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67720c63fa469535b9343b2c | 13 | First, the quantum DW approximation is performed, which assumes that the pump and probe pulses are well separated, meaning that the time delay τ between the pulses is (much) longer than the pulse durations. Second, the short-pulse approximation is adopted, meaning that the nuclear dynamics during the pulse can be neglected. With these two assumptions, the integral TA PP signal takes the DW form |
67720c63fa469535b9343b2c | 14 | where R g and P g represent the initial nuclear coordinates and momenta in the electronic ground state sampled according to the Wigner distribution ρ Wig g (R g , P g ), R g (τ) and P g (τ) denote the nuclear coordinates and momenta propagated in the electronic ground state up to t = τ, and R e (τ) |
67720c63fa469535b9343b2c | 15 | µ µ µ ge , µ µ µ ge(τ) and µ µ µ e(τ) f are the matrix elements of the TDMs operators between the corresponding electronic states, while U eg (R g (τ)), U e(τ)g (R e (τ)) and U f e(τ) (R e (τ)) are the transition frequencies (or, equivalently, energy gaps) between the corresponding electronic states. The notion e(τ) means that a trajectory initiated in an excited state e may jump into another electronic state. |
67720c63fa469535b9343b2c | 16 | The above derivations have been made under the assumption that NAC-induced transitions between manifolds 0, I, and II can be neglected on the timescale of interest. Once the internal conversion (IC) e(τ) → g is allowed, Eq. ( ) remains valid, but the window functions W int k defined per Eq. ( ) have to be replaced by the new window functions W int k,IC which are defined in terms of the original window functions as follows 115 : |
67720c63fa469535b9343b2c | 17 | Owing to the e(τ) → g IC, two GSB contributions arise: the cold and the hot. The cold contribution is the conventional GSB signal which reveals the nuclear wavepacket on the electronic ground state. It is described by the window function W int 0 of Eq. (33). The hot contribution is the ICinduced GSB signal, that reveals the manifold-I trajectory which jumps to the electronic ground state after the e(τ) → g IC. This trajectory contributes to the GSB with a minus sign, -W int 0 in Eq. ( ) 115 . |
67720c63fa469535b9343b2c | 18 | Cotton and Miller showed that the electronic part of the density matrix can be calculated within the SQC/MM framework by "binning" the trajectory to different windows which define the currently occupied electronic states in the mapping dynamics . With this method, we obtain information about the involved electronic states and transitions and can straightforwardly evaluate the DW functions of Eqs. ( ) and (32). Several comments are appropriate though. First, using the binning procedure to specify the DW functions correlates nicely with the central idea of the SQC/MM dynamics to use binning for defining the state occupations. Second, this method defines the active state in the trajectory propagation and only the diagonal elements of the density matrix are used to calculate the spectra. Therefore the current way to calculate the DW functions is very similar to that used in the on-the-fly TSH dynamics . Third, we admit limitations of the current approach. In the applications of the present work, these limitations are not crucial, because manifold I contains just a single electronic state. For molecular systems with several simultaneously excited bright electronic states in manifold I, TA PP and other nonlinear spectroscopic signals will have contributions from electronic coherences between these electronic states. The SCM/MM approach can handle these coherences, and this will require the appropriate modification of the DW algorithm. Work in this direction is currently in progress. |
67720c63fa469535b9343b2c | 19 | To illustrate the performance of the SQC/MM-DW methodology, we chose two well-known molecules, cis-azobenzene and cis-hepta-3,5,7-trieniminium cation (PSB4), which are sketched in Fig. (a) and (b). Optimizations of the S 0 minima of both systems were performed by employing the complete active space self-consistent field (CASSCF) in the Gaussian 16 package where azobenzene is optimized at CASSCF(6,6)/6-31G level while PSB4 at CASSCF(8,8)/6-31G(d). In the on-the-fly SQC/MM dynamics simulations, the MOLPRO2022 package 118 was used for the electronic structures calculations. |
67720c63fa469535b9343b2c | 20 | Initial nuclear coordinates and momenta were generated by the Wigner sampling of the lowest vibrational level on the S 0 state. In the SQC/MM dynamics, the initial sampling and final assignment of quantum states for electronic DoFs were conducted using the symmetrical triangle window function with the trajectory-adjusted ZPE correction γ . All electronic mapping coordinates and momenta were sampled by the action-angle method. The time steps for the propagation of the nuclear and electronic motions were 0.2 fs and 0.002 fs, respectively. All dynamics calculations were carried out with the JADE package . |
67720c63fa469535b9343b2c | 21 | In azobenzene, manifold I contains a single state S 1 and manifold II consists of 4 states, from S 2 to S 5 . In PSB4, manifold I also contains a single state S 1 and manifold II contains 6 states, from S 2 to S 7 . 100 BOMD trajectories on the S 0 state were run up to 200 fs in the simulation of the GSB cold signal. Other 100 trajectories starting from the S 1 state were propagated to simulate the hot GSB, SE, and ESA signals. We chose snapshots per 10 steps from every trajectory to obtain the vertical excited energies (VEEs) and TDMs. |
67720c63fa469535b9343b2c | 22 | We chose Gaussian envelopes of the pump and probe pulses, E a (t) = exp{-(t/τ a ) 2 } and E a (ω) = exp{-(ωτ a ) 2 /4} (a = pu, pr), in which the pulse duration τ a is set to 5 fs. This yields the pulse bandwidth 0.44 eV (full width at half maximum). In our simulations, polarization-sensitive effects and orientational averaging are not explicitly considered, which is equivalent to replacing the scalar products of the kind |ε ε ε pu µ µ µ ge (R g )| 2 by scalar coefficients |µ µ µ ge (R g )| 2 in the DW functions. Within the DW formalism, the aforementioned effects can be taken care of as demonstrated in Ref. . |
67720c63fa469535b9343b2c | 23 | Considering isomerization of azobenzene and PSB4, we chose the following criterion to distinguish between the cis and trans photoproducts. If the dihedral angle falls within the range from -30 to 30 degrees between 175 and 200 fs, the product is of cis-structure. If the dihedral angle falls within the range of 150 to 210 degrees, the product is of trans-structure. Specifically, the dihedrals C3-N1-N2-C1 and C4-C5-C6-C7 were chosen for azobenzene and PSB4, respectively (cf. Ref. ). |
67720c63fa469535b9343b2c | 24 | While interpreting the TA PP spectra, it is useful to keep in mind that the SE and ESA contributions reflect the pump-pulse induced wavepacket motion in manifold I, projected on the electronic ground state (SE) or on the higher-lying electronic states of manifold II (ESA). The cold GSB signal mirrors the ground state wavepacket, while the hot GSB signal reveals the wavepacket initiated and propagated in manifold I but transferred to the electronic ground state after the IC. |
67720c63fa469535b9343b2c | 25 | Photoisomerization of azobenzene finds a wide range of applications in high-density storage devices , light-driven molecular motors and protein probes . Femtosecond spectroscopy revealed the important role of the low-lying excited states nπ * and ππ * in the course of isomerization . From the theoretical perspective, azobenzene's nonadiabatic dynamics initiated in the nπ * or ππ * states were investigated extensively 120, . |
67720c63fa469535b9343b2c | 26 | Dynamical responses of azobenzene initiated in its lowest excited state S 1 are shown in Fig. . Panel (a) displays the S 1 (orange) and S 0 (blue) population evolution. Since the total, S 1 + S 0 , population is conserved, we concentrate on the S 1 population dynamics, which can be subdivided in several stages. The population remains constant within the first 25 fs. This establishes a characteristic time which the photoinduced wavepacket needs to travel from the initial Franck-Condon region to the IC region. From 25 fs to 90 fs, the population exhibits a fast decay: S 1 looses half of its initial value at around 50 fs. Then the slower decay is observed. . |
67720c63fa469535b9343b2c | 27 | The ESA spectrum in Fig. ) is initially concentrated around 3.6 eV, which corresponds to the S 1 -S 4 VEE in Table . At around 10 fs, the ESA spectrum splits into two components, of which the lower one oscillates around 1.0 eV and the upper one oscillates around 5.0 eV. |
67720c63fa469535b9343b2c | 28 | As the wavepacket moves away from the Franck-Condon region, both the SE and ESA signals exhibit significant quenching owing to the two main reasons. First, TDMs become smaller, which is a manifestation of the significance of the non-Condon effects in azobenzene . Second, IC depopulates the the excited state. After 170 fs, the S 1 population becomes small and both the SE and ESA signals tend to vanish (see Fig. ). |
67720c63fa469535b9343b2c | 29 | The time evolution of the SE and ESA spectra correlates with the torsional motion of the C3-N1-N2-C4 dihedral angle, as shown in Fig. . The C3-N1-N2-C4 dihedral angle is around 5 degrees in the first 5 fs, indicating that the trajectories are near the S 0 minimum, and the SE and ESA maxima reveal the VEEs in the Franck-Condon region. Since the S 1 -S 4 TDM dominates the short-time dynamics, the ESA maximum coincides with the S 1 -S 4 VEE. The subsequent decrease of the S 1 -S 4 TDM and increase of the S 1 -S 5 and S 1 -S 2 TDMs lead to the splitting of the ESA signal. Interestingly, the time evolutions of the SE and ESA spectra correlate with those of the C3-N1-N2-C4 dihedrals in many aspects: timescales, oscillation patterns, and so on. For example, maxima of the SE and ESA spectra around 120 fs in panels (b) and (c) correlate with the minimum of the dihedral angle in panel (d). |
67720c63fa469535b9343b2c | 30 | in Fig. ). The figure reveals two peaks of vibrational origin: the first peak located around 2000 cm -1 (the period ∼ 17 fs) is attributed to the N --N stretch and the second peak located around 600 cm -1 (the period ∼ 56 fs) is attributed to the C-H out-of-plane motion. These two modes are assigned according to Table . Oscillations with a period of ∼ 17 fs are clearly seen in in Fig. . Furthermore, since the first-peak frequency is roughly thrice larger than the second-peak frequency vibration, every forth peak of the cold GSB signal in panel (b) is more pronounced. Physically, the strong oscillation patterns in the cold GSB signal are a manifestation of the significant dependence of TDMs on nuclear coordinates (non-Condon effect). Fig. shows the hot GSB signal. It emerges at 25 fs, indicating the starting of IC. Then the hot GSB signal exhibits quite irregular oscillations which somewhat resemble those in the SE and ESA signals in Fig. (b) and (c). For example, note a pronounced recurrence around 120 fs. |
67720c63fa469535b9343b2c | 31 | The two can be identified by monitoring the oscillatory patterns in the hot GSB signals. Fig. (d) shows the hot GSB signal for the trajectories producing the trans-azobenzene. After 25 fs, the signal shifts to the blue following the torsional motion in panel (f). Then the signal remains in the domain around 3.0 eV, which is consistent with the behavior of the trajectories producing trans-azobenzene. The hot GSB signal in panel (e) is calculated for the trajectories producing cis-azobenzene. The first stage of its evolution is quite similar to that of its transcounterpart, since both move to the blue following the torsional motion in panel (f). At longer times, however, a portion of trajectories producing the cis-signal returns to the low-energy domain. The reason is as follows: these trajectories experience further torsional motion after the cis-configuration is achieved. The cis-azobenzene has a stronger TDM to the excited states than the trans-azobenzene (see Tables and). Hence the total hot GSB signal is dominated by the cis-azobenzene. |
67720c63fa469535b9343b2c | 32 | Summarizing, the SE and ESA signals reveal the S 1 population dynamics and the C3-N1-N2-C4 torsion on the S 1 state. As the SE signal overlaps spectrally with the GSB signal (Fig. ), the ESA signal is much easier to follow. The cold GSB signal gives information on the vibrational wavepacket motion on the S 0 state. The hot GSB signal reflects the C3-N1-N2-C4 torsion on the S 0 after IC. The cis and trans photoreaction channels may be distinguished by monitoring the hot GSB signals. |
67720c63fa469535b9343b2c | 33 | The retinal protonated Schiff base (rPSB) is a chromophore of the rhodopsin family which is crucial for the vision process and its ultrafast cis-trans photoisomerization is the key step for such biological functionality. The model systems protonated Schiff bases CH 2 (CH) 2n-2 NH + 2 (PSBn) were often used to study photochemistry of rPSB 121, . Here, PSB4 was selected as a representative of PSBn. |
