Understanding the Effect of Conformation on Hole Delocalization in

Aug 16, 2018 - ACS Editors' Choice: Using Data Analysis to Evaluate and Compare Chemical Syntheses. This week: Using data analysis to evaluate and ...
0 downloads 0 Views 2MB Size
Download PDF
Subscriber access provided by University of South Dakota

Communication

Understanding the Effect of Conformation on Hole Delocalization in Poly(dimethylsilane) Milena Jovanovic, and Josef Michl J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.8b05829 • Publication Date (Web): 16 Aug 2018 Downloaded from http://pubs.acs.org on August 16, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Journal of the American Chemical Society

Understanding the Effect of Conformation on Hole Delocalization in Poly(dimethylsilane) Milena Jovanovic and Josef Michl* Department of Chemistry and Biochemistry, University of Colorado, Boulder, CO 80309-0215 and Institute of Organic Chemistry and Biochemistry, Academy of Sciences of the Czech Republic, Flemingovo nám. 2, 16610 Prague 6, Czech Republic Supporting Information Placeholder _________________________________________________ ABSTRACT: Density functional theory calculations confirm that the simple explanation of the origin of the striking conformational dependence of ó-electron localization/delocalization in polysilanes offered by the extremely simple Ladder C model is correct. _______________________________________ ó-Electron delocalization affects the properties of oligosilanes (R1 R2 Si)n , such as hole mobility,1 ionization potentials,2 and electronic transitions3,4,5,6 much more strongly than those of alkanes (R1 R2 C)n ,7,8,9,10,11,12 and is exquisitely sensitive to the conformation of silicon backbone. Depending on conformation, the response of the energy of the HOMO6LUMO excitation to chain extension can be almost as strong as that of a polyene13 or be absent altogether.14 In a regular helix with SiSiSiSi dihedral angles ù close to 180E (allanti), the HOMO is delocalized evenly over the chain, as in a polyene, whereas for ù close to 0E(all-syn), it consists of disconnected islands of large amplitude, resembling the mid-band MO of a polyene. A simple intuitive explanation is available15 in terms of the Hückel-type Ladder C model.16 This extension of the Sandorfy model C17 has two sp3 hybrid orbitals on each silicon atom (one on terminal Si atoms), interacting through three kinds of resonance integrals: primary (âp), geminal (âg), and vicinal (âv). Unlike the negative integrals âp and âg, âv is a function of ù, and is negative at small ù and positive at large ù (Figure 1). Although the Ladder C model appeals by its simplicity and accounts for many properties of polysilanes,18 its primitive nature raises doubts about the validity of any explanation it provides. We now demonstrate that its explanation of the origin of conformational effects on ó delocalization in polysilanes is duplicated by standard density functional theory (DFT), which accounts well for optical and other properties of oligosilanes,10,19,20 but does not provide comparable intuitive insight. For a juxtaposition of Ladder C and DFT results we treat regular helical [(CH3 )2 Si]4 using band theory with cyclic boundary conditions. As a measure of ó delocalization, we use a physicist's measure, effective hole mass, and a chemist's measure, the unevenness of the crystal orbital structure, which is related to the location of the maximum of the top valence band in k space. When the maximum is located at the à point (k = 0) or the X point (k = ð) in the Brillouin zone (à or X' point in the Jones zone21), the orbital amplitude is distributed evenly along the chain and the hole is delocalized. When it is located centrally in the Brillouin (or Jones)

Figure 1. Ladder C model. Top: skeletal atomic hybrid orbitals and definition of resonance integrals â. Bottom, â as a function of the SiSiSiSi dihedral angle ù. zone, the orbital amplitude consists of a series of nearly perfectly separated islands and the hole is localized. We deal with the valence band, because the Ladder C model does not consider Si-C bond orbitals and cannot describe the conduction band correctly. For an infinite polysilane, g±(k) = á ± [âp2 + âg2 + âv2 + 2âp âg cos(ka) + 2âv âg cos(ka) +2âp âv cos(2ka)]½ ,

