Different electronic structure of phosphonyl radical adducts of N-heterocyclic carbenes, silylenes and germylenes: EPR spectroscopic study and DFT calculations

Abstract

Stable N-heterocyclic carbenes and germylenes were allowed to react with a phosphonyl radical, (i-PrO)₂(O)P˙ (7), generated by photolysis of [(i-PrO)₂(O)P]₂Hg. The products were identified by EPR spectroscopy. An unsaturated carbene (1) and germylene (3) react with 7 at the divalent atom to give unstable radical products (τ_½ = 0.2 s). A benzo-annulated carbene (4) and a saturated germylene (6) react with 7 to give more active radicals. An unsaturated (2) and a saturated silylene (5) undergo rapid reaction (in the dark) with [(i-PrO)₂(O)P]₂Hg to yield unusual silyl phosphites. In these cases only secondary radicals were observed. DFT (PBE0/TZVP//B3LYP/6-31+G(d)) calculations of the radical adducts of the different (C, Si, Ge) unsaturated N-heterocyclic divalent species with the phosphonyl radical show that the unpaired electron is delocalized over the five-membered ring; the spin density on the central atoms decreases in the order C, 39% > Si, 14% > Ge, 2%. These trends can be understood in terms of a zwitterionic structure of the radical adducts. The calculations of the radical adducts of 4, 5 and 6 with 7 indicate larger spin density on the central atom, 47%, 58% and 42% on C, Si, Ge, respectively.

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Introduction

Divalent compounds of group 14 elements are among the most important reactive intermediates.¹ For a long time species involving divalent carbon and its heavier congeners could only be directly observed by spectroscopic techniques, either in the gas phase² or in low-temperature matrices,³ but could not be isolated in macroscopic amounts at room temperature. Considerable progress in the chemistry of these compounds was achieved with the synthesis and isolation of stable N-heterocyclic carbenes^4a–4c and later of its heavier analogs.^4d–4i

These discoveries have stimulated research on the electronic structure of these novel divalent species and on the reasons for their unusual stability.⁵

Carbene 1 and its heavier group 14 congeners have lone pair electrons as well as a low-lying vacant pπ orbital, which implies that they can act both as electron donors, e.g.: in carbene–, silylene–, germylene–transition metal complexes,⁶ and as electron acceptors, e.g.: in reduction by alkali metals.⁷ These species therefore may possess high reactivity towards free radicals with different donor–acceptor properties. Interaction of the divalent species with radicals to form a new bond and change their valency from two to three can involve, in the first step, a single electron transfer. An analogous case of interaction of free radicals with compounds containing lone pair electrons may be found in the radical chemistry of phosphites or phosphines, where radical addition to trivalent organophosphorus species leads to formation of four-valent, phosphorus-centered intermediates (eqn (1)).⁸

X₃P: + Y˙ → X₃P˙–Y (1)

Although many reactions of stable N-heterocyclic divalent compounds have now been described,⁹ few reports on the chemistry of radicals of these compounds are available.¹⁰ Several radical adducts of unsaturated 1–3 with free radicals of different chemical nature, such as O-, P-, Re-, Co-, Mo-centered radicals (eqn (2)), have been studied by EPR and DFT calculations and were reported recently by us^10a–c and by other groups.^10d–k These adducts represent a new type of neutral radicals stabilized by various degrees of delocalization, which depend on the central divalent atom.^10a–c The first isolations of diamagnetic products of free radical addition to silylenes and germylenes have been reported recently.^10h,i

We present here a first systematic study of phosphonyl radical (i-PrO)₂(O)P˙ (7) adducts of N-heterocyclic stable carbenes, silylenes and germylenes by EPR spectroscopy and DFT calculations. We consider the following: (i) spectral features of the radical adducts, (ii) the effect of the divalent atom E (E=C, Si, Ge) on the spin density distribution in radical adducts, (iii) the effect of a saturated or unsaturated N-heterocycle on the electronic and molecular structure of the generated adducts. Additionally, we report a new type of reaction of silylenes 2 and 5 with phosphonyl mercury which yields silyl phosphites.

Results and discussion

In the following sections we discuss the structures and EPR spectra of radical adducts of 1–6 with the phosphonyl radical 7. Selected calculated geometrical parameters are given in Table 1 and the hfc constants and spin density distribution are provided in Table 2.