67720c63fa469535b9343b2c | 34 | We begin our discussion with the S 1 and S 0 population evolutions presented in Fig. (a). Similar to azobenzene and due to the same reasons, the nonadiabatic S 1 evolution starts with a delay. For PSB4, however, the delay is longer, around 50 fs, and the population decay is slower. Namely, the S 1 population of PSB4 halves at about 125 fs, and reaches some 20% of its initial value at 200 fs. Fig. displays the SE signal. It is located around 4 eV (which corresponds to the S 0 -S 1 VEE in Table ) and exhibits pronounced slightly damped oscillations with a period of ∼ 30 fs. After 120 fs, the signal retains oscillatory behavior, but becomes more erratic and does not reveal a specific oscillation frequency. The ESA signal of Fig. (c) shows a qualitatively similar behavior, but consists of two leading components: The upper component oscillating around 3.5 eV is produced by the S 1 -S 4 and S 1 -S 5 transitions, while the lower component oscillating around 1 eV corresponds to the S 1 -S 2 transition (Table ). The ESA signal is governed by the stronger Let us now turn to the GSB signals. The cold GSB signal in Fig. (a) exhibits oscillates around 4.0 eV corresponding to the S 0 -S 1 VEE in Table . Fig. , which shows the Fouriertransformed cold GSB signal defined per Eq. ( ), exhibits three peaks located at 300 cm -1 , 1300 cm -1 and 1700 cm -1 . These frequencies correspond to the vibrational periods of 111 fs, 26 fs, and 20 fs, respectively. They are attributed to the torsion of the C 5 --C 6 bond, the waging of the C-C-H or N-C-H modes, and the stretching motion of the C --C bonds, which are assigned according to Table . The three vibrational modes are responsible for the GSB dynamics in Fig. (a): the second and the third mode produce oscillations while the first one causes a slight increase of the oscillation amplitude around ∼ 100 fs. towards the final products. Since vibrational relaxation and dissipation are not accounted for in simulations, it is quite tricky to estimate the final branching ratio of the products. However, as we discussed previously, the C 5 --C 6 torsional motion is of primarily importance in the wavepacket evolution. We thus tried to divide all trajectories according to the dihedral angle of this bond. |
67720c63fa469535b9343b2c | 35 | The results are shown in Fig. , which displays the SE, ESA, and hot GSB spectra corresponding to the trans (upper panels) and cis (lower panels) isomers. The trajectories leading to the trans- The methodology has been tested and illustrated by the ab initio evaluation of TA PP spectra of realistic molecular systems, azobenzene and the PSB4. For both molecules, the SE and ESA spectra were demonstrated to give a direct fingerprint of the excited state wavepacket dynamics and permit the monitoring of the isomerization pathways en route to the final photoproducts. |
67720c63fa469535b9343b2c | 36 | At the moment, the ab initio DW methodology has been combined with three most popular quasiclassical trajectory simulation protocols: TSH (including Tully's fewest switches method 115,116,120 , Landau-Zenner method , and machine-learning enhanced Landau-Zenner method ), Ehrenfest 150 , and SQC/MM in the present work. In this context, two comments are in order. For the molecular systems with a single excited electronic state, the DW methodology results in the computational protocol which is essentially the same for all three (semi)classical methods. Hence, the differences in the predictions of the spectroscopic signals can be directly pinned down to the differences in the approximations used in a specific dynamical method. For molecular systems with several bright excited electronic states, TA PP and other nonlinear spectroscopic signals will have contributions from electronic coherences. In this latter case, different variants of the mapping approach may have advantages over the TSH and Ehrenfest counterparts . This latter argument may broaden the applicability of spectroscopic DW simulations performed with SQC/MM and other variants of the mapping approach. |
6122751251cfec491e978ca8 | 0 | Per-and polyfluoroalkyl substances (PFASs) are artificially-made compounds with strong carbon-fluorine (C-F) bonds that endow them with exceptional chemical stability. Because of their intrinsic longevity, these compounds have been used in a multitude of technologies, including nonstick coatings, water-resistant membranes, and fire-resistant foams. However, the very same characteristics that enable this stability also poses severe health hazards since their presence in drinking-water sources is toxic and carcinogenic to humans. In particular, the intrinsic strength of the C-F bond in PFASs prevents most organisms from decomposing these persistent contaminants, which further exacerbates their bio-accumulation and toxicity. Moreover, due to their strong chemical stability, conventional treatments (such as chemical oxidation methods) are less effective in the degradation of PFASs, making them extremely difficult to remove. Because of their resistance to conventional chemical treatments, immense interest has recently focused on photo-induced processes for directly decomposing PFAS contaminants. In contrast to conventional filtration techniques that merely remove PFAS (which still require subsequent treatment after filtration), very recent studies have suggested that PFAS degradation can be accelerated with electromagnetic/optical fields, such as those used in photocatalysis or commercially available laser sources. While these recent findings hold immense promise for directly treating PFAS, the exact mechanisms in these degradation processes remain unknown, and a guided path for rationally identifying photoactive materials and experimental conditions remains elusive. |
6122751251cfec491e978ca8 | 1 | To shed crucial mechanistic insight into these new degradation processes, we present the first application of real-time time-dependent density functional theory (RT-TDDFT) for understanding photo-induced degradation mechanisms in PFAS. While DFT calculations have become more common in environmental research, prior DFT studies on PFAS have only focused on reactions on the electronic ground-state potential energy surface. In contrast, the RT-TDDFT formalism used in this work can describe electronic excited-state dynamics beyond conventional ground-state DFT to explore photo-induced mechanisms and bring a fundamental understanding of these degradation processes. In other words, the photo-induced degradation mechanisms in PFAS inherently occur on electronic-excited-state potential surfaces that cannot be treated with ground-state DFT, and excited-state RT-TDDFT is required for capturing the resulting photochemical reaction dynamics. |
6122751251cfec491e978ca8 | 2 | To this end, the present work constitutes the first quantum dynamical study of photo-induced degradation mechanisms of perfluorooctanoic acid (PFOA) and perfluorooctanesulfonic (PFOS) contaminants. We first give a brief description of the RT-TDDFT formalism and our computational methods, which includes our custom implementation of optical electromagnetic fields in the GPAW software package. We then present a series of RT-TDDFT calculations and electronic diagnostics showing that this photo-induced process selectively degrades PFOA/PFOS while keeping the water molecules in the surrounding environment intact. Our results are complemented by a variety of analyses, including real-time electronic properties and timedependent orbital occupations that explain the underlying excited-state mechanisms of the degradation process. Finally, we conclude with a discussion and summary of our results, with additional perspectives of future applications of RT-TDDFT that can have a broad impact in probing photo-induced interactions of environmental contaminants. |
6122751251cfec491e978ca8 | 3 | We used RT-TDDFT with Ehrenfest-based molecular dynamics to probe the degradation of PFAS/PFOS solvated with 43 explicit water molecules under the influence of electromagnetic radiation. Previous work by us on PFAS/PFOA has shown that 43 water molecules was sufficient to capture explicit solvent effects, which is necessary to mimic the natural solvation environment required for exploring the photo-induced dynamics of PFOA/PFOS. The use of explicit solvent in this work also provides a more accurate simulation of fluorine dissociation dynamics (and the possible formation of photo-induced reaction products) since hydrogen-bonding effects are more accurately captured by explicit solvent compared to coarse-grained polarizable continuum model approaches. The RT-TDDFT formalism with Ehrenfest-based molecular dynamics allows us to accurately capture non-adiabatic processes, such as the optically-induced, excited-state degradation dynamics examined in this work. The time-dependent orbitals were obtained by solving the self-consistent time-dependent Kohn-Sham equations: |
6122751251cfec491e978ca8 | 4 | where 𝐸 0 , 𝑡 0 , 𝜏 0 , and 𝜔 are the amplitude, center, width, and frequency of the electromagnetic pulse, respectively. We used the PBE exchange-correlation functional within the projector augmented wave formalism 17 and a 0.3-Å real-space grid spacing for both the geoemetry optimizations and RT-TDDFT calculations. The use of a 0.3-Å real-space grid in our simulations is on par with the settings recommended for RT-TDDFT simulations in GPAW. To further assess the accuracy of our simulation settings, we also carried out two separate benchmark DFT calculations of a single PFOA molecule with a 0.3 and 0.1 Å real-space grid. Our benchmark calculations show that the density of states obtained with a 0.3-Å real-space grid is very similar to those obtained with 0.1 Å. Since the orbital energies near the Fermi level (which are responsible for most of the excitations) are very similar for both grid spacings, the use of a 0.3-Å real-space grid supports the robustness of our results (further details are given in the Supporting Information). |
6122751251cfec491e978ca8 | 5 | The geometry of PFOA/PFOS + 43 H2O molecules in a 29×24×22 Å 3 simulation box was first optimized such that the residual forces were less than 0.01 eV/Å (a large box size was chosen to prevent periodic images of the system from interacting with each other). This optimized geometry was then used as an initial condition for the excited-state, photo-induced Ehrenfest dynamics, and the resulting atomic positions were monitored at each time step. We used an optical pulse with ω set to either 6 or 7.5 eV with a ~10 W/cm 2 intensity, which is commensurate with field strengths used in photocatalysis experiments. Our simulations were carried out for a total of 36 fs with a timestep of 10 attoseconds (the electromagnetic optical pulse (c.f. Figure ) acts on the system for the first 20 fs). Finally, it is worth noting that these excited-state RT-TDDFT calculations are significantly more expensive than conventional ground-state DFT calculations, and this work utilized a total of over 570,000 CPU hours on the XSEDE Comet computing cluster. |
6122751251cfec491e978ca8 | 6 | The RT-TDDFT methodology described previously was used to probe the dissociation of PFOA/PFOS with a variety of optical fields. For clarity, we only discuss the dissociation dynamics of PFOA in the main text, and the results for PFOS (which are similar) are described in the Supporting Information. To choose a relevant excitation energy (ω), we first computed the absorption spectrum of PFOA + 43 H2O molecules (depicted in Fig. (a)) using a standard RT-TDDFT procedure described in our previous work. Specifically, the Kohn-Sham orbitals for these optical absorption calculations were propagated for 25 fs with a time step of 8 as, and a 0.23 eV full-width-at-half-maximum Gaussian broadening was used to plot the spectrum. The optical absorption spectrum in Fig. (b) shows a near continuum of excitations beyond the optical gap of ~5 eV, which indicates that the system does not strongly absorb below 5 eV. As such, we set the excitation frequency (ω) of the optical pulse to 6 eV for all our photo-induced studies. Fig. ) depicts the temporal dependence of the electric field of the optical pulse used in our calculations. |
6122751251cfec491e978ca8 | 7 | The polarization of the electric field is oriented perpendicular to the axis of the PFOA molecule. Finally, to further examine the polarization and subsequent dissociation dynamics of the C-F bonds in PFOA, we computed the Kohn-Sham orbitals as a function of time in Fig. . Since these orbitals are complex-valued (i.e., Eq. ( ) is a complex-valued integro-differential equation), we used the following visualization scheme in Fig. : the opacity denotes the magnitude of the complex-valued orbital, and its color (ranging from red to blue) represents its phase. At t = 0, the highest occupied molecular orbital (HOMO) is real-valued and almost entirely localized on nearby water molecules. As time progresses, the HOMO starts to delocalize onto the PFOA molecule during 8-16 fs, and some electronic charge transfers from the water to PFOA. This excess charge occupies the previously empty 3sF and 2pC atomic orbitals on PFOA, which possesses a strong σ* anti-bonding character. Once these empty orbitals become occupied, a dissociative electron attachment (DEA) process occurs: the subsequent electron-nuclei motion causes the C-F bond to elongate and destabilize (since the HOMO now has an anti-bonding character) until it irreversibly dissociates. This dynamic mechanism is reminiscent of the pseudo-Jahn-Teller effect that enables a charge density redistribution and produces highly directional ionic forces that destabilize specific bonds in chemical/material systems. Finally, the positively charged hole remaining in the solvent (which arises from a charge-transfer excitation) becomes stabilized by the surrounding water molecules thereafter. This general dissociation mechanism is also similar to that observed in highresolution gas-phase electron-collision experiments in which electron attachment to a CF4 molecule also leads to C-F bond dissociation. However, the major difference is that electrons in these prior experiments were artificially produced with an electron beam/gun, whereas the source of electrons in our solvated PFAS system naturally arises from nearby water molecules that are dynamically excited with an optical pulse. Finally, it is worth mentioning that our approach highlights the importance of utilizing these RT-TDDFT techniques for probing excited-state, photo-induced degradation of PFAS contaminants, which have started to garner immense attention in the scientific community. |
