Two-photon excited deep-red and near-infrared emissive organic co-crystals

Two-photon excited near-infrared fluorescence materials have garnered considerable attention because of their superior optical penetration, higher spatial resolution, and lower optical scattering compared with other optical materials. Herein, a convenient and efficient supramolecular approach is used to synthesize a two-photon excited near-infrared emissive co-crystalline material. A naphthalenediimide-based triangular macrocycle and coronene form selectively two co-crystals. The triangle-shaped co-crystal emits deep-red fluorescence, while the quadrangle-shaped co-crystal displays deep-red and near-infrared emission centered on 668 nm, which represents a 162 nm red-shift compared with its precursors. Benefiting from intermolecular charge transfer interactions, the two co-crystals possess higher calculated two-photon absorption cross-sections than those of their individual constituents. Their two-photon absorption bands reach into the NIR-II region of the electromagnetic spectrum. The quadrangle-shaped co-crystal constitutes a unique material that exhibits two-photon absorption and near-infrared emission simultaneously. This co-crystallization strategy holds considerable promise for the future design and synthesis of more advanced optical materials.

O rganic near-infrared (NIR) absorbing and emitting materials have found applications in fields as broad as bio-imaging 1-3 , photothermal therapy [4][5][6] , drug release 7 , night-vision technologies, and advanced optoelectronics 8,9 , for the simple reason that NIR light exhibits superior optical penetration, lesser photodamage, and lower optical scattering compared to visible light [10][11][12] . In order to fabricate NIR absorbing or emitting materials, several strategies are generally applied to tune the energy gap in these materials. They involve the extension of the length of π-conjugation in unsaturated molecules 13 and the introduction of metal centers into coordination compounds 8 , as well as the association of electron-donor and acceptor units in molecular materials 14,15 . Moreover, two-photon absorption (TPA) materials, through the absorption of two photons simultaneously, are capable of converting the excitation wavelengths from the visible to the NIR region. This property engenders an alternative approach for the construction of NIR absorbing materials. Two-photon excited NIR-emitting materials, with inherent multifunctionality, are ideal candidates for cell imaging 16 , photodynamic therapy 17,18 , microfabrication 19 , and optical data storage 20,21 . Consequently, the exploration of effective design strategies, along with the development of new twophoton excited NIR emissive materials, constitutes an attractive objective in materials science.
Recently, organic co-crystals, wherein donor and acceptor molecules assemble into highly ordered superstructures, based on intermolecular noncovalent bonding interactions, have emerged as a category of supramolecular materials with the following advantages [22][23][24] . (i) The preparation methods of co-crystals are similar to those of traditional single-component crystallization, which are feasible and easy to perform 25 . (ii) The properties of the co-crystals are related to their molecular packing and morphology, both of which can be modulated through co-crystal engineering without the requirement for further chemical synthesis 26 . (iii) Co-crystals not only maintain the properties of the individual components, but also, on some occasions, display unusual properties [27][28][29] . For instance, a co-crystal based on tetrathiafulvalene (TTF) and tetracyanoquinodimethane (TCNQ) exhibits metallic electrical conductivity, in sharp contrast with the semiconductor characteristics of their individual crystals 30 . Although low molecular weight organic ferroelectrics are few and far between, charge transfer co-crystals, with lock-arm supramolecular ordering (LASO) motifs, exhibit 31 ferroelectric behavior at room temperature. Inspired by these advances, extensive investigations of organic co-crystals have been pursued by scientists in different areas of materials science 32,33 . To date, abundant properties, such as ambipolar charge transport 34 , optical waveguide modulation 35 , piezochromic behavior 36,37 , thermal-mechanical response 38 , photothermal conversion 39 , and room-temperature phosphorescence 40 , have been achieved by simple co-crystallization. The engineering of NIR emissive cocrystals that exhibit TPA, however, remains as a challenge.
