Five Stereoactive Orbitals on Silicon: Charge and Spin Localization in

Apr 19, 2013 - usual conformation with charge and spin delocalized over the Si backbone, ... delocalization in the silicon compounds.1 Thus, like poly...
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Five Stereoactive Orbitals on Silicon: Charge and Spin Localization in the n‑Si4Me10−• Radical Anion by Trigonal Bipyramidalization Matthew K. MacLeod† and Josef Michl*,†,‡ †

Department of Chemistry and Biochemistry, University of Colorado, Boulder, Colorado 80309, United States Institute of Organic Chemistry and Biochemistry, Academy of Sciences of the Czech Republic, Flemingovo nám., 2, 166 10 Praha 6, Czech Republic

‡

S Supporting Information *

ABSTRACT: RIUMP2/def2-TZVPPD calculations show that in addition to its usual conformation with charge and spin delocalized over the Si backbone, the isolated Si4Me10−• radical anion also has isomeric conformations with localized charge and spin. A structure with localization on a terminal Si atom has been examined in detail. In vacuum, it is calculated to lie 11.5 kcal/mol higher in energy than the charge-and-spin delocalized conformation, and in water the difference is as little as 1.6 kcal/mol. According to natural orbital and localized orbital analyses, the charge-and-spin-carrying terminal Si atom uses five stereoactive hybrid orbitals in a trigonal bipyramidal geometry. Four are built mostly from 3s and 3p atomic orbitals (AOs) and are used to attach a Si3(CH3)7 and three CH3 groups, whereas the larger equatorial fifth orbital is constructed from 4s and 4p AOs and acts as a nonbonding (radical) hybrid orbital with an occupancy of about 0.65 e. SECTION: Molecular Structure, Quantum Chemistry, and General Theory

A

tetrahedral (T), in the small-radius exciton, either one Si atom is trigonal bipyramidal (TBP) or two adjacent Si atoms are halfway between T and TBP, and bond lengths are altered. The TBP atom or atoms carry excess negative charge, and positive charge is accommodated in one or more σSi−Si bonds. Much of the excess negative charge is accommodated in the σ* antibond orbitals formed by the distorted Si atom or atoms, but ∼20% of an electron charge is carried by their fifth “valence” orbital directed in the TBP equatorial plane and composed primarily of 4s, 4p, and 3d atomic orbitals. Although the fifth hybrid orbital is more diffuse than the usual first four, it is much smaller than a Rydberg orbital. The objective of the present paper is to ascertain the possible existence and the nature of small-radius polarons in permethylated oligosilane chains. There is some similarity between the addition of an electron to make a radical anion and an electronic excitation of the neutral system, in that in each case, an additional electron is placed into an antibonding orbital. It is of theoretical interest to ask (i) whether the nature of the site distortion is similar in the two cases and whether TBP Si atom or atoms also appear in the radical anion, and (ii) whether they again carry some of their electron density in a fifth “valence” atomic hybrid. A localized radical anion should be differentially stabilized by ion pairing with a small cation and by solvation in highly polar solvents. We have selected the radical anion of n-decamethyltetrasilane, Si4(CH3)10−•, for our RIMP2/def2-TZVPPD investiga-

