Precise Regulation of Distance between Associated Pyrene Units and Control of Emission Energy and Kinetics in Solid State

Open AccessCCS ChemistryRESEARCH ARTICLE1 Dec 2021Precise Regulation of Distance between Associated Pyrene Units and Control of Emission Energy and Kinetics in Solid State Jiaqiang Wang, Qianxi Dang, Yanbin Gong, Qiuyan Liao, Guochang Song, Qianqian Li and Zhen Li Jiaqiang Wang Sauvage Center for Molecular Sciences, Department of Chemistry, Wuhan University, Wuhan 430072 Google Scholar More articles by this author , Qianxi Dang Sauvage Center for Molecular Sciences, Department of Chemistry, Wuhan University, Wuhan 430072 Google Scholar More articles by this author , Yanbin Gong Sauvage Center for Molecular Sciences, Department of Chemistry, Wuhan University, Wuhan 430072 Google Scholar More articles by this author , Qiuyan Liao Sauvage Center for Molecular Sciences, Department of Chemistry, Wuhan University, Wuhan 430072 Google Scholar More articles by this author , Guochang Song Sauvage Center for Molecular Sciences, Department of Chemistry, Wuhan University, Wuhan 430072 Google Scholar More articles by this author , Qianqian Li Sauvage Center for Molecular Sciences, Department of Chemistry, Wuhan University, Wuhan 430072 Google Scholar More articles by this author and Zhen Li *Corresponding author: E-mail Address: [email protected] E-mail Address: [email protected] Sauvage Center for Molecular Sciences, Department of Chemistry, Wuhan University, Wuhan 430072 Institute of Molecular Aggregation Science, Tianjin University, Tianjin 300072 Joint School of National University of Singapore and Tianjin University, International Campus of Tianjin University, Fuzhou 350207 Google Scholar More articles by this author https://doi.org/10.31635/ccschem.020.202000556 SectionsSupplemental MaterialAboutAbstractPDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareFacebookTwitterLinked InEmail Many approaches have been explored to tune emission behaviors of organic luminogens. However, precise regulation of distances in dimers is seldom reported. Here, four pyrene derivatives are presented, and we precisely regulate the distance between pyrene units of X2P. Its crystal manifests unusual deep-blue excimer emission at 424 nm, while the crystal of X1P with only one pyrene unit for each molecule gives sky-blue emission with a maximum emission peak at 475 nm, which even shows an unexpected bathochromic shift effect compared with the emission of the needle crystal of X2EP with the largest conjugated structure and tunable tristate kinetics of excimer emissions upon different stimuli. Notably, the excimer decay time of the X2P crystal (26.4 ns) is apparently shorter than that of the X1P crystal (106.0 ns). The qualitative and quantitative analysis of π–π interactions with different distances between pyrene units in crystals was performed for the first time, leading to the conclusion that short distance and strong π–π interactions are vital to lower excited-state energy and weaken delayed fluorescence. This study introduces an easy and efficient way to precisely regulate distances in dimer and control the emission energy and kinetics of the decay process in the solid state for unique applications, as well as to predict the distance based on emission wavelength. Download figure Download PowerPoint Introduction Optoelectronic materials work in liquid, solid, and even gaseous physical states. However, under most circumstances, materials play a certain role as aggregates.1–5 It is common that materials have very different photophysical properties in the aggregated state, especially in crystals with orderly arrangements, from those in solution.6–11 For example, the emission color of pyrene in dilute solution is bluish violet, which could be assigned to the monomolecular emission with a maximum emission wavelength at 375 nm, whereas the pyrene crystal exhibits maximum emission wavelength at 468 nm.12,13 It is clear that in crystal there are π–π interactions between two adjacent pyrene molecules as dimers with a distance between two pyrene planes of 3.528 Å (Figure 1).12 Actually, for other luminogens, strong intermolecular interactions also influence the emissive behaviors of luminogens to a large degree.14–17 Figure 1 | The design schematic of pyrene derivatives to precisely regulate the π–π interactions in crystals and the distance between pyrene substituents, the maximum emission wavelength and the corresponding inherent excimer decay time of X1P and X2P crystals. The photographs of crystals were taken upon excitation at about 365 nm by optic microscope Leica M123. Download figure Download PowerPoint Recently, extensive studies