Probe 1 as depicted in Fig. 1 is composed of an electron-donating anisole substituent and an electron-deficient tris(picolyl)amine Zn²⁺ receptor linked through an oxazole bridge. The tris(picolyl)amine unit often acts as the Zn²⁺ receptor in the TP probe. The nitrogen atom could coordinate with the zinc ion by donating a lone electron pair into an empty metal orbital. In probe 2, we replace the anisole donor with the dimethylamino terminal because the dimethylamino group has stronger ability to donate and transport electrons. In probe 3, the hydroxy group with weaker donation ability is used. These push-pull structures can improve the ICT and induce a large TPA response. The geometry optimization of probe 1 gives as many as six equilibrium conformations 1a--1f as shown in Fig. 2. The frequency calculations for these geometries do not produce any imaginary frequencies. It can be seen that the six isomers differ by the orientations of two picolyl groups at the end of the ligands. The optimized geometries of zinc complexes are also presented in Fig. 2. Two Cl⁻ ions are incorporated explicitly in order to include counter ion effects and give the charge-neutral complex.^[19,22] It is interesting to find that different coordination geometries are obtained. In Zn1a structure, the zinc ion prefers to chelate with four nitrogen atoms of the tris(picolyl)amine receptor to complete the six-coordination geometry. The bond length between the nitrogen atom and zinc ion has a typical value of 2.1 Å–2.3 Å, which is similar to the general x-ray crystal structure.^[35] The Zn1b and Zn1c have similar structures, in which the zinc ion connects with the three nitrogen atoms of the dipicolylamine group at the end of the ligands. The Zn1d also has a five-coordination geometry, but one of the connecting nitrogen atoms belongs to the picolyl unit in the middle of the ligand. In Zn1e and Zn1f, only two nitrogen atoms take part in the coordination. In Zn1f, the zinc ion does not connect with the picolyl unit in the middle of the ligand. By examining these complexes' structures, one can find that the zinc ions in Zn1b, Zn1c, and Zn1f are a little farther away from the oxazole cores than the zinc ions in the other structures. It is also noticed that each of all the backbones for these structures has good planarity.

Fig. 2.

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	Fig. 2. (color online) Optimized geometries of 1a–1f and the corresponding zinc complexes.

The optimized geometries of probe 2 and the corresponding zinc complexes are displayed in Fig. 3. The result is the same as that of probe 1. Six isomers of probe 2 and six coordination conformations are also obtained. The corresponding geometries of probe 3 are also fully optimized.

Fig. 3.

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	Fig. 3. (color online) Optimized geometries of 2a–2f and the corresponding zinc complexes.

It is expected that the various conformations will give rise to different electronic structures, which are closely related to the TPA transition matrix element according to Eq. (2). The permanent dipole moments and the energies of these structures are examined and the results are listed in Table 1. It shows that the permanent dipole moments of isomers 1a–1f are quite different: 1c has the largest dipole moment (7.584 deb, 1 deb = 3.33564 × 10⁻³⁰ C·m), and 1d has the smallest one (3.037 deb). In the corresponding zinc complexes, the permanent dipole moments still maintain almost the same order. This result is consistent with the characteristics of the structures. It is found that 1f has the lowest energy among six isomers of probe 1, and the energy differences between the other structures and 1f are very small in general. The energy difference ΔE ranges from 1.8 kcal/mol to 4.1 kcal/mol. Such small energy barriers indicate that these isomers could be thermally populated. It is surprising that Zn1a has the lowest energy among the zinc complexes and the energy difference between Zn1e and Zn1a has the largest value, which is 11.04 kcal/mol. This is probably because Zn1a has a six-coordination geometry while Zn1e only has four coordination bonds. It is also found that the energy differences between Zn1a and Zn1b and between Zn1a and Zn1d are only 0.667 kcal/mol and 0.733 kcal/mol, which means that these structures can be populated at considerable percentages according to the Boltzmann distribution. The case of probe 2 is similar to that of probe 1. The difference in permanent dipole moment among the isomers becomes more obvious. However, for probe 3, the difference in permanent dipole moment among the isomers is a little smaller than for probe 1.

