J. Phys. Chem. B 2008, 112, 7631–7644
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Chelation of Transition Metal Ions by Peptide Nanoring Shuichiro Kihara, Hiroyuki Takagi, Kazumasa Takechi, and Kyozaburo Takeda* Department of Materials Science and Engineering, School of Science and Engineering, Waseda UniVersity, Tokyo 169-8555, Japan ReceiVed: January 8, 2008; ReVised Manuscript ReceiVed: April 7, 2008
We have computationally studied the energetics and electronic structures of a chelate system where the guest cation is a transition metal (TM) and the host ligand is a peptide nanoring (PNR). The trapping of a TM cation by a cyclic peptide skeleton is primarily caused by the electrostatic interaction. The exchange interaction plays a secondary role in determining the relative stability in accordance with the spin multiplicity. An interesting feature of this chelate system is that a TM cation can also be trapped by the side-chain aromatic groups of the PNR via π-d hybridization. However, the spin multiplicity of the system changes the trapped form. When the chelate system has spin singlet multiplicity, a Fe2+ cation, for example, is not trapped by the single-phenyl group but is preferentially sandwiched by the two phenyl groups. In contrast, a Fe2+ cation can be trapped by single as well as by double-phenyl groups when the chelate system has higher spin multiplicity, such as triplet and quintet. These two different trapping forms are caused by the difference in the number of valence electrons of TM cations. For this chelate system, the newly occupied molecular orbital (MO) has an interbenzene antibonding character. Therefore, an electron occupying this MO state favors the mutual separation of two benzene molecules. Because the electron occupation of this MO varies in accordance with the spin multiplicity, one can predict the preference for the single-phenyl-group trapping process rather than the doublephenyl-group process systematically as well as consistently. I. Introduction Peptide nanorings (PNRs) are cyclic proteins first reported by Ghadiri et al.1 These proteins have a well-defined peptide skeleton consisting of an alternate sequence of D- and L-amino acid residues (D,L-peptide) and provide (sub)nanometer-scale inner pores. O(dC 100 kcal/mol, whereas the chelate system is realized even by using the SφT process when ∆I < 100 kcal/mol. We now expand our consideration to other X2+ metal cations, Cr2+, Ni2+, and Mg2+, the ion radii of which are similar to that of the Fe2+ cation. We first optimize the hypothetical chelate compounds of X2+/Bz and Bz/X2+/Bz, where the metal cation X2+ is simply captured by the SBT and DBT processes,
J. Phys. Chem. B, Vol. 112, No. 25, 2008 7641 respectively. We then calculate the energy differences ∆I(X2+) DBT/I 2+ 2+ ) ESBT/I coh (X ) - Ecoh (X ), which are given in Table 3. On the basis of the present ∆ prediction, the Cr2+ cation is expected to be trapped by the DφT process but not by the SφT process when the chelate system has spin singlet or triplet multiplicity, whereas even the SφT process is feasible for the chelate system having spin quintet multiplicity. The figures in Table 3 further indicate that both the SφT and DφT processes are preferable for Ni2+ (singlet and triplet) and Mg2+ cations (singlet). We verify this ∆ prediction by ab initio calculations. The resulting molecular structures are shown in Figure 10, where we initially placed the X2+ cation in the SφT form and optimized the molecular structure energetically. As expected from the ∆ prediction of ∆S(Cr2+) ) 129.7 kcal/mol, the present ab initio calculation demonstrates that the SφT process is ineligible energetically and is switched into the DφT process via the energetical optimization. Thus, the DφT process is clearly verified to be preferable when the Cr2+ chelate compound has spin singlet multiplicity. The value of ∆Q(Cr2+) ) 81.58 kcal/ mol indicates the feasibility of the SφT process for the chelation of the Cr2+ cation when the system has spin quintet multiplicity. Figure 10 reveals that this prediction is also consistent with the ab initio result. Analogously, the values of ∆S(Ni2+) ) 103.84 kcal/mol and ∆T(Ni2+) ) 98.99 kcal/mol indicate that the Ni2+ cation can be trapped even by the SφT process when the chelate system has spin singlet or triplet multiplicity. These features are also confirmed by ab initio calculations as shown in Figure 10. One should, however, note that the present ∆ prediction causes the following inconsistency with ab initio results. The value of ∆T(Cr2+) ) 122.41 kcal/mol indicates the lack of preferability of the SφT process when the system has spin triplet multiplicity, but ab initio calculations demonstrate the prefer-
Figure 14. Illustration of π-s and π-p mixings found in DBz (Bz/Mg2+/Bz) sandwich cluster (a) and calculated MOs (B3LYP/6-31G//) of the optimized Mg2+/6φPNR in which the cation Mg2+ is trapped by the DφT process (b). All the MOs in the DBz sandwich cluster (a) are schematically illustrated by using the result of the minimal-basis HF calculation and are classified by using the irreducible representations of D6h. We also illustrate several wave functions of the typical π-d MOs.