6122751251cfec491e978ca8 | 8 | In conclusion, we have carried out the first RT-TDDFT study of excited-state dynamics in PFAS pollutants to understand their photo-induced degradation mechanisms. By explicitly accounting for non-adiabatic excited-state interactions in solvated PFOA/PFOS, we show that these photo-induced excitations enable a charge-transfer process that polarizes the C-F bond, resulting in a dynamic dissociation on a femtosecond time scale. Moreover, we show that this photo-induced process is highly selective and only affects the PFOA/PFOS molecules while keeping the surrounding water molecules intact. The parameters used in these calculations are commensurate with commercially available monochromatic light/laser sources and shed crucial mechanistic insight into their excited-state degradation dynamics. |
6122751251cfec491e978ca8 | 9 | Looking forward, we anticipate that these state-of-the-art RT-TDDFT approaches could accelerate PFAS remediation efforts in two immediate ways. First, our predictive calculations demonstrate that electromagnetic/optical fields are a viable and direct approach to degrade PFAS pollutants as opposed to conventional filtration techniques that merely remove PFAS (which still require treatment after filtration). Second, these RT-TDDFT approaches can guide ongoing experimental efforts by rationalizing or high-throughput screening of new photocatalytic materials/surfaces, which have started to garner immense attention for enhanced PFAS degradation. As such, the RT-TDDFT techniques used in this work provide fresh opportunities for exploring excited-state, photo-induced degradation dynamics that are actively being explored in the remediation of PFAS and other environmental contaminants. |
6626393a418a5379b05fb6c4 | 0 | Over the past few decades, many studies have been conducted on -conjugated molecules, which have unique electronic properties based on an effective -electron delocalization. Since -conjugated molecules with rigid and planar structures, in general, have p-orbitals overhanging perpendicular to the molecular plane, stacking of two or more molecular planes can affect the molecular orbitals themselves, leading to significant changes in physical properties such as absorption properties. Therefore, when two -conjugated units are close to a separation distance of 3.4 Å (the sum of van der Waals (vdW) radii of carbon atoms) or less by a stacked structure that can induce an interaction between their molecular orbitals by forming new orbitals through linear combination of the components, it is expected that they could exhibit unprecedented properties that are not seen with monomeric -conjugated units. There have been several reports that the stacking of aromatic compounds can modify their intrinsic properties such as conductive/energy transfer properties and absorption/emission properties due to the formation of H-or J-aggregates. Recently, a unique property of three-dimensional (3D) aromaticity based on stacked anti-aromatic molecules has been reported by Shinokubo et al (Figure ). A similar 3D (anti)aromaticity was also predicted by closely stacked aromatic units, and thus the stacking of planar -systems is key for the development of molecules with novel functions. Cationic -conjugated molecules often exhibit a long-wavelength absorption with a large molar extinction coefficient due to the narrow HOMO-LUMO gap based on the effective delocalization of both charge and -electrons. In addition, since well-designed organic cations can interconvert with neutral species upon electron transfer (Figure ), cationic -conjugated molecules are promising candidates for functional organic materials such as chromic materials and organic semiconductors. |
6626393a418a5379b05fb6c4 | 1 | When two or more cationic units can be stacked, they can show novel properties and functions, which can be switched by an external stimulus, such as an electric potential. However, under dispersed conditions, such as in solution, cation units cannot be stacked effectively to interact with each other, due to Coulombic repulsion and/or entropical disadvantage. Therefore, there are very few successful examples of realizing the proximity of cationic species, when compared to the results with neutral molecules. Moreover, the redox behavior of stacked cations has not yet been well studied, and thus there is still room to explore novel properties of stacked multi-cationic species. |
6626393a418a5379b05fb6c4 | 2 | To date, three methods have been mainly used to construct stacked structures. First, by introducing functional groups and/or side chains into -conjugated molecules with a wide -plane, attractive interaction between molecules can induce aggregation, where the formation of aggregates is more enthalpically favorable in the crystalline state or under conditions of high concentration and low temperature. Second, by the inclusion of two or more -conjugated molecules in a cage-shaped molecule, molecules are forced to be stacked and interact with each other. Third, by using cyclophanetype structures with two or more linkers, the -planes are forced to be closely arranged and form a faceto-face stacked structure. Among them, we considered that cyclophane-type structures are suitable for realizing the stacking of cationic -systems because the other two approaches would be less promising due to electrostatic repulsion between cationic units. We envisaged that, by stacking of the cationic units, considerable changes in color (e.g., blue-or red-shift) and reduction behavior (e.g., stepwise one-electron reduction) would be expected compared to the results with the corresponding monomeric cation. Thus, we designed cyclophane-type dications 2 2+ with coplanar xanthylium units, which would have a stacked geometry of reference monocations 1 + (Figure ). In this study, we investigated the effect of the cyclophane-type structure on the physical properties and redox behavior of 2 2+ . Due to the close proximity of cationic units realized by the above molecular design, the intramolecular interaction between cation units enables a change in absorption. Furthermore, this cation-stacking approach can stabilize their reduced species, allowing us to observe clean electrochromic behavior, even though the reduced states are open-shell species. |
6626393a418a5379b05fb6c4 | 3 | Based on the above concept, cyclophane-type dications 2 2+ with planar 3,6-dialkoxyxanthylium units were designed, with the expectation that the stacking of cationic units could be realized by effective interaction through three-carbon linkers. In addition, since reduction of 2 2+ efficiently decreases electrostatic repulsion between -conjugated units to make further proximity between them, the redox interconversion with the one-or two-electron reduced species could allow reversible control of the photophysical properties based on a change in the stacking environment (Figure ). Regarding the additional aryl group at the 9-position of xanthylium, 4-methoxyphenyl and 4-dimethylaminophenyl groups with different electron-donating properties were selected to investigate the influence of electronic properties. We also introduced a 5-(4-methoxyphenyl)-thienyl group, which is expected to stabilize radical cationic and biradical species based on the effective delocalization of a positive charge or an unpaired electron due to extension of the conjugated system. As shown in Scheme 1, cyclic diketone 7 was prepared by the reaction of 3,6-dihydroxyxanthen-9-one 4 with tosylated 2,2-diethyl-1,3-propanediol 5 in a stepwise manner. For the latter cyclic reaction, we adopted high dilution conditions (5 mM in DMF). The gem-diethyl-substituted linkers would contribute to the efficient formation (Thorpe-Ingold Effect ) of an intramolecular cyclic compound rather than linear oligomers, and the desired macrocyclic diketone 7 was isolated in 63% yield. When diketone 7 was reacted with the corresponding aryl lithium reagents, precursor diols 8a-8c were obtained in 70%, 54%, and 73% yields, respectively. |
6626393a418a5379b05fb6c4 | 4 | X-ray analyses of 2a 2+ (BF 4 -) 2 and 1a + BF 4 -using a single crystal obtained by recrystallization from CH 2 Cl 2 /Et 2 O revealed that there are the shortest intermolecular C•••C contacts of 3.3799(19) Å for 1a + BF 4 -and 3.189(5) Å for 2a 2+ (BF 4 -) 2 , respectively, both of which are smaller than the sum of the vdW radii of carbon atoms (3.4 Å) (Figure ). The value for 2a 2+ is smaller than that for 1a + . Therefore, obvious intramolecular interactions due to - stacking between cation units were expected for the cyclophane-type dications. Another feature of the packing structure is that, in cyclophane-type dication salt 2a 2+ (BF 4 -) 2 , two chromophores in the crystal are facing each other and stacked in a parallel manner, unlike that of monocation salt 1a + BF 4 -(Figure ). Compared to the dihedral angle [11.15(6)°] between the triarylmethyl moieties for 1a + BF 4 -, the smaller value [7.71( )°] was observed for 2a 2+ (BF 4 -) 2 , i.e., cation units are almost overlapped in parallel thanks to the cyclophane structure. These results show that the molecular design of the introduction of the highly planar -system is effective for stacking of the cationic units. |
6626393a418a5379b05fb6c4 | 5 | All macrocyclic dications exhibit strong absorptions in the visible region [ max /nm (log ): 420 (5.00) for 2a , respectively], a blue shift and an increase in full width at half-maximum (FWHM) of the absorption band at around 420 nm were observed for cyclophane-type dications 2 2+ (Figure ). This means that there is a contribution from H-type aggregates, and thus, even in solution, cation units in dication 2 2+ have a stacking geometry similar to those in the single crystal. Furthermore, the absorption maxima of the first band for these cations drastically changes depending on the donating ability of the substituent on the aryl group due to the significant change in the HOMO level. To gain insight into the stabilization energy by the stacking of cation units for cyclophane-type dications 2 2+ , the relative energies among the conformers was investigated using DFT calculations at the B97X-D/6-31G* level. As shown in Figures and-S21, the relative energies for the semi-open form and the open form are much higher than that for the closed form with the stacked geometry, which is calculated to be the most stable structure for all dications (semi-open form: E rel = 6.79 kcal mol -1 for 2a 2+ , 15.11 kcal mol -1 for 2b 2+ , and 6.68 kcal mol -1 for 2c 2+ and open form: E rel = 19.55 kcal mol -1 for 2a 2+ , 20.68 kcal mol -1 for 2b 2+ , and 18.77 kcal mol -1 for 2c 2+ ). This result indicates that the stacking of cationic units has a stabilization effect, which is greater than the electrostatic repulsion. Indeed, the noncovalent interaction (NCI) plots of 2 2+ at the B97X-D/6-31G* level show that, due to the delocalization of a positive charge that efficiently reduces electrostatic repulsion, the cation units facing each other of 2 2+ exert attractive rather than repulsive effects (Figures and). and -0.34 for 1c + ) when there is no interaction between the cation units, the stepwise reduction processes indicate that the cation units are close enough to interact with each other even in solution. In addition, unlike with monocations 1 + which exhibit an irreversible process, reversible redox waves were observed for dications 2 2+ , indicating that the cyclophane structure can stabilize both radical cation and biradical species. Although the closed-shell species might be obtained by the bond formation between the two radicals upon the 2e-reduction of 2 2+ , the reversible waves show that the -bond was not formed. |
6626393a418a5379b05fb6c4 | 6 | Such species with a -bond should have a much lower HOMO level, leading to an anodic shift of the oxidation potential, however, it is not the case. DFT calculations also suggest that the most stable structure is the open-shell species 2 •• , and thus, the -bonded species can be excluded in the later discussion. The differences in reduction potentials among the three dications 2 2+ with different substituents are small (~0.2 V) for both E 1 red and E 2 red /V, suggesting that the coefficients of LUMO of 2 2+ are mainly located on the xanthylium units. Furthermore, a twisted geometry of the aryl group to the xanthylium unit also suppresses effective conjugation. Thus, the donating ability of aryl groups does not affect the reduction potentials. |
6626393a418a5379b05fb6c4 | 7 | In addition, continuous electrochromic behavior was demonstrated upon constant-current electrochemical reduction and subsequent oxidation in CH 2 Cl 2 for 2 2+ (BF 4 -) 2 , which was monitored by UV/Vis spectroscopy. For 2a 2+ (BF 4 -) 2 and 2b 2+ (BF 4 -) 2 , clean electrochromism was observed via radical cation species in both redox processes, and the original spectra were regenerated by electrochemical oxidation of as-prepared biradical species (Figures and). Clean electrochromic behavior is noteworthy even when it is realized by involving the biradical state. Therefore, the stacked geometry can certainly stabilize radical cation and biradical species, due to the effective interaction between planar units, as found in the dications. |
