Relaxation of the Lowest Singlet Excited State of Octamethyltrisilane

Article pubs.acs.org/JPCA

Fifth Stereoactive Orbital on Silicon: Relaxation of the Lowest Singlet Excited State of Octamethyltrisilane Matthew K. MacLeod,† Lukás ̌ Kobr,† 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: We address relaxation pathways in the excited singlet states S1 of saturated molecules, specifically alkylated oligosilanes. Unlike their longer peralkylated homologues, disilanes and trisilanes do not fluoresce even at low temperatures. An examination of the S1 potential energy surface of Si3Me8 with density functional (TDDFT, LC-TDDFT), and ab initio (RICC2, RIADC(2)) methods with TZVP basis sets revealed only extremely shallow minima in the vicinity of funnels, accounting for the absence of fluorescence, rapid internal conversion, and photoproducts. Relaxed singlet excited state structures either contain one approximately trigonal bipyramidal Si atom or two that are halfway between tetrahedral and trigonal bipyramidal. Four of the ligands are those that the Si atom had in the ground state. Natural bond orbital analysis suggests that the fifth one is a nonbonding hybrid orbital of the lone-pair type and size intermediate between valence and Rydberg, with an only very small occupancy, yet stereochemically active. The fifth natural hybrid orbital is composed primarily of 4s, 4p, and usually to a lesser degree, also 3d atomic orbitals. The trigonal bipyramidal structure allows an optimal accommodation of the presence of both a negative and a positive charge in the Lewis structures. The excess negative charge on the distorted Si atom is shared between the nonbonding fifth hybrid orbital and σ* antibonding orbitals associated with its bonds. The positive charge resides in an adjacent σ SiSi bond orbital. A Rydberg minimum also occurs on the S1 surface at the geometry of the radical cation.

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Molecular Orbitals and Excited States in Si3Me8. Symmetry with respect to the xz plane of the Si atoms can be used to label orbitals σ and π and excited states σσ* and σπ* (x stands for the Si(1)−Si(3) direction). With certain approximations, such labels can also be used for longer oligosilanes with nonplanar backbones.10,13 At its ground-state equilibrium geometry, Si3Me8 has two low-lying nearly degenerate valence excited states: σσ* (x polarized) and σπ* (symmetry forbidden).14,15 In both, excitation is from the highest energy σSiSi orbital (HOMO). The terminating σ* orbital is the lowest energy σ*SiSi orbital and π* is the lowest energy antisymmetric combination of the σ*SiC orbitals. The observed σσ* excitation energy is 47 100 cm−1 and the oscillator strength is 0.13, in agreement with the computed (MS-CASPT2/ANOL)16 values, 45 100 cm−1 and 0.32. The σπ* transition has not been observed, but its presence has been inferred16 from the observed temperature dependence of the absorption spectra; calculations16 yield 46 200 cm−1. They place the lowest Rydberg state significantly higher, at ∼55 200 cm−1. Because we are interested in the interpretation of observations made in the condensed phase,

INTRODUCTION Electronic Excitation in Saturated Molecules. Lowestenergy electronic excitation in saturated molecules involves the very σ-bond electrons that hold the molecule together and can therefore be expected to induce large structural rearrangements, dissociative in the triplet state, but not necessarily1 in the S1 state. Experimental evidence for strongly distorted relaxed S1 states is provided by the enormously Stokes shifted fluorescence of alkanes2 and their silicon analogs, oligosilanes,3−5 which are easier to study. The equilibrium structures of these emitting species have been mysterious for decades. The fluorescence quantum yields are often small, implying nonradiative deactivation (internal conversion and photoproduct formation, presumably through conical intersections,1,6−8 and possibly also intersystem crossing). Anticipating similarities along the homologous series, we have embarked on a systematic examination of the S1 potential energy surfaces of permethylated oligosilanes, starting with the shortest, Si2Me6.9 The short peralkylated oligosilanes, disilanes and trisilanes (such as SinMe2n+2, n = 2, 3), do not fluoresce detectably and their S1 states must therefore have efficient deactivation pathways. For trisilanes, one decay mechanism, involving the reductive elimination of an internal silylene, was studied earlier.10−12 The present paper deals with octamethyltrisilane (1) and identifies additional deactivation pathways. © 2012 American Chemical Society

Received: July 10, 2012 Revised: September 8, 2012 Published: September 14, 2012 10507

dx.doi.org/10.1021/jp3068393 | J. Phys. Chem. A 2012, 116, 10507−10517

The Journal of Physical Chemistry A

Article

methods (Turbomole 6.2) and with the LC-TDDFT method in the Tamm−Dancoff approximation (TDA) with the LC-BLYP functional and def2-TZVP19 basis set (GAMESS). Standard TDDFT with the random phase approximation (RPA) tends to stretch bonds in sigma bound systems excessively,36 and this was also found to be the case for Si3Me8 (Supporting Information). Excited state vibrational analysis was used to identify minima. The LC-TDDFT vertical emission energies were compared with those originally found with the standard TDDFT approach to assess the credibility of the S1 minima found. Whenever a region of S1−S0 energy differences smaller than 2 000 cm−1 was located, we assumed that a funnel was present. These funnels correspond to those found at the RIADC(2)/TZVP level of theory. Vertical excitation (emission) energies at each relaxed S1 stationary point were calculated in the RPA approximation. The RPA oscillator strengths are preferred over TDA because they obey the sum rule and are the same in the dipole length and dipole velocity formulations. Also, the literature37 and our experience with the longer oligosilanes suggest that RPA excitation energies are in somewhat better agreement with experiment. We used the LC-BLYP functional and the def2TZVP basis set (GAMESS), which contains diffuse functions on C and Si. LC-BLYP calculations were also carried out with the def2-TZVPD+ basis set, which is the def2-TZVPD basis set38 augmented with an additional diffuse function for H added from the aug-cc-pVTZ basis set.21 The site distortion energy, ESD, was then computed as the difference between the vertical Franck−Condon and relaxed S1 energies, and the Stokes shift, ESS, was obtained as the difference between the vertical absorption and emission electronic energies. Natural bond orbital (NBO) analysis39 of the LC-TDDFT S1 density matrix was performed at the LC-BLYP/def2-TZVP level of theory with the NBO 5.940 program linked to the GAMESS program suite using the 3-center 4-electron bond search parameter. Analysis of the NBO description and the σσ*/σπ* nature of the excited states was carried out according to a literature procedure13 (Supporting Information). The second Cartesian moment ⟨r2⟩ expectation values of the resulting natural hybrid orbitals (NHOs) were calculated with MOLCAS 7.641 (Supporting Information).

where transitions to Rydberg states are broadened, shifted to higher energies, and essentially inobservable, they are of little interest in the present context. Minima and Funnels in the S1 Surface. The search for minima in the S1 surface of Si3Me8 is complicated by the proximity of valence and Rydberg states. To minimize the likelihood of convergence to Rydberg minima and to locate only valence minima on the S1 surface, the initial examination of the S1 surface by stochastic methods did not use diffuse functions in the basis set. This increased the energy of Rydberg states artificially and made it less probable that they would contaminate the lowest excited states reached from the ground state equilibrium structure. Once the minima were approximately located, the calculations were repeated with diffuse functions included in the basis set, allowing a verification of the valence nature of S1 at these geometries. The search for valence minima also revealed regions of near S0−S1 degeneracy. Their importance in inducing jumps from the S1 to the S0 surface was recognized long ago and they were referred to as funnels.17 Once a funnel region is reached, nonadiabatic coupling and internal conversion to S0 dominate and further travel on the S1 surface is highly unlikely. Funnels are often associated with conical intersections, regions of nuclear geometries at which the S0−S1 degeneracy is exact. A knowledge of these regions would be critical for molecular dynamics calculations and the prediction of quantum yields of the various possible photoproducts but is unimportant for our purposes. Their calculation would require a multireference method and we made no attempt to find them.