lthough they are fully saturated, peralkylated linear oligosilanes and polysilanes n-SimR2m+2 display many similarities with conjugated π-electron systems. These analogies have been much investigated and long attributed to σ delocalization in the silicon compounds.1 Thus, like polyenes, polysilanes readily undergo one-electron reduction2−6 or oxidation7,8 to form the radical ions9,10 n-SimR2m+2−• or nSimR2m+2+•. Generally, in long chains, the added charge and spin are delocalized over many adjacent silicon atoms (“large radius polaron”). One can expect the size of the polaron to be dictated by the polaron−phonon coupling constant, which reflects the relative magnitude of the stabilization of charge by delocalization and by site distortion. In shorter chains, quantum confinement reduces the conjugative stabilization, while the site distortion energy hardly changes at all. There may then be a chain length for which the latter prevails, and in shorter chains the polaron can be expected to localize on a small number of sites or perhaps a single site. To our knowledge, such “selftrapped small-radius polarons” with localized charge have not been identified in oligosilanes by experiment or computation. In the analogous case of electronic excitation in electroneutral permethylated silicon chains, the collapse of a largeradius to a small-radius self-trapped exciton occurs when the chain lengths is reduced to seven silicon atoms.11 Permethylated oligosilanes with eight or more Si atoms carry delocalized excitation, those with six or fewer Si atoms carry localized excitation, and in permethylated heptasilane, chain conformation dictates which case occurs.12 The nature of the geometrical distortion in the excited site has only been elucidated recently.13−15 Whereas in the ground state and in the delocalized excited states all Si atoms are approximately © 2013 American Chemical Society

Received: February 25, 2013 Accepted: April 19, 2013 Published: April 19, 2013 1649

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Table 1. RIUMP2/def2-TZVPPD Optimized Geometries of Ground Statesa ω SiSiSiSi/deg

∠SiSiSi/deg

∠CSitC/deg

∠CiSiiSit/deg

∠SiiSitCt/deg

SiSi/Å

SiiCi/Å

SitCt/Å

162.8

109.7 109.7

109.2 109.6 109.2 109.6

1.896 1.896 1.896 1.896

176.5

127.3 127.3

2.368 2.399 2.368

1.912 1.911 1.911 1.912

1b C1

164.7

112.8d 111.4

110.2 110.2 109.7 110.2 110.2 109.7 123.7b 109.0 109.1 109.0 109.1 123.7 98.7f 99.7 103.7 110.6 112.3 111.9

2.357 2.357 2.357

1a C2h

108.7 109.1 108.9 108.7 109.1 108.9 103.9 106.2 103.8 103.9 106.2 103.8 96.8e 96.9 153.7i 107.6 106.9 107.2

2.358 2.353 2.352

1.900 1.897 1.908 1.910

1.886 1.886 1.885 1.886 1.886 1.885 1.917c 1.902 1.902 1.902 1.902 1.917 1.935g 1.969h 1.968 1.891 1.892 1.896

structure 1 C2

105.3 105.5 105.3 105.5

107.5 106.3 112.6 112.2

Neutral Si4Me10 (1) and the charge-and-spin delocalized (1a) and terminally charge-and-spin localized (1b) isomers of the Si4Me10−• radical anion. The subscript t indicates a terminal and the subscript i an internal atom. All angles and bond lengths are listed and the important ones are identified in Figure 1 and in the following footnotes. bThe Si(1)−Si(1)−C(1) valence angle. cThe Si(1)−C(1) bond length. dThe Si(1)−Si(2)−Si(3) valence angle. eThe C(3)−Si(1)−C(1) valence angle. fThe Si(1)−Si(2)−C(3) valence angle. gThe Si(1)−C(1) bond length. hThe Si(1)−C(3) bond length. i The C(2)−Si(1)−C(3) valence angle. a