Table 1 Calculated sum of angles (Σθ(E)) around the central atom [°] and selected bond lengths (Å) of radicals 1–6

Radical	E	Σθ(E)	E–P	E–N^a	N–C^b	C–C′
a Average of E–N and E–N′. b Average of N–C and N′–C′.
1a	C	352.3	1.781	1.421	1.395	1.349
4a	C	340.9	1.836	1.423	1.399	1.416
2a	Si	284.2	2.400	1.841	1.365	1.374
5a	Si	313.0	2.339	1.754	1.472	1.533
3a	Ge	270.0	2.493	1.961	1.348	1.390
6a	Ge	303.6	2.463	1.856	1.463	1.529

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Table 2 Experimental and calculated ¹³C, ²⁹Si, ⁷³Ge, ³¹P and ¹⁴N hfc constants (a, G), and calculated Löwdin atomic spin densities (SD)

	a(E) exp	a(E) calc	SD(E)	a(P) exp	a(P) calc	SD(P)	a(2N) exp^a	a(2N) calc^a	SD(2N) ^b
a Average value on two atoms. b Sum of values on two atoms. c No experimental data. d Calculated data for model 4a′. e Not observed due to low signal-to-noise ratio.
1a	25.6	21.9	39.3%	48.7	34.9	7.5%	4.7	3.1	34.3%
2a	—^c	−75.0	14.4%	—	243.5	10.5%	—	4.4	45.8%
3a	15.0	−13.9	2.4%	186.0	182.9	8.1%	6.4	5.3	54.2%
4a	n/o^e	46.8	46.7%	81.0	122.2	7.1%	3.6	2.5	27.3%
5a	—	−192.3	57.8%	—	264.0	11.6%	—	3.7	16.8%
6a	n/o	−78.3	42.0%	199.6	302.1	14.5%	7.6	4.6	23.7%

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Radical 7 is pyramidal and the unpaired electron occupies an orbital with nearly sp³ hybridization.^11a (the EPR spectrum and a DFT calculated structure of 7 are presented in the ESI, Fig. S1†). The radical addition product of phosphonyl radicals in which the phosphorus atom is β to the radical center yield large a_P values (40–140 G), which are easy to detect. Thus, the EPR spectra can provide important information about the structures of the radical adducts.^10c,11b–d

a) Carbene adducts

i) Radical adduct of carbene 1. In a preliminary communication^10c we reported the generation of radical 1a (eqn (3)).

The following hyperfine coupling (hfc) constants were measured for radical 1a (g = 2.0027, τ_½ = 7.1 s): a(³¹P) = 48.7 G, a(2¹⁴N) = 4.7 G, a(2¹H′) = 1.1 G, a(¹³C*) = 25.6 G (Table 2). According to DFT calculations, the central carbon atom in 1a is slightly pyramidal, Σθ(C*) = 352° and the heterocycle is almost planar. The calculated Löwdin atomic spin density of 1a shows that 39% of the spin density is localized on the central carbon atom (C*) and 37% on the other ring atoms.

ii) Radical adduct of carbene 4. Unfiltered UV irradiation of the benzene solution of 4 and [(i-PrO)₂(O)P]₂Hg (eqn (4)) leads to an EPR spectrum consistent with radical 4a [a(2¹⁴N) = 3.6 G; a(³¹P) = 81.0 G; g = 2.0028; τ_½ < 1 s] (Fig. 1a, Table 2). Hyperfine coupling of the unpaired electron with the ¹³C* nucleus was not observed due to a low signal-to-noise ratio.

Fig. 1 (a) EPR spectrum of 4a recorded under UV-irradiation at 298 K, (b) DFT calculated spin density of 4a′ at 0.003 au contour level. Calculated g-factor = 2.0032.

To investigate the structure and the spin density distribution in radical 4a DFT quantum mechanical calculations were carried out on a model radical (4a′), in which 1-adamantyl groups were replaced by tert-butyl groups. The heterocycle of 4a′ is nearly planar (∠C*NCC′ = −5.6° and ∠C*N′C′C = 6.7°), with a more pyramidal central carbon atom (Σθ(C*) = 341°) than that in 1a (Table 1). Calculations show that 47% of the spin density is localized on the central carbon atom, and 36% of the spin density is distributed on the other atoms of the heterocycle and annulated aromatic ring (Table 2). The difference between the calculated (a_P = 122 G) and experimental (a_P = 81.0 G) ³¹P hfc constant can be attributed to conformational and vibrational averaging and general method error.

b) Germylene adducts

i) Radical adduct of germylene 3. Addition of phosphonyl radical 7 to germylene 3 in a toluene solution leads to an intense EPR spectrum consistent with radical 3a (eqn (5)) [a(2H) = 4.4 G; a(2¹⁴N) = 6.38 G; a(³¹P) = 186.0 G; a(⁷³Ge) = 15.0 G; g = 2.0021] (Fig. 2, Table 2).