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METHODS Density functional theory (DFT) ground state (S0) geometry optimizations for Si3Me8 were carried out with the long-range corrected (LC) functional LC-BLYP18 with the def2-TZVP19 basis set as implemented in GAMESS, version August 1, 2011 R.120 and with the aug-cc-pVDZ21 basis set using Turbomole 6.2.22 In all LC-BLYP calculations, the range correction cutoff parameter μ was set to 0.23 a0−1, a value that reproduces the observed σσ* excitation energy15 of Si3Me8 when used with the LC-BLYP/def2-TZVP method. Ab initio optimizations with the resolution of identity approximate singles and doubles coupledcluster (RICC2)23−25 and the polarization propagator RIADC(2) (algebraic diagrammatic construction through second order) methods26 with TZVP27 basis sets were also carried out. The ground state of the radical cation Si3Me8+• was optimized with the RIUMP2/def2-TZVP method28 (Turbomole 6.2). A stochastic search for local minima in the S1 excited state of Si 3Me8 used time-dependent density functional theory (TDDFT).29 Here 100 structures were generated from the ground state equilibrium geometry in a stochastic manner according to parameters published previously9 and subsequently optimized with the PBE0,30,31 B3LYP,32 and BHLYP33 functionals using the TZVP27 basis set (Turbomole 6.2). The B3LYP functional used was the version that employs the VWN5 correlation functional.34 These calculations employed large integration grids (size 5).35 Selected excited state valence angle scans where all other coordinates were optimized were carried out using Turbomole 6.2 with the above functionals and basis sets. The final excited state (S1) geometry optimizations were carried out starting at the minima located in the excited state stochastic search with the ab initio RICC2 and RIADC(2)

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RESULTS To summarize briefly, multiple methods of calculation located four characteristic minima in the S1 surface 1 (1a−d). Inclusion of diffuse functions in the basis set did not significantly affect the emission energies of the structures 1a−1d, and at these geometries S1 is of valence nature. In contrast, at the minimum geometry 1e, S1 is of diffuse (Rydberg) nature. Additional minima were found but were deemed less relevant because they are either very similar to one of the minima 1a−1e, or were only found with one method of calculation (cf. Supporting Information). All of the structures 1a−e involve considerable structural relaxation away from the initial ground state equilibrium (vertical) geometry. In the case of 1a and 1b the relaxation produces two Si atoms with geometries intermediate between tetrahedral and trigonal bipyramidal (TBP), and in the next two cases, geometries with one internal (1c) or terminal (1d) Si atom with a nearly exactly TBP geometry. In the case of 1e, the relaxation produces the geometry of the radical cation of 1. The silicon atoms that have approached or reached the TBP geometry also house a fifth orbital of 4s4p3d nature in the 10508



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equatorial position of the trigonal bipyramid. Electron density is taken from the σSiSi HOMO and placed into this fifth atomic orbital and also into the σ*SiSi and σ*SiC orbitals on the distorted Si atom. One of the structures, 1a, resembles that of the recently reported9 blue minimum of Si2Me6 and also those structures which have been recently found responsible for the blue emission from somewhat longer oligosilanes.42 The other minima, 1b−d, are more vaguely related to the structures responsible for the anomalous green emission of certain longer oligomers.5 Several S0−S1 funnels, 1α−1δ, have also been identified. Valence Excited State Geometry Relaxation. To increase the likelihood that the S1 optimization leads to minima and funnels in valence states of octamethytrisilane, the optimization was performed without diffuse functions in the basis set. The optimization started at various choices of geometry. (i) The ground state C2 equilibrium geometry 1, at which the lowest excited singlet state is of σπ* nature. This optimization led to the same funnel 1α irrespective of the method used. It has a square planar geometry at the central Si atom with both internal C atoms approximately in the Si−Si−Si plane (Figure 1). (ii) The other choice was a set of geometries 1* derived from structure 1 by stochastic kicks to Si, C and H.

Figure 2. S1 valence minima 1a−d (LC-BLYP/def2-TZVP) and the Rydberg minimum 1e (RICC2/aug-cc-pVDZ). Si−Si bond lengths are given in Å and valence angles in deg.

The narrow Si−Si−Si minimum 1b was found with stochastic searches and all functionals. The internal dimethysilylene extrusion funnel 1γ was not found in the stochastic search and resulted from reoptimization of the narrow Si−Si−Si minimum 1b with ab initio methods. A series of constrained optimizations along the Si−Si−Si bending coordinate with the BHLYP method indicated a very flat potential energy surface with a barrier to the dimethylsilylene extrusion funnel 1γ of only 360 cm−1 at a Si−Si−Si valence angle of 69°. The PBE0 and B3LYP stochastic searches found the wide Si−Si−Si valence angle minimum 1c. All stochastic searches found the funnel 1β whose geometry is similar in many respects to the wide Si−Si−Si angle minimum 1c but mainly differs by an inversion of the Si−Si−Si valence angle. A crude internal C−Si−C valence angle scan at the B3LYP level indicates a barrier of 410 cm−1 when traveling from the wide Si−Si−Si valence angle minimum to a value of approximately 140°. The excited state stochastic searches located the 1d minimum and the 1δ funnel, related to 1d through an increase of the C−Si−C valence angle beyond 180°. Ab initio reoptimization of 1d also yielded 1δ, whereas TDDFT and LC-TDDFT indicated 1d to be a minimum on the S1 surface. A series of constrained optimizations at the BHLYP level along the C(1)−Si(1)−Si(2) bending coordinate indicates the barrier from 1d to 1δ, located at ∼130°, to be only ∼70 cm−1. Blue Minimum 1a. The geometry of 1a belongs to the C1 symmetry group and was found with ab initio, TDDFT, and LC-TDDFT approaches. It is referred to as “blue” because its analogs in somewhat longer silanes are believed42 to be responsible for their reported4 blue emission. For 1a, both Si−Si bonds are stretched compared to the ground state, but Si(2)−Si(3) is elongated much more than Si(1)−Si(2). The Si(1)−Si(2) bond lengths range from 2.372 (RIADC(2)) to 2.379 Å (RICC2) and the Si(2)−Si(3) bond lengths range from 2.454 (LC-BLYP) to 2.609 Å (RIADC(2)) (Table 1). There are other important geometrical distortions besides the Si(2)−Si(3) stretch. The Si−Si−Si valence angle is increased from 110.3° in the ground state (LC-BLYP, Table 2) to 138.8° (LC-BLYP). The C(5)−Si(2)−Si(3) angle is reduced to 88.7° (LC-BLYP) to 89.6° (RIADC(2)). The most Si−C bond stretching occurs between atoms Si(2) and C(5) (to 1.929 Å, LC-BLYP) or between atoms Si(3) and C(6), to 1.920

Figure 1. S0−S1 funnels 1α−δ (RIADC(2)/TZVP). Si−Si bond lengths (Å) and selected valence angles (deg) as well as two views of the 1α and 1β funnels are shown.