Table 1.

Table 1.

Table 1. Values of permanent dipole moment μ and energy difference ΔE. . μ/D ΔE/kcal·mol−1 μ/D ΔE/kcal·mol−1 1a 4.276 4.050 Zn1a 17.955 0 1b 7.459 2.006 Zn1b 21.716 0.667 1c 7.584 3.603 Zn1c 23.215 9.074 1d 3.037 1.878 Zn1d 13.684 0.733 1e 4.403 0.062 Zn1e 14.841 11.040 1f 3.511 0 Zn1f 18.721 9.823 2a 3.631 4.056 Zn2a 16.623 0 2b 7.998 2.032 Zn2b 24.105 0.725 2c 9.355 3.603 Zn2c 26.522 9.134 2d 2.248 1.910 Zn2d 11.376 0.762 2e 6.281 0.092 Zn2e 12.611 10.749 2f 5.320 0 Zn2f 18.934 9.656 3a 4.423 4.046 Zn3a 18.150 0 3b 7.326 1.990 Zn3b 21.412 0.752 3c 7.138 3.578 Zn3c 22.553 9.039 3d 3.476 1.877 Zn3d 14.248 0.732 3e 4.085 0.043 Zn3e 15.684 10.864 3f 3.323 0 Zn3f 18.516 9.785

Table 1. Values of permanent dipole moment μ and energy difference ΔE. .

Our calculated OPA wavelength λ_op, oscillator strength f_op, and transition nature of all the studied molecules are listed in Table 2. It shows that the maximum OPA peaks of these compounds are all derived from the transition between ground state (S₀) and the first excited state (S₁), which is mainly dominated by the transition from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO).

For probe 1, one can see that the OPA wavelengths of the six isomers 1a–1f are all located at about 360 nm and their oscillator strengths only have a little difference. When the molecule binds to a zinc ion, the λ_op is red-shifted or blue-shifted to some extent. The Zn1a, Zn1d, Zn1e, and Zn1f have 16-, 21-, 28-, and 7-nm red-shifts respectively, while Zn1b and Zn1c have 4- and 3-nm blue-shift. The largest red-shift occurs in Zn1e. As a result, various coordination conformations have different OPA wavelengths. It also shows that the differences in oscillator strength among these zinc complexes increase in comparison with those among free ligands. The f_op of Zn1e is 0.7, which is much lower than the value of Zn1f, 0.99. These results indicate that the coordination modes have some effects on OPA properties. One can conclude that when the zinc ion coordinates with the nitrogen atom, which belongs to the picolyl unit in the middle of the ligand, the OPA wavelength has a considerable red-shift.

From probe 1 to probe 2 it follows that the OPA wavelengths of 2a–2f are red-shifted to around 410 nm due to the stronger electron donor. The isomerism still has very little effect on the OPA properties of the free ligands. However, when it comes to the zinc complexes, the various coordination modes have quite different OPA properties. The OPA wavelengths of Zn2a, Zn2d, and Zn2e are red-shifted obviously with respect to their free ligands. The largest red-shift still occurs in Zn2e, arriving at 48 nm. In addition, the difference in λ_op between Zn2b and Zn2e becomes 47 nm.

Table 2.

Table 2.