Fig. 2 (a) EPR spectrum of a toluene solution of 3a recorded under UV-irradiation at 298 K (asterisk marks lines belonging to side products¹²), (b) simulated spectrum of 3a, (c) expanded low field multiplet.

When the irradiating light is turned off a fast (and reversible) decrease in the intensity of the EPR signal of 3a is observed (τ_½ = 0.2 s) (Fig. S3†). The rate of decay of 3a is not markedly dependent on temperature (230–290 K) and we believe that radical 3a decays via dimerization (dimer structure unknown). We estimate the dimerization rate constant as 2k_dim = 5 × 10³ M⁻¹ s⁻¹.

According to DFT calculations, the heterocycle of 3a is nearly planar (∠GeNCC′ = −2.4° and ∠GeN′C′C = 1.4°), with a significant pyramidality at the germanium atom, Σθ(Ge) = 270.0°. The calculated g-factor (2.0027), hfc constants for ⁷⁹Ge, ¹⁴N, ¹H, ³¹P and the calculated spin density (Fig. 3, Table 2) show good agreement with the experimental EPR data of 3a, indicating that only 2% of the spin density is localized on the germanium atom, and 81% of the spin density is distributed over the other atoms of the heterocycle. The calculations indicate that 12% of the spin density is localized on the phosphonyl group, accounting for the high hyperfine splitting by the ³¹P nucleus. Thus, the spin density is transferred from germanium into the five-member ring and into the phosphonyl group, leading to an unusual zwitterionic structure (eqn (5)). An analogous case of a nearly complete transfer of spin density away from a heteroatom occurs in the phosphorus-centered radical ˙PPh(OEt)₂(OBu-t), where the spin density is delocalized onto the aromatic ring.¹³

Fig. 3 DFT calculated spin density of 3a at 0.003 au contour level. Calculated g-factor, absolute values of hfc constants and Löwdin atomic spin densities (in parentheses) at the particular nucleus of radical 3a: g = 2.0027, a(¹³C) = 1.0 G (14.8%), a(¹³C′) = 2.2 G (11.9%), a(¹H) = 4.1 G (−1.0%), a(¹H′) = 3.5 G (−1.0%).

The hyperfine coupling of germanium in 3a, a(⁷³Ge) = 15.0, is much smaller than that in the stable pyramidal radical [(Me₃Si)₂N]₃Ge˙ (171.0 G),¹⁴ and in fact even smaller than reported for the planar radical (t-Bu₂MeSi)₃Ge˙ (20.0 G).¹⁵ The relatively low ⁷³Ge hyperfine coupling constant in radical 3a is consistent with delocalization of the unpaired electron away from the Ge atom. Similar to 3a, a low ⁷³Ge hyperfine coupling constant (9.6 G) was observed for the isoelectronic Cl-substituted germanium radical 3b, which was isolated as deep red crystals in the reaction of the anion radical of 1,2-bis[(2,6-diisopropylphenyl)imino]acenaphthene and GeCl₂.^10j We believe that in this case, full stabilization of the radical was achieved by additional delocalization of the unpaired electron over the annulated acenaphthene fragment of the molecule (a DFT calculated structure of 3b is presented in the ESI, Fig. S4†).

ii) Radical adduct of germylene 6. Unfiltered UV-irradiation of a toluene solution containing [(i-PrO)₂(O)P]₂Hg and saturated germylene 6 leads to an EPR spectrum consistent with radical 6a [a(2H) = 2.5 G; a(2¹⁴N) = 7.64 G; a(³¹P) = 199.6 G; g = 2.0036] (eqn (6), Fig. 4, Table 2). This spectrum demonstrates the interaction of the unpaired electron with only two methylene protons out of four. Evidently, the two pairs of methylene protons are not magnetically equivalent relative to the orbital of the unpaired electron (see calculations below). At room temperature the rate of dynamic conformational changes (ring inversion) of the saturated heterocycle (in the timescale of EPR) is not enough to average the hyperfine interaction with the four protons. This effect is typical for EPR spectra of saturated cyclic radicals.^10a,16 The very large ³¹P-coupling constant of 199.6 G in 6a is one of the largest observed for ³¹P nuclei in radical adducts of phosphonyl radicals.