1 ACS Paragon Plus Environment

Journal of the American Chemical Society 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

where g!(k) and g+(k) are the energies of the top valence and bottom conduction band, respectively, and á is the Hückel Coulomb integral. We use literature values of âp, âg, and âv,18 and ù ranges from 0E to 180E. Our DFT calculations use the PBE0 functional,22,23 which works well for oligosilanes and polysilanes, 24,25 and the POB-TZVP basis set.26 Band structure was computed at geometries fully optimized within a cyclic line group,27 using CRYSTAL01728 and EMC29 for effective mass. Steric hindrance limited the range to 25E # ù # 180E. Figure 2 shows the top valence band calculated with DFT and Ladder C, plotted in the Jones zone for three helices (ù = 180E, 101.3E, and 26.6E, see also Figure S1). Translationally invariant unit cell size reflects the number n of SiMe2 units per helical turn [(SiMe2 )2 : ù = 180E, (SiMe2)28: ù = 101.3E, (SiMe2)33: ù = 26.6E]. This cell does not utilize the full helical symmetry, but preserves the interpretation of k as a reciprocal lattice vector. An alternative formalism30 uses helical symmetry and the smallest unit cell (SiMe2). The Jones zone edge X' equals 2ð for ù = 180E, 28ð for ù = 101.3E, and 33ð for ù = 26.6E. The central point of the Jones zone X" is ð for ù = 180E, 14ð for ù = 101.3E, and 33ð/2 for ù = 26.6E. The valence band structure demonstrates the qualitative similarity of the Ladder C and the DFT results and illustrates the complexity that can arise in helical systems.31,32 At large ù, the valence band has a local maximum at the à point (k = 0) and a global maximum at the X' point (k = nð). At intermediate ù, it has a maximum at X' and a minimum at the à point, and at small ù, it has minima at both à and X' points and a maximum near the middle of the Jones zone. As ù decreases, the Fermi level drops until at ù = 26.6E the bottom of the valence band crosses another band. This lower energy band is of SiC nature and is absent in the Ladder C model. The broad peak in the ù = 101.3E curve at ~ !7.3 eV is missing in the Ladder C model for similar reasons.

They are the most stable when âv < 0 and the least stable when âv > 0. The orbitals at X" and !X" (both shown at X") have a node across each vicinal interaction, and are the most stable when âv > 0 and the least stable when âv < 0. The number of nodes across vicinal interactions increases from the à and Xr points toward the Xrr point as dictated by symmetry. The band structure is symmetric with respect to the Xrr point because at âg = 0 there is no energy difference between the in-phase (left of X") and out-of-phase (right of X") combination of orbitals of the two subchains. Next, we introduce geminal interactions described by a negative âg, which cause the two subchains to be combined into a single chain. In Figure 3, the dashed lines are converted into the full lines, as indicated by the vertical arrows. Symmetry with respect to the Xrr point is lost, because the in-phase combinations to the left of X" are stabilized and the out-of-phase combinations to the right of X" are destabilized. The magnitude of the energy shift increases with distance from X", where the geminal interactions at each silicon atom cancel and the dashed and full curves cross. The most stabilized newly formed orbital is at the à point, which has no nodes across geminal interactions, and the most destabilized orbital is at Xr, which has a node across each geminal interaction. The effects of these geminal interactions are profound and fully account for the resulting shapes of the full curves in Figure 3. At large ù, the maximum at the à point becomes a merely local maximum, while the one at the Xr point becomes the global maximum. As the energy at the Xrr point does not change, the minimum shifts to the left. At small ù, the maximum shifts from the Xrr point to the right, to an orbital that is destabilized by both vicinal and geminal interactions. The minimum at the à point is additionally stabilized, while the one

Figure 2. Band structure. A: from DFT; B: from Ladder C. Green: ù = 180E (Xr = 2ð); orange: ù = 101.3E(Xr = 28ð); purple: ù = 26.6E(Xr = 33ð). The origin of the behavior observed in Figure 2 is understandable similarly as in oligosilanes of finite length.15 Consider a zeroth order Hamiltonian in which âg = 0. Then, the two hybrids on a silicon atom do not interact, and the chain splits into two similar subchains, each containing half of the SiSi bonds, with a valence band analogous to that of a strongly alternating polyene (dashed lines in Figure 3). When ù is large, it has maxima at à and Xr points, and a minimum in the center of the Jones zone (Xrr point). The opposite is true at small values of ù. This is understandable in terms of valence band eigenvectors, which contain no nodes across primary interactions. At à and Xr, they also have no nodes across vicinal interactions and their energies are dictated by the sign of âv.