have been carried out to explore the links between some interesting phenomena and crystal packing modes, such as aggregation-induced emission (AIE), mechanochromism (MC), mechanoluminescence (ML), and room-temperature phosphorescence (RTP).18–23 Thanks to the efforts of scientists, many ways have been found to change the structure of compounds to influence the packing modes of crystals so as to achieve different properties.24–29 For instance, dimers, as one of the most important types in crystal packing, are always mentioned, and a great deal of research focuses on how to tune the π–π interactions in them.30–36 Nevertheless, this research does not focus on controlling the distance of π-planes in dimers and precisely regulating the π–π interactions, while such results are likely to provide new insights on new molecular design with expected molecular packing in aggregates. Since the distance of the naturally formed dimers in single crystals could not be conveniently controlled, we considered the introduction of a typical aromatic compound to a special frame with adjustable distance between π-planes by changing the molecular structure. Pyrene has been used as an important research model for fundamental research as well as a common luminogen for practical applications, such as sensors, organic light-emitting diodes (OLEDs), organic field-effect transistors (OFETs), and organic photovoltaic cells (OPVs).37–41 As mentioned above, a significant difference of emission color can be observed in pyrene crystal compared with its dilute solution, due to the formation of excimers. In addition, combined with the triplet–triplet annihilation (TTA) process, there are also long-lived excited states.42–45 Actually, the control of emission energy and lifetime is a distinct advantage for designing materials with special optoelectronic properties in the solid state.46–48 However, it is still unclear what the influence of distances between π-conjugated planes in pyrene excimers is on their photophysical properties in solid state, let alone the qualitative and quantitative analysis of their π–π interactions in the solid state. Accordingly, we designed and synthesized four pyrene derivatives of X1P, X2P, X1EP, and X2EP by using xanthene as the template frame (Figure 1 and Scheme 1). After introducing the pyrene rings to 4- and 5-positions of xanthene simultaneously, the fixed distance between pyrene units of intramolecular excimer in the X2P crystal could be kept, and the precise regulation of π–π interactions in the dimer-like structure was partially realized. Scheme 1 | Synthetic approach to the four pyrene derivatives. Download figure Download PowerPoint In the X2P crystal, the distance between pyrene units is determined to be 3.675 Å with maximum emission wavelength at 424 nm, while in crystal of X1P with only one pyrene unit for each molecule, the maximum emission wavelength is 475 nm, and there are intermolecular pyrene excimers existing with distance between pyrene units to be 3.358 Å. Besides, the excimer decay time (τE) of the X2P crystal (26.4 ns) is much shorter than that of the X1P crystal (106.0 ns), leading to different orders of magnitude of the rate constant of excimer decay and intersystem crossing (ISC). The influence of different distances between associated pyrene units on noncovalent interactions (NCIs) was investigated by the qualitative and quantitative analysis for the first time. We found that longer distance reduced repulsion between pyrene units and weakened π–π interactions, which contributed to shorter τE and longer lifetimes for delayed fluorescence. Experimental Methods Synthesis The synthetic approach to the four pyrene derivatives is presented in Scheme 1. Using xanthene as the template frame, pyrene substituents were bonded to its 4- and 5-positions, through Suzuki coupling reactions between Xan-2Br and Py-Bpin to yield X1P and X2P. Tertiary butyl groups were introduced to prevent the bromination reacting at 2,7-position and offer good solubility for target compounds. The bromo atom was removed by treating X1P-Br with n-butyllithium (n-BuLi) and H2O to produce X1P. We used alkynylene substituents to improve the flexibility of the compounds to some extent and verify the important role of a rigid xanthene frame in precisely regulating the distance between pyrene substituents. Thus, X1EP and X2EP were prepared through Sonogashira coupling reactions between 1-bromopyrene and xanthene derivatives. Detailed synthetic procedures and characterization of the compounds are presented in the Supporting Information Figures S35–S52. Characterization 1H and 13C NMR spectra were recorded on a 400 and 600 MHz Bruker ASCEND spectrometers (Bruker Corporation, Switzerland). Elemental analyses of carbon and hydrogen were measured on a PerkinElmer microanalyzer (PerkinElmer, United States). Mass spectra were measured on a Thermo DSQ II GC/MS spectrometer (ThermoFinnigan, California, United States). UV–vis spectra were measured on a Shimadzu UV-2550 (Shimadzu Corporation, Kyoto, Japan). Photoluminescence (PL) spectra and low-temperature delayed spectra were performed on a Hitachi F-4600 fluorescence spectrophotometer (Hitachi Ltd, Tokyo, Japan). The powder X-ray diffraction (PXRD) patterns were recorded by a Bruker D8 ADVANCE using Cu-Kα radiation from 5 to 50°. The single-crystal XRD data were collected in a Bruker Smart APEX CCD diffractometer. The ML spectra were collected from an Ocean Optics QE65 Pro spectrometer (Ocean Optics, Inc., Dunedin, FL, United States). Lifetimes monitoring at the maximum emission wavelengths were determined with an Edinburgh Instruments FLS980 spectrometer (Edinburgh Instruments Ltd., Livingston, United Kingdom) by fitting time-correlated single-photon counting (TCSPC) data, and PL quantum yields were determined by FLS980 spectrometer with an integrating sphere. Time-dependent density functional theory (TD-DFT) calculations were performed on the Gaussian 09 program (Revision D01). The NCI analysis was performed for studying weak interaction in the single crystals.49 The hydrogen atoms in single crystals were positioned by constraint optimization at B3LYP-D3(BJ)/6-311G* level, and the NCI analysis was investigated via Multiwfn50 and VMD (Visual Molecular Dynamics) programs. Energy decomposition analysis based on molecular force-field (EDA-FF) methods was proposed by the Multiwfn author, which could decompose the total interaction energy into disparate energy terms with exact physical significance. The ground-state (S0) geometries were optimized with Becke’s three-parameter exchange functional along with the Lee Yang Parr’s correlation functional (B3LYP) using 6–31G (d) basis sets. Results and Discussion The UV–vis absorption spectra of these four compounds were measured in tetrahydrofuran (THF) solution. Similar absorption bands for X1P and X2P as well as for X1EP and X2EP disclosed their similar electronic structures, respectively, while X1EP and X2EP have larger conjugated structures ( Supporting Information Figure S1a). Distinctly different from their similar absorption spectra, the PL spectra of the four compounds in solution all have different emission peaks ( Supporting Information Figure S1b). The solutions of X1P and X1EP exhibit multiple emission peaks with maximum emission wavelengths at 386 and 400 nm, respectively. However, the structureless PL spectra of the other two compounds show emission peaks at 435 nm for X2P and 503 nm for X2EP. These peaks should be ascribed to intramolecular excimer emissions, as further confirmed by the appearance of new emission peaks at longer wavelength regions for X1P and X1EP in THF/water mixture solvent with a high water fraction and in a THF solution with high concentration ( Supporting Information Figures S2 and S3) and the absence of any spectral changes in the PL spectra for X2P and X2EP in THF/water mixture solvent with different water fraction and in the THF solution with different concentrations ( Supporting Information Figures S4 and S5).13,51–53 Crystals of the four compounds were cultured from mixture solvents of THF and methanol, including two kinds of crystals of X2EP (one is bulk-like while the other is needle-like). As shown in Figures 2a–2e, the X1P crystal presents its maximum emission peak at 475 nm with a shoulder peak at about 420 nm, while the emission peak of the X2P crystal locates at 424 nm, which is blue-shifted to a great extent in comparison with the X1P crystal. Thus, even though there are more pyrene units in the chemical structure of X2P, it exhibits an obviously bluer fluorescence (see inset pictures in Figures 2a and 2b). The calculated CIE (Commission internationale de l'éclairage) coordinates in CIE 1931 color space chromaticity diagram facilitate a quantitative analysis of the emission color ( Supporting Information Figure S11). The emission is calculated at CIE coordinates of (0.16, 0.20) for X1P crystal and (0.16, 0.07) for X2P crystal. It is worth mentioning that the needle crystals of X2EP show blue emission with CIE coordinates of (0.17, 0.12), demonstrating an even smaller y value than that of the X1P crystal regardless of the largest conjugated structure of X2EP. Figure 2 | (a and b) PL spectra of X1P crystal and X2P crystal (λex = 340 nm), respectively. (c–e) PL spectra of X1EP crystal, X2EP bulk crystal, and X2EP needle crystal (λex = 380 