Fig. 4 (a) EPR spectrum of 6a recorded under UV-irradiation at 298 K, (b) expanded low field multiplet.

After the irradiating light is turned off the signal of 6a immediately disappears. The signal intensity of 6a is lower by an order of magnitude than the signal of 3a at a similar reactant concentration and condition of UV-irradiation. This fact indicates that the rate of 6a dimerization is markedly faster than for 3a.

DFT calculations of hfc constants in radical 6a predict a somewhat larger a_P = 302.1 G. The calculated spin density distribution shows that in radical 6a 42% of the spin density is localized on the central germanium atom, and 24% of the spin density is distributed on the ¹⁴N atoms (Fig. 5), in contrast to the spin density distribution in 3a in which only 2% of the spin density resides on the Ge. Such a spin distribution difference between 3a and 6a is reasonable, because 6a has no conjugated π-system which can delocalize the spin.

Fig. 5 DFT calculated spin density of 6a at 0.003 au contour level. Calculated g-factor, absolute values of hfc constants and Löwdin atomic spin densities (in parentheses) at the particular nucleus of radical 6a: g = 2.0031, a(¹³C) = 0.5 G (0.7%), a(¹³C′) = 0.4 G (−0.2%), a(¹H) = 0.8 G (−0.1%), a(¹H*) = 2.3 G (0.2%), a(¹H′) = 5.6 G (0.7%), a(¹H*′) = 7.5 G (0.9%).

c) Silylene adducts

i) Reaction of silylene 2 with [(i-PrO)₂(O)P]₂Hg. In contrast to carbenes and germylenes, spontaneous reaction of a toluene solution of [(i-PrO)₂(O)P]₂Hg with unsaturated silylene in a 1 : 2 ratio begins immediately even at 200 K and gives an unexpected red-yellow Hg-containing product (2b), which was characterized by ¹H, ¹³C, ³¹P and ²⁹Si NMR spectroscopy (Scheme 1). 2b is not stable at r.t. and completely disappears after 12 h (in the dark) forming a new compound 2c, also observed by NMR spectroscopy. Additionally, traces of (i-PrO)₂(O)PH have been observed by NMR spectroscopy, indicating that radical processes are involved. Both products 2b and 2c are very air and moisture sensitive. Matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF MS) of the reaction mixture shows signals corresponding to 2c and of the Hg-elimination product of 2b (Fig. S5†).

Scheme 1

Reactions of silylene with dialkylphosphite and its derivatives are new and interesting, however evidently, we cannot use [(i-PrO)₂(O)P]₂Hg for formation of Si–P bonds in radical addition reactions.

The EPR monitoring of a toluene solution containing [(i-PrO)₂(O)P]₂Hg and 2 in the dark and under UV irradiation reveals only minor secondary products of various radical reactions (for details see ESI, Fig. S6–S7†).

Although we could not observe the primary radical adducts (2a) of the phosphonyl radical with 2, we carried out computations for radical 2a in order to compare it with the analogous adducts of the carbenes and germylenes discussed above. DFT calculations of the structure (Scheme 1) and hfc constants in 2a predict a(³¹P) = 243.5 G. Fig. 6 shows the calculated structure of 2a and its spin density. The heterocycle of 2a is planar (∠SiNCC′ = −0.5° and ∠SiN′C′C = 0.5°), with a pyramidal central silicon, Σθ(Si*) = 284.2°. The calculated spin densities show that in primary radical 2a 14% of the spin density is localized on the central silicon atom and 65% of the spin density is distributed on the other atoms of the heterocycle. The spin delocalization pattern is similar to that in radical 3a (E = Ge), but with slightly higher spin density on the central silicon atom.

Fig. 6 DFT calculated spin density of 2a at 0.003 au contour level. Calculated g-factor, absolute values of hfc constants and Löwdin atomic spin densities (in parentheses) at the particular nucleus of radical 2a: g = 2.0032, a(¹³C) = 0.9 G (13.4%), a(¹³C′) = 1.6 G (9.5%), a(¹H) = 3.0 G (−0.86%), a(¹H′) = 2.4 G (−0.61%).

ii) Radical adduct of silylene 5. Saturated silylene 5 reacts with [(i-PrO)₂(O)P]₂Hg similarly to unsaturated silylene 2 (Scheme 2). However, the reaction is slower and less clean, and additional unidentified minor products were observed.

