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A general formulation of the strong coupling between photons confined in a cavity and molecular electronic states is developed for the state-interaction state-average spin-restricted ensemble-referenced Kohn–Sham method. The light–matter interaction is included in the Jaynes–Cummings model, which requires the derivation and implementation of the analytical derivatives of the transition dipole moments between the molecular electronic states. The developed formalism is tested in the simulations of the nonadiabatic dynamics in the polaritonic states resulting from the strong coupling between the cavity photon mode and the ground and excited states of the penta-2,4-dieniminium cation, also known as PSB3. Comparison with the field-free simulations of the excited-state decay dynamics in PSB3 reveals that the light–matter coupling can considerably alter the decay dynamics by increasing the excited state lifetime and hindering photochemically induced torsion about the C=C double bonds of PSB3. The necessity of obtaining analytical transition dipole gradients for the accurate propagation of the dynamics is underlined. [ABSTRACT FROM AUTHOR]

The photophysical properties of a series of recently synthesized single benzene fluorophores were investigated using ensemble density functional theory calculations. The energetic stability of the ground and excited state species were counterposed against the aromaticity index derived from local vibrational modes. It was found that the large Stokes shift of the fluorophores (up to ca. 5800 cm −1) originates from the effect of electron donating and electron withdrawing substituents rather than π‐delocalization and related (anti‐)aromaticity. On the basis of nonadiabatic molecular dynamics simulations, the absence of fluorescence from one of the regioisomers was explained by the occurrence of easily accessible S 1/S 0 conical intersections below the vertical excitation energy level. It is demonstrated in the manuscript that the analysis of local mode force constants and the related aromaticity index represent a useful tool for the characterization of π‐delocalization effects in π‐conjugated compounds. [ABSTRACT FROM AUTHOR]

An extended variant of the spin-restricted ensemble-referenced Kohn-Sham (REKS) method, the REKS(4,4) method, designed to describe the ground electronic states of strongly multireference systems is modified to enable calculation of excited states within the time-independent variational formalism. The new method, the state-interaction state-averaged REKS(4,4), i.e., SI-SA-REKS(4,4), is capable of describing several excited states of a molecule involving double bond cleavage, polyradical character, or multiple chromophoric units. We demonstrate that the newmethod correctly describes the ground and the lowest singlet excited states of a molecule (ethylene) undergoing double bond cleavage. The applicability of the new method for excitonic states is illustrated with π stacked ethylene and tetracene dimers. We conclude that the new method can describe a wide range of multireference phenomena. [ABSTRACT FROM AUTHOR]

State-averaged (SA) variants of the spin-restricted ensemble-referenced Kohn-Sham (REKS) method, SA-REKS and state-interaction (SI)-SA-REKS, implement ensemble density functional theory for variationally obtaining excitation energies of molecular systems. In this work, the currently existing version of the SA-REKS method, which included only one excited state into the ensemble averaging, is extended by adding more excited states to the averaged energy functional. A general strategy for extension of the REKS-type methods to larger ensembles of ground and excited states is outlined and implemented in extended versions of the SA-REKS and SI-SA-REKS methods. The newly developed methods are tested in the calculation of several excited states of ground-state multi-reference systems, such as dissociating hydrogen molecule, and excited states of donor-acceptor molecular systems. For hydrogen molecule, the new method correctly reproduces the distance dependence of the lowest excited state energies and describes an avoided crossing between the doubly excited and singly excited states. For bithiophene-perylenediimide stacked complex, the SI-SA-REKS method correctly describes crossing between the locally excited state and the charge transfer excited state and yields vertical excitation energies in good agreement with the ab initio wavefunction methods. [ABSTRACT FROM AUTHOR]

Electron transfer in the ground and excited states of a model donor-acceptor (D-A) system is investigated using the single-reference and multi-reference density functional theory (DFT) methods. To analyze the results of the calculations, a simple two-site multi-reference model was derived that predicts a stepwise electron transfer in the S0 state and a wave-like dependence of the S1 electron transfer on the external stimulus. The standard single-reference Kohn-Sham (KS) DFT approach and the time-dependent DFT (TDDFT) method failed to describe the correct dependence of the S0 and S1 electron transfer on the external electric field applied along the donor-acceptor system. The multi-reference DFT approach, the spin-restricted ensemble-referenced KS (REKS) method, was able to successfully reproduce the correct behavior of the S0 and S1 electron transfer on the applied field. The REKS method was benchmarked against experimentally measured gas phase charge transfer excitations in a series of organic donor-acceptor complexes and displayed its ability to describe this type of electronic transitions with a very high accuracy, mean absolute error of 0.05 eV with the use of the standard range separated density functionals. On the basis of the calculations undertaken in this work, it is suggested that the non-adiabatic coupling between the S0 and S1 states may interfere with the electron transfer in a weakly coupled donor-acceptor system. It is also suggested that the electronic excitation of a D+-A- system may play a dual role by assisting the further electron transfer at certain magnitudes of the applied electric field and causing the backward transfer at lower electric field strengths. [ABSTRACT FROM AUTHOR]

The formulations and performances of spin‐restricted ensemble‐referenced KS and mixed‐reference spin‐flip time‐dependent density functional theory incorporating strong correlations into density functional theories are documented. As a result of balanced dynamic and nondynamic correlation, they are capable of describing strongly correlated challenging systems including diradicals, bond dissociation, conical intersections, doubly excited states, and so on, overcoming the limitations of current density functional theories. [ABSTRACT FROM AUTHOR]