nm), respectively. Inset: The corresponding fluorescence images of them taken by optical microscope under 365 nm UV excitation. (f and g) The decay curves at the maximum emission wavelength of dilute solution of X1EP and X2EP (10−5 M in toluene) before and after removal of oxygen. Download figure Download PowerPoint To verify that the emissions of these crystals should be assigned to excimer emissions, we further make a comparison between the PL spectra of crystals, dilute solution (10−5 mol L−1), concentrated solution (10−1 mol L−1), and aggregation state ( Supporting Information Figure S6). Actually, the maximum emission wavelength and fluorescence lifetime of crystals are close to those of excimer emissions of the four compounds in solution or aggregation state. In addition, the broad and structureless emission bands of crystals indicate that they solely exhibit excimer emissions in the crystalline state as well ( Supporting Information Figures S6–S10). Interestingly, the crystals of the four compounds not only show different emission colors but also markedly different fluorescence lifetimes. In general, X1P and X2P crystals without alkynyl groups have much longer lifetimes than X1EP and X2EP crystals. From decay curves of crystals ( Supporting Information Figure S12), we find the significantly smallest excimer decay rate constant of X1P and its excimer lifetime (τE) is 106.0 ns. The τE of X2P crystal is 26.4 ns, which is dramatically decreased compared with that of X1P crystal. For the other three crystals, the excimer fluorescence has a shorter lifetime, and the values are presented in Table 1. Moreover, high PL quantum yields (PLQY; Φ) of the crystals could also be found. Table 1 | Fluorescence Lifetime, PLQY, Kinetic, and EDA Dataa of Crystals of X1P, X2P, X1EP, and X2EP Sample λem (nm) τE (ns) PLQY (%) kE (s−1) kr (s−1) kISC (s−1) EE (kJ/mol) ER (kJ/mol) ED (kJ/mol) X1P 475 106.0 25.7 9.43 × 106 2.42 × 106 7.01 × 106 3.84 44.16 −92.38 X2P 424 26.4 50.5 3.79 × 107 1.91 × 107 1.88 × 107 6.49 26.85 −76.37 X1EP 465 5.0 13.8 2.00 × 108 2.76 × 107 1.72 × 108 N/A N/A N/A X2EP-Bb 490 7.0 37.8 1.43 × 108 5.40 × 107 8.88 × 107 6.54 38.16 −91.14 X2EP-Nc 440 3.9 13.1 2.56 × 108 3.36 × 107 2.23 × 108 4.45 28.57 −70.29 aCalculated according to single-crystal data and not applicable for X1EP. bBulk crystal of X2EP. cNeedle crystal of X2EP. It is known that oxygen can quench the pyrene fluorescence and increase the rate of decay of the singlet excited states by promoting the ISC process from singlet to triplet, which is further quenched by oxygen54: Py S → Py T Py T + O 2 → Py The fluorescence decay curves of X1P, X2P, X1EP, and X2EP solution (10−5 mol L−1 in toluene) before and after removal of oxygen were further measured to verify the oxygen-sensitive property and different ISC process of these pyrene derivatives. The solution of X1P and X2P shows a similar fluorescence lifetime and intensity enhancing after nitrogen blowing ( Supporting Information Figure S13). However, the result after nitrogen blowing of the X1EP solution is differentiated from that of X2EP solution (Figures 2f and 2g). Obvious enhancement in both fluorescence lifetime and intensity could be observed in the X2EP solution after removal of oxygen, while they were almost unchanged for X1EP solution, indicating that excimer constituent reduces the energy gap between singlet and triplet due to the lower energy of the excimer state, which is in favor of the population of triplet excitons. At the same time, since the radiative transition process of X1P solution without excimer emission involves triplet excitons, this may also suggest that alkynyl groups might be harmful for conversion from singlet to triplet excited states. Here, alkynyl groups play a role in increasing the transition moment and enhancing the coupling of the singlet state to the ground state.55–57 The rate constants of the radiative transition from the S1 to S0 and the nonradiative transition from the S1 to Tn are calculated and presented in Supporting Information Table S1. As expected, after introducing the alkynyl group, the rate constant of the radiative transition from S1 to S0 was enhanced greatly for X1EP, while the nonradiative transition from S1 to Tn was also apparently decreased for X1EP and X2EP. Such results may lower the formation of the T1 state. The formation of intramolecular excimer and decrease of the energy gap between excited singlet and triplet states could increase the rate constant of the nonradiative transition, which could lead to the lower PLQY of X2EP. Generally, there are two types of delayed fluorescence, including E- and P-types.58–60 P-type delay fluorescence is so named