Comparison of the electronic structure of different perylene‐based dye‐aggregates

Aggregates of functionalized polycyclic aromatic molecules like perylene derivatives differ in important optoelectronic properties such as absorption and emission spectra or exciton diffusion lengths. Although those differences are well known, it is not fully understood if they are caused by variations in the geometrical orientation of the molecules within the aggregates, variations in the electronic structures of the dye aggregates or interplay of both. As this knowledge is of interest for the development of materials with optimized functionalities, we investigate this question by comparing the electronic structures of dimer systems of representative perylene‐based chromophores. The study comprises dimers of perylene, 3,4,9,10‐perylene tetracarboxylic acid bisimide (PBI), 3,4,9,10‐perylene tetracarboxylic acid dianhydride (PTCDA), and diindeno perylene (DIP). Potential energy curves (PECs) and characters of those electronic states are investigated which determine the optoelectronic properties. The computations use the spin‐component‐scaled approximate coupled‐cluster second‐order method (SCS‐CC2), which describes electronic states of predominately neutral excited (NE) and charge transfer (CT) character equally well. Our results show that the characters of the excited states change significantly with the intermolecular orientation and often represent significant mixtures of NE and CT characters. However, PECs and electronic structures of the investigated perylene derivatives are almost independent of the substitution patterns of the perylene core indicating that the observed differences in the optoelectronic properties mainly result from the geometrical structure of the dye aggregate. It also hints at the fact that optical properties can be computed from less‐substituted model compounds if a proper aggregate geometry is chosen. © 2012 Wiley Periodicals, Inc.     

Calculation of the Vibrationally Resolved,Circularly Polarized Luminescence of d‐Camphorquinone and (S,S)‐trans‐β‐Hydrindanone

Circularly polarized luminescence (CPL), the differential emission of left‐ and right‐handed circularly polarized light from a molecule, is modeled by using time‐dependent density functional theory. Calculations of the CPL spectra for the first electronic excited states of d‐camphorquinone and (S,S)‐trans‐β‐hydrindanone under the Franck–Condon approximation and using various functionals are presented, as well as calculations of absorption, emission, and circular dichroism spectra. The functionals B3LYP, BHLYP, and CAM‐B3LYP are employed, along with the TZVP and aug‐cc‐pVDZ Gaussian‐type basis sets. For the lowest‐energy transitions, all functionals and basis sets perform comparably, with the long‐range‐corrected CAM‐B3LYP better reproducing the excitation energy of camphorquinone but leading to a blue shift with respect to experiment for hydrindanone. The vibrationally resolved spectra of camphorquinone are very well reproduced in terms of peak location, widths, shapes, and intensities. The spectra of hydrindanone are well reproduced in terms of overall envelope shape and width, as well as the lack of prominent vibrational structure in the emission and CPL spectra. Overall the simulated spectra compare well with experiment, and reproduce the band shapes, emission red shifts, and presence or absence of visible vibrational fine structure.     

Phenylene Ethynylene‐Tethered Perylene Bisimide Folda‐Dimer and Folda‐Trimer: Investigations on Folding Features in Ground and Excited States

In this work, we have elucidated in detail the folding properties of two perylene bisimide (PBI) foldamers composed of two and three PBI units, respectively, attached to a phenylene ethynylene backbone. The folding behaviors of these new PBI folda‐dimer and trimer have been studied by solvent‐dependent UV/Vis absorption and 1D and 2D NMR spectroscopy, revealing facile folding of both systems in tetrahydrofuran (THF). In CHCl₃ the dimer exists in extended (unfolded) conformation, whereas partially folded conformations are observed in the trimer. Temperature‐dependent ¹H NMR spectroscopic studies in [D₈]THF revealed intramolecular dynamic processes for both PBI foldamers due to, on the one hand, hindered rotation around C?N imide bonds and, on the other hand, backbone flapping; the latter process being energetically more demanding as it was observed only at elevated temperature. The structural features of folded conformations of the dimer and trimer have been elucidated by different 2D‐NMR spectroscopy (e.g., ROESY and DOSY) in [D₈]THF. The energetics of folding processes for the PBI dimer and trimer have been assessed by calculations applying various methods, particularly the semiempirical PM6‐DH2 and the more sophisticated B97D approach, in which relevant dispersion corrections are included. These calculations corroborate the results of NMR spectroscopic studies. Folding features in the excited states of these PBI foldamers have been characterized by using time‐resolved fluorescence and transient absorption spectroscopy in THF and CHCl₃, exhibiting similar solvent‐dependent behavior as observed for the ground state. Interestingly, photoinduced electron transfer (PET) process from electron‐donating backbone to electron‐deficient PBI core for extended, but not for folded, conformations was observed, which can be explained by a fast relaxation of excited PBI stacks in the folded conformation into fluorescent excimer states.     