Starting from structures 1*, generated by the excited state stochastic search, several minima in S1 were found. The TDDFT BHLYP method yielded the “blue” minimum 1a (Figure 2). Reoptimization of 1a with ab initio methods (RICC2 and RIADC(2)) also showed it to be a minimum on the S1 surface, whereas its reoptimization with the other TDDFT methods produced the wide Si−Si−Si valence angle minimum 1c. If the structure 1a is perturbed by decreasing the terminal C(6)−Si(3)−C(7) valence angle in a constrained optimization (BHLYP), the minimum 1a can reorganize over a barrier of only 25 cm−1 to the wide Si−Si−Si angle structure 1c. Subsequent reoptimization of 1c with both ab initio and BHLYP methods resulted in the S0−S1 funnel 1β. 10509



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Table 1. Optimized Geometries of S1 Valence Minima 1a−1d of Octamethyltrisilane ∠SiSiSi/deg

∠CiSiiCi/deg

∠CiSiiSit/deg

∠SiiSitCt/deg

SiSi/Å

SiiCi/Å

SitCt/Å

Si3Me8 RIADC(2)/TZVP C1 1a

134.9

112.5

89.6 112.4 94.5 110.8

2.372 2.609

1.902 1.914

Si3Me8 RICC2/TZVP C1 1a

137.5

112.5

89.1 111.1 95.3 109.4

2.379 2.576

1.907 1.924

Si3Me8 LCBLYP/def2-TZVP C1 1a

138.8

112.6

88.9 108.5 99.7 106.8

2.373 2.454

1.884 1.924

Si3Me8 LCBLYP/def2-TZVP C1 1b

78.1

98.9

99.9 96.2 120.5 153.1

2.441 2.499

1.896 1.923

Si3Me8 LCBLYP/def2-TZVP Cs 1c

172.5

129.2

90.9 92.2 90.9 92.2

2.426 2.426

1.969 1.969

Si3Me8 LCBLYP/def2-TZVP Cs 1d

101.0

110.1

108.7 113.9 108.7 113.9

90.5 95.1 144.3 107.1 119.4 106.6 90.7 96.6 142.8 107.0 119.8 106.3 89.5 103.5 138.4 108.1 120.2 105.2 96.1 113.8 116.4 133.6 108.8 92.1 104.6 108.3 119.7 104.6 108.3 119.7 92.7 92.7 97.8 104.5 111.0 111.0

2.553 2.352

1.869 1.889

1.920 1.908 1.910 1.898 1.909 1.900 1.923 1.907 1.911 1.899 1.910 1.901 1.921 1.878 1.892 1.880 1.880 1.882 1.888 1.869 1.894 1.899 1.879 1.901 1.882 1.880 1.885 1.880 1.885 1.882 1.961 1.961 1.900 1.880 1.880 1.866 1.866

structure

shows that on Si(2), a fifth NHO is constructed from 4s, 4p, and 3d atomic orbitals and has an occupancy of 0.04 e− in the S1 state. This can be compared with an occupancy of 0.87 e− for the hybrid pointing toward Si(3). The Si(3) atom has a similar fifth NHO with an occupancy of 0.03 e− in the S1 state, which can be compared with an occupancy of 0.90 e− for the hybrid pointing toward Si(2). The nonbonding fifth orbital populations represent only 1% of the total electron counts of 3.3 e− and 2.8 e− in the Si valence orbitals for Si(2) and Si(3), respectively. The axial hybrid orbitals that are used to make the Si(2)−Si(3) bond have increased p character and the equatorial Si(2) and Si(3)−C NHOs have increased s character (sp2), as does the Si(2) hybrid that points toward Si(1), with a 20° deviation from the line connecting the atomic centers. The latter orbital has a large NHO occupation of 1.15 e−. The S0−S1 electronic transition dipole moment lies along the elongated Si−Si bond and the dipole moment of the S1 state ranges from 0.77 to 1.10 D for the RIADC(2) and LC-BLYP structures, respectively. Narrow Si−Si−Si Angle Minimum 1b. This S1 state is of σμ* mixed nature (where the amounts of σ* and π* contained in μ* depend on the functional used in the optimization

(RIADC(2)) to 1.923 Å (RICC2). The Si(2)−Si(3)−C(8) angle is increased to 138.4 (LC-BLYP) to 144.3° (RIADC(2)). Excited state vibrational analysis of 1a revealed that the structures obtained with TDDFT, LC-TDDFT, and ab initio methods correspond to an energy minimum on the S1 surface. Even though octatrimethylsilane does not fluoresce, the vertical emission energies obtained by these methods at the 1a geometry (e.g., 25 200 cm−1 at the RICC2 minimum geometry) agree with the value of 25 400 cm−1 extrapolated from the observed4 blue emission in the permethylated oligosilane series. Relaxation to this minimum corresponds to a large site distortion energy ESD of 3 500 cm−1 and a huge Stokes shift of 18 900 cm−1. The LC-BLYP 1a structure yields an emission energy of 26 600 cm−1, close to the ab initio values (Table 3). The S1 excited state of the blue structure 1a corresponds to a HOMO to LUMO σσ* transition from the ground state. The HOMO (σ) is localized mostly on the elongated Si(2)−Si(3) bond but has contributions from the C(5) and C(6) 2pz atomic orbitals, too. The LUMO (σ*) is delocalized over all Si atoms via contributions from 3s and 3pz atomic orbitals and also has minor contributions from the in-plane C(1) and C(8) 2px atomic orbitals. NHO analysis on the LC-BLYP 1a structure 10510



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Table 2. Optimized Equilibrium Structures of the Ground State Neutral S0, and Radical Cation D0, and S1 Rydberg Minimum 1e ∠SiSiSi/deg

∠CiSiiCi/deg

∠CiSiiSit/deg

∠SiiSitCt/deg

SiSi/Å

SiiCi/Å

SitCt/Å

Si3Me8 RIADC(2)/TZVP C2 S0

110.6

108.4

109.6 109.4

2.356 2.356

1.907 1.907

Si3Me8 RICC2/TZVP C2 S0

110.4

108.4

109.6 109.4 109.6 109.4

2.355 2.355

1.909 1.909

Si3Me8 LCBLYP/def2-TZVP C2 S0

110.3

108.2

110.0 109.1 110.0 109.1

2.340 2.340

1.888 1.888

Si3Me8 RICC2/aug-cc-pVDZ C2 S0

108.9

109.5

109.9 109.3 109.9 109.3

2.358 2.358

1.915 1.915

Si3Me8 RICC2/aug-cc-pVDZ C2 D0

94.0

116.1

111.9 110.4 111.9 110.4

2.460 2.460

1.884 1.884

Si3Me8 RICC2/aug-cc-pVDZ C2 1e

94.0

116.1

111.9 110.4 111.9 110.4

110.0 110.5 110.1 110.0 110.5 110.1 111.0 110.5 110.2 111.0 110.5 110.2 110.0 110.7 109.1 110.0 110.7 109.1 110.0 110.0 109.0 110.0 110.0 109.0 111.8 105.5 93.7 111.8 105.5 93.7 111.8 105.5 93.7 111.8 105.5 93.7