6626393a418a5379b05fb6c4 | 8 | To isolate the biradical species and confirm the reversibility of redox interconversion, chemical reduction and subsequent oxidation of 2 2+ (BF 4 -) 2 were performed. As shown in Scheme 2, upon twoelectron reduction of cyclophane-type dicationic salts 2a 2+ (BF 4 -) 2 , 2b 2+ (BF 4 -) 2 , and 2c 2+ (BF 4 -) 2 with two equivalents of cobaltocene in dry MeCN, biradical species 2a ). Very weak signals assignable to the species with open-shell characters were observed, indicating that the singlet state is more stable for these biradicals. Therefore, for 2 •• , although there is a marginal contribution from the thermally excited triplet species in solution, the singlet state can be stabilized by a spin-spin interaction in the cyclophane-type structure. This study demonstrates that the cyclophane structure composed of planar -conjugated cations is an effective way not only to modulate physical properties such as absorption and redox properties but also to stabilize the corresponding reduced species including a biradical state. |
6626393a418a5379b05fb6c4 | 9 | In conclusion, we designed and synthesized cyclophane-type dications 2a 2+ -2c 2+ , composed of two units of planar -units xanthylium 1 + with the alkylene linkers. X-ray analyses of dication salts 2a 2+ (BF 4 -) 2 -2c 2+ (BF 4 -) 2 showed that the cation units are closely stacked and facing each other in the crystal due to the non-covalent interaction between planar -units, which was demonstrated by NCI plots. |
6626393a418a5379b05fb6c4 | 10 | Furthermore, by modifying the electron-donating ability of the substituent on the aryl group, the color tone of the dications can be modulated without changing the LUMO level. Such a stacking structure observed in 2 2+ can also stabilize their radical cation and biradical species, and thus cyclophane-type dications 2 2+ exhibit clean electrochromic behavior via an intermediary radical cation and biradical. In addition, biradical species 2a •• -2c •• were successfully isolated upon two-electron reduction of cyclophane-type dicationic salts 2a 2+ (BF 4 -) 2 -2c 2+ (BF 4 -) 2 . Therefore, the cation-stacking approach can be a versatile method for developing stimuli-responsive molecules and stabilizing intrinsically unstable open-shell species. |
6745c60ff9980725cf05c167 | 0 | Cyclic systems are fundamental structural motifs prevalent in a vast array of pharmacologically active compounds. By introduction of the fully saturated cyclic fragments the potential drug molecule, one could modulate the most important drug substance properties, including but not limited to alterations in molecular conformations, physicochemical characteristics or metabolic stability. Saturated cyclic ethers represent a broad subclass of cyclic motifs that have garnered significant attention in modern drug discovery. Widely distributed among natural products, O-heterocyclic compounds rapidly became one of the key components in numerous synthetic drugs (Figure ). Often being used as mimetics of naturally occurring fragments, saturated oxygen heterocycles can improve the compound's hydrophilicity, enhance its metabolic stability or biological activity when introduced into a molecule of interest. Incorporation of fluorine atoms into cyclic compounds has recently emerged as a cornerstone strategy in medicinal chemistry for enhancing therapeutic efficacy. Fluorination offers unique opportunities to modulate the physicochemical characteristics of (hetero)cyclic structures, thereby influencing their interactions with biological targets and pharmacokinetic behavior. Along with notable influence on the acidity/basicity of ionizable groups and lipophilicity of the whole molecule, fluorination-based strategy could offer the possibility of radio-labelling active therapeutics for in vivo probing purposes or eliminate the instable functionalities via the bioisosteric replacement approach. Despite the growing number of examples of late-stage fluorination of the complex organic structures, fluorinated building blocks are still keeping their dominating role as a source of Fluorine in complex fluorinated compounds. Extensive application of the fluorinated fragments raised a question of their rational exploitation, thus encouraging a series of systematic studies in this area. The groups of Müller, O'Hagan, Linclau, and others revealed a number of valuable insights on the effects of the fluorination pattern on the compound's physicochemical properties (Figure ). In our group, we continuously extended this knowledge by investigation of fluorinated alicyclic, aza-heterocyclic, and (recently) oxetane-derived (3,3-diFox) building blocks. As a part of this ongoing project, in this work we performed a comprehensive characterization of gem-difluorinated five-and six-membered O-heterocycles. We studied physicochemical parameters of their model derivatives (i.e., pKa and LogP) with a focus on the gem-difluorination and O-substitution effects. Furthermore, we have performed synthesis and biological evaluation of fluorinated analogues of p38α mitogen-activated protein kinase (MAPK) inhibitor R-1487 to illustrate the utility of the title fluorinated building blocks for the pharmacokinetic properties modulation. |
6745c60ff9980725cf05c167 | 1 | Physicochemical studies. The pKa values for carboxylic acids 1, 2 and protonated amines 3, 4 were measured by standard acid-base titration (Figure ). As anticipated, introduction of the Oxygen atom into the ring led to a significant decrease in the pKa value that correlated with its inductive effect (i.e., the through-bond distance to the functional group). In particular, the most significant decrease was observed for the 1[1,0]/1[2,0] and 2[0,0]/2[2,0] carboxylic acid pairs. For amines, this effect was even more pronounced, with ΔpKa = 1.7-1.8 units for 3[1,0]/3[3,0] and 4[0,0]/4[3,0] pairs. gem-Difluorination of both alicyclic and O-heterocyclic carboxylic acids and amines also led to an expected pKa decrease, with its absolute value following the trend: β > γ > δ position. Again, acidity of protonated amines was more susceptible to the CF2 group effects, with the largest ΔpKa of 3.1 units observed for the 3[0,0]/3[0,β] and 4[3,0]/4[3,β] pairs. The LogP values were measured for anilides 5, 6 and benzamides 7, 8 (prepared by reaction of carboxylic acids 1, 2 with aniline in the presence of EDC, DMAP, and Et3N, or amines 3, 4 with benzoyl chloride in the presence of Et3N) using the classical shake-flask method combined with HPLC quantitative analysis (Figure ). It was found that introducing the Oxygen atom resulted in lowered lipophilicity (by 0.83-1.57 ΔLogP units), with the largest difference (1.57) for the 7[3,0]/7[0,0] pair. Notably, the effect of gem-difluorination of alicyclic and Oheterocyclic compounds on their lipophilicity was different. In particular, gem-difluorination of cycloalkane derivatives 5-8[0,0] typically resulted in the lipophilicity decrease (by 0.16-0.56 LogP units). The highest ΔLogP values were observed for the ,difluorinated isomers (up to 0.56 for the 7[0,0]/7[0,β] pair). To gain a deeper insight into the nature of the O/CF2 effects on the compound's lipophilicity in the studied series, we calculated average pKa and LogP values for the corresponding amide pairs (i.e., with/without O or CF2 group) for each position of the five-and six-membered rings (2, 3, or 4 for O, and , , or for CF2). separate fragments in the discussed positions. For example, to evaluate effect of introducing Oxygen atom at the position 2 of the six-membered ring on the COOH group acidity, pKa values of all available tetrahydropyran-3carboxylic acids (1[2,0], 1[2,γ], and 1[2,δ]) were compared to those of cyclohexane counterparts (1[0,0], 1[0,γ], and 1[0,δ]), and average pKa was determined within this subset. The resulting pKa and LogP increments are summarized in Figure , A. This deliberately selected example is given for illustration purposes; see Table for the full dataset. |
6745c60ff9980725cf05c167 | 2 | Furthermore, we have evaluated if the above increments are additive by prediction of ΔpKa and ΔLogP of gem-diflurinated O-heterocyclic compounds 1-4[2-4,-] relatively to parent nonfluorinated cycloalkane derivatives 1-4[0,0] (Figure , B; Table ). For the ΔpKa values, the additivity was confirmed: the corresponding prediction error (ΔΔpKa = -0.08±0.56) was within the 3 confidence interval, which correlated with the literature data. For the LogP values, the predictions had much larger errors (ΔΔLogP=0.56±0.79) and were systematically higher than the corresponding experimental values. In other words, the lipophilicity decrease from both O and CF2 moieties acting simultaneously was lower than anticipated from the separate increments of these fragments. Notably, higher prediction errors were observed for the amine and benzamide series. These results show that mutual influence of both Oxygen and gem-CF2 fragments should be taken into account when discussing their effects on the compound's lipophilicity. Interestingly, the prediction error (ΔΔLogP) of the simple additive model was higher for the compounds with higher ΔpKa values (see the Supporting Information, Figure ). Since ΔpKa correlates with electronic distribution changes in the molecules of the corresponding building blocks (and hence in partof their model derivatives), this result shows that the properties of the amide functional group attached to the saturated ring may be also important for the compound's lipophilicity. It should be noted that we have already observed similar trends for the gemdifluorinated cycloalkane series. Biological evaluation. To evaluate the utility of the discussed building blocks for bioisosteric replacements, we prepared five analogs of R-1487 (10a)a known highly potent and selective p38α mitogen-activated protein kinase (MAPK) inhibitor developed by Roche scientists. R-1487 (10a) and its analogs 10b-f were prepared by SNAr reaction of known key intermediate 9 (synthesized in five steps from a commercially available pyrimidine derivative) and amines 3 or 4. As in the case of model amide derivatives 7 and 8, replacing the tetrahydropyran moiety in the molecule of 10a with gemdifluorinated analogs resulted in slightly increased lipophilicity. Notably, the changes in LogD7.4 values of compounds 10a-f in correlated with LogP trends observed for benzamides 7 and 8 (with a single exception of compounds 10d/3 [3,0]). This result confirms suitability of the model systems used by us in this work for the lipophilicity studies. |
6745c60ff9980725cf05c167 | 3 | Kinetic aqueous solubility of compounds 10a-f correlated with the LogD7.4 data: more lipophilic gem-difluorinated representatives were by 30-100 μM less soluble in PBS as compared to non-fluorinated counterparts. Metabolic stability (measured as intrinsic clearance, CLint) demonstrated 1.5-fold improvement for some representatives (14 and 15 µL/min/mg for 10e and 10f vs 23 µL/min/mg for 10a). Importantly, the potency of all the fluorinated derivatives against human recombinant fulllength p38α MAPK remained in the nanomolar range, albeit 5-to 8-fold decrease was observed. These results show that gemdifluorinated O-heterocyclic substituents discussed in this work can indeed be used for isosteric replacements in medicinal chemistry. |
6745c60ff9980725cf05c167 | 4 | Fluorination of cyclic compounds represents a potent strategy in drug discovery, offering fine control over physicochemical properties and pharmacological profiles. In this work, we demonstrated this by a comprehensive study of gemdiflurinated saturated O-heterocyclic building blocks (carboxylic acids and primary amines) along with their non-fluorinated and carbocyclic counterparts. Increments of introducing an Oxygen atom or a gem-CF2 group to the compound's physicochemical properties were established for each position of five-and sixmembered saturated ring. It was found that whereas for acidity (pKa), these increments demonstrated additivity and correlated with the substituent's inductive effects, for lipophilicity (LogP), a more complex behavior was characteristic. In particular, while gem-fluorination of cyclohexane-and cyclopentane-derived amides typically led to decrease in their lipophilicity, gem-difluorinated O-heterocyclic derivatives were typically more lipophilic than their non-fluorinated counterparts. Finally, we demonstrated potential of gem-difluorinated O-heterocyclic substituents for bioisosteric replacements by the synthesis and evaluation of was demonstrated by the synthesis of p38α MAPK inhibitorsanalogs of Roshe's clinical candidate R-1487. The synthesized fluorinated mimetics retained nanomolar potency against their biological target, had somewhat higher lipophilicity and lower aqueous solubility but improved metabolic stability. We believe that these results will help the fluorinated five-and six-membered O-heterocyclic fragments to find their place in the medicinal chemists' toolbox and promote their wider applications in early drug discovery. |
6745c60ff9980725cf05c167 | 5 | The solvents were purified according to the standard procedures. Compound 9 was synthesized according to the literature method. General procedure for the synthesis of anilides 5 and 6. To a solution of corresponding acid (1.00 mmol) and aniline (93 mg, 1.00 mmol) in CH3CN (5 mL), 1-methylimidazole (246 mg, 3.00 mmol) and TCFH (308 mg, 1.10 mmol) were subsequently added. The resulting mixture was stirred at room temperature overnight and concentrated under reduced pressure to dryness The residue was dissoved in EtOAc (15 mL) and washed with saturated aq NaHCO3 (3 10 mL), 10% aq citric acid (3 10 mL), brine (3 10 mL), dried over Na2SO4, and evaporated under reduced pressure to give pure anilide. |