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Figure 15. Illustration of the trapping and extracting processes of Mg2+ cation by 6PNR. We have performed the calculations by B3LYP/6-31G** while varying the interatomic distance d. We have found the two local minimum (LM1 and LM2) structures in the energetics against d. The LM1 corresponds to the trapping of the OHC, and the LM2 corresponds to the extraction of the target cation.
ability of the SφT process. Similarly, ab initio calculations elucidate that the trapping process for the Mg2+ cation is switched to the DφT process, although the small value of ∆S(Mg2+) ) 79.14 kcal/mol strongly indicates the preferability of the SφT process when the system has a spin singlet state. What causes the above consistency or inconsistency and predictability or unpredictability in the ∆ prediction? We discuss this subject on the basis of electron occupation with connecting the orbital nature of the newly occupied MOs. In Figure 11a, we schematically illustrate the π-d MOs and their electron occupation when the DBT process traps the Cr2+, Fe2+, or Ni2+ cation. One should note that the occupation of the π-d MOs changes in accordance with the trapped TM cation because of the difference in the number of valence electrons among these three TM cations: the Cr2+ cation has two fewer valence electrons than the Fe2+ cation, whereas the Ni2+ cation has two more electrons. Consequently, the excited electrons causing a spin triplet multiplicity in the Cr2+ chelate system still occupy the π-d HOMO - 1 (a1g) state (Figure 6c). The electron occupation of the π-d LUMO (e/1g) should first occur when this Cr2+ chelate system has spin quintet multiplicity. In contrast, two extra electrons in the Ni2+ cation allow this π-d LUMO (e/1g) to be occupied by electrons even when the chelate system has a spin singlet state. In a higher spin state, electron(s) should occupy the other π-d LUMO. This difference in the electron occupation causes the preferability or lack of preferability between the SφT and DφT processes, because the molecular deformation is efficiently determined by the newly occupied MOs in accordance with their orbital characters. The newly occupied MO is the π-d LUMO (e/1g) which has an interbenzene antibonding character in addition to the antibonding coupling between π (Bz) and d (TM) orbitals as shown in Figure 11b. Accordingly, the electron occupation of this state causes the mutual separation of the two Bz molecules to stabilize its own MO state energetically and causes the preferability of the SBT (SφT) process in the formation of the chelate system. The resulting feasibility of both SφT and DφT processes is consistent with ab initio results except for the Cr2+ chelate system having a spin triplet state (Appendix B). Thus, the occupation of the π-d LUMO (e/1g) by the electron(s) allows us to predict the preferability or otherwise of the SφT and DφT processes systematically as well as consistently (such as 18 electrons rule). V. Conclusion We have computationally studied the energetics and electronic structures of an X2+/PNR chelate system in the gase phase (Appendix D) and obtained the following results.