2.46 2.46

1.884 1.884

1.897 1.898 1.897 1.897 1.898 1.897 1.898 1.899 1.898 1.898 1.899 1.898 1.878 1.879 1.878 1.878 1.879 1.878 1.905 1.906 1.905 1.905 1.906 1.905 1.881 1.882 1.870 1.881 1.882 1.870 1.881 1.882 1.897 1.881 1.882 1.897

structure

Table 3. LC-BLYP/def2-TZVPD+ Vertical Emission Energies EVE, S0−S1 Oscillator Strengths f, S0−S1 Λ Values, S1 Dipole Moments, Distortion Energies ESD, and Stokes Shifts ESS for the S1 Minima 1a−1e of Octamethyltrisilane structure

method

state

EVE/cm−1

f

Λ

S1 dipole/debye

1a

RIADC(2) RICC2 LCBLYP LCBLYP LCBLYP LCBLYP RICC2

σσ*

24 900 25 200 26 500 16 000 21 900 18 400 32 000

0.137 0.125 0.083 0.004 0.004 0.009 0.003

0.63 0.62 0.59 0.56 0.66 0.40 0.22

0.77 0.86 1.10 1.31 1.04 3.69 2.60

1b 1c 1d 1e a

σμ* σσ*a σσ* σ4sb

ESD/cm−1 3 3 2 8 3 5 4

500 500 900 700 700 600 400

ESS/cm−1 19 200 18 900 17 300 27 800 21 900 25 400 11 700

The ⟨r2⟩ expectation value for the fifth NHO for this state is 333.2 au. bThe ⟨r2⟩ expectation value for the fifth NHO for this state is 1325.9 au.

NHO of sp3 nature that points to Si (1), an sp4 orbital of nearly normal occupancy (0.96 e−) which points toward Si(3), an sp3 orbital pointing to C(4) with a typical Si−C NHO occupancy of around 0.6 e−, and an sp2 hybrid orbital to C(5) which has higher than normal occupancy (0.79 e−). There is an additional hybrid orbital made of 4s, 4p, and 3d orbitals on Si(2) which occupies the wide C(5)−Si(2)−Si(3) angle. Its occupancy is 0.04 e−, only 1% of the total Si(2) NHO population. In contrast, Si(3) has rehybridized to house a sp4 hybrid pointing toward Si(2) and an sp2 hybrid pointing toward C(6). Here the

procedure, cf. Supporting Information). In the LC-BLYP 1b minimum both Si−Si bonds are elongated, Si(1)−Si(2) to 2.442 and Si(2)−Si(3) to 2.500 Å. The Si−Si−Si valence angle is only 78.2°. The internal Si(2)−C(5) bond is extended to 1.900 Å. This bond also makes a wide C(5)−Si(2)−Si(3) angle of 153.2° with the Si(2)−Si(3) bond, whereas the angle Si(2)−Si(3)−C(6) is only 133.6°. The hybridization of the NHOs on Si(2) and Si(3) correlates with the geometrical arrangements at these two atoms. For the 1b LC-BLYP structure, Si(2) houses a low occupancy (0.82 e−) 10511



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nonbonding fifth orbital inside the wide Si(2)−Si(3)−C(6) angle has an occupancy of only 0.02 e−. The vertical emission energy of 1b is very dependent on the method of calculation (Supporting Information) and of S1 optimization. The LC-BLYP structure yields an EVE value of 16 000 cm−1. The S1 dipole moments of this minimum is also sensitive to the optimization method. For example, the 1b BP86 structure yields an S1 dipole moment of 4.32 D, which is more than three times that of the LC-BLYP structure (1.25 D, Supporting Information). The site-distortion energies, irrespective of the functional used in the structural optimization procedure, gave the largest ESD values (∼10 000 cm−1) among all minima. The 1b minimum has an extremely large calculated Stokes shift of 27 800 cm−1. Wide Si−Si−Si Angle Minimum 1c. The PBE0, B3LYP, and LC-BLYP minima are similar and we focus on the LCBLYP structure. This Cs symmetry minimum has equally stretched Si−Si bonds (2.426 Å). The C(4)−Si(2)−C(5) symmetry plane is orthogonal to the Si−Si−Si backbone. The structure 1c is very close to having C2v symmetry, and only deviates from it by a very minute methyl twist and unequal internal Si−C bond lengths. The Si(2)−C(4) and Si(2)−C(5) bonds are stretched to 1.961 and 1.969 Å, respectively, and the Si−Si−Si valence angle is remarkably wide, 172.5°. There are also wide terminal in-plane C−Si−Si angles of 119.7°. The internal C−Si−Si angles are 92.2°. The internal C−Si−C valence angle is 129.2°. The two NHOs on Si(2) that point toward the terminal Si atoms have an increased p character (∼sp5), and the two Si(2) hybrids that point toward the internal Me groups have an increased s character (∼sp2). NHO analysis shows the fifth valence orbital on the internal Si in 1c to have high 3pz, 4pz, and 3dx2‑y2 character. In contrast to the fifth Si orbital in the minima 1a, 1b, and 1d, here the 3d contribution is of a size similar to that of the 4pz component (cf. Figure 4 and Supporting Information). This fifth valence orbital on Si(2) has the largest NHO occupation (0.22 e−) of all the nonbonding fifth valence orbitals in the minima 1a-d. This value represents 6% of the total Si(2) NHO occupation. This orbital has an ⟨r2⟩ expectation value of 332.2 au, intermediate between valence and Rydberg (cf. Supporting Information). The S1 state of 1c has an increased σσ* character along the Si−Si backbone as evidenced by larger Si−Si NHO coefficients for the HOMO and LUMO compared with those of the ground state equilibrium structure. The LC-BLYP/def2-TZVPD+ calculated emission energy is 21 900 cm−1. The very weak S0−S1 transition ( f = 0.004) is polarized along the short axis of the molecule (z). The S1 state has a dipole moment of ∼1 D, pointing along the z axis. The site-distortion energy is rather small, ∼3 700 cm−1, only slightly larger than that for the blue minimum 1a. Importantly, the emission energy for 1c does not change significantly if calculated without diffuse functions, and the LC-BLYP/def2-TZVP method predicts 22 000 cm−1. Symmetric Wide Terminal C−Si−C Angle Minimum 1d. The structure of 1d contains a mirror plane that cuts through atoms Si(1), Si(2), Si(3), C(1), and C(8), and two of the hydrogen atoms. The Si−Si bond lengths are unequal. In the LC-BLYP minimum, the Si(1)−Si(2) bond length (2.553 Å) exceeds the Si(2)−Si(3) bond length (2.352 Å). The longest Si−C bonds (1.961 Å, equivalent by symmetry) are from Si(1) to C(2) and C(3). The C(2)−Si(1)−C(3) valence angle is wide (166.5°) and the C(2,3)−Si(1)−Si(2) angle is narrow (92.7°).