Figure 3. Zeroth order (dashed) and first order (full) perturbation theory Ladder C results for (SiMe2)4 (green, ù = 180E, purple, ù = 26.6E). Schematic orbital drawings: Top, at the à (left) and X' (right) points of the Jones zone; center, at k (and -k) corresponding to the Fermi level in the ù = 26.6E helix; bottom, at the X" and -X" points. Circle radii represent orbital amplitudes at hybrid orbitals and color represents their signs.

2 ACS Paragon Plus Environment

Page 2 of 5

Page 3 of 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Journal of the American Chemical Society at Xr point is destabilized. As ù increases, the introduction of geminal interaction shifts the maximum from the Xrr point toward the Xr point. In the process, the valence band flattens to the right of its maximum, increasing the effective hole mass hugely. When the maximum reaches the X' point, the effective hole mass drops. Figure 4 shows plots of the effective mass calculated for a hole at the global maximum of the valence band as a function of ù. For both DFT and Ladder C calculations, they follow the expectations that we have developed above. The smallest effective hole mass is predicted for loose helices, and a larger one for tight helices. For intermediate values of ù, where the valence band changes from the loose to the tight helix behavior, the effective hole mass increases and approaches infinity, as the valence band flattens. The exact value of ù at which this happens is not the same in the DFT calculation and in the Ladder C model, and depends on the choice of functional in the former and choice of parameters in the latter. We conclude that the arguments made earlier15 for oligosilanes of finite length apply also in the infinite chain limit, and most importantly, that the significant features of the Ladder C results for delocalization of sigma electrons in poly(dimethylsilane) are reproduced by DFT calculations. The results validate the simpleminded explanation of the origin of conformational effects on óelectron delocalization provided by the Ladder C model.

AUTHOR INFORMATION Corresponding Author [email protected]

ACKNOWLEDGMENT This material is based upon work supported by the National Science Foundation under CHE-1566435.