Table 2. One-photon absorption wavelength properties of the molecules in water solvent. . λop/nm fop Transition nature λop/nm fop Transition nature 1a 361 0.89 S0–S1 H–L(99%) Zn1a 377 0.71 S0–S1 H–L(96%) 1b 362 0.90 S0–S1 H–L(89%) Zn1b 358 0.98 S0–S1 H–L(99%) 1c 364 0.85 S0–S1 H–L(86%) Zn1c 361 0.93 S0–S1 H–L(99%) 1d 357 1.01 S0–S1 H–L(99%) Zn1d 378 0.76 S0–S1 H–L(99%) 1e 359 0.98 S0–S1 H–L(99%) Zn1e 387 0.70 S0–S1 H–L(99%) 1f 359 1.02 S0–S1 H–L(97%) Zn1f 366 0.99 S0–S1 H–L(99%) 2a 411 0.73 S0–S1 H–L(99%) Zn2a 438 0.57 S0–S1 H–L(99%) 2b 408 0.84 S0–S1 H–L(99%) Zn2b 410 0.76 S0–S1 H–L(96%) 2c 408 0.83 S0–S1 H–L(99%) Zn2c 414 0.74 S0–S1 H–L(96%) 2d 405 0.84 S0–S1 H–L(99%) Zn2d 442 0.60 S0–S1 H–L(99%) 2e 409 0.81 S0–S1 H–L(99%) Zn2e 457 0.54 S0–S1 H–L(99%) 2f 406 0.86 S0–S1 H–L(99%) Zn2f 412 0.80 S0–S1 H–L(99%) 3a 358 0.84 S0–S1 H–L(98%) Zn3a 374 0.67 S0–S1 H–L(99%) 3b 360 0.82 S0–S1 H–L(86%) Zn3b 358 0.88 S0–S1 H–L(99%) 3c 363 0.72 S0–S1 H–L(79%) Zn3c 355 0.93 S0–S1 H–L(99%) 3d 354 0.92 S0–S1 H–L(96%) Zn3d 375 0.72 S0–S1 H–L(99%) 3e 357 0.93 S0–S1 H–L(98%) Zn3e 385 0.65 S0–S1 H–L(99%) 3f 357 0.96 S0–S1 H–L(96%) Zn3f 363 0.94 S0–S1 H–L(99%)

Table 2. One-photon absorption wavelength properties of the molecules in water solvent. .

The OPA properties of probe 3 are similar to those of probe 1 due to the little difference in the donation ability between the methoxy and the hydroxy groups. Nearly all the OPA wavelengths of 3a–3f and Zn3a–Zn3f are slightly blue-shifted compared with those of the corresponding structures 1a–1f and Zn1a–Zn1f.

The TPA wavelength λ_tp and cross section α in water solvent for all the studied molecules are calculated by the response theory in the Dalton program. The TPA cross sections of the three lowest excited states for probes 1 and 2 are presented in Table 3.

Table 3.

Table 3.

Table 3. Values of two-photon absorption wavelengths λtp and cross section σ of the three lowest excited states of probes 1 and 2 in water solvent. . State λtp/nm σ/GM State λtp/nm σ/GM 1a S1 732 224 Zn1a S1 773 367 S2 678 7 S2 668 1 S3 599 94 S3 649 6 1b S1 740 97 Zn1b S1 736 279 S2 704 290 S2 685 2 S3 609 43 S3 670 1 1c S1 743 74 Zn1c S1 745 317 S2 703 373 S2 691 3 S3 606 52 S3 620 17 1d S1 727 237 Zn1d S1 778 403 S2 707 14 S2 672 1 S3 606 9 S3 647 13 1e S1 732 260 Zn1e S1 808 439 S2 689 12 S2 709 16 S3 597 91 S3 586 37 1f S1 736 195 Zn1f S1 752 375 S2 674 233 S2 713 1 S3 597 69 S3 612 69 2a S1 822 538 Zn2a S1 893 658 S2 667 11 S2 761 14 S3 659 45 S3 730 16 2b S1 824 538 Zn2b S1 838 596 S2 693 240 S2 790 16 S3 661 29 S3 770 1 2c S1 824 524 Zn2c S1 850 627 S2 703 285 S2 800 19 S3 659 30 S3 705 2 2d S1 816 570 Zn2d S1 906 716 S2 695 3 S2 766 14 S3 646 93 S3 754 13 2e S1 824 586 Zn2e S1 951 723 S2 678 10 S2 819 66 S3 658 37 S3 670 31 2f S1 824 567 Zn2f S1 865 761 S2 668 252 S2 841 1 S3 656 27 S3 695 43

Table 3. Values of two-photon absorption wavelengths λtp and cross section σ of the three lowest excited states of probes 1 and 2 in water solvent. .