Calculated values of the vertical emission energy at the green minimum 1d are sensitive to the method used. However, the nature of the excited state is similar for all the methods and involves an excitation from the Si−Si HOMO (a′) to the LUMO (a′), localized on Si(1), mainly at the C(2)−Si(1) and Si(1)−C(3) bonds and on a nonbonding fifth orbital. The Si(1) hybrids pointed toward C(2) and C(3) are approximately sp2 hybridized and have higher than average occupation. In the 1d LC-BLYP structure, the Si(1) hybrid pointed toward C(1) has a high p character (∼80%, with 3px and 3pz contributions) and lower than average occupation (0.65 e−) whereas the Si(1)−C(2) and Si(1)−C(3) hybrids have increased s character (30%) and higher occupation (0.78 e−). The 1d structures obtained with different methods were similar in terms of geometrical parameters, but the NHO hybridization varied. It showed a removal of electron density from the orbitals forming the Si−Si bond, especially the hybrid on Si(1), and its movement to both a nonbonding fifth “valence” orbital located on Si(1) and to the σ*SiC and σ*SiSi orbitals. For example, the LC-BLYP 1d structure favored excitation into σ*Si(1)C(2) (0.36 e−), σ*Si(1)Si(2) (0.15 e−) and to the nonbonding fifth orbital (0.12 e−). According to our NHO analysis at the 1d LC-BLYP minimum, the fifth valence hybrid orbital on Si is made up mostly of 4s and 4p atomic orbitals, with a smaller contribution from 3d orbitals, and carries a population of 0.12 e−, which represents 4% of the total 2.95 e− count in the Si(1) valence orbitals. The bonds carrying the four substituents are ordinary 2-electron bonds, each involving a single hybrid orbital on Si, and a NBO search did not locate a 3-center 4-electron bond. The LC-BLYP relaxed structure 1d has a large S1 dipole moment, 3.69 D, and a small S0−S1 oscillator strength ( f = 0.009), polarized along the stretched Si−Si bond. The emission energy is 18 400 cm−1, on the low side of the broad green emission of longer oligosilanes, which has a maximum near 20 000 cm−1.5,43 The 5 600 cm−1 site distortion energy of 1d is large compared to those at the other minima, except for 1b. Rydberg Minimum 1e. This C2 structure was obtained upon optimization of excited 1 with the LC-BLYP/aug-ccpVDZ (Supporting Information) and RICC2/aug-cc-pVDZ methods. We present the latter geometry here. The Si−Si bond lengths (2.460 Å) are extended equally relative to the ground state, where both are 2.358 Å at this level of theory. The Si−C bond lengths are not significantly different from those in the ground state. The largest C−Si−Si valence angle distortion to 93.7°, from the ground state value of 109.0°, is located at C(1)−Si(3)−Si(2). The Si−Si−Si valence angle is also reduced, to 94.0° in 1e from 108.9° in the ground state equilibrium structure. As in hexamethyldisilane,9 the Rydberg minimum structure 1e is practically identical to that of the radical cation (cf. Table 2). The excitation is from the Si−Si HOMO (localized in the Si−Si bonds) and the terminal orbital is of 4s nature (Figures 3 and 4). Natural population analysis44 (NPA) reveals the S1 density to contain a significant increase in Rydberg population with respect to the S0 density and the populations of the valence minima 1a−d (Supporting Information). Even without diffuse functions in the basis set, this structure yields an S1 wave function with high Rydberg character. The transition from the ground state is forbidden. The vertical emission energy is 32 000 cm−1, the site distortion is 4 400 cm−1 and the calculated Stokes shift is 11 700 cm−1 when calculated with the LC-BLYP/def2-TZVPD+ method. 10512



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angle is 88° and the internal C−Si−C valence angle is 90°. A slight twist of the methyl groups reduces the symmetry of this funnel from C2v to C1. The Si−Si−Si inversion funnel 1β is characterized by an extremely wide Si−Si−Si angle of 198°. The internal C−Si−C valence angle is also large, 161°. Both the Si−Si bonds and internal C−Si bonds are stretched, to 2.46 and 2.04 Å, respectively. These bonds form narrow C−Si−Si valence angles of 90°. The dimethylsilylene extrusion funnel 1γ has a very narrow Si−Si−Si valence angle of 61° and a wide C(5)−Si(1)−Si(2) valence angle of 159°. This funnel has increased Si−Si bond lengths at 2.47 and 2.75 Å for the Si(1)−Si(2) and Si(2)−Si(3) bonds, respectively. In accord with the silylene extrusion process in which a new bond is formed between terminal Si atoms, the Si(1)−Si(3) distance is reduced to 2.72 Å. In the C−Si−C inversion funnel 1δ the C(2)−Si(1)−C(3) angle is now 200°. The C(1)−Si(1)−Si(2) angle is also large, 156°. The Si(1)−Si(2) bond is stretched to 2.95 Å, whereas the remaining Si−Si bond (2.33 Å) hardly deviates from the ground state equilibrium bond distance. Funnels associated with the additional minima discussed in the Supporting Information were located as well. The S0 and S1 energies of the funnels and S1 minima are depicted in Figure 5, where the dashed lines are merely guides for the eye and not approximations to cuts through the S1 potential energy surface, which may contain barriers.

Figure 3. HOMO and LUMO at geometries of octamethyltrisilane minima in S1. Molecular orbitals are shown with the isodensity surface value of 0.04 for valence minima 1a−d and at 0.014 for the Rydberg minimum 1e (LC-BLYP/def2-TZVPD+).

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DISCUSSION Even though fluorescence is not observed in trisilanes and therefore minima in the S1 surface would seem to be absent or too shallow to be of interest, their identification is valuable in two ways: (i) They serve as a conceptual link to similar minima in longer oligosilanes that apparently are deeper and do fluoresce, and (ii) they can serve as fleeting intermediates along deactivation pathways. In the still relatively small Si3Me8 molecule they are easier to examine in detail than their analogs will be in the longer permethylated oligosilanes. Similar information has already been obtained from a study of Si2Me6 but was limited by the presence of only two silicon atoms in the molecule. Concepts from the present work may also be helpful in understanding fluorescence in other species, such as silicon clusters.45 For 2-methyltrisilane, no excited state minima were found in previous work12 and it was proposed that the return through a conical intersection leading to the extrusion of a silylene is responsible for the absence of fluorescence. Reliability of the Results. Our first concern is the difference in the results obtained with different methods of calculation. The minima highlighted in this study were found with multiple approaches. Although only one minimum (1a) was found with both density functional and ab initio methods, in longer chains analogs of 1b and 1d have been found with both types of calculation.42,46 It thus seems that the latter structures are reasonable but the shallow potential minima make them very hard to find in octamethyltrisilane. The vertical emission energies of the structures of 1a obtained with the various methods, e.g., 25 200 or 26 500 cm−1 with the RICC2 and LC-TDDFT methods, respectively, are both in line with fluorescence energy extrapolation (25 400 cm−1) from longer oligosilanes.4 A second concern is the introduction of artificial charge transfer through the TDDFT approach and its effect on the

Figure 4. NHOs on Si(2) at the 1c minimum energy structure: (A) the four traditional NHOs directed to the Si and internal C atoms shown at the 0.13 contour; (B) the fifth orbital valence contribution shown at the 0.07 contour; (C) the Si(2) NHO that points to Si(3) at an intermediate contour level of 0.04; (D) the fifth orbital at the 0.04 contour level; (E) the fifth orbital at the 0.02 contour level; (F) the 4s Rydberg orbital at the Rydberg minimum 1e at the 0.02 contour level. NHOs for both 1c and 1e were generated from the LC-BLYP/ 6311+G(d,p) S1 density matrix.

