Impact of helical elongation of symmetric oxa[n]helicenes on their structural, photophysical, and chiroptical characteristics

The adjustment of the main helical scaffold in helicenes is a fundamental strategy for modulating their optical features, thereby enhancing their potential for diverse applications. This work explores the influence of helical elongation (n = 5-9) on the structural, photophysical, and chiroptical features of symmetric oxa[n]helicenes. Crystal structure analyses revealed structural variations with helical extension, impacting torsion angles, helical pitch, and packing arrangements. Through theoretical investigations using density functional theory (DFT) calculations, the impact of helical extension on aromaticity, planarity distortion, and heightened chiral stability were discussed. Photophysical features were studied through spectrophotometric analysis, with insights gained through time-dependent DFT (TD-DFT) calculations. Following optical resolution via chiral high-performance liquid chromatography (HPLC), the chiroptical properties of both enantiomers of oxa[7]helicene and oxa[9]helicene were investigated. A slight variation in the main helical scaffold of oxa[n]helicenes from [7] to [9] induced an approximately three-fold increase in dissymmetry factors with the biggest values of|glum| of oxa[9]helicene (2.2 × 10-3) compared to|glum|of oxa[7]helicene (0.8 × 10-3), findings discussed and supported by TD-DFT calculations.

The effect of particle size on the optical and electronic properties of hydrogenated silicon nanoparticles

We use a combination of many-body perturbation theory and time-dependent density functional theory to study the optical and electronic properties of hydrogen terminated silicon nanoparticles. We predict that the lowest excited states of these silicon nanoparticles are excitonic in character and that the corresponding excitons are completely delocalised over the volume of the particle. The size of the excitons is predicted to increase proportionally with the particle size. Conversely, we predict that the fundamental gap, the optical gap, and the exciton binding energy increase with decreasing particle size. The exciton binding energy is predicted to counter-act the variation in the fundamental gap and hence to reduce the variation of the optical gap with particle size. The variation in the exciton binding energy itself is probably caused by a reduction in the dielectric screening with decreasing particle size. The intensity of the excited state corresponding to the optical gap and other low energy excitations are predicted to increase with decreasing particle size. We explain this increase in terms of the 'band structure' becoming smeared out in reciprocal space with decreasing particle size, increasing the 'overlap' between the occupied and unoccupied quasiparticle states and thus, the oscillator strength. Fourier transforms of the lowest excitons show that they inherit the periodicity of the frontier quasiparticle states. This, combined with the delocalisation of the exciton and the large exciton binding energy, means that the excitons in silicon nanoparticles combine aspects of Wannier-Mott, delocalisation and effect of periodicity of the underlying structure, and Frenkel, large exciton binding energy, excitons.

The influence of heteroatoms on the circularly polarized luminescence performance of [7]helicene derivatives: aromatic vs. non-aromatic five-membered rings

Helicenes are promising candidates for circularly polarized luminescence (CPL) materials, although the performance is poor due to the unsatisfactory dissymmetric factor (glum) and fluorescence quantum efficiency (ΦF). Herein, the influence of heteroatoms (C, Si, Ge, O, S and Se) on the electronic structures and chiroptical properties of [7]helicene derivatives is systematically investigated using density functional theory (DFT) and time-dependent DFT calculations combined with the thermal vibration correlation function theory. The results reveal that the non-radiative energy consumption processes for helicene systems are closely related to the variation of bond length upon electronic excitation. Moreover, by introducing five-membered rings and heteroatoms, the dipole-forbidden S1 → S0 emission of [7]helicene changes to dipole-allowed transition due to the rearrangement of occupied orbitals and lifting of the nearly degenerate orbitals, resulting in an enhancement of ΦF. As the heteroatomic radius increases, ΦF decreases while the glum increases. Compared with the derivatives containing aromatic five-membered rings ([7]H-O, [7]H-S, and [7]H-Se), the non-aromatic counterparts ([7]H-C, [7]H-Si, and [7]H-Ge) exhibit a balance in ΦF and glum values. The present study helps to clarify the relationship between structures and chiroptical properties and offers a feasible strategy for the future design of helicene-based CPL materials.

Effect of Terminal Fluorination on Chiroptical Properties of Carbo[5-8]helicenes: A Systematic Computational Study at the RI-ADC(2) Level

In this article, effects of di-, tetra-, and octafluorination on the structural and chiroptical properties of carbo[5-8]helicenes are reported. Three fluorinated derivatives are designed from each parent carbohelicene by substituting either one, two, or four hydrogens at each terminal ring with fluorine atoms. Excited states properties such as UV-vis and CD spectra of all the six fluorinated carbohelicenes are computed at the ADC(2)/def2-TZVP level, and the results are compared against the results of their respective parent carbohelicene. In addition, CPL properties are also computed at the same level of theory. In the case of carbo[5]helicene (5H), g_CPL decreases with an increase in the degree of fluorination. A similar observation is made in carbo[6]helicene (6H) too, although the value for tetrafluorinated 6H is slightly larger than for difluorinated 6H. Di- and tetrafluorination in carbo[7]helicene (7H), and all types of considered fluorination in carbo[8]helicene (8H) produce improved g_CPL results. Results for fluorescence rate constants are also shown. Results are analyzed in terms of the transition dipole moment vectors and the angles between those.