Additionally, the organic naphthalenediimide-based triangle ( Fig. 1a and Supplementary Figs. 2-7), namely NDI-Δ 41 , consisting of three electron-deficient NDI units, linked by trans-1,2cyclohexano bridges, has been applied widely in supramolecular chemistry. On account of its well-defined inner cavity, NDI-Δ is capable 42 of undergoing selective assembly into either helical or non-helical nanotubes upon the encapsulation of halogenated solvent molecules, e.g., XCH 2 CH 2 X where X=Cl, Br, I. The NDI-Δ, which is electron-deficient, is capable of encapsulating 41 linear I 3 − anions, resulting in the formation of single-handed helices in the solid state. Also, the electron-poor NDI-Δ and electron-rich TTF can, as a result of [π···π] interactions, co-assemble into twodimensional (2D) crystalline superstructures 43 . On the other hand, NDI-Δ-based rechargeable lithium-ion batteries exhibit 44 ultrahigh rate capability, as a result of the through-space electron sharing between NDI units in NDI-Δ molecules. The optical properties of NDI-Δ and its supramolecular assemblies, however, have hardly been investigated.
Herein, we examine a two-photon excited NIR emissive supramolecular material based on the co-crystallization of NDI-Δ and coronene (COR, Fig. 1b). Owing to the good match of their molecular sizes, the electron acceptor NDI-Δ and the electron donor COR can form two COR-NDI-Δ co-crystals (CNCs) with different morphologies-triangular and quadrangular in shapewhich have been denoted by CNC-T and CNC-Q, respectively. The selective co-crystallization can be controlled by varying both the nature of solvents and the donor-acceptor stoichiometries. Analyses of the solid-state superstructures reveal that CNC-Q exhibits a more efficient donor-acceptor [π···π] overlap compared with that of CNC-T, which engenders a stronger charge-transfer interaction in CNC-Q. Consequently, CNC-Q has a narrower bandgap and emits deep-red and NIR fluorescence centered on 668 nm, while CNC-T displays deep-red fluorescence with a peak at 638 nm. The TPA properties of NDI-Δ and COR are retained in the co-crystals. Benefiting from intermolecular charge-transfer interaction, CNC-T and CNC-Q possess higher TPA crosssections and longer two-photon excitation wavelengths that extend up into the NIR-II region when compared to their individual components. Overall, CNC-T and CNC-Q, not only constitute two rare co-crystals that exhibits TPA, as well as deep-red and NIR emission, but also serve as a powerful tool for uncovering the superstructure-property relationships. This investigation provides insights into tuning the optical properties in supramolecular systems and sheds light on the possibility of employing co-crystallization as a strategy for the production of multifunctional materials.

Results
Growth of NDI-Δ crystals and NDI-Δ-based co-crystals. NDI-Δ molecules are known 42 to adopt different packing arrangements in different solvents, indicating that their selection wields a significant influence on the crystallization of NDI-Δ molecules. In order to slow down the rate of crystal growth and obtain highquality crystals of NDI-Δ, PhCl was selected as the solvent because of its high boiling point. Upon slow evaporation of PhCl, colorless one-dimensional (1D) needle NDI-Δ crystals were obtained ( Supplementary Fig. 19). Single-crystal X-ray diffraction (XRD) analysis of the crystals reveals ( Supplementary Fig. 11 Fig. 18a) of the NDI-Δ crystals is consistent with the simulated pattern based on the single-crystal XRD data, indicating the high quality of the NDI-Δ crystals.
COR, an aromatic electron donor with good optoelectrical properties ( Supplementary Fig. 21) 45,46 , possesses a strong ability 38 to interact with electron acceptors. Owing to the larger size of COR compared to that of the NDI-Δ cavity, COR is only capable of interacting with the outer surface of NDI-Δ by means of [π···π] interactions. This mode of packing will increase the [π···π] overlap throughout the entire superstructure, enriching the potential optoelectrical properties of the co-crystals. Hence COR is employed to enter into co-crystallization with electronaccepting NDI-Δ molecules. High-quality crystals of COR could be grown ( Supplementary Fig. 18b) by slow evaporation of its CH 2 Cl 2 solution. These crystals also exhibit (Supplementary Fig. 19) a 1D morphology.
The electron acceptor NDI-Δ and the COR donor, as a result of intermolecular charge transfer interactions, form (Supplementary Fig. 20) selectively two COR-NDI-Δ co-crystals (CNCs). One of them exhibits a unique triangular morphology, and the other possesses a quadrangular shape ( Supplementary Fig. 19). Based on their morphologies, the two CNCs were named CNC-T and CNC-Q, respectively. The CNCs were found to be sensitive to the crystallization solvents and the respective donor-acceptor stoichiometries used in their preparation. For example, with a donor-acceptor molar ratio of 1:2, CNC-T can be obtained ( Supplementary Fig. 18c) selectively by slow vapor diffusion of MeOH into a THF solution. Alternatively, with a donor-acceptor molar ratio of 1:1, CNC-Q can be obtained ( Supplementary  Fig. 18d) selectively by slow vapor diffusion of Et 2 O into a CH 2 Cl 2 solution.