6745c60ff9980725cf05c167 | 6 | Compounds 10a,b,d. To a stirred solution of compound 9 (367 mg, 1.00 mmol) in toluene (10 mL) amine (1.50 mmol) and Na2CO3 (228 mg, 2.15 mmol) were subsequently added. The resulting mixture was heated to 80 °C in an oil bath, stirred at the same temperature overnight and concentrated under reduced pressure to dryness. The residue was dissolved in EtOAc (15 mL) and washed with saturated aq NaHCO3 (3 10 mL), 10% aq citric acid (3 10 mL), brine (3 10 mL), dried over Na2SO4, and evaporated under reduced pressure. Crude material was purified with reverse-phase HPLC to give pure product 10. |
623dd513202c069887e0e12c | 0 | Numerous unconventional forms of aromaticity have been identified experimentally in the last decades; Möbius aromaticity in macrocycles and metallacycles, all-metal σ-aromaticity in the solid state, aromaticity in electronically excited states, and several other forms. Three-dimensional aromaticity (3D-aromaticity) is an intriguing topic introduced by Aihara in 1978 when he analyzed polyhedral boranes using a Hückel-type molecular orbital theoretical approach. Closo-boranes, such as [B12H12] 2-first synthesized in the 1950s, are highly stable compounds and emblematic 3D-aromatic compounds. Today, 3D-aromaticity is also found in metal clusters and some charged fullerenes, where the aromaticity of the latter is also classified as spherical aromaticity that follows Hirsch's 2(n+1) rule. The tetrahedral P4 molecule (white phosphorous) and Group 14 element E4 4-Zintl ions have been labelled as 3Daromatic, and this also applies to the Zn I 8 (Zn I 8(HL)4(L)8 12- |
623dd513202c069887e0e12c | 1 | , L = tetrazole dianion) metal cluster which additionally can be described as cubic aromatic since it exhibits an electron delocalization over the entire Zn I 8 cube. The unifying feature of these molecules is that they, besides extensive electron delocalization, have a number of degenerate molecular orbital (MO) levels which are at least triply degenerate, including the highest occupied and the lowest unoccupied MOs (HOMO and LUMO). We will henceforth call these molecules truly 3D-aromatic molecules. The MO diagram of a typical 2D-aromatic molecule such as benzene and a truly 3D-aromatic molecule like B6H6 , as shown in Figure , reveals that a closed -electron shell results with 4n + 2 electrons in a 2D-aromatic molecule, while a closed shell requires 6n + 2 highly delocalized electrons in 3D-aromatic molecules with tetrahedral or octahedral structures. Monocyclic 2Daromatic molecules with lower symmetries (e.g., C2v symmetric pyridine) lack the doubly degenerate -MOs but still have -MOs that strongly resemble those of the highly symmetric archetypes (see Figure for a comparison between the -MOs of pyridine and benzene). The same applies to 3D-aromatic carboranes in relation to the highly symmetric closo-boranes (see Figure for CB5H6 -and B6H6 2-). Indeed, Schleyer and co-workers concluded that the 4-center-2-electron 3D-aromaticity of the 1,3,5,7-bisdehydroadamantane dication manifests itself in a tetrahedral orbital topology, even though the molecule does not belong to the Td point group. 3D-aromatic molecules are traditionally -conjugated. Therefore, the search for conjugated 3D-aromatic molecules and aromaticity that extends in three dimensions has recently intensified. Indeed, the term 3D-aromaticity has been used to label several different compound classes that exhibit electron delocalization in 3D. One form of aromaticity in three dimensions is the through-space (face-to-face or stacked-ring) aromaticity first observed through computations by Corminboeuf, Schleyer, and Warner in methano-bridged superphanes involving π-stacked [4n]annulenes (Figure ), and further explored both theoretically and experimentally in cyclophanes and hexaphyrin dimers. π-Capped annulenes with six interstitial electrons have also been described as 3D aromatic. However, here it should be realized that among the three aromaticity forms in Figure , it is only spherical aromaticity that fulfills the criterion of triply or higher orbital degeneracy, justifying the classification of C60 10+ as 3D-aromatic. |
623dd513202c069887e0e12c | 2 | New and highly interesting compounds are the π-conjugated cage compound 1 (Figure ), its cations up to the hexacation 1 , and related compounds, which were reported by Wu and co-workers and considered to be "3D globally aromatic". This bicyclic macrocycle consists of three equally long -conjugated arms, and in its neutral form was computationally found to possess one Hückel aromatic cycle with 38π-electrons while the lack of aromaticity in the other two cycles is a result of the C2 symmetric structure and poor conjugation in the third bridge. Yet, when the structure of 1 was enforced to D3 symmetry, it was reasoned that the aromaticity involves the complete molecule. The same was found for 1 which has a D3 symmetric global minimum. Since the macrocycle 1 has 56 -electrons, i.e., a 6n + 2 number (n = 9), and exhibits three diatropic ring-currents, it was concluded that 1 is 3Daromatic when D3 symmetric. This also applies to the hexacation which has 50 -electrons, a 6n + 2 number with n = 8. Additionally, Casado and Martín considered 1 and its hexacation 1 in terms of spherical aromaticity, and argued that the hexacation with 50 -electrons follows Hirsch's 2(n + 1) 2 rule for spherical aromaticity with n = 4. However, this rule applies to electron systems that can described as uniformly distributed spherical electron gases for which the wavefunctions are described by the angular momentum number l (l = 0, 1…) and where each energy level is 2l + 1 degenerate. Yet, despite that the -electron counts of 1 and 1 6+ in D3 symmetry are in accord with, respectively, the 6n + 2 and 2(n + 1) 2 rules, this symmetry provides for only double degeneracy. Furthermore, in D3 symmetry 1 and 1 6+ must exhibit three equivalent cyclic paths as their electronic structures must be symmetry-adapted. Earlier, a set of compounds related to 1, the dithiopheno-bridged octaphyrins 2 and 3 (Figure ), were explored by Kim and co-workers. These compounds showed two diatropic ring currents with 26 and 34 -electrons, respectively, a feature that the authors described as dual aromaticity. Yet, the authors also used the term bicycloaromaticity, a concept introduced by Goldstein in 1967 to describe through-space aromatic (homoaromatic) interaction in charged bicyclic macrocycles with puckered structures. Results from 1 H NMR spectroscopy showed that the ring currents of 2 are diatropic, and the aromatic character was further corroborated by Sundholm and co-workers through computations of magnetically induced current densities. Clearly, most molecules are three-dimensional, but the mere combination of a 3D molecular geometry along with (aspects of) aromaticity is not a sufficient condition for 3Daromaticity. As a first example, helicenes are aromatic molecular scaffolds with 3D structures, however, they are not 3D-aromatic. Neither is an octahedral supramolecular scaffold with isolated aromatic compounds. Both are examples of 2D-aromatic systems embedded in 3D scaffolds, i.e., a 3D-aromatic system that cannot be reduced to a set of 2D-aromatic moieties. |
623dd513202c069887e0e12c | 3 | Helicenes do not fulfill the 6n + 2 electron count and the supramolecular scaffold with isolated aromatic compounds (by taking a large distance between them) would also show no delocalization between the individual compounds. From Figures and it is apparent that a variety of compound types have been labelled as 3D-aromatic throughout time, yet, is the term meaningful if used that broadly? In our view, there is a high need for a strict definition, and we build on what is known for the closo-boranes, labelled by Aihara as 3D aromatic. We further relate to what is generally accepted for 2D aromaticity (Figure ). Hence, the four necessary conditions for true 3D-aromaticity that all must be fulfilled are (i) (at least) triply degenerate MOs or a closely related orbital topology which exists for tetrahedral or higher symmetry molecules, (ii) a closed-shell electronic structure, which leads to a 6n + 2 electron count for tetrahedral or octahedral molecules (or molecules that are nearly so), (iii) extensive electron delocalization involving the complete molecule leading to a resonance stabilization, and (iv) similar (electronic and magnetic) properties in the three xyz directions. None of these conditions by itself is a sufficient condition. Notably, a definition requiring the fulfilment of all of these conditions is in line with Aihara's original observations for closo-boranes as 3D-aromatics. Now, how do 1 -3 and 1 6+ comply with the essential features and the established definitions for 3D-aromaticity and bicycloaromaticity? As the D3 point group in 1 does not induce triply or higher-order orbital degeneracies, is the aromaticity in 1 -3 and 1 6+ instead related to the Hückel-aromaticity of two-dimensional polycyclic aromatic hydrocarbons (PAHs)? Compounds 1 -3 and 1 6+ are unusual and intriguing, yet, even though their aromatic character is apparent from both experimental and computational observations, the cause of this aromaticity has not been analyzed in depth. In particular, there has been no search for macrocycles that potentially disprove the hypothesis that 1 and its hexacation comply with the 6n + 2 rule for 3D-aromaticity and Hirsch's 2(n + 1) 2 rule for spherical aromaticity. In this work we present a deeper theoretical analysis of 1 -3 and related compounds, along with a computational analysis to establish the precise nature of the aromaticity of these compounds. |
623dd513202c069887e0e12c | 4 | The analyses and discussions of our findings are split in three sections; a first with the qualitative theory on bicycloaromaticity, 3D-aromaticity, and 2D-aromaticity in threedimensional compounds (briefly, 2D-aromaticity-in-3D), a second with computational results of these compounds discussed within the theoretical framework described in the first section, and a third where we explore species that can be truly -conjugated 3D-aromatics. |
623dd513202c069887e0e12c | 5 | On the alleged bicycloaromaticity of 2 and 3. We start with the two dithiophenobridged octaphyrins 2 and 3 as they link PAHs with the cage-type macrocycles. Macrocycles 2 and 3 were recently labelled as bicycloaromatic, a form of aromaticity defined by Goldstein as a case where three separate -conjugated polyene segments (ribbons) in a bicyclic CmHm hydrocarbon interact through-space in either a longicyclic or a laticyclic topology (Figure ). Two criteria must be fulfilled for a bicycloaromatic interaction; (i) m must be an odd number (i.e., odd number of C and H atoms), and (ii) the total number of π-electrons must equal 4n. |
623dd513202c069887e0e12c | 6 | A potentially bicycloaromatic species is the bicyclo[2.2.1]heptadienyl cation (C7H7 + ) as it has four -electrons and m = 7. Conversely, bicyclo[3.2.2]nonatrienyl (C9H9 + ) with m = 9 should in theory be bicycloantiaromatic as it has in total six π-electrons and the even-odd bridge interaction is destabilizing as it involves four π-electrons. Based on the original definition of bicycloaromaticity, it is clear that 2 and 3 do not satisfy the criteria for bicycloaromaticity as (i) they possess 42 π-electrons (a 4n + 2 number corresponding to bicycloantiaromaticity), (ii) the three bridges (ribbons) are not separate from each other as they all interact conjugatively with the two bridgehead atoms which are sp 2 instead of sp 3 hybridized, and (iii) all bridges have even numbers of atoms in the -conjugated paths (16, 16 and 8) (Figure ). With two bridgehead atoms this implies that they are not CmHm compounds with m odd as the sum equals 42 (16 + 16 + 8 + 2). Thus, the description of bicycloaromaticity by Kim and co-workers as a concept where "two (or more) potentially aromatic circuits are contained within the same non-planar molecular framework and share the same electrons" is not in line with the original definition (Figure ). |
623dd513202c069887e0e12c | 7 | On the alleged 3D-aromaticity of 1 and 1 . Next, we now turn to the claimed 3Daromaticity of compounds 1 and 1 6+ . To determine if a compound is 3D-aromatic one must analyze its electronic structure. As noted in the Introduction, a 3D-aromatic molecule should have (at least) triply degenerate orbitals, but this degeneracy will be lifted when heteroatoms are incorporated in the molecular scaffold (see CB5H6 -, Figure ) or when effects such as bond length alterations lower the symmetry. Compounds 1 and 1 6+ are aromatic in their D3-symmetric structures, they are three-dimensional, have 6n + 2 -electron counts and extensive electron delocalization. We argue that 1 -3 as well as 1 6+ are expanded and puckered versions of PAHs, instead of true 3D-aromatics, where the π-electrons are shared between a set of circuits that each fulfil the 4n + 2 rule (Figure ) (for 2 and 3 with different n). The total ring-current picture of a PAH is constructed from all the different circuits that can be drawn. Naphthalene has three circuits; where the two hexagons (a and b) correspond to local six-electron circuits (A and B), while both hexagons are involved in the ten-electron circuit C. Furthermore, the induced diatropic ring-currents of circuits A and B, generated in an external magnetic field, are equivalent and cancel each other in the central C-C bond so that naphthalene exhibits an induced diatropic ring current exclusively along the perimeter. A similar analysis can be made for anthracene and other PAHs. Now, to what extent is the aromaticity of macrocycles 2 and 3 reminiscent of that of naphthalene? Also, can naphthalene be altered/modified to the extent that its ring currents resemble those of the two bicyclic macrocycles 2 and 3, and should one not consider three aromatic cyclic paths in 2 and 3? |