• The trapping of the Fe2+ cation by the 6PNR skeleton is primarily caused by the electrostatic potential between the Fe2+ guest cation and the 6PNR host. The exchange interaction plays a secondary role in determining the energetic relation due to the spin multiplicity. This is because unoccupied d orbitals hardly hybridize with the MOs of the PNR skeleton, and less CT occurs between the guest cation and the PNR host, even when the PNR has aromatic side chains. • The TM cation can be also trapped at the aromatic side chain(s) via the π-d interaction when the PNR has aromatic side chains. However, the spin multiplicity of the system changes the trapped form. When the chelate system has spin singlet multiplicity, an Fe2+ cation, for example, is not trapped by the single-phenyl group but is preferentially sandwiched by the double-phenyl group. In contrast, an Fe2+ cation can be trapped by single as well as by double-phenyl group when the chelate system has higher spin multiplicity such as triplet and quintet. • These two different trapping forms are caused by the difference in the number of valence electrons of TM cations. An electron occupying the LUMO state favors the mutual separation of two benzene molecules, and this electron occupation varies in accordance with the spin multiplicity. Accordingly, one can predict the preference for the single-phenyl-group trapping process rather than the double-phenyl-group process systematically as well as consistently. Acknowledgment. The authors would like to express their thanks to Dr. Hajime Okamoto for fruitful discussions on the ion trapping processes by PNRs and to Mr. Yasuhiro Suzuki for his kind help in preparing the manuscript. They also express their thanks to Prof. Atsushi Nakajima of Keio University for his fruitful discussion. Parts of the calculations have been carried out at IMS (BUNSHIKEN), Okazaki, Japan. This work was partly supported by a Grant-in-Aid for Scientific Research on High Technology (2006) from the Ministry of Education, Culture, Sports, Science and Technology. Appendix A Change in Spin Phase We here study how the energetical stability in the SBT (Fe2+/ Bz) and DBT (Bz/Fe2+/Bz) processes changes while varying the interatomic distance ξ as well as the spin multiplicity. We show the calculated changes for these processes in Figure 12a,b, respectively. Figure 12a reveals that the ground state of the SBT system is expected to have spin quintet multiplicity when the SBT system has a larger value of the interatomic distance ξ
Chelation of Transition Metal Ions by Peptide Nanoring (>1.55 Å), because the large ξ weakens the energy separations among the π-d orbitals and Hund’s rule is increasingly evident. One can, however, find that the ground state changes its multiplicity into the triplet state when ξ < 1.55 Å. One should further note that the SBT system with spin singlet multiplicity has less potential to be the ground state of this system. On the other hand, the DBT process with spin singlet multiplicity has more potential to be the ground state when ξ is less than 1.85 Å (Figure 12b). This is because the enhanced π-d interaction widens the energy differences among the resulting π-d MOs more than the exchange interaction energy. One can then find the energetically optimized DBT system (S/ D6h) at ξ ) 1.6 Å. However, the ground state of the DBT system changes its spin multiplicity from a singlet state to a quintet state when ξ is larger than 1.85 Å. Thus, the Fe2+ cation is unlikely to be trapped by the single-phenyl group but can feasibly be captured by the double-phenyl group when the system has spin singlet multiplicity, whereas it can be trapped by both the single and double-phenyl groups when the system has spin quintet multiplicity. Appendix