The fluorescence microscopy images reveal ( Fig. 1c-f) that both CNC-T and CNC-Q emit bright red fluorescence, which is significantly different from the green fluorescence of individual NDI-Δ and COR crystals, indicating the influence of cocrystallization upon the optical behavior. With identical supramolecular co-constitutions but different donor-acceptor stoichiometries, CNC-T and CNC-Q serve as ideal models to unravel the superstructure-property relationships 47 in these co-crystals. Meanwhile, reports relating to the influence of donor-acceptor stoichiometry on the luminescence behavior of co-crystals are rare 48,49 . These facts motivated us to gain in-depth understanding to the superstructures and optical properties of CNC-T and CNC-Q.
Solid-state superstructures and morphologies of co-crystals. Single-crystal XRD analysis of CNC-T, in which the molar ratio between the donor and acceptor is 1:2, reveals that it belongs (Supplementary Table 3) to the monoclinic C2 space group. NDI-Δ and COR adopt (Fig. 2a) Fig. 13) the cyclohexano hydrogen atoms in NDI-Δ and the plane of COR with distances ranging from 2.60 to 2.88 Å. The donor-acceptor pairs of COR and NDI-Δ stack in a 1D columnar superstructure (Fig. 2c), through [C−H···O] hydrogen bonding between aromatic hydrogen and carbonyl oxygen atoms in two adjacent NDI-Δ molecules  CNC-T displays a triangular morphology, an observation which is not common in organic crystals. In order to gain more insight into the formation of this geometry, powder XRD analysis and morphology simulation were carried out on CNC-T. The powder XRD pattern of CNC-T, grown on a glass substrate, displays (Supplementary Fig. 18c) strong (001) and (002) diffraction peaks, indicating 35 that the triangular growth face of the co-crystal is parallel to the (00l) lattice plane. This experimental data is confirmed by the simulated morphology of the co-crystals. CNC-T possesses ( Supplementary Fig. 14) an isosceles triangular geometry, wherein the (001) and (00-1) growth faces account for (Supplementary Table 1) the largest facet area percentage of 42.5% as a result of their lowest attachment energy (E att ). The vertex angle of a simulated isosceles triangle is 62°, an angle which is consistent with that (62°) between the (110) and (1-10) lattice planes observed (Supplementary Fig. 15) in the single-crystal XRD data. Benefiting from the high symmetry in the C2 space group, the (110) and (1-10) growth faces display identical E att and the exposed facet area percentage in the simulated morphology, so that CNC-T adopts an isosceles triangular geometry.
In contrast, CNC-Q, with a 1:1 donor-acceptor stoichiometry, crystallizes (Supplementary Table 3) in a triclinic P1 space group. With the change in donor-acceptor ratio, NDI-Δ molecules are surrounded (Fig. 3a) by one more equivalent of COR molecules in CNC-Q than that observed in CNC-T. This stoichiometry  Table 2) −64.3, −66.4, and −81.0 kcal/ mol, respectively. These energies lead to the percentages of their exposed facet areas in the simulated morphology being 34.6, 33.6, and 26.8%, respectively, explaining why we observe the quadrangle-shaped CNC-Q.
In summary, comparing these two co-crystals, we can conclude that (i) NDI-Δ and COR prefer to adopt a face-to-face packing motif driven by charge-transfer interactions even in different solvents, (ii) NDI-Δ is prone to assemble into 1D supramolecular arrays supported by multiple [C−H···O] hydrogen bonds, and (iii) alteration in donor-acceptor stoichiometries results in dramatic differences in the solid-state superstructures and morphologies.