tion. It is small enough for adequate calculations, yet large enough to display the effects of backbone conformation.16 A previous B3LYP/6311+G(d,p) calculation17 on the charge-andspin delocalized form of this radical anion found the potential energy minimum to be structurally very similar to the neutral transoid18 ground state, T on all Si atoms, and our calculations confirm this result (1a in Table 1, cf. the strictly T neutral ground state 1). To find charge-and-spin localized isomers of Si4(CH3)10−•, we optimized the ground state starting at geometries favorable in the first excited singlet state of neutral Si4Me1015and performed vibrational frequency analysis. In addition to the charge-and-spin delocalized minimum 1a and its backbone conformational isomer, we found several higher energy local minima in which one of the Si atoms is TBP and carries highly localized charge and spin (Supporting Information). We have selected a minimum with a TBP terminal Si atom for a detailed examination (Figure 1, 1b in Table 1). The computed vertical detachment energies of 1a and 1b are weakly negative, −0.09 and −0.22 eV, respectively, making the radical anion metastable, but cannot be considered accurate at the present level of calculation. The Charge-and-Spin Delocalized Minimum (1a, Table 1, Figure 1). Our C2 symmetry structure 1a is similar to the reported17 density functional theory (DFT) structure, but we find the optimal dihedral angle to be 175.6° instead of 180°, which is a transition state. We also find somewhat larger Si−Si−Si and in-plane C−Si−Si valence angles and longer Si−Si bonds. Both the singly occupied molecular orbital (SOMO; Figure 2) and the spin density (Figure S1) of 1a are delocalized over the backbone and in-plane Si−C bonds. Natural charges19 (Table 2) show that the excess electron is delocalized over the Si backbone with a slight preference for the internal Sii (Δq = −0.14 e) over the terminal Sit (Δq = −0.10 e) atoms. Spin densities are also delocalized over the Si backbone and favor the Sii atoms by about a factor of 2. The natural

Figure 1. Optimized RIUMP2/def2-TZVPPD structures for ground states of transoid neutral Si4Me10 (1) and for the charge-and-spin delocalized (1a) and the terminally charge-and-spin localized isomer (1b) of the Si4Me10−• radical anion.

hybrid orbitals (NHOs) directed along the Si backbone have a slight excess of s character and are sp2.75. The excess electron is chiefly carried by the Si backbone σ*Si−Si antibonds, with occupation numbers of 0.25 at SiiSii, 0.15 at SiiSit, and 0.10 at SiiCt. The Terminally Charge-and-Spin Localized Minimum (1b, Table 1, Figure 1). The most striking feature is the wide C(2)− Si(1)−C(3) valence angle of 153.7°. Other valence angles at Si(1) are also distorted from tetrahedral, but the geometry of the rest of the molecule is almost the same as in the ground 1650

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The excess charge resides on Si(1), where the SOMO (Figure 2), the spin density (Figure S1), and the difference density of the anion and the neutral (Figure S2) are highly localized. Structure 1b is 11.5 kcal/mol above 1a in energy in the isolated ion, but only 1.6 kcal/mol in water (ε = 78.39) according to the continuum conductor-like screening (COSMO) model. The natural bond orbital (NBO) analysis and the localized orbital (LO) analysis agree that Si(1) uses five valence orbitals. The NHO composition of the fifth orbital in terms of natural atomic orbital (NAO) contributions shows active participation of 4s and to a lesser degree 4p atomic orbitals (AOs). The ⟨r2⟩ value of this orbital is roughly twice those of the other four (Table 3), and is somewhat smaller than that of the 4s NAO (⟨r2⟩ = 51.4 Å2). The Si(1) hybrid orbitals used to make the Si(1)−C(2) and Si(1)−C(3) bonds that form the wide C(2)− Si(1)−C(3) valence angle on Si(1) are enlarged and possess some 4s and 4pz character. The Si(1) hybrid pointing to Si(2) has high p character (sp4), and the Si(1) hybrids pointing to the terminal methyl groups have increased s character. Boys localization of the MOs20 yields an LO picture similar to that provided by the NBO analysis (Table 3). Here again five orbitals are used by Si(1) to produce the occupied molecular orbitals, and the fifth orbital (⟨r2⟩ = 37.4 Å2) is not much more extended than the four traditional valence orbitals (Figure 4). The Si(1)−C(1) LO is the next most extended orbital at 28.6 Å2 and the Si(1)−Si(2) LO is the least extended at 9.0 Å2. Based on the AO contributions to the LO summed for each atom, all the LOs on Si(1) show significant atomic contributions from Si(2). The Si(1)−Si(2) LO is the most localized with AO contributions from only two atoms that yield a large (79.2%) contribution to the LO, and it has the smallest ⟨r2⟩ value. The other LOs on Si(1) have significant weights over three atoms. The nonbonding fifth orbital on Si(1) is more delocalized than the other Si(1) LOs and contains AO contributions from Si(1), Si(2), C(2), and C(3).