623dd513202c069887e0e12c | 8 | Figure shows the two general bicyclic structures to which the three compounds of Wu, Kim and co-workers belong; the difference between the two structures being the total number of π-electrons in the three arms, i.e., 4n (Type A) and 4n + 2 (Type B). Here it should be pointed out that the single -electrons at the two bridgehead C atoms displayed in the generalized structures do not represent radical centers but instead indicate that these -electrons are involved in -bonds to either of the three linkers. Indeed, the three-dimensional bicyclic structures can all be viewed as expanded naphthalenes (Figure ). Starting at naphthalene we increase the -electron count by expanding the six-membered rings through linkers while keeping the topology of Figure to ensure that each circuit allows for 2D Hückel-aromaticity. How do the -electron counts vary in these bicyclic compounds? Especially, when do they equal 6n + 2? For Type A expanded naphthalenes the -electron counts generally equal 4k + 4l + 4m + 2, which when k = l = m becomes 3×4k + 2 = 6×2k + 2. With n = 2k we get the -electron count 6n + 2. Thus, with three linkers of equal length the -electron counts of expanded naphthalenes happen to coincide with the -electron counts of truly 3D-aromatic molecules. This also applies for the Type B expanded naphthalenes with six extra electrons, still resulting in a 6n' + 2 count (n' = n + 1). Among 1 -3 and 1 6+ it is therefore only 1 and 1 6+ |
623dd513202c069887e0e12c | 9 | that have 6n + 2 total -electron counts. Yet, will similar bicyclic cages as 1 and 1 6+ exhibit aromatic character also when n ≠ m and/or k? If the tether lengths are just slightly different, e.g., k = l + 1 = m + 1, then the -electron count is not a 6n + 2 number, although, the structure should still allow for strong -conjugation and Hückel-aromaticity in the three individual macrocyclic paths. Now, if these latter species are calculated to be aromatic, that will disprove that 1 and 1 6+ are 3D-aromatics. These two species would instead be three times locally 2D |
623dd513202c069887e0e12c | 10 | Design of true -conjugated 3D-aromatics. Having refuted the claims of the bicycloaromaticity of 2 and 3 as well as the 3D-aromaticity of 1 and 1 6+ , how to design conjugated (macrocyclic) cage molecules that are truly 3D-aromatic? As it is the higher-order point groups that exhibit irreducible representations with triple (or higher) degeneracies, leading to species that possibly can be 3D-aromatic, a -conjugated macrocycle which is 3D-aromatic must have (approximate) tetrahedral, octahedral or icosahedral, or even higher symmetry. |
623dd513202c069887e0e12c | 11 | Importantly, the local -orbitals of the -conjugated linkers must be oriented radially outward if they are to interact with the local p orbitals at the vertex atoms. We have also analyzed such tetrahedral and cubic species through computations (Figure and vide infra). These species must have radial orientations of their π-orbitals similar to charged fullerenes C60 10+ and C20 2+ , which have been explored computationally and found to follow Hirsch's 2(n + 1) 2 rule as they are spherically aromatic. Yet, Hirsch's rule has a limitation as it seems applicable only to species with 50 -electrons or less. A further caveat with regard to the cubic species is that each of the faces has 4m -electrons (m ≠ n), meaning that these can be Hückel-antiaromatic. |
623dd513202c069887e0e12c | 12 | Hence, the cubes can in theory be both globally 3D-aromatic and six-fold locally 2Dantiaromatic. Compounds which are Baird-aromatic follow Baird's rule which tells that the lowest ππ* triplet state of [4n]annulenes is aromatic, and it applies to electronically excited states and to openshell ground states. For a (macro)cyclic two-dimensional molecule which is Hückelaromatic one can achieve a Baird-aromatic triplet state by either removal or addition of two electrons, exemplified by, respectively, the benzene dication and dianion for which there are derivatives shown experimentally to have either triplet ground states or low-lying triplet states. Similar to the 2D-Baird-aromatic benzene dication and dianion, true 3D-Bairdaromaticity will occur for the trication and trianion as their -electron occupancies allow for half-filled triply degenerate orbitals with an electron count of 6n -1. Hence, true open-shell 3D-Baird-aromaticity will not occur for the triplet dication even though 1 , which has a triplet ground state, has a NICS(0) value of -2.6 ppm 48 which (at best) suggests a modest Bairdaromatic character. Instead, the triplet dication of a true 3D-aromatic species would have an electron configuration with four -electrons in the triply degenerate HOMOs, an electron configuration that due to the Jahn-Teller effect should lead to a distortion away from the highsymmetry. Now, what is the electron count for Baird-aromaticity in a bicyclic macrocycle which is 2D-aromatic-in-3D? If one goes by simple -electron counts, the quartet trication of both Type A and Type B expanded naphthalenes with k = l = m can be Baird-aromatic as each linker will have 4k -1 -electrons for Type A and 4k + 1 -electrons for Type B providing for three Baird-aromatic 4n circuits (n = 2k). Additionally, the triplet dication can be Bairdaromatic in one single cycle, as found by Wu and co-workers. For 3D-aromatic species, in contrast, only the trication in its quartet state can exhibit Baird-aromaticity. |
623dd513202c069887e0e12c | 13 | Tetra-tethered 2D-aromatics-in-3D: A final feature of 2D-aromatic-in-3D structures is that they can be expanded to (hypothetical) macrocyclic compounds with additional arms (Types C and D, Figure ). Here, it is noteworthy that a macrocyclic cage molecule with four tethers, yet with -conjugated (aromatic) Ni-porphyrin units at its two poles, was recently reported by Wu and co-workers. It was argued that the dication of this species "discloses the close correlation between 3D global aromaticity and 2D Hückel aromaticity". Yet, does it? |
623dd513202c069887e0e12c | 14 | Gedanken-molecules which are 2D-aromatic-in-3D with six Hückel-aromatic 4n + 2 cycles and with total -electron counts of 8n + 2; a -electron count which is not in line with true 3Daromaticity. As pointed out in the Introduction, 3D aromaticity cannot be reduced to a set of 2D aromatic moieties. This also becomes obvious via the origins of, respectively. the 4n + 2 and 6n + 2 electron counts (Figure ) as the electron counts stem from the different orbital degeneracies in the two aromaticity types. |
623dd513202c069887e0e12c | 15 | Computational analysis: Here we use quantum chemical calculations to probe the conceptual theories described above. We start by examining the electronic structure and aromaticity of naphthalene (4), puckered naphthalene (5), and the benzocyclooctatetraene dication (6) as 10-electron bicyclic molecules, and connect these to the nonplanar dithiophenobridged octaphyrins 2 and 3 which have one short and two long bridges. Subsequently, we study bicyclic macrocycles with three bridges of (approximately) equal lengths whereby these compounds adopt cage-type structures. We especially analyze compounds that allow us to contest the presumption that 1 and 1 6+ are 3D-aromatics that follow the 6n + 2 and 2(n + 1) 2 rules. At the end, we explore tetrahedral and cubic -conjugated compounds (Figure ) with potentials to be 3D-aromatics. |
623dd513202c069887e0e12c | 16 | It should be stressed that the study is aimed at establishing the type of aromaticity, not the quantitative extent of aromaticity. We utilize primarily the B3LYP functional with the 6-311G(d,p) basis set. This functional is known to exaggerate aromaticity in macrocycles when compared to long-range corrected functionals (e.g., CAM-B3LYP), which are recommended for such molecules and for aromatic compounds in general. Calculations with CAM-B3LYP are, however, performed on selected species (see Tables and in the SI). |
623dd513202c069887e0e12c | 17 | Aromaticity analyses are performed through the electron density of delocalized bond (EDDB) function, nucleus independent chemical shifts (NICS), anisotropy of induced current density (ACID), as well as current densities and strengths of the integrated current densities calculated perturbatively with the GIMIC program. The EDDB function discloses electron delocalization, and hence, electron density that cannot be attributed exclusively to a particular chemical bond. EDDB reveals that in archetypical Hückel's 4n + 2 aromatics the cyclic (Kekuléan) delocalization predominates and is very effective (82-89% for 6π-systems) while in the case of Hückel's 4n antiaromatics cyclic delocalization almost entirely vanishes although some local resonance effects still remain in their π-systems (see Discussion B in the Supporting Information and Figure for further examples). This clarifies the wide span in the electron delocalization between aromatic and antiaromatic annulenes. As we are aware that electron-sharing and magnetic response properties are not always connected, we follow the common practice of using a set of descriptors to characterize the aromatic character of a given species. It should, however, be noted that we emphasize results on electron delocalization as provided by EDDB. |
623dd513202c069887e0e12c | 18 | Nonplanar dithiopheno-bridged octaphyrins as expanded naphthalenes: The fact that naphthalene exhibits two circuits with six -electrons and one with ten becomes apparent through electronic aromaticity indices. EDDB reveals delocalization through both the perimeter and the central CC bond (4, Figure ), and as the electronic structure is a superposition of the -dectet and the two -sextet resonance forms, the EDDB-based percentage effectiveness of cyclic delocalization of -electrons in each cycle is similar. In contrast, and as noted above, magnetic indices give an obscured picture since the induced ring currents from the two hexagons circuits of 4 cancel each other perfectly in the central CC bond (Figure ). This is also clear from the current densities obtained with GIMIC as the average current strength in the perimeter bonds is ~13 nAT -1 (diatropic) while the current strength in the central CC bond is nil (for a definition of the strengths of the integrated current densities see ref. 86). Yet, when gradually distorting one of the hexagons leading to a puckered Cs symmetric structure (5, Figure ) the ring current in the puckered hexagon is attenuated whereby the two 6-electron ring currents do not cancel anymore and a current density in the inter-ring CC bond emerges (for current densities of gradually more distorted naphthalenes see Tables and). One can also see that the -electron delocalization is very attenuated in the puckered hexagon while it is enhanced in the planar hexagon (Figure ). Yet, it is also possible to achieve a differentiation in the 6-electron currents, and a current density in the inter-ring CC bond, by going to the nearly planar benzocyclooctatetraene dication (6, Figure ). For 6, a NICS-XY scan shows that the local 6-electron aromaticity in the hexagon dominates over that in the octagon (Figure ), whereby the resulting current density in the central CC bond is 4.7 nAT -1 . Clearly, a structural differentiation between the two 6-electron cycles, achieved either by distortion or altered ring size, provides for a differentiation in the ring currents of the two cycles, leading to an imperfect cancellation of the currents in the inter-ring CC bond. In 2 and 3, the dissimilarities between the two 26-electron cycles come about because of the orientation of the dithienothiophene (DTT) bridge which leads to a better -conjugation with one half of the octaphyrin than with the other half, reflected in C-C-C-C dihedral angles to the DTT bridge which are 7 and 33º, respectively. This provides a better electron delocalization in one 26-electron cycle than in the other (41.7 vs. 35.6%), although the best delocalization is along the perimeter (42.5%). |
623dd513202c069887e0e12c | 19 | C2v symmetric structure (a first-order saddle point). However, the DTT bridge is too long by ~0.9 Å to fit into an [34]octaphyrin (see Figure ), and its incorporation leads to the strongly puckered compound. Indeed, a planar C2v symmetric structure of 2 is a higher-order saddle point 87.0 kcal/mol above the minimum. The importance of the nonplanarity for the observations made by Kim and co-workers becomes obvious through an ACID plot of the planar C2v structure because now the two 26π-electron ring currents are of similar weights and cancel on the bridge whereas the current through the perimeter remains (Figure ). In the planar structure of 2 there is a slight reduction in the difference in the extent of delocalization between the two 26-electron cycles (34 vs. 39%) (Table ). Hence, it is the non-equivalence of the two 26-electron resonance structures of 2 and 3, effectuated through the non-planar structures and the larger C-C-C-C dihedrals within one macrocyclic path than within other, that leads to the observation of two strong ring currents with, respectively, 34 and 26 -electrons and one with weakened strength (Figure ). It is apparent that these macrocycles resemble distorted naphthalene. |