because of its first discovery from pyrene and phenanthrene.61,62 The different ISC process also indicates that there might be a different TTA process and delayed fluorescence. The photophysical properties of the compounds at 77 K were further investigated. In frozen glassy 2-methyltetrahydrofuran at 77 K, only monomer emissions were found from steady PL spectra of X2P, X1EP, and X2EP in dilute solution (Figure 3a and Supporting Information Figure S14). This is reasonable, since the excimer formation will occur after excitation in dilute solution, and it is hard for this process to take place. An excimer emission peak is found on the steady PL spectrum of X1P solution, which is consistent with the maximum emission of the delayed luminescence spectra of X1P and X2P solution ( Supporting Information Figure S15). Such emissions should be classified as delayed excimer fluorescence, since pyrene derivative phosphorescence should be observed at around 600 nm.63,64 Such results indicate that more efficient TTA process happens in X1P solution, and the same emission of delayed fluorescence of X1EP and X2EP solution further suggests the pyrene-based TTA process. The efficient TTA and strong delayed fluorescence of X1P solution could be ascribed to the lack of π–π interactions constraining triplet excitons compared with X2P and X2EP. The more efficient conversion from singlet to triplet excited states than X1EP is also an important reason, which is consistent with results after being deoxygenated at room temperature. The situation in crystals is different (Figure 3b and Supporting Information Figure S16). X1P crystal exhibits blue-shifted emission at 77 K, which is similar to bulk crystal of X2EP with lower excimer emission energy at room temperature than those of other crystals with similar structure. The delayed fluorescence spectrum of X1P crystal is consistent with its steady PL spectrum at room temperature but different from that at 77 K, while the delayed fluorescence spectrum of X2P crystal is consistent with its steady PL spectrum at 77 K. Along with longer delayed fluorescence lifetime ( Supporting Information Figure S17), it suggests TTA is enhanced in X2P crystal. Figure 3 | (a) The steady PL spectra of X1P and X2P solution (10−5 mol L) at room temperature and 77 K and their delayed spectra at 77 K. (b) The steady PL spectra of X1P and X2P crystals at room temperature and 77 K and their delayed fluorescence spectra at 77 K. Download figure Download PowerPoint Single-crystal structures and molecular packing of the compounds were examined carefully so as to gain deeper insight into the origin of the above phenomena ( Supporting Information Figures S18–S22 and Table S2). Since the pyrene units in intramolecular excimers are not exactly parallel to each other, we define the distances between pyrene units as the longer distance from the center of one pyrene unit to another pyrene plane. Figures 4a and 4b show packing modes of crystal cells of X1P and X2P. In a single crystal of X1P, one crystal cell contains two kinds of dimers (dimer1 and dimer2), in which the pyrene units are parallel to each other with distances of 3.358 and 3.713 Å, respectively. There are four molecules with the same configuration in the crystal cell of X2P, and we found that pyrene units prefer to generate intramolecular dimer-like interactions rather than intermolecular dimers. In the molecule of the X2P crystal, the dihedral angle between two pyrene planes is 5.505°. As defined above, the distance between pyrene units is determined to be 3.675 Å, which is much longer than that in dimer1 of X1P crystals but slightly shorter than that in dimer2 (Figures 4a and 4b). Likewise, in bulk crystals of X2EP the dihedral angle between pyrene planes is 3.254°, and the distance between pyrene units is 3.528 Å. In needle crystals of X2EP, there are two different configurations, one of which shows a dihedral angle as large as 7.535° with a distance between pyrene units to be 3.638 Å, while that in another configuration is 2.394° with a distance of 3.634 Å ( Supporting Information Figure S22). Figure 4 | (a) Packing mode of X1P crystal and the distance between pyrene units in dimer1 and dimer2. (b) Packing mode of X2P crystal and the distance between pyrene units in the molecule. (c) Gradient isosurfaces for dimer1 in X1P crystal and the value of dispersion energy between pyrene units. (d) The scatter diagram for RDG versus sign(λ2)ρ of dimer1 in X1P crystal. (e) Gradient isosurfaces for molecule in X2P crystal and the value of dispersion energy between pyrene units. (f) The scatter diagram for RDG versus sign(λ2)ρ of molecule in X2P crystal. Download figure Download