A Twisted Bay‐Substituted Quaterrylene Phosphorescing in the NIR Spectral Region

The preparation of the first soluble quaterrylene derivative featuring peripheral tert‐butyl substituents and sterically hindering, core‐anchored triflate groups has been achieved. This involves a facile synthetic route based on an oxidative coupling of perylene precursors in the presence of H₂O₂ as oxidant. The steric hindrance between the TfO substituents at the central bay position of the quaterrylene board triggers a strong deformation of the central perylene planarity, which forces the quaterrylene platform to adopt a twisted geometry as shown by X‐ray analysis. Exceptionally, photophysical investigations show that the core‐twisted quaterrylene phosphoresces in the NIR spectral region at 1716 nm. Moreover, third‐order nonlinear optical measurements on solutions and thin film containing the relevant molecule showed very large second hyperpolarizability values, as predicted by theoretical calculations at the CAM ‐B3LYP /6‐31G** level of theory, making this material very appealing for photonic applications.     

Comparison of aromatic NH···π, OH···π, and CH···π interactions of alanine using MP2, CCSD, and DFT methods

A comparison of the performance of various density functional methods including long‐range corrected and dispersion corrected methods [MPW1PW91, B3LYP, B3PW91, B97‐D, B1B95, MPWB1K, M06‐2X, SVWN5, ωB97XD, long‐range correction (LC)‐ωPBE, and CAM‐B3LYP using 6‐31+G(d,p) basis set] in the study of CH···π, OH···π, and NH···π interactions were done using weak complexes of neutral (A) and cationic (A⁺) forms of alanine with benzene by taking the Møller–Plesset (MP2)/6‐31+G(d,p) results as the reference. Further, the binding energies of the neutral alanine–benzene complexes were assessed at coupled cluster (CCSD)/6‐31G(d,p) method. Analysis of the molecular geometries and interaction energies at density functional theory (DFT), MP2, CCSD methods and CCSD(T) single point level reveal that MP2 is the best overall performer for noncovalent interactions giving accuracy close to CCSD method. MPWB1K fared better in interaction energy calculations than other DFT methods. In the case of M06‐2X, SVWN5, and the dispersion corrected B97‐D, the interaction energies are significantly overrated for neutral systems compared to other methods. However, for cationic systems, B97‐D yields structures and interaction energies similar to MP2 and MPWB1K methods. Among the long‐range corrected methods, LC‐ωPBE and CAM‐B3LYP methods show close agreement with MP2 values while ωB97XD energies are notably higher than MP2 values. © 2010 Wiley Periodicals, Inc. J Comput Chem 2010     

Which density functional is close to CCSD accuracy to describe geometry and interaction energy of small noncovalent dimers? A benchmark study using Gaussian09

A benchmark study on all possible density functional theory (DFT) methods in Gaussian09 is done to locate functionals that agree well with CCSD/aug‐cc‐pVTZ geometry and Ave‐CCSD(T)/(Q‐T) interaction energy (E_int) for small non‐covalently interacting molecular dimers in “dispersion‐dominated” (class 1), “dipole‐induced dipole” (class 2), and “dipole‐dipole” (class 3) classes. A DFT method is recommended acceptable if the geometry showed close agreement to CCSD result (RMSD < 0.045) and E_int was within 80–120% accuracy. Among 382 tested functionals, 1–46% gave good geometry, 13–44% gave good E_int, while 1–33% satisfied geometry and energy criteria. Further screening to locate the best performing functionals for all the three classes was made by counting the acceptable values of energy and geometry given by each functionals. The meta‐generalized gradient approximation (GGA) functional M06L was the best performer with total 14 hits; seven acceptable energies and seven acceptable geometries. This was the only functional “recommended” for at least two dimers in each class. The functionals M05, B2PLYPD, B971, mPW2PLYPD, PBEB95, and CAM‐B3LYP gave 11 hits while PBEhB95, PW91B95, Wb97x, BRxVP86, BRxP86, HSE2PBE, HSEh1PBE, PBE1PBE, PBEh1PBE, and PW91TPSS gave 10 hits. Among these, M05, B971, mPW2PLYPD, Wb97x, and PW91TPSS were among the “recommended” list of at least one dimer from each class. Long‐range correction (LC) of Hirao and coworkers to exchange‐correlation functionals showed massive improvement in geometry and E_int. The best performing LC‐functionals were LC‐G96KCIS and LC‐PKZBPKZB. Our results predict that M06L is the most trustworthy DFT method in Gaussian09 to study small non‐covalently interacting systems. © 2013 Wiley Periodicals, Inc.     