Quantum Chemical Characterization and Design of Quantum Dots for Sensing Applications

The ability to tune the optoelectronic properties of quantum dots (QDs) makes them ideally suited for the use as fluorescence sensing probes. The vast structural diversity in terms of the composition and size of QDs can make designing a QD for a specific sensing application a challenging process. Quantum chemical calculations have the potential to aid this process through the characterization of the properties of QDs, leading to their in silico design. This is explored in the context of QDs for the fluorescence sensing of dopamine based upon density functional theory and time-dependent density functional theory (TDDFT) calculations. The excited states of hydrogenated carbon, silicon, and germanium QDs are characterized through TDDFT calculations. Analysis of the molecular orbital diagrams for the isolated molecules and calculations of the excited states of the dopamine-functionalized quantum dots establish the possibility of a photoinduced electron-transfer process by determining the relative energies of the electronic states formed from a local excitation on the QD and the lowest QD → dopamine electron-transfer state. The results suggest that the Si₁₆₅H₁₀₀ and Ge₈₄H₆₄ QDs have the potential to act as fluorescent markers that could distinguish between the oxidized and reduced forms of dopamine, where the fluorescence would be quenched for the oxidized form. The work contributes to a better understanding of the optical and electronic behavior of QD-based sensors and illustrates how quantum chemical calculations can be used to inform the design of QDs for specific fluorescent sensing applications.

Effects of Heterocyclic Ring Fusion and Chain Elongation on Chiroptical Properties of Polyaza[9]helicene: A Computational Study

In the present work, the effect of lateral and helical extensions on the physical and chiroptical properties of azahelicenes is reported. Starting with the experimentally reported polyaza[9]helicene (9Ha), three derivatives, two with laterally fused electron-withdrawing rings and the third with larger helical length, are designed. For the excited-state properties such as UV-vis and CD spectra, performances of different DFT functionals are evaluated by comparing the energies and characters of the excited states against the ADC(2) results. CPL properties are calculated at DFT level. Among the three designed systems, pyrazine-based 9HaP shows an improved g_CPL value compared to that for parent 9Ha. However, quinoxaline-based 9HaQ is found to be the worst CPL emitter with the lowest dissymmetry factor. The helically extended derivative, 11Ha, shows good CPL results, but g_CPL remains smaller than that for the parent system. The CPL results are analyzed in terms of electric dipole transition moment (EDTM) and magnetic dipole transition moment (MDTM) vectors, and angles between these two vectors.

Tuning Transition Electric and Magnetic Dipole Moments: [7]Helicenes Showing Intense Circularly Polarized Luminescence

Helicenes are promising candidates for chiral optoelectronic materials because of their helically twisted π-conjugated system. However, the emission intensity of unsubstituted helicenes is very weak (Φ_f < 0.05) due to a small oscillator strength for the S₁ → S₀ transition. In this work, we investigated the substitution position of the [7]helicene framework so that the S₁ → S₀ transition has a large transition magnetic dipole moment (TMDM) and is partially symmetry-allowed. A [7]helicene derivative thus designed showed a large fluorescence emission rate (k_f = 0.02 ns^-1) and a large TMDM for the S₁ → S₀ transition (|m| = 2.37 × 10^-20 erg·Gauss^-1), which are more than 10 times greater than those of unsubstituted [7]helicene (k_f = 0.001 ns^-1, |m| = 0.045 × 10^-20 erg·Gauss^-1). As a result, we achieved the [7]helicene derivative whose dissymmetry factor of CPL and fluorescence quantum yield were both high (|g_CPL| = 1.3 × 10^-2, Φ_f = 0.17) in the solution phase.

Fluorescence Behavior of Bis(cyanostyryl)pyrrole Derivatives Depending on the Substituent Position of Cyano Groups in Solution and in Solid State

We synthesized a novel fluorophore of distyrylpyrrole derivatives possessing cyano groups at different positions on olefin. Their fluorescence properties in solution and solid state were investigated by photoluminescence quantum yield and lifetime measurements, which provided a radiative decay constant ( k_f) and nonradiative decay constant ( k_nr). The derivative with cyano groups at the inner position of the molecule, inner isomer, shows a high fluorescence quantum yield (Φ_f = 0.43) in solution, while another derivative with a cyano group at the outer position, outer isomer, hardly shows fluorescence (Φ_f < 0.01) due to the large nonradiative decay ( k_nr > 10 ns^-1). Upon formation of a single crystal or nanoparticles, these difference were inverted; the quantum yield of the outer and inner isomer was enhanced and diminished, respectively. We explained these differences between in solution and solid state by means of analysis of a single X-ray structure and computation study.