Funnels: Structures of Near S0−S1 Degeneracy. The square planar funnel 1α is characterized by having a square planar tetracoodinate Si atom with both internal Si−C bonds in the Si−Si−Si plane. In the RIADC(2) structure of 1α, the Si−Si bonds are only slightly stretched to 2.48 Å and the internal Si−C bonds are 1.97 Å long. The Si−Si−Si valence 10513



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Table 4. Octamethyltrisilane S1−S0 Funnel Geometries (RIADC(2)/TZVP) structure

∠SiSiSi/deg

∠CiSiiCi/deg

∠CtSitCt/deg

∠CiSiiSit/deg

SiSi/Å

SiiCi/Å

SitCt/Å

1α

88

90

91 178 91 177

2.49 2.48

1.97 1.97

1β

198

161

88 90 90 87

2.46 2.46

2.04 2.05

1γ

63

102

114 160 100 98

2.47 2.75

1.91 1.92

1δ

100

106

104 110 109 104 110 108 109 105 108 109 105 108 102 113 103 109 103 109 201 96 98 109 108 109

111 116 111 113

2.33 2.95

1.92 1.92

1.90 1.90 1.90 1.90 1.90 1.90 1.90 1.90 1.90 1.90 1.90 1.90 1.91 1.92 1.89 1.90 1.89 1.93 1.92 1.90 1.90 1.90 1.90 1.90

optimizations for structures 1a-d with the TDDFT/aug-ccpVDZ method produced valence minima. The LC-TDDFT/ def2-TZVP minima 1a−d were checked with single point LCTDDFT/def2-TZVPD+ calculations, which showed the valence character to remain and yielded insignificant changes to the emission energies. This is very different from the case of the Rydberg minimum 1e, whose EVE values varied wildly with the choice of functional and basis set. Finally, a fourth concern is that with stretched bonds multireference methods are often needed. However, the bonds in the minima 1a−1e are not extremely stretched. The D1 values55 and multistate complete active space plus second order perturbation theory (MS-CASPT2)41 reference weights at the S1 minima indicate sufficient reliability (Supporting Information). Concerning the funnels, we expect more expensive multireference methods to locate structures closer to the real conical intersections but expect them to be structurally analogous to the funnels we have found here. Multireference calculations12 have located a true conical intersection in 2methyltrisilane which is indeed very similar to the extrusion funnel 1γ located in this work. Stationary Points in the S1 State. An oversimplified but useful overall characterization of the valence S1 minima is that they are essentially of two types. A type I minimum contains two Si atoms at a geometry intermediate between tetrahedral and trigonal pyramidal (TBP) and a type II minimum has one Si atom at a full TBP geometry. In both cases, the remaining Si atoms are tetrahedral. The blue minimum (1a) and the narrow Si−Si−Si valence angle minimum (1b) are of type I, whereas the wide Si−Si−Si (1c) and C−Si−C valence angle (1d) minima are of Type II. Valence Minima of Type I. In both 1a and 1b the silicon atoms with intermediate geometries are labeled Si(2) and Si(3). If the distortion toward a trigonal bipyramidal arrangement were completed, in 1a the axial positions at Si(2) would be

Figure 5. RIADC2/TZVP S0 (blue) and S1 (red) energies of the S1 valence minima (LC-TDDFT/def2-TZVP) and funnels (RIADC2/ TZVP) in octamethyltrisilane.

minima. The LC-TDDFT method, which has been found to provide reliable results elsewhere,18,47−52 was able to locate four minima, 1a−d. Judging from the values of the vertical excitation energy EVE, oscillator strength f, and the Λ criterion53 it seems that S1 optimization with TDDFT and any functional tested led to acceptable structures for the blue minimum 1a and the wide Si−Si−Si valence angle minimum 1c. Calculations for the narrow Si−Si−Si valence angle minimum 1b and for the wide C−Si−C valence angle minimum 1d were more difficult. They were easily contaminated with spurious CT (Supporting Information) and required the LC-TDDFT method. A third issue faced was the mixing of valence and Rydberg orbitals, which is strong at the ground state equilibrium geometry of Si3Me8. From MS-CASPT2 calculations with basis sets designed for Rydberg states, this mixing has been shown to be artificial,16 and therefore the valence minima on the S1 surface remain our main focus. Generally, as electronically excited molecules relax, Rydberg-valence mixing decreases.1,54 Though the B3LYP method was not able to locate the Rydberg minimum 1e (Supporting Information), the geometries obtained with the LC-BLYP and RICC2 methods seem to be reliable as they resemble those of the radical cation. Additional 10514



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slightly more from the tetrahedral starting point. This is reflected in the unequal degrees of rehybridization on the two Si atoms and their difference in the fifth natural hybrid orbital electron occupations. These differences likely bias the 1b structure toward internal rather than terminal dimethyltrisilane extrusion found with ab initio optimization of 1b. The S1 wave functions at the minima 1a−d are different from that at the Rydberg minimum 1e, where the excitation is into a Rydberg 4s orbital and whose EVE depends strongly on the presence of diffuse functions in the basis set. The low 1e Λ value of 0.20 fits nicely into the range of typical values for Rydberg states (0.06 < Λ < 0.28).53 Valence Shell Expansion in the S1 State. The presence of a fifth stereochemically active orbital on one or two Si atoms is remarkable. Although this nonbonding orbital has a low occupancy and carries only about 5% of the total valence electron count, its presence has a large effect on the molecular geometry. This orbital is necessarily more diffuse that a valence orbital would be, because it is built from 4s, 4p, and 3d atomic orbitals. Yet, it clearly is not a Rydberg orbital, as is obvious from its ⟨r2⟩ value, NAO composition, NPA Rydberg populations, Λ values, and the fact that EVE does not change upon addition of diffuse functions to the basis set (the largest change upon going from def2-TZVP to def2-TZVPD+ for 1a− d is 200 cm−1). Similar expansion of the Si valence shell to five or even six hybrid orbitals using orbitals of the 3d shell used to be invoked commonly for the ground states of various compounds containing a pentacoordinate or hexacoordinate Si atom,56,57 but more recent calculations showed convincingly that in these structures a Si atom uses only four hybrid orbitals and formally carries no more than eight electrons in its valence shell.58−60 The bonding in these compounds is now understood by recognizing that, in the first approximation, each of the two lobes of a single Si 3p orbital is used to attach one axial ligand through a 3-center 4-electron bond. This is quite distinct from the situation encountered presently. Localized molecular orbital calculations on the radical anion optimized geometries in analogous permethylated oligosilanes yield results similar to that of the NBO analysis, i.e., that a fifth orbital occupies the wide valence angle on the TBP Si atom. Qualitatively, it is much more acceptable to postulate a participation by a fifth high-energy orbital in an expansion of the valence shell of a high-energy excited state than in the ground state, but this result is still quite remarkable. Funnels and Photophysics. After σσ* excitation at or near the ground state equilibrium geometry, both the σπ* and σσ* states of octamethyltrisilane will be soon accessed. The molecules that are excited into the σπ* surface will be able to electronically deactivate by twisting the internal Si−C bonds into the Si−Si−Si plane. Here the π* orbital is lowered in energy as the Si−C antibonds are rotated into the nodal plane. This mechanism could contribute to the loss of fluorescence in octamethyltrisilane but would be less likely for structures that have extended Si−Si bond lengths or in longer oligosilane chains, both of which have smaller σ−σ* orbital energy gaps. Because only very small barriers are in the way, the σσ* excited state of both 1a and 1c can easily relax via inversion of the Si backbone to find the 1β funnel. The central Si atom goes from trigonal bipyramidal in the 1c minimum to a bent structure in 1β. The inversion of the Si−Si−Si valence angle allows the LUMO to be lowered in energy as the number of nodes along the Si backbone is reduced from three to two via

occupied by Me3Si ligands and two of the equatorial positions by methyls, and the axial positions at Si(3) would be occupied by Me2Si and an in-plane methyl, whereas two of the equatorial positions would carry out-of-plane methyls. The structure 1b can be described in similar terms. The axial substituents at Si(2) would now be a methyl group and the terminal Si(3)Me3 group. The equatorial substituents at Si(2) would be a methyl and terminal SiMe3 groups. In 1a and 1b, the third equatorial position on each partly TBP Si atom is taken up by an additional low occupation orbital carrying a small electron density equal to a fraction of that found in the single TBP Si atom in 1c and 1d that fills the void left by the large valence angles, Si(1)−Si(2)−Si(3) and Si(2)−Si(3)−C(8) in 1a, and C(5)−Si(2)−Si(3) along with C(6)−Si(3)−Si(2) in 1b. Both 1a and 1b are related to the blue minimum of hexamethyldisilane9 and differ only in how the additional SiMe3 (TMS) group is added to the parent disilane (Figure 6).