PowerPoint The π–π interactions between pyrene units as well as C–H···π interactions within the distance of 4 Å were also investigated. The amounts and distances of such interactions in each crystal cell are listed in Supporting Information Tables S3 and S4. Thus, it is significant to note that X1P crystals exhibit the shortest distances for π–π interactions (3.632–3.650 Å). Nonetheless, X2P crystals exhibit the most multiple interactions with relatively shorter distances, while in needle crystals of X2EP, there are fewer multiple interactions and relatively longer distances. Such multiple interactions might provide restrictions on nonradiative transition at room temperature and low temperature. Thus, a lower PLQY of the needle crystal of X2EP compared with its bulk crystal is found. In addition, the apparently lower PLQY of X1EP crystal compared with that of its dilute solution might be caused by the lack of such multiple interactions, while it should also be attributed to the enhancement of nonradiative transition after formation of excimer and the decrease of the energy gap between excited singlet and triplet states as mentioned above. In addition, some theoretical calculations were carried out to learn about the energy gaps and energy levels of the singlet and triplet states of the compounds. Both the calculated results of frontier molecular orbitals based on optimized structures ( Supporting Information Figure S24) and single-crystal data ( Supporting Information Figure S25) demonstrate that the electron clouds in the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) are mainly located on pyrene units, revealing the interruption of structural π-conjugation by the central xanthene core across the entire molecule and the subtle influence of the xanthene core on the compounds emissions. In Supporting Information Figure S24, we show that X2P and X2EP with symmetrical structures forming intramolecular excimers both have similar energy levels and molecular orbitals (MOs) for LUMO and LUMO+1 as well as for HOMO and HOMO-1, which could not be found on X1P and X1EP. The singlet and triplet energies are summarized in Supporting Information Tables S5 and S6 and Figures S27 and S28. NCIs can also be investigated by theoretical calculations. Figure 4c presents gradient isosurfaces for dimer1 in the X1P crystal, which depicts the multiple NCIs. We find that an area colored green lies between two pyrene units, while some isosurfaces colored red and green are located in the surrounding area of tertiary butyl and methyl groups. The colors of gradient isosurfaces are defined based on values of sign(λ2)ρ. Here, λ2 is the eigenvalue of the electron-density Hessian (second derivative) matrix, while ρ is the quantum-mechanical electron density. Thus, sign(λ2) could help to differentiate the bonded interactions (λ2 < 0) from nonbonded interactions (λ2 > 0), and ρ could help us learn about strength of interactions. When sign(λ2) is negative and the absolute value of it is large, it indicates the existence of strong-bonded interactions such as hydrogen bonds and isosurfaces with blue color. Conversely, large and positive values of sign(λ2) indicate the existence of nonbonded interactions and isosurfaces with red color. Green isosurfaces suggest that values of sign(λ2) are near zero and van der Waals interactions exist. Reduced density gradient (RDG) represents the deviation from a homogeneous electron distribution.45 Figure 4d illustrates that some green points and some red points lie in the area with low RDG values, indicating that π–π interactions occur between two pyrene units in dimer1 of X1P crystal exactly, and repulsive interactions also occur close to tertiary butyl and methyl groups. Similar results are found in molecules of the X2P crystal but it seems more green points with low RDG values have very near-zero values of sign(λ2) (Figure 4e and 4f). The EDA-FF provides quantitative analysis of such interactions (Table 1). Without a polar group, the crystals all show minor electrostatic potential energy (EE), while the X2P crystal has a much smaller value of dispersion energy (ED = −76.37 kJ/mol) than that of dimer1 in X1P crystal (ED = −92.38 kJ/mol), demonstrating weaker π–π interactions between pyrene units in our target molecule after we regulate their distance. It is worth mentioning that repulsive energy (ER) would also be larger with shorter distance between pyrene units. Furthermore, green isosurfaces could also be found between pyrene units in bulk and needle crystal of X2EP ( Supporting Information Figure S26) and the smallest value of dispersion energy among the four crystals could be calculated for needle crystal of X2EP. As th