Variation of the precession K along the torsion C2-C6 BCP bond-path of fulvene for the S 0 (left panel) and S 1 (right panel) electronic states for a series of values of the torsion θ = 0.0° (Franck-Condon) to θ = 64.3° (conical intersection). Bond critical points (BCP s) are located at a distance = 0.0 a.u along the bond-path. • Determined the precessions K of the path-packets for the S 0 and S 1 states of fulvene. • The precessions K of the path-packets quantified the bond rigidity and flexibility. • An asymmetry is found for the S 1 state variation in the bond-path rigidity with torsion. • The S 1 state at torsion θ = 0.0° possesses maximum bond-rigidity along the entire bond. • The S 1 state possessed a higher degree of bond-anharmonicity than the S 0 state. Here we have determined the precessions K and K' of the { p , p ′} and { q , q ′} path-packets for the excited state deactivation reaction of fulvene in terms of bond-flexing, bond-torsion and bond-anharmonicity that includes the tendencies towards bond-path-rigidity and bond-path-flexibility. An asymmetry is found for the S 1 state resulting in an unpredictable variation in the direction of the bond-path-rigidity as a function of the torsion coordinate. Uniquely, the S 1 state at torsion θ = 0.0° possesses the possible maximum bond-path-rigidity, along the entire bond-path but then drops lower than for the S 0 state at the conical intersection indicating photo-excitation facilitates the torsion. [ABSTRACT FROM AUTHOR]

A balanced treatment of the covalent and ionic contributions to the ground and excited states originating from torsion about double bonds is known to be strongly dependent on the presence of dynamic electron correlation. We undertake an analysis of the minimum energy pathways corresponding to deactivation of the first excited singlet state of PSB3. In doing so we consider torsion about the three double bonds including other intramolecular degrees of freedom, such as the bond length alternation. The 3‐D bond‐path analysis provides a new 'bond‐localized orbital‐like' directional interpretation of bonding. Therefore, we present a more sophisticated method of determination of the degree of covalent and ionic contributions known to be responsible for altering the relative stability of the S1/S0 conical intersections. The results presented suggest that the commonly used simplified multi‐reference methodologies that often result in incorrect predictions for the excited state deactivation reaction mechanism. The bond‐path framework set B visualization of the spectrum of the chemical character (covalent–biradical‐ionic) displayed of each of the back‐bone bonds as well as the influence on neighboring bonds. The most preferred directions of accumulation of charge density, q‐ and q′‐paths along the backbone bond‐path (r) corresponding to the torsional C10‐N12 BCP for the S0 (top) and S1 (below) states at a value of the torsion q = 90.0°. [ABSTRACT FROM AUTHOR]

The factors underlying the experimentally observed branching ratio (70:30) of the (1,3‐cyclohexadiene) CHD → HT (1,3,5‐hexatriene) photochemical ring‐opening reaction are investigated. The ring‐opening reaction path is optimized by a high‐level multi‐reference DFT method and the density along the path is analyzed by the quantum theory of atoms in molecules (QTAIM) and stress tensor methods. The performed density analysis suggests that, in both S1 and S0 electronic states, there exists an attractive interaction between the ends of the fissile σ‐bond of CHD that steers the ring‐opening reaction predominantly in the direction of restoration of the ring. It is suggested that opening of the ring and formation of the reaction product (HT) can only be achieved when there is a sufficient persistent nuclear momentum in the direction of stretching of the fissile bond. As this orientation of the nuclear momentum vector can be expected relatively rare during the dynamics, this explains the observed low quantum yield of the ring‐opening reaction. Experimentally observed branching ratio (70:30) of the (1,3‐cyclohexadiene) CHD → HT (1,3,5‐hexatriene) photochemical ring‐opening reaction is investigated by first‐principles calculations and next‐generation quantum theory of atoms in molecules. It is suggested that opening of the ring and formation of the reaction product can only be achieved when there is a sufficient persistent nuclear momentum in the direction of stretching of the fissile bond. [ABSTRACT FROM AUTHOR]

A vector‐based representation of the chemical bond is introduced, which we refer to as the bond‐path framework set B = {p, q, r}, where p, q, and r represent 3 eigenvector‐following paths with corresponding lengths H*, H, and the familiar quantum theory of atoms in molecules (QTAIM) bond‐path length (BPL). The intended application of B is for molecules subjected to various types of reactions and distortions, including photoisomerization reactions, applied torsions θ, or normal modes of vibration. The lengths H* and H of the eigenvector‐following paths are constructed using the e1 and e2 Hessian eigenvectors, respectively, along the bond path, these corresponding to the least and most preferred directions of charge density accumulation. In particular, the paths p and q provide a vector representation of the scalar QTAIM ellipticity ε. The bond‐path framework set B is applied to the excited state deactivation of fulvene that involves distortions along various intramolecular degrees of freedom, such as the bond stretching/compression of bond‐length alternation and bond torsion distortions. We find that the H* and H lengths can differentiate between the ground and excited electronic states, in contrast to the QTAIM BPL. Five unique paths were presented for B= {(p0,p1), (q0,q1), r} for the ground and first excited states where the profile of the scaling factor, the ellipticity ε, reveals a large unexpected asymmetry for the excited state. A "next‐generation" quantum theory of atoms in molecules (QTAIM) is introduced to analyze all types of bonding in molecules subjected to various types of reactions and distortions, including photoisomerization reactions, applied torsions θ, or normal modes of vibration. The double‐bond isomerization of fulvene is used as test model for this "next‐generation" QTAIM approach. [ABSTRACT FROM AUTHOR]