Figure 6. Derivation of the geometries of the blue and green minima 1a and 1b, respectively, from Si2Me6. Optimized S1 valence angles (deg) and bond lengths (Å) for hexamethyltrisilane and octamethyltrisilane are indicated at the BHLYP/TZVP level of theory.

Valence Minima of Type II. In 1c, the central silicon atom Si(2) and in 1d, the terminal atom Si(1) is trigonal bipyramidal. In 1c, both axial ligands are SiMe3 and the two equatorial ligands are Me, whereas in 1d the axial ligands are Me, one of the equatorial ligands is Me, and the other is Si2Me5. In both cases, the third equatorial position at the trigonal bipyramidal Si atom is occupied by a non-bonding orbital of the “lone pair” type, but carrying only a small electron density. Excited State Wave Functions at S1 Minima. An interesting relationship between 1a and 1b concerns the nature of the LUMO orbital. In 1a the LUMO is delocalized over the Si backbone and in-plane methyl groups, whereas in 1b the LUMO is more localized over the C(5)−Si(2)−Si(3)−C(6) moiety. In both cases, the LUMO is mainly composed of atomic orbital contributions from axial ligands of the two intermediate TBP Si atoms (cf. Figure 3). Although 1a has EVE values in the blue spectral region, the narrow Si−Si−Si minimum 1b has emission energies more strongly Stokesshifted toward the green. However, the actual calculated emission energy of 1b varies considerably, because it is sensitive to spurious charge transfer. An analogous structure in tetrasilane has been found with ab initio methods46 and this likely reflects its increasing stability as the chain length is increased. Although the 1b minimum contains two Si atoms with intermediate TBP structure, the central Si atom deviates 10515



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The fifth orbital carries some of the excess negative charge that was removed from the HOMO and the rest goes into the Si−Si and Si−C antibonding orbitals. This low occupancy orbital is made of 4s, 4p, and 3d atomic orbital contributions. Special care needs to be taken regarding the TDDFT excited state optimization of saturated systems. Artificial charge transfer can easily be built into the relaxed structure, as is the case for minima 1b and 1d, which gave rise to large variation in emission energies, oscillator strengths and S1 dipole moments. Also, the geometry of the Rydberg minimum found by the TDDFT B3LYP/aug-cc-pVDZ method was very different from 1e and thus from the structure of the radical cation. LCTDDFT optimization seems to improve the description of the minima 1a−e satisfactorily.

this mechanism. Ab initio optimizations lead from 1c directly to the 1β funnel. The C−Si−C inversion funnel 1δ and a similar funnel (cf. Supporting Information, 1ε) are the main deactivation mechanisms uncovered by the excited state stochastic search. As the narrow Si−Si−Si angle structure 1b represents the global minimum on S1 located in this work, it is likely that many vibrationally hot molecules will approach this well and continue to the nearby silylene-extrusion funnel 1γ. Combined with previous computational results,10,12 this supports the notion that this mechanism is the major deactivation path for excited octamethyltrisilane. Indeed, internal dimethylsilylene is the most prominent photoproduct found from irradiation of oligosilane chains.10 Commentary on the Lack of Fluorescence in Octamethytrisilane. Why do trisilanes not emit, but longer oligosilanes do? Although we have only made crude scans, it is clear that in 1, the barriers around the blue and green minima are very small. Relaxed C−Si−C and Si−Si−C angle scans yielded barriers of mere 30 to 410 cm−1 for the cost of travel from a minimum to a funnel region. A relaxed Si−Si−Si angle scan with TDDFT suggests the barrier for 1b to reach the dimethylsilylene extrusion funnel is 360 cm−1, whereas ab initio approaches predict that this rearrangement is barrierless. As site distortion energies are huge in comparison to these numbers, vertical excitation will deposit a large amount of electronic potential energy that will be converted into nuclear kinetic energy and allow the molecule to explore large regions of its potential energy surface even in a condensed medium. If the minima are accessed at all, it is thus likely to be only briefly, and given the weak S1−S0 oscillator strengths at the minima, it is no surprise that fluorescence has a difficult time competing with travel to funnels and return to S0. This situation is similar to that found for hexamethyldisilane,9 but only more complicated as there are additional shallow minima that can also be thought of as brief intermediates on the S1 surface. Analogous minima in longer oligosilane chains apparently gain relative stability as the length of the chain is increased and lead to higher fluorescence quantum yields.

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ASSOCIATED CONTENT

S Supporting Information *

Ab initio versus RPA and TDA TDDFT based S1 state optimized geometries, octamethyltrisilane absorption at the ground state equilibrium geometry, geometries of the S1 TDDFT valence minima, analysis of σσ−σπ* mixing at the narrow Si−Si−Si valence angle minimum, natural population analysis, NHO composition, second Cartesian moments, and additional S1 minima and S0−S1 funnels. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS We are grateful to Prof. Raül Crespo (Valencia, Spain) and Frank Weinhold (Madison, WI) for useful discussions. This material is based upon work supported by the National Science Foundation under Grant No. (CHE0848477).

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REFERENCES

(1) Michl, J.; Bonačić-Koutecký, V. Electronic Aspects of Organic Photochemistry; Wiley-Interscience: New York, 1990. (2) Hirayama, F.; Lipsky, S. J. Chem. Phys. 1969, 51, 3616−3617. (3) Sun, Y. P.; Michl, J. J. Am. Chem. Soc. 1992, 114, 8186−8190. (4) Raymond, M. K.; Michl, J. Int. J. Quantum Chem. 1999, 72, 361− 367. (5) Fogarty, H.; Casher, D.; Imhof, R.; Schepers, T.; Rooklin, D.; Michl, J. Pure Appl. Chem. 2003, 75, 999−1020. (6) Worth, G. A.; Meyer, H.-D.; Cederbaum, L. S. In Conical Intersections: Electronic Structure. Dynamics and Spectroscopy; Domcke, W., Yarkony, D. R., Köppel, H., Eds.; World Scientific: Hackensack, NJ, 2004; Vol 15. (7) Martínez, T. J. Acc. Chem. Res. 2006, 39, 119−126. (8) Yarkony, D. Chem. Rev. 2012, 112, 481−498. (9) MacLeod, M. K.; Michl, J. Collect. Czech. Chem. Commun. 2011, 76, 2085−2116. (10) Michl, J.; Balaji, V. In Computational Advances in Organic Chemistry: Molecular Structure and Reactivity; Ö gretir, C., Csizmadia, I., Eds.; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1991. (11) Miller, R. D.; Michl, J. Chem. Rev. 1989, 89, 1359−1410. (12) Venturini, A.; Vreven, T.; Bernardi, F.; Olivucci, M.; Robb, M. A. Organometallics 1995, 14, 4953−4956. (13) Bande, A.; Michl, J. Chem.Eur. J. 2009, 15, 8504−8517. (14) Obata, K.; Kira, M. Organometallics 1999, 18, 2216−2222. (15) Rooklin, D.; Schepers, T.; Raymond-Johansson, M.; Michl. J. Photochem. Photophys. Sci. 2003, 2, 511−517. (16) Piqueras, M. C.; Michl, J.; Crespo, R. Mol. Phys. 2003, 104, 1107−1112.