Absorption and fluorescence spectra. In order to elucidate the photophyscial properties of CNC-T and CNC-Q, solid-state UV-Vis absorption and fluorescence spectra were recorded. NDI-Δ crystals show (Fig. 4a) strong absorption in the region of 240-420 nm, and COR crystals absorb primarily at 240-450 nm. Distinctive absorption spectra were observed after co-crystallization. CNC-T exhibits a broad absorption ranging from 240 to 596 nm, which is significantly red-shifted in comparison with the individual NDI-Δ and COR crystals, on account of the intermolecular charge-transfer interaction in the co-crystal. By contrast, the absorption band of CNC-Q extends up to 617 nm, which is 21 nm red-shifted compared to that of CNC-T. This difference may arise from a more efficient donor-acceptor [π···π] overlap in the solidstate superstructure of CNC-Q than in that of CNC-T.
Fluorescence spectra reveal (Fig. 4b) that the two co-crystals display a red-shifted emission compared to that of the individual molecular crystals, an observation which is in agreement with the fluorescence microscopy images (Fig. 1). NDI-Δ and COR crystals show green fluorescence with emission peaks centered on 488 and 506 nm, respectively. Their corresponding solid-state photoluminescence quantum yields (PLQYs, Ф F ) are 1.4 and 3.2%. In comparison with their solution-state fluorescence spectra (Supplementary Fig. 21), the solid-state fluorescence spectra of NDI-Δ and COR crystals are red-shifted, on account of their particular packing modes in the solid state 50 . NDI-Δ molecules have a rigid triangular geometry, which prevents the formation of H-type aggregates, while COR molecules adopt ( Supplementary Fig. 12) a slipped face-toface packing mode with J-type aggregation in their crystalline state. CNC-T exhibits (Fig. 4b) deep-red fluorescence 51 with a peak at 638 nm, while CNC-Q displays (Fig. 4b) deep-red and NIR fluorescence with a maximum emission wavelength at 668 nm, which is red-shifted by 162 nm compared to that of the COR crystals. The solid-state PLQYs of CNC-T and CNC-Q are 0.9 and 2.2%, respectively, values which are comparable to those of the individual component crystals. These observations underline the viability of the co-crystallization strategy in producing solidstate NIR functional materials 11,52 . Time-resolved fluorescence measurements reveal that both CNC-T and CNC-Q exhibit ( Supplementary Fig. 22) a double-exponential fluorescence decay curve with an average lifetime of 11.4 and 9.7 ns, respectively. The radiative rate constant (k r ) and non-radiative rate constant (k nr ) of CNC-T are (Supplementary Table 4   Two-photon absorption. TPA is a third-order nonlinear optical process, which occurs upon exposure of materials to highintensity lasers. Upon excitation by a 700 nm laser, NDI-Δ crystals were observed (Fig. 6a) by a two-photon microscope. Their emission was collected in the green detection channel (detection region: 470-550 nm), corresponding closely to their fluorescence emission (488 nm). Similar fluorescence emission by NDI-Δ crystals can also be detected (Fig. 6b-d) in the green channel of the two-photon microscope when excited at 800, 900, and 1000 nm. These observations indicate that NDI-Δ crystals are capable of emitting light at a shorter wavelength upon excitation at a longer wavelength, a process which corresponds to photon upconversion. When the excitation wavelength is fixed at 740 nm, the fluorescence intensity of NDI-Δ crystals is proportional to the square of the incident laser power (Fig. 7a and Supplementary  Fig. 23), implying that the upconversion emission of NDI-Δ crystals originates from a TPA process 53 . COR crystals display a similar TPA process (Fig. 6e-h) to that of NDI-Δ crystals. Upon excitation at 700, 800, 900, and 1000 nm, the upconversion emission by COR crystals, which agrees with their fluorescence emission (506 nm), is also collected in the green detection channel. At a fixed excitation wavelength of 740 nm, the fluorescence intensity of COR crystals increases ( Fig. 7b and Supplementary Fig. 24) linearly with the square of laser power, indicating an active TPA process. Similarly, the two co-crystals also exhibit nonlinear optical responses. At laser irradiation from 700 to 1000 nm, the upconversion emission of CNC-T is collected (Fig. 6i-l) in the red detection channel (detection region: 550-650 nm), which corresponds closely to the fluorescence emission (638 nm) of CNC-T. At a fixed excitation wavelength of 1000 nm, the fluorescence intensity of CNC-T displays ( Fig. 7c and Supplementary Fig. 25) a linear dependence on the square of the laser power. The TPA of CNC-Q is also detected (Fig. 6m-p) by two-photon imaging in the red channel, in accordance with its fluorescence emission band in the region of 580-950 nm. The corresponding excitation power dependence of fluorescence intensity is illustrated in Fig. 7d and Supplementary Fig. 26. In addition, the TPA of the co-crystals is further supported by time-dependent densityfunctional theory (TDDFT) calculations (Supplementary Fig. 35 and Table 6). In the calculated one-photon absorption spectra, the lowest-energy excited state of CNC-T corresponds to the wavelength of 677 nm with a negligible oscillator strength of 0.009 a.u.. CNC-Q exhibits three lowest-energy excitations at the wavelength of 725, 770, and 827 nm, with quite small oscillator strengths of 0.027, 0.001, and 0.020 a.u., respectively. Consequently, the emission of the co-crystals at excitation wavelengths of 1000 nm stems mainly from the TPA rather than the one-photon absorption of their lowest-energy excited states.