Figure 2. RIUMP2/def2-TZVPPD highest two occupied molecular orbitals (MOs) at Si4Me10−• radical anion minima (isodensity contour, 0.04).

Table 2. Ground State UMP2/6-311+G(d,p) Natural Charges (q, in units of e) for α and β Spin Orbitals, and Spin Densities (ρ) for Radical Anions 1a and 1b structure

atom

qtot (1)

qαa

qβ

qtot

Δ qtot

ρ

1a

Si(1) Si(2) Si(3) Si(4) Si(1) Si(2) Si(3) Si(4)

1.18 0.72 0.72 1.18 1.09 0.70 0.70 1.17

0.46 0.17 0.17 0.46 0.10 0.36 0.33 0.58

0.62 0.43 0.43 0.62 0.68 0.34 0.36 0.58

1.08 0.60 0.60 1.08 0.78 0.74 0.71 1.16

−0.11 −0.12 −0.12 −0.11 −0.31 0.00 −0.01 −0.01

0.16 0.25 0.25 0.16 0.58 −0.01 0.03 0.00

1b

a

The excess electron resides in an α spinorbital.

state of neutral 1. The structure is approximately TBP at Si(1), with the C(2)−Si(1)−C(3) atoms as the axis and the in-plane terminal methyl and adjacent SiMe2 group as two equatorial substituents. The third equatorial site is taken up by a fifth hybrid orbital.

Table 3. AO Contributions to NHOs and LOs on Si(1) of 1b, UHF/6-311+G(d,p) NHO

⟨r2⟩/Å2

na

comp. (%)b

NAOc

LOd

⟨r2⟩/Å2

comp. (%)e

atom

Si(1)−C(1)

23.8

0.53

28.6

23.0

0.60

Si(1)−C(2)

18.6

37.7 28.9 18.0 36.4 22.4 14.4

C(1) Si(1) Si(2) Si(1) C(2) Si(2)

Si(1)−C(3)

19.3

0.65

Si(1)−C(3)

17.1

38.2 19.4 14.5

Si(1) C(3) Si(2)

Si(1)−Si(2)

15.0

0.83

Si(1)−Si(2)

9.0

54.3 24.9

Si(2) Si(1)

Si(1) nbf

46.5

0.65

3s 3px 3pz 3s 4s 3py 3pz 4pz 3s 4s 3py 3pz 3s 3px 3pz 3s 4s 3pz 4pz

Si(1)−C(1)

Si(1)−C(2)

22.1 48.6 25.6 22.0 12.5 41.3 16.3 5.5 25.3 5.9 56.2 8.3 19.2 48.7 28.2 10.5 43.7 19.3 23.7

Si(1) nbf

37.4

25.5 25.3 13.6 6.7

Si(1) Si(2) C(2) C(3)

a

NHO occupation number. bContributions larger than 5%. cThe Si(1)−Si(4) direction is defined as x. dPrimary localization. eContribution of AO orbitals larger than 5% to the LO. fThe fifth Si(1) orbital (nonbonding). 1651