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SUMMARY Singlet excited octamethyltrisilane has several radiationless deactivation pathways. If the low lying σπ* state is accessed, twisting of the central SiMe2 unit into the Si−Si−Si plane leads directly to a square planar S0−S1 funnel and deactivates the molecule back to the ground state. The ways to deactivate the σσ* state include the previously proposed silylene extrusion mechanism as well as new deactivation pathways, such as Si backbone inversion or C−Si−C angle inversion. This accounts for the absence of fluorescence in octamethyltrisilane. The minima found in the S1 surface of octamethyltrisilane are useful models for excitation localization in oligosilane chains. Both 1a and 1b keep the excitation delocalized symmetrically on two Si atoms by distorting both halfway toward a trigonal bipyramidal geometry, whereas 1c and 1d distort only one of them, but almost all the way to a trigonal bipyramid. The quasilinear axis of the trigonal bipyramidal geometry can be defined by Si−Si−Si (as in the minima 1a and 1c), Si−Si−C (1b), or C−Si−C (1d) atoms. The Si−Si−C and C−Si−C axes can occur on terminal or internal Si sites. Silicon atoms in excited state minima show deviations from the standard sp3 ground state hybridization to make way for an additional fifth orbital added to the equatorial position of one or two TBP Si atoms. 10516



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(53) Peach, M. J. G.; Benfield, P.; Helgaker, T.; Tozer, D. J. J. Chem. Phys. 2008, 128, 044118−044125. (54) Mori, T.; Glover, W. J.; Schuurman, M. S.; Martínez, T. J. J. Phys. Chem. A 2012, 116, 2808−2818. (55) Janssen, C.; Nielsen, I. Chem. Phys. Lett. 1998, 290, 423−430. (56) Gillespie, R. J.; Silvi, B. Coord. Chem. Rev. 2002, 233, 53−62. (57) Woon, D. E.; Dunning, T. H. J. Phys. Chem. A 2009, 113, 7915− 7926. (58) Reed, A. E.; Weinhold, F. J. Am. Chem. Soc. 1986, 108, 3586. (59) Reed, A. E.; Schleyer, P. v. R. J. Am. Chem. Soc. 1990, 112, 1434−1445. (60) Weinhold, F.; West, R. Organometallics 2011, 30, 5815−5824.

(17) Michl, J. Top. Curr. Chem. 1974, 46, 1−59. (18) Tawada, Y.; Tsuneda, T.; Yanagisawa, S.; Yanai, T.; Hirao, K. J. Chem. Phys. 2004, 120, 8425−8433. (19) Weigend, F.; Ahlrichs, R. Phys. Chem. Chem. Phys. 2005, 7, 3297−3305. (20) 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, J.; et al. J. Comput. Chem. 1993, 14, 1347−1363. (21) Dunning, T. H. J. Chem. Phys. 1989, 90, 1007−1023. (22) TURBOMOLE V6.2 2010, a development of University of Karlsruhe and Forschungszentrum Karlsruhe GmbH, 1987−2007, TURBOMOLE GmbH, since 2007; available from http://www. turbomole.com. (23) Hättig, C.; Weigend, F. J. Chem. Phys. 2000, 113, 5154−5161. (24) Hättig, C. J. Chem. Phys. 2003, 118, 7751−7761. (25) Köhn, A.; Hättig, C. J. Chem. Phys. 2003, 119, 5021−5036. (26) Hättig, C. In Advances in Quantum Chemistry: Response Theory and Molecular Properties; Sabin, J. R., Brändas, E., Jensen, H., Eds.; Academic Press: New York, 2005; Vol. 50. (27) Schäfer, A.; Huber, C.; Ahlrichs, R. J. Chem. Phys. 1994, 100, 5829−5835. (28) Weigend, F.; Häser, M.; Patzelt, H.; Ahlrichs, R. Chem. Phys. Lett. 1998, 294, 143−152. (29) Furche, F.; Ahlrichs, R. J. Chem. Phys. 2002, 117, 7433−7447. (30) Perdew, J. P.; Ernzerhof, M.; Burke, K. J. Chem. Phys. 1996, 105, 9982−9985. (31) Adamo, C.; Scuseria, G. E.; Barone, V. J. Chem. Phys. 1999, 111, 2889−2899. (32) Becke, A. D. J. Chem. Phys. 1993, 98, 5648−5652. (33) Becke, A. D. J. Chem. Phys. 1993, 98, 1372−1377. (34) Vosko, S. H.; Wilk, L.; Nusair, M. Can. J. Phys. 1980, 58, 1200− 1211. (35) Treutler, O.; Ahlrichs, R. J. Chem. Phys. 1994, 102, 346−1354. (36) Casida, M. E.; Gutierrez, F.; Guan, J.; Gadea, F. X.; Salahub, D.; Daudey, J. P. J. Chem. Phys. 2000, 113, 7062−7071. (37) Dreuw, A.; Head-Gordon, M. Chem. Rev. 2005, 105, 4009− 4037. (38) Rappoport, D.; Furche, F. J. Chem. Phys. 2010, 133, 134105− 13415. (39) Reed, A. E.; Curtiss, L. A.; Weinhold, F. Chem. Rev. 1988, 88, 899−926. (40) NBO 5.9 E. D. Glendening, J, Badenhoop, K.; Reed, A. E.; Carpenter, J. E.; Bohmann, J. A.; Morales, C. M.; , Weinhold, F. Theoretical Chemistry Institute, University of Wisconsin, Madison, 2001. (41) 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. Comput. Mater. Sci. 2003, 28, 222−239. (42) MacLeod, M. K. Ph.D. Dissertation, University of Colorado, Boulder, 2011. (43) Fogarty, H. Ph.D. Dissertation, University of Colorado, Boulder, 2005. (44) Reed, A. E.; Weinstock, R. B.; Weinhold, F. J. Chem. Phys. 1985, 83, 735−746. (45) Torricelli, G.; Akraiam, A.; von Haeften, K. Nanotechnology 2011, 22, 315711. (46) Teramae, H.; Michl, J. Chem. Phys. Lett. 1997, 276, 127−132. (47) Rohrdanz, M. A.; Herbert, J. M. J. Chem. Phys. 2008, 129, 034107−034114. (48) Kuritz, N.; Stein, T.; Baer, R.; Kronik, L. J. Chem. Theory Comput. 2011, 7, 2408−2415. (49) Vydrov, O. A.; Scuseria, G. E. J. Chem. Phys. 2006, 125, 234109−234117. (50) Chiba, M.; Tsuneda, T.; Hirao, K. J. Chem. Phys. 2006, 124, 144106−144116. (51) Govind, N.; Valiev, M.; Jensen, L.; Kowalski, K. J. Phys. Chem. A 2009, 113, 6041−6043. (52) Kronik, L.; Stein, T.; Refaely-Abramson, S.; Baer, R. J. Chem. Theory Comput. 2012, 8, 1515−1531. 10517


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