Taking into consideration that the TPA is governed by different quantum-mechanical rules, in comparison with onephoton absorption, the TPA spectra can display distinct line shapes compared to their one-photon spectra 54 . The two-photon excitation spectra of these crystals were recorded to explore the excitation wavelength dependence of their upconversion emission intensity . For this purpose, an in-situ two-photon imaging experiment was conducted at a constant laser power, while the laser excitation wavelengths were varied in the range of 700-1000 nm by intervals of 20 nm. The upconversion emission intensity was collected from the same sample region and then plotted as the function of the excitation wavelength. The resulting two-photon excitation spectra (Fig. 8) reveal that NDI-Δ and COR crystals display the strongest upconversion fluorescence at 700 nm. In sharp contrast, the twophoton excitation spectra of CNC-T and CNC-Q exhibit a similar shape with peaks centered on 980 nm. These profiles indicate that co-crystallization leads to a red-shifted TPA spectrum compared to the individual molecular crystals. Remarkably, CNC-Q serves as a co-crystal that exhibits two-photon response and NIR emission simultaneously, implying that the co-crystallization strategy serves as a convenient and efficient design approach towards multifunctional optical materials.
Two-photon excitation spectra simulations. Second linear response TDDFT calculations were performed using an in-house code to gain a theoretical understanding of the TPA spectrum 55,56 . The calculated TPA spectra (Fig. 9) of all four materials are consistent with the experimental results (Fig. 8). The NDI-Δ crystals display a broad TPA spectrum in the region of 600-800 nm, and exhibit a maximum TPA cross-section (σ TPA ) of 60 GM at 690 nm. The COR crystals display a sharp twophoton excitation peak at 658 nm with a weak σ TPA of 8.8 μGM.
The maximum σ TPA of CNC-T and CNC-Q are 1939 GM at 643 nm and 256 GM at 624 nm, respectively. These values are 32 and 4.3 times larger than that for NDI-Δ crystals. CNC-T possesses higher σ TPA than that for CNC-Q, a difference which may arise from the fourth-power dependency of σ TPA on the transition dipoles and the average values of transition dipoles for CNC-T are 48% higher than those for CNC-Q. Moreover, in the calculated TPA spectra of the co-crystals, a new absorption band was identified in the range from 1000 to 1300 nm in the NIR-II region 57,58 , with a maximum σ TPA of 92 GM at 1290 nm and 65 GM at 1177 nm for CNC-T and CNC-Q, respectively. The possible reasons for the increased TPA cross-sections and red-shifted TPA spectra of co-crystals include the following. (i) The donor and acceptor molecules adopt a face-to-face packing motif, facilitating the [π···π] overlap throughout the entire superstructure. (ii) The intermolecular charge-transfer interaction induces the π-electron delocalization from the donor to the acceptor molecules, contributing to the supramolecular electronic polarization in the co-crystals 53,59 . These results imply that the design of charge transfer co-crystals emerges as an alternative approach for the synthesis of TPA materials with enhanced twophoton response. In the rational design of two-photon excited NIR emissive co-crystals, two fundamental points can be taken into consideration-namely, selecting TPA-active precursors in order to induce nonlinear optical properties, and introducing intermolecular charge-transfer interactions in order to achieve NIR emission and enhanced two-photon responses.