For 1a, 1d, and 1e, the first excited state has the largest TPA intensity. The largest cross sections of 1a, 1d, and 1e are located at about 730 nm with 224, 237, and 260 GM respectively. As for 1b and 1c, the second excited state has the largest TPA intensity and the corresponding TPA wavelength λ_tp is centered at around 700 nm. The values of σ are equal to 290 GM and 373 GM. For 1f, both the first and the second excited states have considerable TPA cross sections. We note that the isomerism effects cannot be neglected. If all the isomers are taken into account, the obtained TPA spectrum could have several separated absorption maxima at about 670 nm, 700 nm, and 730 nm respectively.

When coordinated with Zn²⁺, the first excited state has the largest TPA intensity for all the zinc complexes. One can see that the coordination mode has an important effect on the TPA property. There are big differences in not only TPA intensity but also wavelength among zinc complexes. The largest cross section of Zn1a is 367 GM at 773 nm. The TPA wavelengths of Zn1b and Zn1c are 736 nm and 745 nm respectively, which are much shorter than that of Zn1a. Zn1b has the smallest cross section, which is only 279 GM. The λ_tp of Zn1d is similar to that of Zn1a, but the σ increases to 403 GM. Zn1e has the longest λ_tp, 808 nm, and the largest σ, 439 GM. That is, the absorption position ranges from 736 nm to 808 nm, which means that the absorption bands have large shifts between each other. From the cross section, we find that the TPA intensity is in the order Zn1e>Zn1d>Zn1f>Zn1a>Zn1c>Zn1b. The difference between the maximum and the minimum cross sections is large, which is 160 GM, about 36% of the maximum. By the inspection of the structures of the zinc complexes, one can quickly realize that the coordination mode with the connection between the zinc ion and the nitrogen atoms, which belongs to the picolyl unit in the middle of the ligand, always brings about the large cross sections in a long wavelength region. According to Eq. (2), we know that the TPA transition matrix element is determined by the electronic structures including the dipole moments and the excitation energies. So the lowest excitation energy of Zn1e is one of the probable reasons for the strongest TPA intensity among the zinc complexes. Comparing with corresponding free ligands, λ_tp has a large red-shift and σ is increased greatly for Zn1a, Zn1d, and Zn1e. These results are in good agreement with experimental observations.^[22] The arrangement where the metal ion binds to the acceptor site should yield an increased cross section.^[19,22]

In the case of probe 2, the first excited state has the largest TPA intensity for all the free ligands and zinc complexes. For 2b, 2c, and 2f, the second excited state also has considerable intensity. The largest cross sections of 2a–2f are all located at about 820 nm with different cross sections. The maximum and the minimum cross sections are 524 GM and 586 GM for 2c and 2e respectively. Both 2b and 2c have two absorption maxima at about 820 nm and 700 nm and the absorption intensities at 700 nm cannot be neglected. As for probe 1, if all the isomers 2a–2f are considered together, the obtained TPA spectrum could have several separated absorption maxima. One can also see that the TPA wavelengths have large red-shifts and the intensities increase greatly due to the stronger electron donor with respect to probe 1.

Table 4.

Table 4.

Table 4. Value of two-photon absorption wavelength λtp and cross section σ of three lowest excited states of probe 3 in water solvent. . State λtp/nm σ/GM State λtp/nm σ/GM 3a S1 730 207 Zn3a S1 775 345 S2 681 8 S2 670 1 S3 597 84 S3 646 5 3b S1 738 86 Zn3b S1 745 297 S2 701 281 S2 689 6 S3 609 37 S3 672 1 3c S1 743 46 Zn3c S1 738 271 S2 703 391 S2 697 1 S3 609 29 S3 621 1 3d S1 725 218 Zn3d S1 783 386 S2 707 16 S2 676 1 S3 608 8 S3 653 13 3e S1 732 244 Zn3e S1 816 414 S2 685 8 S2 715 22 S3 596 75 S3 586 31 3f S1 732 153 Zn3f S1 754 360 S2 674 226 S2 717 1 S3 595 58 S3 615 57

Table 4. Value of two-photon absorption wavelength λtp and cross section σ of three lowest excited states of probe 3 in water solvent. .