B Cr2+ Chelate System Having a Spin Triplet Multiplicity In Figure 13, we show the ab initio MOs for the resulting Cr2+ SφT chelate system having spin triplet multiplicity. One can find the characteristic CT between the π-d MOs and the naked π MOs. This CT fills one of the π-d LUMO (e/1g) by an R electron via the energetical optimization (Figure 13b). The DBT sandwiching process is then not undergone, and the two φ groups mutually separate, because the newly occupied π-d LUMO has an antibonding character among the Bz, Cr, and Bz (Bz/Cr2+/Bz). Thus, the SφT process occurs in spite of the larger ∆ value. Appendix C Mg2+ Chelate System We illustrate the orbital mixing in the DBT process for the Mg2+ cation (Bz/Mg2+/Bz) in Figure 14a. The valence states of the alkali earth metal Mg correspond to the 3s and also 3px, 3py, and 3pz AOs. Although these AOs are unoccupied by electrons in the Mg2+ cation state, the π-p and π-s orbital mixings play an important role in the Mg2+ cation trapping by the DBT sandwiching process. Different from d orbitals, p orbitals have an odd symmetry around the center. Therefore, π orbitals caused by the double Bz molecules can now be hybridized with p orbitals when these π orbitals have an ungerade symmetry. The π-p and π-s orbital mixings, then, stabilize three of the four occupied π orbitals (a1g, a2u, and e1u) energetically, whereas the π orbital (HOMO, e1g) remains without the hybridization, as shown in Figure 14a. Thus, the π-p and π-s couplings cause the energetical stabilization siginificantly. This feature is in strong contrast to that found in the π-d hybridization, where two π orbitals having an ungerade symmetry (a2u and e1u) remain without the energetical stabilization (Figure 6). This is the reason why the π-p and π-s couplings in the Mg2+ cation are more likely to undergo the DBT sandwiching process and why the ∆ prediction is not appropriate. We show the calculated MOs of the energetically optimized Mg2+/6φPNR having spin singlet multiplicity in Figure 14b. The π-p and π-s couplings described above can be clearly recognized. The discrepancy from the ideal DBT geometry having a D6h symmetry causes the strong resolution in the
J. Phys. Chem. B, Vol. 112, No. 25, 2008 7643 degenerated π, π-s, and π-p states. However, no CTs occur directly from these naked π states to the Mg2+ cation, because the naked π orbitals are lower than the π HOMO. One should further note that the trapping of the Mg2+ cation deforms the hexagonal ring skeleton into a rectangular ring (Figure 10). This deformation induces the orbital mixing between the φ (benzyl) side chains and the peptide skeleton, and extreme electronic localization results (Figure 14b). Appendix D Trapping of the Hydrated Cation Cluster and Extraction of the Metal Cation All the calculations reported here have been carried out in the gas phase. Then, one should take into account the influence of solvation in the calculation for a direct comparison with experiments. We have started this subject through the case where the PNR traps the metal cation hydrated by water molecules. We considered two cations of Mg2+ and Fe2+ surrounded by six water molecules. The energetical optimization reveals that six water molecules encircle the target cation octahedrally, causing a Th point group symmetry (octahedrally hydrated cluster, OHC). The further deformation into the Ci point group symmetry is induced by Jahn-Teller distortion when the [Fe(H2O)6]2+ cluster has a higher spin multiplicity as a triplet or a quintet. It also elucidates that the resulting OHCs give the similar sidelines of 2.90Å for [Mg(H2O)6]2+ and 2.83Å for [Fe(H2O)6]2+ because of their analogous ion radii. Our calculation on the supramolecule [X(H2O)6]2+/6PNR