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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]

Conical intersections control excited state reactivity, and thus, elucidating and predicting their geometric and energetic characteristics are crucial for understanding photochemistry. Locating these intersections requires accurate and efficient electronic structure methods. Unfortunately, the most accurate methods (e.g., multireference perturbation theories such as XMS-CASPT2) are computationally challenging for large molecules. The state-interaction state-averaged restricted ensemble referenced Kohn–Sham (SI-SA-REKS) method is a computationally efficient alternative. The application of SI-SA-REKS to photochemistry was previously hampered by a lack of analytical nuclear gradients and nonadiabatic coupling matrix elements. We have recently derived analytical energy derivatives for the SI-SA-REKS method and implemented the method effectively on graphical processing units. We demonstrate that our implementation gives the correct conical intersection topography and energetics for several examples. Furthermore, our implementation of SI-SA-REKS is computationally efficient, with observed sub-quadratic scaling as a function of molecular size. This demonstrates the promise of SI-SA-REKS for excited state dynamics of large molecular systems. [ABSTRACT FROM AUTHOR]

The use of the mixed reference (MR) reduced density matrix, which combines reduced density matrices of the MS = +1 and -1 triplet-ground states, is proposed in the context of the collinear spin-fliptime-dependent density functional theory (SF-TDDFT) methodology. The time-dependent Kohn-Sham equation with the mixed state is solved by the use of spinor-like open-shell orbitals within the linear response formalism, which enables to generate additional configurations in the realm of TD-DFT. The resulting MR-SF-TDDFT computational scheme has several advantages before the conventional collinear SF-TDDFT. The spin-contamination of the response states of SF-TDDFT is nearly removed. This considerably simplifies the identification of the excited states, especially in the "black-box" type applications, such as the automatic geometry optimization, reaction path following, or molecular dynamics simulations. With the new methodology, the accuracy of the description of the excited states is improved as compared to the collinear SF-TDDFT. Several test examples, which include systems typified by strong non-dynamic correlation, orbital (near) degeneracy, and conical intersections, are given to illustrate the performance of the new method. [ABSTRACT FROM AUTHOR]

The spin-restricted ensemble-referenced Kohn-Sham (REKS) method is based on an ensemble representation of the density and is capable of correctly describing the non-dynamic electron correlation stemming from (near-)degeneracy of several electronic configurations. The existing REKS methodology describes systems with two electrons in two fractionally occupied orbitals. In thiswork, the REKS methodology is extended to treat systems with four fractionally occupied orbitals accommodating four electrons and self-consistent implementation of the REKS(4,4) method with simultaneous optimization of the orbitals and their fractional occupation numbers is reported. The new method is applied to a number of molecular systems where simultaneous dissociation of several chemical bonds takes place, as well as to the singlet ground states of organic tetraradicals 2,4-didehydrometaxylylene and 1,4,6,9-spiro[4.4]nonatetrayl. [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]

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]

Quantum-chemical computational methods are benchmarked for their ability to describe conical intersections in a series of organic molecules and models of biological chromophores. Reference results for the geometries, relative energies, and branching planes of conical intersections are obtained using ab initio multireference configuration interaction with single and double excitations (MRCISD). They are compared with the results from more approximate methods, namely, the state-interaction state-averaged restricted ensemble-referenced Kohn-Sham method, spin-flip time-dependent density functional theory, and a semiempirical MRCISD approach using an orthogonalization-corrected model. It is demonstrated that these approximate methods reproduce the ab initio reference data very well, with root-mean-square deviations in the optimized geometries of the order of 0.1 À or less and with reasonable agreement in the computed relative energies. A detailed analysis of the branching plane vectors shows that all currently applied methods yield similar nuclear displacements for escaping the strong non-adiabatic coupling region near the conical intersections. Our comparisons support the use of the tested quantum-chemical methods for modeling the photochemistry of large organic and biological systems. [ABSTRACT FROM AUTHOR]

Ensemble density functional theory ( DFT) is a novel theoretical approach that is capable of exact treatment of non-dynamic electron correlation in the ground and excited states of many-body fermionic systems. In contrast to ordinary DFT, ensemble DFT has not found so far a way to the repertoire of methods of modern computational chemistry, probably owing to the lack of practically affordable implementations of the theory. The spin-restricted ensemble-referenced Kohn-Sham ( REKS) method represents perhaps the first computational scheme that makes ensemble DFT calculations feasible. The REKS method is based on the rigorous ensemble representation of the energy and the density of a strongly correlated system and provides for an accurate and consistent description of molecular systems the electronic structure of which is dominated by the non-dynamic correlation. This includes the ground and excited states of molecules undergoing bond breaking/bond formation, the low-spin states of biradicals and polyradicals, symmetry forbidden chemical reactions and avoided crossings of potential energy surfaces, real intersections between the energy surfaces of the ground and excited states (conical intersections), and many more. The REKS method can be employed in connection with any local, semi-local and hybrid (global and range-separated) functional and affords calculations of large and very large molecular systems at a moderate mean-field cost. WIREs Comput Mol Sci 2015, 5:146-167. doi: 10.1002/wcms.1209 Conflict of interest: The author has declared no conflicts of interest for this article. For further resources related to this article, please visit the . [ABSTRACT FROM AUTHOR]