Predictive power of long-range corrected functionals on the spectroscopic properties of tetrapyrrole derivatives for photodynamic therapy

Porphyrin and chlorin based compounds possess promising properties to be utilized as photosensitizers in photodynamic therapy (PDT). However, the photosensitizers available on the market today are not ideal for use in PDT, which has emphasized the need for new photosensitizers with improved photodynamic properties to be developed. Computational drug-design can be utilized in the search for improved pharmaceutical compounds, provided that the methods used are able to reproduce experimental data. In the present study we investigated, by the use of time-dependent density functional theory (TD-DFT), the performance of the long-range corrected functionals ωB97, ωB97X and ωB97XD on their ability to predict low-lying singlet excitations (>600 nm) of a set of well-known photosensitizing compounds. It was found that ωB97X reproduced the experimental red-most absorption band most satisfactorily. The use of either B3LYP, ωB97XD or M06 in geometry optimizations has a minor effect on the spectra in most cases. Calculated energy differences between the optimized singlet ground states and optimized first excited triplet states show consistent and overall higher triplet state energies for B3LYP, M06, and PBE0 compared with ωB97, ωB97X, and ωB97XD. The calculated triplet state energies are, however, sufficient to generate singlet oxygen in most cases.     

Theoretical analysis of excited states and energy transfer mechanism in conjugated dendrimers

The excited states of the phenylene ethynylene dendrimer are investigated comprehensively by various electronic‐structure methods. Several computational methods, including SCS‐ADC(2), TDHF, TDDFT with different functionals (B3LYP, BH&HLYP, CAM‐B3LYP), and DFT/MRCI, are applied in systematic calculations. The theoretical approach based on the one‐electron transition density matrix is used to understand the electronic characters of excited states, particularly the contributions of local excitations and charge‐transfer excitations within all interacting conjugated branches. Furthermore, the potential energy curves of low‐lying electronic states as the functions of ethynylene bonds are constructed at different theoretical levels. This work provides us theoretical insights on the intramolecular excited‐state energy transfer mechanism of the dendrimers at the state‐of‐the‐art electronic‐structure theories. © 2014 Wiley Periodicals, Inc.     

Analytical nuclear excited‐state gradients for the Tamm–Dancoff approximation using uncoupled frozen‐density embedding

We report the derivation and implementation of analytical nuclear gradients for excited states using time‐dependent density functional theory using the Tamm–Dancoff approximation combined with uncoupled frozen‐density embedding using density fitting. Explicit equations are presented and discussed. The implementation is able to treat singlet as well as triplet states and functionals using the local density approximation, the generalized gradient approximation, combinations with Hartree–Fock exchange (hybrids), and range‐separated functionals such as CAM‐B3LYP. The new method is benchmarked against supermolecule calculations in two case studies: The solvatochromic shift of the (vertical) fluorescence energy of 4‐aminophthalimide on solvation, and the first local excitation of the benzonitrile dimer. Whereas for the 4‐aminophthalimide–water complex deviations of about 0.2 eV are obtained to supermolecular calculations, for the benzonitrile dimer the maximum error for adiabatic excitation energies is below 0.01 eV due to a weak coupling of the subsystems. © 2017 Wiley Periodicals, Inc.     

Theoretical investigations of the perylene electronic structure: Monomer,dimers, and excimers

The structural and electronic properties of perylene molecule, dimers, and excimers have been computationally studied. The present work represents the first systematic study of perylene molecule and dimer forms by means of long‐range corrected time‐dependent density functional theory (TDDFT) approaches. Initially, the study explores the photophysical properties of the molecular species. Vertical transitions to many excited singlet states have been computed and rationalized with different exchange‐correlation functionals. Differences between excitation energies are discussed and compared to the absorption spectrum of perylene in gas phase and diluted solution. De‐excitation energy from the relaxed geometry of the lowest excited singlet is in good agreement with the experimental fluorescence emission. Optimization of several coplanar forms of the perylene pair prove that, contrary to generalized gradient approximation (GGA) and hybrid exchange‐correlation functionals, corrected TDDFT is able to bind the perylene dimer in the ground state. Excitation energies from different dimer conformers point to dimer formation prior to photoexcitation. The fully relaxed excimer geometry belongs to the perfectly eclipsed conformation with D_2h symmetry. The excimer equilibrium intermolecular distance is shorter than the separation found for the ground state, which is an indication of stronger interchromophore interaction in the excimer state. Excimer de‐excitation energy is in rather good agreement with the excimer band of perylene in concentrated solution. The study also scans the energy profiles of the ground and lowest excited states along several geometrical distortions. The nature of the interactions responsible for the excimer stabilization is explored in terms of excitonic and charge resonance contributions. © 2015 Wiley Periodicals, Inc.     