Upon Zn²⁺ binding, each of all the zinc complexes has a strong TPA peak in a longer wavelength range with enhanced cross section in comparison with each of the corresponding free ligands. It shows that the TPA wavelength and cross section are quite different among the zinc complexes. Zn2b has the smallest cross section 596 GM at 838 nm, while Zn2f has the largest value 761 GM at 865 nm. The cross section increases by 165 GM. Like the zinc complexes of probe 1, the TPA intensity is in the order Zn2f>Zn2e>Zn2d>Zn2a>Zn2c>Zn2b. When the zinc ion connects with the nitrogen atoms from the picolyl unit in the middle of the ligand, Zn2e, Zn2d, and Zn2a give rise to the large cross sections in the long wavelength region. Although Zn2f has the largest cross section, the TPA wavelength is located at 865 nm, which is much shorter than those of Zn2e, Zn2d, and Zn2a. According to our calculations, it can be concluded that the coordination mode plays an important role in TPA intensity and wavelength.

The TPA properties of probe 3 are also calculated and the results are shown in Table 4. The data are similar to those of probe 1. Most of the TPA cross sections decrease a little with respect to the corresponding structures of probe 1 due to the weak donor unit.

It is well known that TPA properties highly depend on the ICT process. The charge will be redistributed when the molecule is excited from the ground state to the excited state. In order to further explore the effects of the coordination mode and obtain a better understanding of the ICT process, we perform the natural bond orbital charge analyses for Zn1a, Zn1b, Zn1d, and Zn1e in their ground states and in the first excited states. To analyze them clearly, these molecules are divided into three parts as shown in Fig. 4. The net charges of parts A, B, and C are specifically calculated and all the calculated results are listed in Table 5.

Fig. 4.

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	Fig. 4. Divided parts of the molecules Zn1a, Zn1b, Zn1d, and Zn1e.

Table 5.

Table 5.

Table 5. Net charges (in units of e) for divided parts of the molecules in the ground states and in the first excited states. . QA0 QA1 ΔQA QB0 QB1 ΔQB QC0 QC1 ΔQC Zn1a –0.186 –0.102 0.084 0.224 0.544 0.320 –0.037 −0.441 −0.404 Zn1b –0.187 –0.114 0.073 0.204 0.430 0.226 –0.017 −0.316 −0.299 Zn1d –0.186 −0.101 0.085 0.226 0.550 0.324 –0.041 –0.450 −0.409 Zn1e –0.185 –0.096 0.089 0.236 0.586 0.350 –0.051 –0.490 −0.439

Table 5. Net charges (in units of e) for divided parts of the molecules in the ground states and in the first excited states. .

Q_A0 and Q_A1 denote the net charge of part A in the ground state and that in the first excited state, respectively. ΔQ_A represents the net charge difference between the ground state and the first excited state in part A. Like this definition, ΔQ_B and ΔQ_C denote the net charge differences between the ground state and the first excited state for part B and part C, respectively. For Zn1a, it is found that the net charge of part A in the first excited state Q_A1 is −0.102e, which is more electropositive than the value in the ground state Q_A0, −0.186e. The net charge of part B in the first excited state (Q_B1, 0.544e) is also more electropositive than in the ground state (Q_B0, 0.224e). In the case of part C, the net charge in the first excited state (Q_C1, −0.441e) is more electronegative than in the ground state (Q_C0, −0.037e). This indicates that part A, together with part B, is the donor, and part C is the acceptor of the molecule. Other structures are similar to those of Zn1a. That is, part A and part B both act as a donor, and part C serves as an acceptor. The net charge difference of the donor should be the sum of ΔQ_A and ΔQ_B. For Zn1a, the net charge difference of the donor is 0.404e, which is very close to the value of Zn1d, 0.409e. Zn1b has the smallest value, 0.299e and Zn1e has the biggest one, 0.439e. This demonstrates that the capacity of ICT is in the order Zn1e>Zn1d>Zn1a>Zn1b, which is consistent with the order of TPA intensity.