Scheme 2

As we did for 2a, we studied computationally the radical adduct (5a) of phosphonyl radical 7 to silylene 5. The DFT calculations predict a(³¹P) = 264.0 G. The calculated spin density distribution shows that in radical 5a 58% of the spin density is localized on the central silicon atom, and 19% of the spin density is distributed over the other atoms of the heterocycle (Fig. 7).

Fig. 7 DFT calculated spin density of 5a at 0.003 au contour level. Calculated g-factor, absolute values of hfc constants and Löwdin atomic spin densities (in parentheses) at the particular nucleus of radical 5a: g = 2.0032, a(¹³C) = 2.3 G (0.9%), a(¹³C′) = 1.1 G (0.1%), a(¹H) = 0.7 G (0.06%), a(¹H*) = 2.9 G (0.29%), a(¹H′) = 1.7 G (0.24%), a(¹H*′) = 5.0 G (1.1%).

Conclusions

Radical reactions of phosphonyl radicals with stable N-heterocyclic carbenes, silylenes and germylenes were studied by EPR spectroscopy and by DFT calculations. The calculations show that for unsaturated radicals 1a, 2a and 3a, the degree of pyramidality at the radical center increases in the order: C (Σθ = 352°) ≪ Si (Σθ = 284°) < Ge (Σθ = 270°), which is accompanied by a decrease in the spin density on the central atom (C (39.3%) ≫ Si (14.4%) > Ge (2%)) and an increased spin delocalization over the 5-membered ring (C ≪ Si < Ge, highest delocalization). These trends can be understood in terms of a larger contribution of zwitterionic resonance structure B (eqn (7)) along the series Ge > Si ≫ C. This trend is consistent with the strength of np-SOMO(E) → π*(N–C=C–N) conjugation which also follows the order Ge > Si > C, as the SOMO(E) energy in e.g., H₃E˙ increases along the series C (−10.5 eV) ≪ Si (−9.1 eV) < Ge (−8.9 eV) (UHF/6-311+G//UB3LYP/6-311+G(d)). In all these trends large differences are observed between C and Si while the differences between Si and Ge are small.

In saturated radicals 5a and 6a, lacking the possibility for cyclic electron delocalization, the calculated spin density at the central atom is much higher (Si, 58%; Ge, 42%) than in the corresponding unsaturated radicals 2a and 3a, as expected.

Silylenes, in contrast to carbenes and germylenes react spontaneously with [(i-PrO)₂(O)P]₂Hg to yield unusual mercury-containing silyl phosphites. This new reaction opens interesting synthetic perspectives (e.g. synthesis of metallosilyl phosphite compounds).

The geometry, spin density distribution and reactivity of radical adducts of group 14 imidazol-2-ylidene and imidazolin-2-ylidene demonstrate a strong dependence on the nature of the heterocycle and on the divalent central atom. Such dependence is unprecedented in radical chemistry. We are continuing to explore this interesting new class of radical reactions.

Experimental section

Standard Schlenk techniques in a vacuum (10⁻² torr) were used for the preparation and manipulations of all samples.

Typical EPR experiment

The phosphonyl radical 7 was generated photolytically in situ from [(i-PrO)₂(O)P]₂Hg. UV-irradiation of solutions containing the N-heterocyclic metallylenes and [(i-PrO)₂(O)P]₂Hg in a Pyrex tube within the cavity of the EPR spectrometer gave rise to the radical adducts of metallylenes whose spectra were recorded. The typical concentration of the metallylenes was 10⁻² M and of Hg[P(O)(OPr-i)₂]₂ was 3 × 10⁻³ M.

Materials

The synthesis of 2,^4d3,^4h4,^4b5,^4f6^4h and [(i-PrO)₂(O)P]₂Hg¹⁷ is described elsewhere. Toluene and benzene were degassed, kept on t-BuLi in a vacuum and distilled prior to use.

EPR spectroscopy

EPR spectra were recorded on a Bruker EMX-10/12 X-band (ν = 9.4 GHz) digital EPR spectrometer equipped with a Bruker N₂-temperature controller. Samples were irradiated with the focused and filtered (λ > 300 nm) or unfiltered (λ > 250 nm) light of a high-pressure mercury lamp (1 kW) (ARC lamp power supply model 69920) in the resonator of the EPR spectrometer.