623dd513202c069887e0e12c | 20 | To achieve a planar octaphyrin-based macrobicyclic species, the DTT bridge was replaced by a shorter butadiyne bridge and the two pyrrole rings adjacent to the bridgehead C atoms were linked pairwise via methylene bridges. This leads to the D2h symmetric molecule 7, a compound that displays only a perimetric ring current with current densities in the range 23 -33 nAT -1 (Figure ). To achieve a differentiation between the two 22-electron macromonocycles in a near-planar macrobicycle, we replaced two CH moieties on one side by two SiH moieties, leading to 8. According to ACID, two clockwise ring-currents can be detected for this species; one over the perimeter and one over one of the 22-electron cycles (Figure ). As seen visually, the 22-electron cycle with the stronger ring current is the ring with CH units. The NICS-XY scans also show that the aromatic character of one of the two macromonocycles decreases when going from 7 to 8. Hence, there is an imperfect cancellation of the two 22-electron ring-currents in the butadiyne-bridge of 8, analogous to the situation in 6 (Figure ). GIMIC reveals current strengths of 11.7 -14.4 nAT -1 at this bridge. Interestingly, EDDB reveals that the extent of delocalization in the two macromonocycles of 8 are, respectively, larger and smaller than in the two equivalent macromonocycles of 7 (Figure ). Furthermore, Kim and co-workers argued that the triplet state of the dication of 2 |
623dd513202c069887e0e12c | 21 | ( 3 2 2+ ) can be described as having one 33-electron cycle in the perimeter and one 25-electron circuit in one of the individual macrocycles. Based on the conceptual theory above, we instead reason that 3 2 2+ is a distorted expanded naphthalene dication which is triplet state 2D-Bairdaromatic in the conventional sense. The naphthalene dication in its triplet state ( 3 4 2+ ) is described by three Baird-aromatic resonance structures; two with 4-electron circuits in either of the hexagons and one with an 8-electron perimeter (Figure and). Upon distortion leading to 3 5 2+ the two 4-electron cycles become inequivalent; one remains unaltered while the other is weakened (Figure ). Similarly, 3 2 2+ should be described primarily by two conventional 4n-electron Baird-aromatic resonance structures; one with a 32 -electron perimetric circuit and one with a 24-electron circuit in one of the two macromonocycles (Figure ). The weakened cyclic conjugation in the ring with two Si atoms is also apparent in the EDDB plot. |
623dd513202c069887e0e12c | 22 | On the aromaticity of fully -conjugated cage macrocycles: Despite the obvious three-dimensional structures of 1 and 1 6+ , and that the globally aromatic characters of the D3 symmetric molecular cages may seem apparent, they are not 3D-aromatic and do not follow the 6n + 2 rule. Instead their aromaticity can be understood in terms of the conventional Hückelaromaticity of polycyclic aromatic hydrocarbons, which in most cases is two-dimensional. We therefore label these compounds as 2D-aromatic-in-3D. Also 1 and 1 6+ can be viewed as expanded naphthalenes (Figure ) where the middle tether has been elongated so that the -electron counts in the three macrocyclic paths become equal. To check the aromatic character of these macrocycles, we use an electronic index, i.e. EDDB, over other descriptors, considering that electron delocalization is a necessary condition for 3D-aromatics. |
623dd513202c069887e0e12c | 23 | As noted above, the D3 symmetry does not provide the compounds with the required orbital degeneracy for 3D-aromaticity. Furthermore, in neutral 1, the dihedral angles between the tethers at the bridgehead atoms (δ1, δ2, and δ3, Figure ) are 26°, 46°, and 48°, which reveals that only one of the three cyclic paths is significantly -conjugated over the two bridgeheads as the -orbital overlap between two p AOs scales as cos with being the angle between the two AOs. Yet, with the other dihedral angles in that (aromatic) cycle being 154 -171°, its conjugation is also attenuated. It was earlier reported that when D3 symmetric there is an equal aromaticity in the three rings, giving 1 aromatic character that seemingly extends over the complete molecule. However, as concluded above, the equal extent of aromaticity in the three local rings is a necessary result of the symmetry-adapted electronic structure and is not due to 3D aromaticity. Thus, it is also not appropriately described as an aromaticity of global character. |
623dd513202c069887e0e12c | 24 | Furthermore, the D3 symmetric structure of 1 6+ maximizes the possibility to mutually separate six positive charges. Accordingly, its enhanced aromatic character is a by-product of charge repulsion, which is in line with earlier observations on oxidized macrocycles when compared to the corresponding neutral macrocycles. In this context, it is notable that 1 6+ has 1 = 2 = 3 = 41°, and with two such dihedrals in each macrocyclic ring the -conjugation will still be attenuated since [cos(41°)] 2 = 0.57. |
623dd513202c069887e0e12c | 25 | As 1 6+ has a -electron count of 50, Casado and Martín described it as spherically aromatic fulfilling Hirsch's 2(n + 1) 2 rule with n = 4. Here, it is noteworthy that Wu and coworkers recently concluded that a similar C2 symmetric cage-type macrocycle with four tethers does not follow this rule. Now, to probe if 1 6+ complies with Hirsch's rule, or if the -electron count is merely coincidental, we analyzed the next larger analogue of 1 6+ , leading to 11 6+ with five instead of four thiopheno rings in each tether. According to EDDB this hexacation exhibits slightly more -electron delocalization than 1 6+ (60.0% in 11 and 59.5% in 1 6+ ) and would be equally aromatic. Yet, 11 6+ has 62 -electrons, a number which is not a 2(n + 1) 2 number (the next is 72 when n = 5). Instead, the slightly enhanced -electron delocalization of 11 seems to be a result of the longer tethers which allow for better -orbital overlap at the bridgehead C atoms because the δ1 -δ3 values are lower in 11 than in 1 6+ (36° vs. 41°). Thus, the reason that the -electron count of 1 6+ is a 2(n + 1) 2 number is coincidental. The -electron count of 11 6+ is a 6n + 2 number. Yet, also this -electron count does not expose 3D-aromaticity since a -electron count of 6n + 2 results coincidentally for a bicyclic molecule with three equal tethers, as described in the qualitative theory section. To confirm this, we examined if cage macrocycles where one linker has four more -electrons (or four less) than the other two linkers are similarly aromatic as 1 6+ and 11 . We tested this through 9 6+ and 10 6+ (Figure ) with total -electron counts of 54 and 58, i.e., counts that are not 6n + 2 numbers. We now find that the extent of -electron delocalization according to EDDB is similar in the four hexacations (Figure ), revealing that it is not the specific 6n + 2 -electron count in 1 and 11 which leads to the high delocalization in these species. Instead, all four species (1 6+ , 9 6+ , 10 6+ , and 11 ) are 2D-aromatic-in-3D, which should be the reason for their high electron delocalization. Notably, similar results were calculated with CAM-B3LYP as with B3LYP (see Table ). Furthermore, by starting at 11 and shortening one of the tethers by either two or three thiopheno rings, we arrive at cage compounds 12 and 13 where the extent of delocalization starts to differ between the macrocyclic paths (see Table ). In 12 the electron delocalization in one circuit reaches 52% while it is 41 -42% in the other two, and in 13 these numbers are 54% and 38%, respectively. This is even a stronger differentiation than seen in 2. in their lowest open-shell quartet states. For the percentage delocalized electrons per cycle, see Table in the SI. |
623dd513202c069887e0e12c | 26 | Finally, it was earlier argued that the dication of 1 in its triplet state ( 3 1 2+ ) is Bairdaromatic in one of the cycles since it has a NICS(0) value of -2.6 ppm, a value that suggests a modest Baird-aromaticity (if any). Following the argumentation in the section on qualitative theory, we tested if Baird-aromaticity is also achieved in the quartet state of the trication, and find that 4 1 3+ is D3 symmetric at its global minimum having an electron delocalization of 59% (EDDB), and a similar delocalization is found in the triplet dication ( and which are true 3D-aromatics? Four conditions should be satisfied according to the definition given in the Introduction. Both the 6n + 2 electron count and the orbital topology requirements must be fulfilled in such molecules, and the molecular properties should be similar in all three directions. Furthermore, they should exhibit extensive electron delocalization in radially oriented -orbitals, and it should be larger than the delocalization for analogous species with other electron counts than 6n + 2. In the theory section, we outlined the design of tetrahedral and cubic -conjugated molecules which may be true 3D-aromatics (see Figure ). |
623dd513202c069887e0e12c | 27 | The design starts at the tetrahedral E4 4-and cubic E8 species, and we insert, respectively, six and twelve -conjugated linkers between the vertex atoms in the two structures. Carbon atoms were chosen at the vertices as they provide for stronger -conjugation than the heavier Group 14 elements which are found in tetrahedral Zintl ions earlier labelled as 3D-aromatic. For the tetrahedral species, we also considered N atoms at the vertices but they lowered the -electron delocalization (see Figure ). With four anionic sp 3 hybridized C atoms (tetrahedral species) |
623dd513202c069887e0e12c | 28 | or eight neutral sp 2 hybridized C atoms (cubic species) we formally have, in both cases, eight radially oriented electrons at the vertices which can conjugate with the electrons in the radial -orbitals of the linkers. Both polyene and polyyne linkers were considered, yet, we start with the rigid polyyne linkers butadiynyl, hexatriynyl or octatetraynyl which contribute with four, six or eight electrons to radially oriented -orbital frameworks. |
623dd513202c069887e0e12c | 29 | When calculated with CAM-B3LYP the delocalization in 16 decreases to 15%, although the molecule keeps its tetrahedral structure. We checked the possible multiconfigurational character of these tetrahedral and cubic systems by computing the T1 diagnostic values for 14 and 15 at CCSD(T)/6-311G(d,p)//B3LYP/6-311G(d,p) level. The values obtained were below 0.02 which is the threshold for single-configurational character of closed-shell species, justifying our use of single-reference methods. Interestingly, for the cubes C8(C4)12 (17) and C8(C6)12 (18) the extent of delocalization of the radial -electrons are higher at 43% and 42%, respectively. Based on the CC bond lengths within the hexatriyne segments of 18 (1.229 -1.330 Å) as compared to those of 1,3,5-hexatriyne (1.209 -1.356 Å), it is furthermore clear that there is some degree of bond length equalization in 18 indicative of enhanced bond delocalization which may suggest aromaticity. Zintl ions such as Si4 4-and white phosphorous P4 have earlier been concluded to be 3D-aromatic based on NICS(0) values computed in the tetrahedron centers. Yet, as the electron delocalization decreases with shorter tethers, it should be the lowest in the E4 4-species. |
623dd513202c069887e0e12c | 30 | Indeed, according to EDDB these species are devoid of electron delocalization in the valence subshell because merely 0.2041 and 0.2075e are delocalized in P4 and Si4 ). Although the HOMO of 16 is triply degenerate and described purely by radially oriented p AOs, HOMO-1 and HOMO-2 are nondegenerate, and HOMO-3 is a mix of radially and in-plane oriented p. Thus, 16 should not be labelled as a 3D-aromatic that fulfills the 6n + 2 rule for tetrahedral or octahedral molecules, and the same applies to 14 and 15. Clearly, as the local bond orbitals with either in-plane or radial orientations mix for the tetrahedra, the polyyne linkers are not suitable for construction of tetrahedral -conjugated 3D-aromatics. In contrast, in the cubic 18, combinations of radially (24) and C8(C6H6)8 ( ) the polyene linkers lead to structures which are distorted (C2 symmetric) with weaker delocalization (35%) than found for the corresponding polyyne-linked species (Figure ). Furthermore, they exhibit significant bond length alternations as seen for |
623dd513202c069887e0e12c | 31 | Using qualitative theory combined with quantum chemical calculations, we came up with key points that help to discern between regular 2D-aromaticity, albeit in a 3D molecular structure, and true 3D-aromaticity in three-dimensional -conjugated (cage) (macro)molecules. Our study revealed that compounds 1 6+ and 2 (and 3) should not be labelled as, respectively, 3D aromatic and bicycloaromatic. The basic prerequisite for 3D-aromaticity, besides 6n + 2 -electron counts and high -electron delocalization, is a highly symmetric structure with at least triply degenerate MOs, features that do not exist in 1 6+ (also not in approximate sense). Yet, there are clear limitations for tetrahedral and cubic cage compounds that formally fulfill the 3Daromaticity requirements because there are negligible differences in electron delocalization between these cage compounds and near-tetrahedral or near-cubic compounds that have electron counts that deviate from 6n + 2. Hence, there seems to be a size limitation for 3Daromaticity, similar as has been observed earlier for spherical aromaticity. Likewise, the main features of bicycloaromatic species do not exist in 2 and 3. |
623dd513202c069887e0e12c | 32 | Hückel-aromatic circuits in three-dimensional molecular scaffolds. In that regard, we showed that not only is there a direct connection between PAHs (e.g., naphthalene) and 1 6+ and 2 (as well as 3), but also a connection between the three macrocycles. It becomes clear that they all can be described as expanded naphthalenes. |
623dd513202c069887e0e12c | 33 | Ideally, in a highly symmetric structure, the 3D aromatic character would only come from radial -MOs, whereas if such orbitals exist in combination with other MO types, then the molecule is not a true 3D aromatic. A second weakness is the fact that the extent of electron delocalization in species that fulfill the 6n + 2 electron count barely differs from those that do not fulfill this count. |
