling on the splitting of quasi-degenerate levels in systems containing multiple chromophores are elucidated on dimers of formaldehyde, water, formic acid, hydrogen fluoride, and carbon monoxide. It is shown that the level structure is mainly determined by the mutual polarization of chromophores and to a lesser extent by the excitonic coupling. The role of symmetry in excitonic coupling in dimers is discussed. The excitonic coupling between all residues in the photoactive yellow protein (PDB: 2PHY) is analyzed.

Detangling Solvatochromic Effects by the Effective Fragment Potential Method

Understanding molecular interactions in complex systems opens avenues for the efficient design of new materials with target properties. Energy decomposition methods provide a means to obtain a detailed picture of intermolecular interactions. This work introduces a molecular modeling approach for decomposing the solvatochromic shifts of the electronic excited states into the contributions of the individual molecular fragments of the environment surrounding the chromophore. The developed approach is implemented for the QM/EFP (quantum mechanics/effective fragment potential) model that provides a rigorous first-principles-based description of the electronic states of the chromophores in complex polarizable environments. On the example of two model systems, water pentamer and hydrated uracil, we show how the decomposition of the solvatochromic shifts into the contributions of individual solvent water molecules provides a detailed picture of the intermolecular interactions in the ground and excited states of these systems. The analysis also demonstrates the nonadditivity of solute-solvent interactions and the significant contribution of solute polarization to the total values of solvatochromic shifts.

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

In this study, the use of self-consistent field quasi-diabats is investigated for calculation of triplet energy transfer diabatic coupling elements. It is proposed that self-consistent field quasi-diabats are particularly useful for studying energy transfer (EnT) processes because orbital relaxation in response to changes in electron configuration is implicitly built into the model. The conceptual model that is developed allows for the simultaneous evaluation of direct and charge-transfer mechanisms to establish the importance of the different possible EnT mechanisms. The method's performance is evaluated using two model systems: the ethylene dimer and ethylene with the methaniminium cation. While states that mediate the charge-transfer mechanism were found to be higher in energy than the states involved in the direct mechanism, the coupling elements that control the kinetics were found to be significantly larger in the charge-transfer mechanism. Subsequently, we discuss the advantage of the approach in the context of practical difficulties with the use of established approaches.

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

The performance of multistate density functional theory (MSDFT) with nonorthogonal state interaction (NOSI) is assessed for 100 vertical excitation energies against the theoretical best estimates extracted to the full configuration interaction accuracy on the database developed by Loos et al. in 2018 (Loos2018). Two optimization techniques, namely, block-localized excitation and target state optimization, are examined along with two ways of estimating the transition density functional (TDF) for the correlation energy of the Hamiltonian matrix density functional. The results from the two optimization methods are similar. It was found that MSDFT-NOSI using the spin-multiplet degeneracy constraint for the TDF of spin-coupling interaction, along with the M06-2X functional, yields a root-mean-square error (RMSE) of 0.22 eV, which performs noticeably better than time-dependent density functional theory (DFT) at an RMSE of 0.43 eV using the same functional and basis set on the Loos2018 database. In comparison with wave function theory, NOSI has smaller errors than CIS(D∞), LR-CC2, and ADC(3) all of which have an RMSE of 0.28 eV, but somewhat greater than STEOM-CCSD (RMSE of 0.14 eV) and LR-CCSD (RMSE of 0.11 eV) wave function methods. In comparison with Kohn-Sham (KS) DFT calculations, the multistate DFT approach has little double counting of correlation. Importantly, there is no noticeable difference in the performance of MSDFT-NOSI on the valence, Rydberg, singlet, triplet, and double-excitation states. Although the use of another hybrid functional PBE0 leads to a greater RMSE of 0.36 eV, the deviation is systematic with a linear regression slope of 0.994 against the results with M06-2X. The present benchmark reveals that density functional approximations developed for KS-DFT for the ground state with a noninteracting reference may be adopted in MSDFT calculations in which the state interaction is key.

Multistate Energy Decomposition Analysis of Molecular Excited States

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.