Benchmarking of density functionals for the kinetics and thermodynamics of the hydrolysis of glycosidic bonds catalyzed by glycosidases

In recent years, there has been an increased interest in understanding the enzymatic mechanism of glycosidases resorting mostly to DFT and DFT/MM calculations. However, the performance of density functionals (DFs) is well known to be system and property dependent. Trends drawn from general studies, despite important to evaluate the quality of the DFs and to pave the way for the development of new DFs, may be misleading when applied to a single specific system/property. To overcome this issue, we carried out a benchmarking study of 40 DFs applied to the geometry optimization and to the electronic barrier height (E _Barrier) and electronic energy of reaction (E _R) of prototypical glycosidase‐catalyzed reactions. Additionally, we report calculations with SCC‐DFTB and four semiempirical MO methods applied to the same problem. We have used a universal molecular model for retaining glycosidases, comprising only a 22‐atoms system that mimics the active site and substrate. High accuracy reference geometries and energies were calculated at the CCSD(T)/CBS//MP2/aug‐cc‐pVTZ level of theory. Most DFs reproduce the reference geometries extremely well, with mean unsigned errors (MUE) smaller than 0.05 Å for bond lengths and 3° for bond angles. Among the DFs, wB97X‐D, CAM‐B3LYP, B3P86, and PBE1PBE have the best performance in geometry optimizations (MUE = 0.02 Å). Conversely, semiempirical MO and SCC‐DFTB methods yielded less accurate geometries (MUE between 0.09 and 0.17 Å). The inclusion of D3 correction has a small, but still relevant, influence in the geometry predicted by some DFs. Regarding E _Barrier, 11 DFs (MPW1B95, CAM‐B3LYP, M06 ‐ 2X, PBE1PBE, wB97X ‐ D, B1B95, BMK, MN12 – SX, M05, M06, and M11) presented errors below 1 kcal.mol^?1, in relation to the reference energy. Most of these functionals belong to the family of hybrid functionals (H‐GGA, HH‐GGA, and HM‐GGA), which shows a positive influence of HF exchange in the determination of E _Barrier. The inclusion of D3 correction has not affected significantly the E _Barrier and E _R. The use of geometries at the accurate but expensive MP2/aug‐cc‐pVTZ level of theory has a small, albeit not insignificant, influence in the E _Barrier when compared with energies calculated with geometries determined with the DFs (usually a few tenths of kcal.mol^?1, with exceptions). In general, semiempirical MO methods and DFTB are associated with larger errors in the determination of E _Barrier, with unsigned errors from 6.9 to 24.7 kcal.mol^?1.     

para‐Quinodimethane‐Bridged Perylene Dimers and Pericondensed Quaterrylenes: The Effect of the Fusion Mode on the Ground States and Physical Properties

Polycyclic hydrocarbon compounds with a singlet biradical ground state show unique physical properties and promising material applications; therefore, it is important to understand the fundamental structure/biradical character/physical properties relationships. In this study, para‐quinodimethane (p‐QDM)‐bridged quinoidal perylene dimers 4 and 5 with different fusion modes and their corresponding aromatic counterparts, the pericondensed quaterrylenes 6 and 7 , were synthesized. Their ground‐state electronic structures and physical properties were studied by using various experiments assisted with DFT calculations. The proaromatic p‐QDM‐bridged perylene monoimide dimer 4 has a singlet biradical ground state with a small singlet/triplet energy gap (?2.97 kcal mol^?1), whereas the antiaromatic s‐indacene‐bridged N‐annulated perylene dimer 5 exists as a closed‐shell quinoid with an obvious intramolecular charge‐transfer character. Both of these dimers showed shorter singlet excited‐state lifetimes, larger two‐photon‐absorption cross sections, and smaller energy gaps than the corresponding aromatic quaterrylene derivatives 6 and 7 , respectively. Our studies revealed how the fusion mode and aromaticity affect the ground state and, consequently, the photophysical properties and electronic properties of a series of extended polycyclic hydrocarbon compounds.     