Control over the Emission Properties of [5]Helicenes Based on the Symmetry and Energy Levels of Their Molecular Orbitals

The effect of different substituents on the fluorescence properties of [5]helicene derivatives was investigated in terms of molecular orbital symmetry. Unsubstituted [5]helicene is nonemissive due to the symmetry-forbidden S₁ → S₀ transition. However, the fluorescence emission rate constant (k_f) of [5]helicenes is efficiently increased by removing the orbital degeneracy involved in the S₁ → S₀ transition. As a result, we achieved a [5]helicene derivative exhibiting a high fluorescence quantum yield (Φ_f = 0.23) and short emission lifetime (⟨τ_f⟩ = 1.5 ns), which is in marked contrast to unsubstituted [5]helicene (Φ_f = 0.04 and ⟨τ_f⟩ = 26 ns).

Calculation of electron-hole recombination probability using explicitly correlated Hartree-Fock method

The electron-hole explicitly correlated Hartree-Fock method (eh-XCHF) is presented as a general strategy for investigation of electron-hole correlation and computation of electron-hole recombination probability. The eh-XCHF method is a variational method which uses explicitly correlated wavefunction that depends on the electron-hole inter-particle distances. It is shown that the explicitly correlated ansatz provides a systematic route to variationally minimize the total energy. The parabolic quantum dot is used as the benchmark system and the eh-XCHF method is used for computation of the ground state energy and electron-hole recombination probability. The results are compared to Hartree-Fock and explicitly correlated full configuration interaction (R12-FCI) calculations. The results indicate that an accurate description of the electron-hole wavefunction at short electron-hole inter-particle distances is crucial for qualitative description of the electron-hole recombination probability. The eh-XCHF method successfully addresses this issue and comparison of eh-XCHF calculations with R12-FCI shows good agreement. The quality of the mean field approximation for electron-hole system is also investigated by comparing HF and R12-FCI energies for electron-electron and electron-hole systems. It was found that performance of the mean field approximation is worse for the electron-hole system as compared to the corresponding electron-electron system.

Reduction of the virtual space for coupled-cluster excitation energies of large molecules and embedded systems

We investigate how the reduction of the virtual space affects coupled-cluster excitation energies at the approximate singles and doubles coupled-cluster level (CC2). In this reduced-virtual-space (RVS) approach, all virtual orbitals above a certain energy threshold are omitted in the correlation calculation. The effects of the RVS approach are assessed by calculations on the two lowest excitation energies of 11 biochromophores using different sizes of the virtual space. Our set of biochromophores consists of common model systems for the chromophores of the photoactive yellow protein, the green fluorescent protein, and rhodopsin. The RVS calculations show that most of the high-lying virtual orbitals can be neglected without significantly affecting the accuracy of the obtained excitation energies. Omitting all virtual orbitals above 50 eV in the correlation calculation introduces errors in the excitation energies that are smaller than 0.1 eV. By using a RVS energy threshold of 50 eV, the CC2 calculations using triple-ζ basis sets (TZVP) on protonated Schiff base retinal are accelerated by a factor of 6. We demonstrate the applicability of the RVS approach by performing CC2/TZVP calculations on the lowest singlet excitation energy of a rhodopsin model consisting of 165 atoms using RVS thresholds between 20 eV and 120 eV. The calculations on the rhodopsin model show that the RVS errors determined in the gas-phase are a very good approximation to the RVS errors in the protein environment. The RVS approach thus renders purely quantum mechanical treatments of chromophores in protein environments feasible and offers an ab initio alternative to quantum mechanics/molecular mechanics separation schemes.

Calculation of absorption and emission spectra of [n]cycloparaphenylenes: the reason for the large Stokes shift

The electronic absorption and emission spectra of the [n]cycloparaphenylenes with n = 6,7,...,11 ([n]CP) have been studied at the time-dependent density functional theory level. The calculations show that the optical gap increases with increasing size of the ring due to reduced ring strain in the larger carbon nanohoops, whereas the energy of the first bright state follows the opposite trend for the studied [n]CPs. For the excited-state structures, the C-C bonds between the phenylene groups have a significant double-bond character giving rise to a continuous electron delocalisation pathway around the ring. The torsion angles between the phenylene moieties are much smaller for the excited state than for the ground state suggesting that the excited state has a stronger electron delocalisation around the carbon nanohoop than for the ground state. The double bond character of the phenylene C-C bonds declines and the phenylene torsion angle increases with increasing ring size. The aromatic stabilisation of the excited state due to the continuous electron delocalisation pathway is probably the main reason for the large Stokes shift. The excited state of the larger [n]CPs are less aromatic than the smaller ones explaining why the Stokes shift decreases with increasing size of the ring. For large [n]CPs, the excitation-energy spectrum forms bands making localisation of the excitons feasible. Localisation of the excitons probably leads to the observed ring-size independence of the electronic excitation spectra for large [n]CPs.