623dd513202c069887e0e12c | 34 | In conclusion, no 3D-aromatic -conjugated molecule has to our knowledge so far been described in experiments. At this point we want to stress that, although we bring a different rationalization of the aromaticity in 1 -3 and 1 6+ than provided earlier, it is truly important that new compounds that stretch and provoke our understanding of chemical bonding phenomena are designed and analyzed. Healthy discussions on their chemical brings chemistry forward as a science. Today, the term 3D-aromaticity is used for a number of different bonding patterns that involve aromatic interaction in three dimensions. Yet, if insufficiently well defined, it will lose its utility as a meaningful concept for chemical bonding analyses and the applications that rest upon such analyses. In our view, it is time the term is put on a solid foundation which applies to both and -bonded systems. This description of 3D aromaticity should comply with Aihara's original finding on the compounds which he labelled as 3D aromatic. Experimental section |
623dd513202c069887e0e12c | 35 | All geometry optimizations were performed with Gaussian 16 at the B3LYP/6-311G(d,p) level, although a selected species were also calculated with CAM-B3LYP. Aromaticity was evaluated in terms of electronic and magnetic indicators at the same level of theory. The electronic delocalization was evaluated by the electron density of delocalization bond (EDDBH), and magnetic properties were assessed using the nucleus-independent chemical shift (NICS), anisotropy of the induced current density (ACID) plots and gauge-including magnetically induced currents (GIMIC). Regarding EDDBH computations, NBO 3.1 and Multiwfn have been employed, where the former together with Avogadro 1.2 was used to obtaining EDDBH surfaces. NICS-XY scans were performed using the Aroma package and ACID plots were produced using AICD 2.0.0 program. |
60c73e16bdbb895770a37da2 | 0 | The discovery of functional molecular materials with targeted properties is hindered by the challenge of predicting the crystal structure that a given molecule will adopt, as well as the often complex relationship between crystal structure and the relevant properties. Computational approaches for guiding materials discovery have attracted significant attention as a means of identifying the most promising synthetic targets and, therefore, reducing experimental effort spent on materials with poor properties. The reliability and scope of methods for computer-guided material discovery have benefited from recent theoretical advances in configurational space sampling , force field and quantum mechanical methods. Developments in these areas mean that not only wider ranges of atomic configurations can be efficiently sampled, but that their physical and chemical properties can also be confidently predicted prior to laboratory synthesis and characterization. In particular, there has been rapid development in the field of crystal structure prediction (CSP) for organic molecules, as exemplified by the latest blind tests in this area. An aim of CSP methods is to produce the full set of stable (low energy) crystal structures available to a molecule and any given molecule usually leads to a large number of possible structures within a small energy range from the global energy minimum. A recent advance in the use of computational methods to guide the discovery of functional materials is the mapping of simulated properties onto the crystal energy landscape produced by CSP methods. The result, which we refer to as the energy-structure-function (ESF) map of a molecule, describes the possible crystal structures, their relative stabilities and expected properties. The assessment of ESF maps of candidate molecules for a targeted function can help rule out molecules with no (or only high energy) predicted structures with the required properties and prioritize the synthesis of molecules with promising predicted structures. The approach has successfully led to the discovery, crystallization and characterization of a porous organic crystal with exceptionally high porosity and methane storage capacity. ESF maps can be produced for any functional material where the relevant property is calculable from the crystal structure. For example, we proposed their use for the assessment of molecules as potential organic semiconductors. To illustrate this, we assessed a series of aza-substituted pentacenes where the targeted property is the electron mobility, which we calculated using Marcus theory. ESF charge mobility maps have also been reported recently for racemic and enantiomerically pure crystal structures of [6]helicene. Because molecular crystals are held together by many weak, competing non-covalent interactions and the possible crystal packing arrangements are typically close in energy, a subtle change in molecular structure can result in completely different molecular arrangements in the low en-ergy crystal structures available to a molecule. In turn, the strong dependence of charge mobilities on relative molecular positions and orientations means that the mobility in the crystal structures of closely related molecules can be very different. We previously proposed several approaches for ranking hypothetical molecules by the likelihood that they will lead to a high mobility crystal structure. One option is to use the predicted mobility of the most probable (lowest energy) predicted crystal structure of each molecule; another choice is the highest mobility among the low energy predicted crystal structures, and a third suggestion was a landscape-averaged mobility that takes into account the distribution of properties among the low energy structures. We believe that this is an advance on previous computational screening methods for molecular organic photovoltaic applications, in which the important influence of crystal packing differences between molecules on the final electronic properties has not been considered. |
60c73e16bdbb895770a37da2 | 1 | To further reveal the interplay between chemical substitution patterns and the resulting crystal packing types for azapentacenes in an automated way, a kernel-based machine learning technique was applied in conjunction with clustering and dimensionality reduction analysis to produce a sketch-map for the individual crystal packing landscapes for pentacene and two azapentacene molecules. These methods provided valuable insight into the profound changes in the overall crystal energy landscapes with changes in molecular substitution pattern. |
60c73e16bdbb895770a37da2 | 2 | In the present study, we build on these previous works by demonstrating the use of CSP in screening a large set of molecules with mixed hydrogen bond donors and acceptors as candidates for small molecule crystalline organic semiconductors. Our study is motivated by the recent report of (pyrido [2,3-b]pyrido [3 ,2 :4,5]pyrrolo[3,2-g]indole) (1, Fig. ), a planar, extended aromatic molecule with C 2v symmetry. 1 adopts a γ-type crystal packing, which features columns of π-stacked molecules, with two orientations of such columns forming a 'cruciform' arrangement. The crystal packing in 1 is directed by hydrogen bonds between the two hydrogen bond donors (-NH from the pyrrole rings) and acceptors (N from pyridine rings). Charge transport calculations on this structure suggested good carrier mobility in the directions of the molecular stacks. |
60c73e16bdbb895770a37da2 | 3 | These results sparked our interest in this class of molecules as an opportunity to explore the use of CSP and the generation of ESF maps in the screening of a large set of related molecules. The question we address is: allowing for reorientation and permutation of the pyridine and pyrrole rings, how does molecular structure affect the crystal packing landscape and what is the impact on the charge transport properties of these molecular materials? For this study, we investigated 1 and an additional 27 isomeric molecules (2-28, Fig. ), performing CSP on each molecule and charge mobility calculations on the low energy crystal structures. The set of molecules includes the twofold symmetrical (C 2v , 1-16) and the 12 asymmetric molecules (C s , 17-28). We did not attempt to exhaust the list of all possible asymmetric possibilities in this study due to the large number of possible combinations. In the end, our goal is to identify the isomer with the the greatest potential to produce a material with large charge carrier mobility. |
60c73e16bdbb895770a37da2 | 4 | To our knowledge, this is the largest set of molecules that has been subjected to CSP and property landscape exploration in a single study to-date. We further applied our recently-developed machine-learning methods to directly compare the differences in crystal packing landscapes across a set of chemically different molecules in a visually appealing and informative way, which can help us to further generalize better molecular design strategies for high-mobility organic semiconductors. |
60c73e16bdbb895770a37da2 | 5 | CSP was performed with our Global Lattice Energy Explorer (GLEE) program. Molecular geometries were optimized at the B3LYP/6-311G** level of theory using GAUSSIAN09 and kept rigid throughout all crystal structure calculations. A total of 49,000 lattice energy minimized crystal structures were produced for each molecule, all with one molecule in the asymmetric unit: 5000 in the most commonly observed space group for organic molecules, P2 1 /c, and 2000 in each of the 22 next most common space groups: |
60c73e16bdbb895770a37da2 | 6 | All lattice energy minimizations were performed using DMACRYS, with space group symmetry constrained throughout the optimizations. Lattice energies were assessed with a revised version of the W99 intermolecular atom-atom potential combined with a distributed multipole electrostatic model based on the molecular charge densities calculated from a distributed multipole analysis of the B3LYP/6-311G** density, with multipoles up to hexadecapole on each atom. |
60c73e16bdbb895770a37da2 | 7 | To remove duplicate crystal structures, an initial screen within individual space groups was performed using the clustering method described in Ref. 22. Overall clustering across all space groups was then performed using the COMPACK method. Classification of crystal packing type was performed using the angles between the planes of nearest neighbour molecules, as described in Ref. 15. |
60c73e16bdbb895770a37da2 | 8 | Electron mobility calculations were performed for all predicted crystal structures of each molecule that are within 7 kJ/mol of that molecule's global lattice energy minimum. This energy window is chosen to include most experimentally observable structures, based on the distribution of calculated lattice energy differences between observed polymorphs. Our mobility calculations use a hopping model and hopping rates from Marcus theory. Details of these calculations are given in the supporting information. |
60c73e16bdbb895770a37da2 | 9 | Similarities between structures from the crystal structure landscapes of all 28 molecules were measured using the SOAP-REMatch Kernel, which assesses similarity of structures based on a comparison of local atomic environments corresponding to spherical regions with cutoff r c around each atom. Based on the kernel-induced distance, the sketch-map dimensionality reduction technique was used to generate a low-dimensional projection of the data in which the proximity between structures is represented as faithfully as possible. Details for constructing the SOAP-REMatch Kernel and sketch-map are provided in our previous publication. A small difference is the choice of r c = 5 Å for the cut-off distance, and γ = 1 as the regularization parameter for the SOAP-REMatch Kernel. For sketch-map we used the parameters 32 σ = 0.12, a = A = 4, b = B = 6. |
60c73e16bdbb895770a37da2 | 10 | We first validate our CSP methodologies on molecule 1, the predicted energy-density landscape for which is shown in Fig. . The experimental crystal structure is located by the CSP search as the global lattice energy minimum. An overlay of the predicted global minimum with the experimental crystal structure is shown in Fig. , with comparison of the lattice parameters given in Table . The small root-mean-squared deviation in atomic positions from a 20-molecule cluster from the crystal structure (RMSD 20 =0.269 Å, Fig. ) and good agreement in lattice constants between the experimental and predicted crystal structure demonstrates excellent performance of our force field energy model. The low energy region of the crystal structure landscape for molecule 1 (Fig. ) is dominated by the γ-type of packing, featuring stacking of the planar molecules in columns (Fig. ). Hydrogen bonds are formed between these columns, arranging them into a 'cruciform' pattern in the lowest energy structure. A few sheet-like structures are also present at low energy. Herringbone packing, as seen in the parent [5]phenacene (picene) crystal structure, is strongly disfavoured for molecule 1. |
60c73e16bdbb895770a37da2 | 11 | In our previous work, the SOAP-REMatch similarity kernel for measuring structural similarity was combined with the HDBSCAN* clustering method and the sketch-map dimensionalityreduction method to produce low-dimensional projections of the individual crystal packing landscapes of pentacene and two azapentacenes. This single-landscape analysis was shown to provide useful information on the packing types available to individual molecules. Here, the method is applied to the more challenging task of analyzing the crystal packing landscapes of multiple molecules in a single sketch-map, which we refer to as multi-landscape analysis. |
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