Design of donor–acceptor–donor (D–A–D) type small molecule donor materials with efficient photovoltaic parameters

Four Donor–Acceptor–Donor (D–A–D) type of donor molecules (M1‐M4) with triphenylamine (TPA) as donor moiety, thiophene as bridge, and thiazolothiazole as acceptor unit were designed and its photovoltaic parameters were equated with reference molecule “R.” DFT functional CAM‐B3LYP/6‐31G (d,p) was found best for geometry optimization and TD‐CAM‐B3LYP/6‐31G (d,p) was found suitable for excited state calculations. Among designed donor molecules, M4 manifests suitable lowest band gap of 4.73 eV, frontier molecular orbital energy levels as well as distinctive broad absorption of 455.3 nm due to the stronger electron withdrawing group. The electron‐withdrawing substituents contribute to red shifts of absorption spectra and better stabilities for designed molecules. The theoretically determined reorganization energies of designed donor molecules suggested excellent charge mobility property. The lower λ_e values in comparison with λ_h illustrated that these four donor materials would be ideal for electron transfer and M4 would be best amongst the investigated molecules with lowest λ_e of 0.0177. Furthermore, the calculated Voc of M4 is 2.04 V with respect to PC₆₀BM (phenyl‐C61‐butyric acid methyl ester). This study revealed that the designed donor materials are suitable and recommended for high performance organic solar cell devices.     

A study of the structure of high-energy states of nitrogen trioxide and the (NO)<Subscript>2</Subscript> dimer: DFT calculations within the symmetrized Kohn-Sham formalism

The electronic structure, geometry, and thermodynamic parameters of the high-energy states of NO₃ and the (NO)₂ dimer are calculated at the DFT B3LYP/6–311++G(3df) level within the symmetrized Kohn-Sham formalism. The results of the DFT calculation of the excited states of NO₃ well agree with the experimental data and precise ab initio calculations. The reactivity of high-energy nitrogen trioxide in the activation of molecular nitrogen and nitrogen protoxide is analyzed. The assumption is substantiated that the Karavaev effect (gain of nitrogen oxides in an air mixture with nitric acid vapors) is due to the photochemical activation of molecular nitrogen in the presence of an NO₃ high-energy state as a decomposition product of nitric acid.     

Adsorption‐induced changes of intramolecular optical transitions: PTCDA/NaCl and PTCDA/KCl

Structural and optical properties of isolated perylene‐3,4,9,10‐tetracarboxylic acid dianhydride molecules adsorbed on (100) oriented NaCl and KCl surfaces were studied theoretically to analyze the recently observed red‐shift of the optical excitation spectrum after adsorption (Müller et al., Phys. Rev. B, 2011, 83, 241203; Paulheim et al. Phys. Chem. Chem. Phys., 2013, 15, 4906). The ground‐state structures were obtained by periodic dispersion‐corrected density functional theory (DFT) calculations. For the excited‐state calculations, nonperiodic time‐dependent DFT methods were applied for a cluster model embedded in point charges. The range‐separated hybrid functional CAM‐B3LYP was used. Correlation‐consistent basis sets were used and the calculated excitation energies were extrapolated to the complete basis set limit. The shift of the first optical excitation energy was analyzed in terms of electronic and geometric contributions. It was found that both the distortion of the molecule due to the interaction with the surface and the electrostatic potential of the surface play an important role. © 2015 Wiley Periodicals, Inc.     

Conformational Analysis and CD Calculations of Methyl‐Substituted 13‐Tridecano‐13‐lactones

Conformational models covering an energy range of 3 kcal/mol were calculated for (13S)‐tetradecano‐13‐lactone ( 3 ), (12S)‐12‐methyltridecano‐13‐lactone ( 4 ), and (12S,13R)‐12‐methyltetradecano‐13‐lactone ( 8 ), starting from a semiempirical Monte‐Carlo search with AM1 parametrization, and subsequent optimization of the 100 best conformers at the 6‐31G*/B3LYP and then the TZVP/B3LYP level of density‐functional theory. CD Spectra for these models were calculated by the time‐dependent DFT method with the same functional and basis sets as for the ground‐state calculations and Boltzmann weighting of the individual conformers. The good correlation of the calculated and experimental spectra substantiates the interpretation of these conformational models for the structure–odor correlation of musks. Furthermore, the application of the quadrant rule in the estimation of the Cotton effect for macrolide conformers is critically discussed.