REFERENCES 1. Kitao, T.; Bracco, S.; Comotti, A.; Naito, M.; Seki, S.; Uemura , T.; Kitagawa, S. J. Am. Chem. Soc. 2015, 137, 5231. 2. Fogarty, H. A.; Tsuji, H.; David, D. E.; Ottosson, C.-H.; Ehara, M.; Nakatsuji, H.; Tamao, K.; Michl, J. J. Phys. Chem. A 2002, 106, 2369. 3. Wallner, A.; Wagner, H.; Baumgartner, J.; Marschner, C.; Rohm, H. W.; Köckerling, M.; Krempner, C. Organometallics 2008, 27, 5221. 4. Tsuji, H.; Fogarty, H. A.; Ehara, M.; Fukuda, R.; Casher, D.; Tamao, K.; Nakatsuji, H.; Michl, J. Chem. Eur. J. 2014, 20, 9431. Corrigendum: Chem. Eur. J. 2015, 21, 1839. 5. Kanazawa, Y.; Tsuji, H.; Ehara, M.; Fukuda, R.; Casher, D. L.; Tamao, K.; Nakatsuji, H.; Michl, J. “Electronic Transitions in Conformationally Controlled Peralkylated Hexasilanes”, ChemPhysChem 2016, 17, 3010. 6. Hlina, J.; Stella, F.; Meshgi, M. A.; Marschner., C.; Baumgartner, J.; Molecules 2016, 21, 1079. 7. Miller, R. D.; Michl, J. Chem. Rev. 1989, 89, 1359. 8. Michl, J.; West, R. in Silicon-Containing Polymers, Jones, R. G.; Ando, W.; Chojnowski, J., Eds.; Kluwer Academic Publishers: Dordrecht, The Netherlands, 2000; p. 499. 9. Matsumoto, N.; Suzuki, H.; Miyazaki, H. in Silicon-Containing Polymers, Jones, R. G.; Ando, W.; Chojnowski, J., Eds.; Kluwer Academic Publishers: Dordrecht, The Netherlands, 2000; p. 531. 10. Fogarty, F. A.; Casher, D. L.; Imhof, R.; Schepers, T.; Rooklin, D. W.; Michl, J. Pure Appl. Chem. 2003, 75, 999. 11. Koe, J.; Fujiki, M. Chapter 6 - Polysilanes. In Organosilicon Compounds: Experiment (Physico-Chemical Studies) and Applications, 1; Lee, V. Y., Ed.; Academic Press: Cambridge, Massachusetts, 2017; 2, 219. 12. Su, T. A.; Li, H., Klausen, R. S.; Kim, N. T.; Neupane, M.; Leighton, J. L.; Steigerwald, M. L.; Venkataraman, L.; Nuckolls, C. Acc. Chem. Res. 2017, 50, 1088. 13. Raymond, M. K.; Michl, J. Int. J. Quant. Chem. 1999, 72, 361. 14. Tsuji, H.; Terada, M.; Toshimitsu, A.; Tamao, K. J. Am. Chem. Soc. 2003, 125, 7486. 15. Jovanovic, M.; Antic, D.; Rooklin, D.; Bande, A.; Michl, J. Chem. Asian J. 2017, 12, 1250. 16. Plitt, H.; Michl, J. Chem. Phys. Lett. 1992, 198, 400. 17. Sandorfy, C. Can. J. Chem 1955, 33, 1337. 18. Schepers, T.; Michl, J. J. Phys. Org. Chem. 2002, 15, 490. 19. Rooklin, D. W.; Schepers, T.; Raymond-Johansson, M. K.; Michl J. Photochem. Photophys. Sci. 2003, 2, 511. 20. Crespo, R.; Piqueras, M. C.; Michl, J. Theor. Chem. Acc. 2007, 118, 81. 21. Jones, H. Proc. Roy. Soc. A (London) 1934, 114, 225. 22. Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3868. 23. Adamo C.; Barone, V. J. Chem. Phys. 1999, 110, 6158. 24. Lehtonen, O.; Sundholm, D. J. Chem. Phys. 2006, 125, 144314. 25. Perdew, J. P.; Yang, W.; Burke, K.; Yang, Z.; Gross, E. K. U.; Scheffler, M.; Scuseria, G. E.; Henderson, T. M.; Zhang, I. Y.; Ruzsinszky, A.; Peng, H.; Sun, J.; Trushin, E.; Görling, A. PNAS, 2017, 114 (11), 2801. 26. Peintinger, M. F.; Oliveira, D. V. J.; Bredow,T. J. Comput. Chem. 2013, 34, 451. 27. Miyazawa, T. J. Polym. Sci. A 1961, 55, 215. 28. Dovesi, R. ; Erba, A.; Orlando, R.; Zicovich-Wilson, C. M.; Civalleri, B.; Maschio, L.; Rerat, M.; Casassa, S.; Baima, J.; Salustro, S.; Kirtman, B. WIREs Comput. Mol. Sci. 2018, e1360. 29. Fonari, A.; Sutton, C. Effective Mass Calculator; The Massachusetts Institute of Technology: Cambridge, MA, United States, 2012.

Figure 4. Effective hole mass in units of electron mass as a function of ù from DFT (blue) and Ladder C (red) theory.

ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publications website. Construction of Jones zone representation. DFT band structure plotted in the first Brillouin zone. DFT optimized geometries.

3 ACS Paragon Plus Environment

Journal of the American Chemical Society 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

30. Blumen, A.; Merkel, C. Phys. Stat. Sol. B 1977, 83, 425. 31. Bozovic, I. Phys. Rev. B, 1984, 29, 6586. 32. Glassey, W. V., Hoffmann, R. Theor Chem Acc, 2002, 107, 272.

4 ACS Paragon Plus Environment

Page 4 of 5

Page 5 of 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Journal of the American Chemical Society TOC Graphic

5 ACS Paragon Plus Environment