system revealed that both of the OHCs, [Mg(H2O)6]2+ and [Fe(H2O)6]2+, approach the 6PNR collectively along the common C3 axis of these OHC and 6PNR. The corresponding supramolecule produces a local minimum point in the energy profile when the interatomic distance d (between the cation and the center of the PNR) is ∼4.0 Å. Both of the OHCs further approach the 6PNR until d ) 2.6-2.9 Å while maintaining their octahedrally hydrated geometry. That is, the 6PNR completely traps the OHC, irrespectively of the species of the included cation Mg2+ and Fe2+. An interesting feature is that the 6PNR extracts the target cation from the OHC when the OHC further approach to the 6PNR. One should note that the target cation should pass the two oxygen planes during when it moves along the C3 axis and intrudes into the center of the PNR. The calculated energy profile demonstrates that the two pseudo-transition states appear just when the cation passes through these oxygen planes. We illustrate the resulting process of a trapping and an extracting for the [Mg(H2O)6]2+/6GPNR system in Figure 15, the details of which will be reported in the next paper. References and Notes (1) Ghadiri, M. R.; Granja, J. R.; Milligan, R. A.; Mcree, D. E.; Khazanovich, N. Nature 1993, 366, 324. (2) Granja, J. R.; Ghadiri, M. R. J. Am. Chem. Soc. 1994, 116, 10785. (3) Sanchez-Quesada, J.; Kim, H. S.; Ghadiri, M. R. Angew. Chem., Int. Ed. 2001, 40, 2503. (4) Fernandez-Lopez, S.; Kim, H. S.; Choi, E. C.; Delgado, M.; Granja, J. R.; Khasanov, A.; Kraehenbuehl, K.; Long, G.; Weinberger, D. A.; Wilcoxenl, K. M.; Ghadiri, M. R. Nature 2001, 412, 452. (5) Kim, H. S.; Hartgerink, J. D.; Ghadiri, M. R. J. Am. Chem. Soc. 1998, 120, 4417. (6) Motesharei, K.; Ghadiri, M. R. J. Am. Chem. Soc. 1997, 119, 11306. (7) Steinem, C.; Janshoff, A.; Vollmer, M. S.; Ghadiri, M. R. Langmuir 1999, 15, 3956. (8) Lewis, J. P.; Pawley, N. H.; Sankey, O. F. J. Phys. Chem. B 1997, 101, 10576. (9) (a) Fukasaku, K.; Takeda, K.; Shiraishi, K. J. Phys. Soc. Jpn. 1997, 66, 3387. (b) 1998, 67, 3751.
7644 J. Phys. Chem. B, Vol. 112, No. 25, 2008 (10) Carloni, P.; Andreoni, W.; Parrinello, M. Phys. ReV. Lett. 1997, 79, 761. (11) Jishi, R. A.; Braier, N. C.; White, C. T.; Mintmeir, J. W. Phys. ReV. B 1998, 58, R16009. (12) Okamoto, H.; Takeda, K.; Shiraishi, K. Phys. ReV. B 2001, 64, 115425. (13) Kim, K. S.; Cui, C.; Cho, S. J. J. Phys. Chem. B 1998, 102, 461. (14) Cui, C.; Kim, K. S. J. Phys. Chem. A 1999, 103, 2751. (15) Yamada, T.; Takechi, K.; Nakanishi, T.; Okamoto, H.; Takeda, K. Jpn. J. Appl. Phys. 2007, 46, 7586. (16) Lehn, J.-M. Supramolecular Chemistry, Concepts and PerspectiVe; VCH: Weinheim, 1995. (17) The resulting radius is naturally dependent on the choice of the calculational method. The HF/6-31G** calculation gives a value of 1.524 Å, whereas the present DFT (B3LYP/6-31G**) gives 1.636 Å.
Kihara et al. (18) (a) Yasuike, T.; Nakajima, A.; Yabushita, S.; Kaya, K. J. Phys. Chem. A 1997, 101, 5360. (b) Yasuike, T.; Yabushita, S. J. Phys. Chem. A 1999, 103, 4533. (19) Okamoto, H.; Nakanishi, T.; Nagai, Y.; Kasahara, M.; Takeda, K. J. Am. Chem. Soc. 2003, 125, 2756. (20) Energetics in an isolated cation is determined by the exchange interaction in accordance with the spin multiplicity. Figure 3 gives an energy difference of 29.6 kcal/mol between FeS2+ and Fe2+ T and of 41.7 kcal/mol 2+ between Fe2+ T and FeQ . Table 2 indicates that the corresponding differences in DφT are 5.6 kcal/mol (between DφT/S and DφT/T) and 25.3 kcal/mol (between DφT/T and DφT/Q). These values are different from those for an isolated Fe2+ cation, because the CT from the naked π orbitals to these π-d MOs changes the original exchange interaction.
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