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(nonbonding) “valence” orbital, composed primarily of 4s and 4p AOs. It carries about two-thirds of the net charge and most of the unpaired spin in the radical anion. Its ⟨r2⟩ value, which can be used to judge spatial extent, is about twice those of the other valence orbitals, but is smaller than that of the 4s NAO. Analysis of the AO contributions to the Boys LOs shows large contributions from Si(2) to the Si(1)−Ct LOs (where Ct indicates a carbon attached to a terminal Si). This localization pattern, and the existence of narrow Ct−Si(1)−Si(2) valence angles, could also be indicative of the propensity for dimethylsilylene extrusion, a process that is known to take place in neutral oligosilanes.1 The charge-and-spin localized minimum 1b is similar to certain excited state minima in neutral Si2Me613 and Si3Me8.14 Ab initio methods have located a similar struture in the first excited singlet state of Si4Me10.15 Thus, both DFT and ab initio methods agree that the Si atom can adopt a TBP geometry and use a fifth orbital when it needs to accommodate an extra electron. The ⟨r2⟩ value of the fifth orbital at the distorted silicon atom in the localized radical anion 1b, 46.5 Å2, is slightly smaller than that of its 4s NAO (51.4 Å2) and that of the fifth orbital at the distorted Si atom in the S1 excited state of the neutral calculated at the same geometry, 51.2 Å2 (Table S9, Supporting Information). The value for the 4s NAO at this Si atom in the S1 state is much larger, 88.9 Å2. Our results for Si4Me10−• suggest a specific geometry and associated electronic structure for the site distortion responsible for localization of charge and spin in radical anions of permethylated oligosilane chains. One of the Si atoms becomes TBP, and it uses five stereoactive “valence” orbitals: four to bind four ligands, and the fifth, primarily of 4s and 4p nature, to hold the additional electron. This result revives the issue of valence shell expansion on atoms of main group elements. In an isolated Si4Me10−• ion, localization on a terminal Si atom occurs with an energetic penalty of 11.5 kcal/mol with respect to the charge-and-spin delocalized minimum, but in water, the two minima are nearly isoergic. One can expect ion pairing to have a similar stabilizing effect on the charge localized state, and we suspect that such structures play a role in the chemical reactions of the radical anions, and possibly as electron trapping sites in irradiated amorphous silicon. The geometry of Si4(CH3)10−• was optimized with the UMP2 method21 using the resolution of identity (RI) approximation22 and the def2-TZVPPD basis set23 with TURBOMOLE 6.3,24 starting at optimized geometries of conformers of Si4Me10 in the lowest singlet excited state.15 Vibrational frequencies were calculated to ensure that stationary points correspond to minima. Spin contamination was checked and was not significant (Supporting Information). NBO analysis25 was carried out with NBO 5.926 in GAMESS (Aug. 2011 R1 version)27 at the UMP2/6-311+G(d,p) and RIUMP2/def2-TZVPPD levels of theory with consistent results (cf. Supporting Information). Boys20 LOs were calculated using Turbomole 6.3 and GAMESS. LOs were also calculated using the Pipek−Mezey28 and Edmiston−Ruedenberg29 methods with GAMESS, and the results were similar (Supporting Information). The ⟨r2⟩ values of the NHOs and LOs were calculated with MOLCAS 7.6.30 Vertical detachment energies were calculated as the difference of the neutral and radical anion energy at the radical anion geometry. The conductor-like screening model (COSMO) was used31,32 with the dielectric screening value of 78.39. Default

Figure 3. Si(1) NHOs for 1b (cf. Table 3). Isodensity values of orbitals in parentheses. Display of (A) all five orbitals (0.14), (B) Si(1) nb (0.10), (C) Si(1)−Si(2) (0.04), (D) Si(1) nb (0.04), (E) the equatorial Si(1)−C(1) NHO (0.04), and (F) an axial Si(1)−C(2) NHO (0.04).

Figure 4. UHF/def2-TZVPPD LOs for 1b shown at the 0.06 isodensity surface value.

Our charge-and-spin delocalized structure 1a is similar to the structure found earlier17 and resembles one of the relaxed geometries of the lowest σσ* excited state of neutral Si4Me10.15 As both structures house an “excess” electron in a σ* orbital, the similarity of the neutral excited state and radical anion structures is understandable. Two significant results have been obtained for 1b, one of the localized forms of the radical anion Si4Me10−•: (i) its site distortion is characterized by an approximately TBP geometry at the terminal Si atom, and (ii) to accommodate the extra negative charge, this silicon atom chiefly uses a fifth 1652

