Multireference approaches for excited states of molecules

Understanding the properties of electronically excited states is a challenging task that becomes increasingly important for numerous applications in chemistry, molecular physics, molecular biology, and materials science. A substantial impact is exerted by the fascinating progress in time-resolved spectroscopy, which leads to a strongly growing demand for theoretical methods to describe the characteristic features of excited states accurately. Whereas for electronic ground state problems of stable molecules the quantum chemical methodology is now so well developed that informed nonexperts can use it efficiently, the situation is entirely different concerning the investigation of excited states. This review is devoted to a specific class of approaches, usually denoted as multireference (MR) methods, the generality of which is needed for solving many spectroscopic or photodynamical problems. However, the understanding and proper application of these MR methods is often found to be difficult due to their complexity and their computational cost. The purpose of this review is to provide an overview of the most important facts about the different theoretical approaches available and to present by means of a collection of characteristic examples useful information, which can guide the reader in performing their own applications

Photorelaxation Induced by Water–Chromophore Electron Transfer

Relaxation of photoexcited chromophores is a key factor determining diverse molecular properties, from luminescence to photostability. Radiationless relaxation usually occurs through state intersections caused by distortions in the nuclear geometry of the chromophore. Using excited-state nonadiabatic dynamics simulations based on algebraic diagrammatic construction, it is shown that this is the case of 9H-adenine in water cluster, but not of 7H-adenine in water cluster. 7H-adenine in water cluster relaxes via a state intersection induced by electron transfer from water to the chromophore. This result reveals an unknown reaction pathway, with implications for the assignment of relaxation mechanisms of exciton relaxation in organic electronics. The observation of photorelaxation of 7H-adenine induced by water–chromophore electron transfer is a proof of principle calling for further computational and experimental investigations to determine how common this effect is

Spatial Factors for Triplet Fusion Reaction of Singlet Oxygen Photosensitization

First-principles quantum-chemical description of photosensitized singlet oxygen generation kinetics is challenging because of the intrinsic complexity of the underlying triplet fusion process in a floppy molecular complex with open-shell character. With a quantum-chemical kinetic model specifically tailored to deal with this problem, the reaction rates are investigated as a function of intermolecular incidence direction, orientation, and distance between O₂ and the photosensitizer. The adopted photosensitizer, 6-azo-2-thiothymine, combines practical interest and prototypical variability. The study quantitatively determined maximum singlet oxygen generation rates for 15 incidence/orientation directions, showing that they span 5 orders of magnitude between the largest and the smallest rate. Such information may provide a hands-on guideline for the experimental molecular design of new photosensitizers as well as further higher-level theoretical research

Divide-to-Conquer: A Kinetic Model for Singlet Oxygen Photosensitization

Photosensitized singlet oxygen generation occurring in a PS–O₂ complex, where PS is a photosensitizer chromophore, is a weakly coupled intermolecular energy-transfer process, a still challenging problem for theoretical chemistry. To investigate the reaction rate directly from quantum-chemical calculations, we built a semiclassical kinetic model that minimizes the computational effort for the calculation of diabatic couplings, activation energies, and reorganization energies, which are the components of the rate. The model splits the system into sets of orthogonal coordinates, which are then explored to compute the reaction rate. This model offers an effective way to evaluate the reaction probability of singlet oxygen generation along different directions and intramolecular distances of the PS–O₂ complex. The model can also be applied to other similar intermolecular energy-transfer problems, to connect the reaction kinetics and quantum-chemical calculations

Hot and Cold Charge-Transfer Mechanisms in Organic Photovoltaics: Insights into the Excited States of Donor/Acceptor Interfaces

The evolution of the excited-state manifold in organic D/A aggregates (e.g., the prototypical P3HT/PCBM) is investigated through a bottom-up approach via first-principles calculations. We show how the excited-state energies, the charge transfer (CT) states, and the electron–hole density distributions are strongly influenced by the size, the orientation, and the position (i.e., on-top versus on-edge phases) of P3HT/PCBM domains. We discuss how the structural order influences the excited-state electronic structure, providing an atomistic interpretation of the photophysics of organic blends. We show how the simultaneous presence of on-top and on-edge phases does not alter the optical absorption spectrum of the blend but does affect the photophysics. Photovoltaic processes such as (i) the simultaneous charge generation obtained from hot and cold excitations, (ii) the instantaneous and delayed charge separation, and (iii) the pump–push–probe charge generation can be interpreted based on our study

Unveiling the Role of <i>Hot</i> Charge-Transfer States in Molecular Aggregates via Nonadiabatic Dynamics

Exciton dynamics governs energy transfer and charge generation in organic functional materials. We investigate high-energy nonadiabatic excited-state dynamics for a bithiophene dimer to describe time-dependent excitonic effects in molecular aggregates. We show that the lowest excited states are populated on the subpicosecond time scale. These states are localized and unproductive in terms of charge separation. Productive high-energy charge-transfer (CT) states are populated within 50 fs during exciton deactivation, but they are short-lived (∼100 fs) and quickly transfer their population to lower states. Our simulations offer molecular-level insights into ultrafast photoinduced charge separation potentially triggered by <i>hot</i> CT states in solid-state organic materials. Design rules are suggested to increase <i>hot</i> exciton lifetimes, favoring the population of CT states as gateways for direct charge generation. These rules may boost the CT quantum yield by depleting unproductive recombination channels