Discussion
We have applied a supramolecular approach to the design of twophoton excited deep-red and NIR emissive materials based on the co-crystallization of NDI-Δ and COR. Two charge transfer cocrystals, CNC-T and CNC-Q, have been obtained by controlling  the nature of the solvents and the donor-acceptor stoichiometries. These co-crystals provide an example of how to gain better insights, through experiments supported by theory, into the relationship between the superstructures of materials and their properties. By altering the donor-acceptor ratio from 1:2 (CNC-T) to 1:1 (CNC-Q), the intermolecular charge-transfer interactions become stronger and the energy bandgap becomes narrower in CNC-Q. Hence CNC-Q exhibits deep-red and NIR emission centered on 668 nm, while CNC-T emits deep-red fluorescence with peak at 638 nm. The TPA properties of the co-crystals are enhanced compared to those of the individual molecular crystals because of the intermolecular charge-transfer interactions. The CNC-T and CNC-Q co-crystals, not only exhibit red-shifted TPA spectra in the NIR-II region, but also possess larger TPA crosssections. Notably, the CNC-Q co-crystal emerges as an innovative two-photon excited NIR-emissive supramolecular material. The co-crystallization strategy presented here possesses the distinct advantage that comes with noncovalent synthesis, providing as it does a facile modular approach to advanced smart materials with multiphoton absorption and tunable emission properties.

Methods
Materials. All chemicals and solvents were purchased from commercial companies and used directly without further purification. (RRRRRR)-NDI-Δ-namely NDI-Δ employed in this research-was synthesized and purified following methods 41 as shown in Supplementary Fig. 1. Coronene (C 24 H 12 , 97%), defined as COR, was purchased from Sigma-Aldrich. Nuclear magnetic resonance (NMR) spectra were recorded on a Agilent 500 MHz spectrometer with a working frequency of 500 MHz in the case of 1 H NMR spectroscopy. Chemical shifts are reported in ppm relative to the signals corresponding to the residual non-deuterated solvents (CDCl 3 : δ 7.26 ppm).
Preparation of co-crystal CNC-T. NDI-Δ (20.8 mg, 20 μmol) was first of all mixed with COR (3.0 mg, 10 μmol) in THF (20 mL) and dissolved by ultrasonic treatment (Supplementary Fig. 9). The solution was filtered with a 0.22-μm syringe filter to remove insoluble impurities. With slow vapor diffusion of MeOH into the filtered solution, high quality red triangle-shaped co-crystals formed after one week.
Preparation of co-crystal CNC-Q. NDI-Δ (20.8 mg, 20 μmol) was first of all mixed with COR (6.0 mg, 20 μmol) in CH 2 Cl 2 (20 mL) and dissolved by ultrasonic treatment (Supplementary Fig. 10). The solution was filtered with a 0.22-μm syringe filter to remove the insoluble impurities. With slow vapor diffusion of Et 2 O into the filtered solution, high quality red quadrangle-shaped co-crystals formed after one week.
Optical and fluorescence microscopies. Optical and fluorescence microscopy images were obtained at room temperature with a Nikon LV150, which was equipped with a high-intensity white light LED source and a 5 mega pixel color camera for image acquisition. Optical microscopy pictures were captured in the bright field mode. Fluorescence microscopy images were captured in the fluorescence mode.
Powder X-ray diffraction analysis. Powder X-ray diffraction (PXRD) was carried out on a STOE STADI MP powder diffractometer, which was equipped with an asymmetric curved Germanium monochromator (Cu K α1 radiation, λ = 1.54056 Å) and a one-dimensional silicon strip detector (MYTHEN2 1K from DECTRIS). The line focused Cu X-ray tube was operated at 40 kV and 40 mA. Samples of micro/ nano-crystals were grown on glass substrates. NDI-Δ crystals were prepared by slow evaporation from a PhCl solution. COR crystals were prepared by slow evaporation from a CH 2 Cl 2 solution. CNC-T was prepared by slow vapor diffusion of MeOH into a THF solution with a 1:2 donor-acceptor molar ratio. CNC-Q was prepared by slow vapor diffusion of Et 2 O into a CH 2 Cl 2 solution with a 1:1 donor-acceptor molar ratio. Paratone oil was used to protect the crystals. Experiments were carried out in reflection geometry mode at room temperature. The simulated powder XRD patterns with Cu K α1 radiation were carried out by Mercury software 4.3.1.