EPR spectra were recorded at microwave power 0.5–1.0 mW, 100 kHz magnetic field modulation of 0.05–1.00 G amplitude. Digital field resolution was 2048 points per spectrum, allowing all hyperfine splitting to be measured directly with an accuracy of better than 0.1 G. Spectra processing and simulation were performed with Bruker WIN-EPR and SimFonia Software. The g-factors values were determined using 2,2,6,6-tetramethylpiperidine-N-oxyl (TEMPO) as reference (g = 2.0058).

NMR spectroscopy

NMR spectra were recorded at room temperature in benzene solutions in J. Young vacuum NMR tubes equipped with DMSO-d₆ capillary as external standard, using Bruker Avance 300 and Bruker Avance 500 instruments. NMR shifts are given in ppm.

2b: ¹H NMR (benzene, DMSO-d₆ capillary): δ 5.95 (4H, s), 4.91 (4H, m, J_H–H = 5.9 Hz), 1.41 (36H, s), 1.30 (24H, m, J_H–H = 5.9 Hz); ²⁹Si NMR: δ 65.7 (d, J_Si–P = 12.7 Hz); ³¹P NMR: δ 129.3; ¹³C NMR: 113.0, 65.4 (d, J_C–P = 10.9 Hz), 51.6, 32.0, 24.8.

2c: ¹H NMR (benzene, DMSO-d₆ capillary): δ 5.71 (2H, s), 4.52 (4H, m, J_H–P = 6.3 Hz, J_H–H = 6.2 Hz), 1.41 (18H, s), 1.19 (24H, dd, J_H–P = 2.0 Hz, J_H–H = 6.2 Hz); ²⁹Si NMR: δ −71.2 (t, J_Si–P = 1.3 Hz); ³¹P NMR: δ 126.2; ¹³C NMR: δ 110.4, 65.5 (d, J_C–P = 11.1 Hz), 51.3, 30.6, 24.5.

5b: ¹H NMR (benzene, DMSO-d₆ capillary): δ 4.94 (4H, m, J_H–H = 6.0 Hz), 2.94 (8H, s), 1.39 (36H, s), 1.33 (24H, d, J_H–H = 6.0 Hz); ²⁹Si NMR: δ 67.9 (d, J_Si–P 16.4 Hz); ³¹P NMR: δ 129.7; ¹³C NMR: 65.0 (d, J_C–P = 10.9 Hz), 51.2, 44.1, 30.8, 24.8.

5c: ¹H NMR (benzene, DMSO-d₆ capillary): δ 4.55 (4H, m, J_H–P = 6.0 Hz, J_H–H = 6.3 Hz), 2.90 (4H, s), 1.66 (18H, s), 1.22 (24H, dd, J_H–P = 5.2 Hz, J_H–H = 6.3 Hz); ²⁹Si NMR: δ −69.1 (t, J_Si–P = 3.2 Hz); ³¹P NMR: δ 126.0; ¹³C NMR: δ 65.2 (d, J_C–P = 10.8 Hz), 50.9, 41.5, 29.3, 25.0.

Computational methods

Geometry optimizations were performed at the DFT B3LYP/6-31+G(d) level. This level was demonstrated to be reliable in predicting ground state geometries of radicals.¹⁸ All structures were confirmed as local minima by calculating second order derivatives. Orbital energies were calculated for optimized geometries using the UHF method because KS energies tend to overestimate the experimental values. However, trends are consistent within the methods.¹⁹ These calculations were carried out using the Gaussian03²⁰ series of programs.

Isotropic hyperfine coupling constants and g-factors were calculated using the PBE0 functional²¹ in conjunction with an uncontracted TZVP²² basis set using the ORCA 2.6.35 software package developed by F. Neese.²³ The PBE0/TZVP level produces more accurate predictions of hfc constants and g-factors.^23b,24

Acknowledgements

We are grateful to Dr Miriam Karni for helpful discussions. This research was supported by the Israel Science Foundation, by the USA-Israel Binational Science Foundation and by the Minerva Foundation in Munich. B.T. is grateful to the Center for Absorption in Science, Israel, Ministry of Immigrant Absorption, State of Israel for support. At the University of Wisconsin this research was sponsored by the National Science Foundation. R. West thanks the WCU program through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology (R33-10082) for support.

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Footnotes

† Dedicated to Professor Wataru Ando, a pioneer of silicon chemistry, on the occasion of his 75th birthday.

‡ Electronic supplementary information (ESI) available: Cartesian coordinates and energies of stationary points in the calculations of 2a, 3a, 4a, 5a, 6a and Fig. S1–S7. See DOI: 10.1039/c0sc00143k

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