The non-adiabatic dynamics of furan excited in the ππ* state (S2 in the Franck–Condon geometry) was studied using non-adiabatic molecular dynamics simulations in connection with an ensemble density functional method. The time-resolved photoelectron spectra were theoretically simulated in a wide range of electron binding energies that covered the valence as well as the core electrons. The dynamics of the decay (rise) of the photoelectron signal were compared with the excited-state population dynamics. It was observed that the photoelectron signal decay parameters at certain electron binding energies displayed a good correlation with the events occurring during the excited-state dynamics. Thus, the time profile of the photoelectron intensity of the K-shell electrons of oxygen (decay constant of 34 ± 3 fs) showed a reasonable correlation with the time of passage through conical intersections with the ground state (47 ± 2 fs). The ground-state recovery constant of the photoelectron signal (121 ± 30 fs) was in good agreement with the theoretically obtained excited-state lifetime (93 ± 9 fs), as well as with the experimentally estimated recovery time constant (ca. 110 fs). Hence, it is proposed to complement the traditional TRPES observations with the trXPS (or trNEXAFS) measurements to obtain more reliable estimates of the most mechanistically important events during the excited-state dynamics. [ABSTRACT FROM AUTHOR]

Next‐generation quantum theory of atoms in molecules was applied to analyze, along an entire bond path, intramolecular interactions known to influence the photoisomerization dynamics of a light‐driven rotary molecular motor. The 3D bond‐path framework set B0,1 constructed from the least and most preferred directions of electronic motion, provided new insights into the bonding leading to different S1 state lifetimes including the first quantification of covalent character of a closed‐shell intramolecular bond path. We undertook the first use of the stress tensor trajectory Tσ(s) analysis on selected nonadiabatic molecular dynamics trajectories with the electron densities obtained using the ensemble density functional theory method. The stress tensor Tσ(s) analysis was found to be well suited to follow the dynamics trajectories that included the S0 and S1 electronic states through the conical intersection and also provided to a new measure to assess the degree of purity of the axial bond rotation for the design of rotary molecular motors. [ABSTRACT FROM AUTHOR]

Various types of interactions between halogen (X) and π moiety (X−π interaction) including halogen bonding play important roles in forming the structures of biological, supramolecular, and nanomaterial systems containing halogens and aromatic rings. Furthermore, halogen molecules such as X2 and CX4 (X = Cl/Br) can be intercalated in graphite and bilayer graphene for doping and graphene functionalization/modification. Due to the X−π interactions, though recently highly studied, their structures are still hardly predictable. Here, using the coupled-cluster with single, double, and noniterative triple excitations (CCSD(T)), the Møller-Plesset second-order perturbation theory (MP2), and various flavors of density functional theory (DFT) methods, we study complexes of benzene (Bz) with halogen-containing molecules X2 and CX4 (X = Cl/Br) and analyze various components of the interaction energy using symmetry adapted perturbation theory (SAPT). As for the lowest energy conformers (S1), X2-Bz is found to have the T-shaped structure where the electropositive X atom-end of X2 is pointing to the electronegative midpoint of CC bond of the Bz ring, and CX4-Bz has the stacked structure. In addition to this CX4-Bz (S1), other low energy conformers of X2-Bz (S2/S3) and CX4-Bz (S2) are stabilized primarily by the dispersion interaction, whereas the electrostatic interaction is substantial. Most of the density functionals show noticeable deviations from the CCSD(T) complete basis set (CBS) limit binding energies, especially in the case of strongly halogen-bonded conformers of X2-Bz (S1), whereas the deviations are relatively small for CX4-Bz where the dispersion is more important. The halogen bond shows highly anisotropic electron density around halogen atoms and the DFT results are very sensitive to basis set. The unsatisfactory performance of many density functionals could be mainly due to less accurate exchange. This is evidenced from the good performance by the dispersion corrected hybrid and double hybrid functionals. B2GP-PLYP-D3 and PBE0-TS(Tkatchenko-Scheffler)/D3 are well suited to describe the X−π interactions adequately, close to the CCSD(T)/CBS binding energies (within ∼1 kJ/mol). This understanding would be useful to study diverse X−π interaction driven structures such as halogen containing compounds intercalated between 2-dimensional layers. [ABSTRACT FROM AUTHOR]