Photophysical characterization. Solution UV-Vis absorption spectra were measured on a UV-3600 Shimadzu spectrophotometer at room temperature. Solution fluorescence spectra were recorded on a HORIBA FluoroMax-4 spectrometer at room temperature. Solid UV-Vis absorption spectra were measured in reflection mode at room temperature on a Shimadzu 3600 UV-visible-NIR spectrophotometer equipped with an integrating sphere. Solid fluorescence spectra were performed with a HORIBA Fluorolog-3 spectrometer. Fluorescence lifetime measurements and solid-state absolute photoluminescence quantum yields were obtained using a HORIBA FluoroMax-4 spectrometer equipped with an integrating sphere (HORIBA Quanta-φ).
Raman spectroscopy. Raman spectra were carried out on a HORIBA LabRAM HR Evolution Confocal Raman instrument. The system was equipped with (i) NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-020-18431-7 ARTICLE multi-laser (473, 532, 633, and 785 nm), (ii) a confocal microscope for high spatial resolution, (iii) a Raman spectrometer detector for high spectral resolution and wide spectral range analysis, (iv) a high-precision DuoScan imaging instrument and (v) an electron multiplying CCD in order to enhance the measured S/N ratios. Two-photon microscopy. The upconversion emission and TPA-related measurements were performed on a Nikon A1R-MP + Multiphoton Microscope with penetration depth up to 1.5 mm. The microscope was equipped with a tunable Chameleon Vision titanium sapphire laser from 700 to 1000 nm. In addition, the GaAsP detectors were applied for increased sensitivity. The resonant scanner was capable of scanning up to~400 frames per second.
Density functional theory computational methods. Structures for the singlemolecule calculations were obtained from X-ray single crystal diffraction data. All electron density functional theory (DFT) single point calculations were performed at the B3LYP/TZP level in the Amsterdam Density Functional program (ADF, version 2018.104) [60][61][62] . The orbital surfaces were visualized with ADFView. The TPA spectra were computed by second linear response TDDFT (SLR-TDDFT), an in-house code implemented within the NWChem suite 63 . This theory computes transition dipoles between different excited states with a computational cost similar to that of traditional linear-response (LR) TDDFT calculations. SLR-TDDFT Calculations can be performed by either "relaxing" the orbitals of the system, or by utilizing an unrelaxed scheme in which the excited-state transition dipoles are determined by a simple numerical differentiation procedure 55 . Given the size of the molecules, in this work the unrelaxed method was used on account of its computational efficiency. In principle, the unrelaxed method is equivalent to employing the auxiliary Casida wave functions 64 , but they can be reliably accurate 65 . For these calculations, the exchange-correlation functional LDA0 was used 66 . This functional-for optical properties-is as accurate as B3LYP, and it provides an additional speed-up for the calculations, which is critical in this case, given the relatively large number of atoms and excited states, especially for CNC-Q. The SLR-TDDFT requires as a first step a regular LR-TDDFT calculation under the Tamm-Dancoff approximation. Also, for computational convenience, the double-ζ basis set and effective-core potential SBKJC were applied. The Davidson convergence threshold is 10 −3 for COR and NDI-Δ, and 10 −2 for CNC-T and CNC-Q. This requirement guarantees the energies are accurate up to a fraction of a meV. In the LR-TDDFT calculation, we neglect virtual orbitals with energies above 12 and 8 eV for CNC-T and CNC-Q, respectively. These ranges are sufficient to cover the TPA spectra: the excited state with largest energy is below 4.14 eV. The SLR-TDDFT algorithm provides all the transition dipoles required to compute the TPA cross-section as a function of the photon wavelength. We assume random circularly polarized light interaction. The frequency-dependent TPA cross-section was computed using the formula for this type of light interaction 67,68 . We assume a Lorentzian line shape function, a broadening factor of 0.05 eV for virtual states, and 0.1 eV for the final states.

Data availability
All the data supporting the conclusions are included in this article and its Supplementary files, or are available from the authors upon reasonable request. The single-crystal diffraction data for NDI-Δ, CNC-T and CNC-Q have all been deposited in the Cambridge Crystallographic Data Centre (CCDC). The deposition numbers are CCDC 2004158-2004160, respectively.

Code availability
The two-photon absorption post-processing code used in this article is available at https://gitlab.com/plusxmartin/insomnia. Received: 18 May 2020; Accepted: 21 August 2020;