Theoretical Characterization of Absorption and Emission Spectra of an Asymmetric Porphycene

The electronic ground and excited states of an asymmetric porphycene, 9-amino-2,7,12,17-tetraphenylporphycene (9-ATPPo), are investigated by electronic structure calculations. Different tautomers are considered to address their contributions to the photophysics of 9-ATPPo. Tautomerization pathways on the ground and excited states are constructed between different isomers. It is found that two trans tautomers are mainly responsible for the absorption and emission spectra of 9-ATPPo. These calculations provide a molecular mechanism to explain recent experimental observations, which show a highly complex Q-band structure in the absorption spectrum and pronounced dual fluorescence in the emission spectrum. Furthermore, the current work shows that tautomerization takes place under the assistance of cavity deformations and that a nonradiative process occurs through weak interstate nonadiabatic couplings near the S₁ minimum rather than strong ones near conical intersections

Nonadiabatic Photodynamics of a Retinal Model in Polar and Nonpolar Environment

The nonadiabatic photodynamics of the <i>all-trans</i>-2,4-pentadiene-iminium cation (protonated Schiff base 3, PSB3) and the <i>all-trans</i>-3-methyl-2,4-pentadiene-iminium cation (MePSB3) were investigated in the gas phase and in polar (aqueous) and nonpolar (<i>n</i>-hexane) solutions by means of surface hopping using a multireference configuration-interaction (MRCI) quantum mechanical/molecular mechanics (QM/MM) level. Spectra, lifetimes for radiationless deactivation to the ground state, and structural and electronic parameters are compared. A strong influence of the polar solvent on the location of the crossing seam, in particular in the bond length alternation (BLA) coordinate, is found. Additionally, inclusion of the polar solvent changes the orientation of the intersection cone from sloped in the gas phase to peaked, thus enhancing considerably its efficiency for deactivation of the molecular system to the ground state. These factors cause, especially for MePSB3, a substantial decrease in the lifetime of the excited state despite the steric inhibition by the solvent

Classification of doubly excited molecular electronic states

Electronic states with partial or complete doubly excited character play a crucial role in many areas, such as singlet fission and non-linear optical spectroscopy. Although doubly excited states have been studied in polyenes and related systems for many years, the assignment as singly vs. doubly excited, even in the simplest case of butadiene, has sparked controversies. So far, no well-defined framework for classifying doubly excited states has been developed, and even more, there is not even a well-accepted definition of doubly excited character as such. Here, we present a solution: a physically motivated definition of doubly excited character based on operator expectation values and density matrices, which works independently of the underlying orbital representation, avoiding ambiguities that have plagued earlier studies. Furthermore, we propose a classification scheme to differentiate three cases: (i) two single excitations occurring within two independent pairs of orbitals leaving four open shells (DOS), (ii) the promotion of both electrons to the same orbital, producing a closed-shell determinant (DCS), and (iii) a mixture of singly and doubly excited configurations not aligning with either one of the previous cases (Dmix). We highlight their differences in underlying energy terms and explain their signatures in practical computations. The three cases are illustrated through various high-level computational methods using dimers for DOS, polyenes for Dmix, and cyclobutane and tetrazine for DCS. The conversion between DOS and DCS is investigated using a well-known photochemical reaction, the photodimerization of ethylene. This work provides a deeper understanding of doubly excited states and may guide more rigorous discussions toward improving their computational description while also giving insight into their fundamental photophysics. </p

Photochemical Deactivation Process of HCFC-133a (C₂H₂F₃Cl): A Nonadiabatic Dynamics Study

The photochemical deactivation process of HCFC-133a (C₂H₂F₃Cl) was investigated by computing excited-state properties with a number of single-reference methods, including coupled cluster to approximated second order (CC2), algebraic diagrammatic construction to second order (ADC(2)), and time-dependent density functional theory (TDDFT). Excited states calculated with these methods, especially TDDFT, show good agreement with our previous multireference configuration interaction (MR-CISD) results. All tested methods were able to correctly predict the properties of the main series of excited states, the n-σ*, n-4p, and n-4s. Nonadiabatic dynamics in the gas phase considering 14 electronic states was simulated with TDDFT starting at the 10 ± 0.25 eV spectral window, to be compared to experimental data measured after 123.6 nm excitation. The excited-state lifetime is 137 fs. Internal conversion to the ground state occurred through several different reaction pathways with different products, including atomic elimination (Cl, F, or H), multifragmentation mechanisms (Cl+F, Cl+H, or F+H), and CC bond-fission mechanisms (alone or with Cl or H elimination). The main photochemical channels observed were Cl, Cl+H, and Cl+F eliminations, representing 54% of all processes