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(16) Albinsson, B.; Teramae, H.; Downing, J. W.; Michl, J. Conformers of Saturated Chains: Matrix Isolation, Structure, IR and UV Spectra of n-Si4Me10. Chem.Eur. J. 1996, 2, 529−538. (17) Tachikawa, H.; Kawabata, H. J. Structures and Electronic States of Permethyloligosilane Radical Ions with All-Trans Form Sin(CH3)2n+2± (n = 2−6): A Density Functional Theory Study. Chem. Theory Comput. 2007, 3, 184−193. (18) Michl, J.; West, R. Conformations of Linear Chains. Systematics and Suggestions for Nomenclature. Acc. Chem. Res. 2000, 33, 821− 823. (19) Reed, A. E.; Weinstock, R. B.; Weinhold, F. Natural Population Analysis. J. Chem. Phys. 1985, 83, 735−746. (20) Foster, J. M.; Boys, S. F. Canonical Configurational Interaction Procedure. Rev. Mod. Phys. 1960, 32, 300−302. (21) Haase, F.; Ahlrichs, R. Semi-direct MP2 Gradient Evaluation on Workstation Computers: The MPGRAD Program. J. Comput. Chem. 1993, 14, 907−912. (22) Sierka, M.; Hogekamp, A.; Ahlrichs, R. Fast Evaluation of the Coulomb Potential for Electron Densities Using Multipole Accelerated Resolution of Identity Approximation. J. Chem. Phys. 2003, 118, 9136−9148. (23) Rappaport, D.; Furche, F. Property-Optimized Gaussian Basis Sets for Molecular Response Calculations. J. Chem. Phys. 2010, 133, 134105−134115. (24) TURBOMOLE V6.3 2011, a development of University of Karlsruhe and Forschungszentrum Karlsruhe GmbH, 1987−2007, TURBOMOLE GmbH, since 2007; available from http://www. turbomole.com. (25) Foster, J. P.; Weinhold, F. Natural Hybrid Orbitals. J. Am. Chem. Soc. 1980, 102, 7211−7218. (26) Glendening, J., Badenhoop, K.; Reed, A. E.; Carpenter, J. E.; Bohmann, J. A.; Morales, C. M.; , and Weinhold, F. NBO 5.9 E. D.; Theoretical Chemistry Institute, University of Wisconsin: Madison, WI, 2001. (27) Schmidt, M. W.; Baldridge, K. K.; Boatz, J. A..; Elbert, S. T.; Gordon, M. S.; Jensen, J. H.; Koseki, S.; Matsunaga, N.; Nguyen, K. A.; Su, S. J.; et al. General Atomic and Molecular Electronic Structure System. J. Comput. Chem. 1993, 14, 1347−1363. (28) Pipek, J.; Mezey, P. G. A Fast Intrinsic Localization Procedure Applicable for Ab Initio and Semiempirical Linear Combination of Atomic Orbital Wave Functions. J. Chem. Phys. 1989, 90, 4916−4926. (29) Edmiston, C.; Ruedenberg, K. Localized Atomic and Molecular Orbitals. Rev. Mod. Phys. 1963, 35, 457−464. (30) Karlström, G.; Lindh, R.; Malmqvist, P. Å.; Roos, B. O.; Ryde, U.; Veryazov, V.; Widmark, P. O.; Cossi, M.; Schimmelpfennig, B.; Neogrády, P.; et al. MOLCAS: A Program Package for Computational Chemistry. Comput. Mater. Sci. 2003, 28, 222−239. (31) Klamt, A.; Schüürmann, G. COSMO: A New Approach to Dielectric Screening in Solvents with Explicit Expressions for the Screening Energy and Its Gradient. J. Chem. Soc., Perkin Trans. 2 1993, 799-805. (32) Klamt, A.; Jonas, V. Treatment of the Outlying Charge in Continuum Solvation Models. J. Chem. Phys. 1996, 105, 9972−9981.

bond-length radii from Turbomole 6.3 were used for cavity construction.

■

ASSOCIATED CONTENT

S Supporting Information *

A discussion of basis set effects, Figures S1−S3, and Tables S1 to S9. This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This material is based upon work supported by the National Science Foundation under Grant No. CHE- 0848477.

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REFERENCES

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