Quantum chemical study of the Si–C bond photodissociation in benzylsilane derivatives: a specific ‘excited-state’ silicon effect

Journal of Molecular Structure (Theochem) 668 (2004) 1–11 www.elsevier.com/locate/theochem

Quantum chemical study of the Si –C bond photodissociation in benzylsilane derivatives: a specific ‘excited-state’ silicon effect Mikhayl F. Budykaa,*, Tatyana S. Zyubinaa, Antonios K. Zarkadisb a

Department of Photochemistry, Institute of Problems of Chemical Physics, Russian Academy of Sciences, Chernogolovka 142432, Moscow region, Russian Federation b Department of Chemistry, University of Ioannina, Ioannina 451 10, Greece Received 1 July 2003; revised 1 July 2003; accepted 22 August 2003

Abstract Structure and properties of the ground ðS0 Þ and lowest excited triplet ðT1 Þ states of benzylsilane derivatives bearing the benzophenone chromophore group, p-PhCO-C6H4-CR00 R000 -SiR30 (R0 , R00 , R000 ¼ H, H, H; Me, H, H; Me, H, Me; Me, Me, Me; Me, H, Ph; Me, Me, Ph; Me, Ph, Ph), were calculated using the semiempirical PM3 method. The bond dissociation energy (BDE) of the Si– C bond in the S0 state and the heat of the bond dissociation reaction ðDHr Þ in the T1 state were found to decrease with increasing substitution at silicon and/or benzylic carbon atom. There exists a straight-line dependence between the BDE and DHr values in the series of the compounds studied. Minimal energy paths for the ‘heterobenzylic’ Si – C bond dissociation in benzylsilane PhCH2-SiH3 and for the benzylic C– C bond dissociation in the carbon analogue ethylbenzene PhCH2-CH3 in T1 states were calculated using PM3 and B3LYP/6-31G**. The activation energies obtained are 13.3 and 36.7 kcal/mol (PM3), and 6.3 and 19.6 kcal/mol (B3LYP/6-31G** with ZPE correction) for benzylsilane and ethylbenzene, respectively. Both methods predict much lower activation barrier for benzylsilane compared to ethylbenzene. The difference in activation energies explains the experimentally observed high quantum yields (up to 0.9) of the Si – C bond photodissociation in silicon derivatives of benzophenone as compared to the C– C bond photodissociation in the corresponding carbon analogues (quantum yields ,0.17). q 2004 Elsevier B.V. All rights reserved. Keywords: PM3; B3LYP; Benzylsilane derivatives; Triplet excited state; Photodissociation

1. Introduction The oxidative cleavage of organosilanes, specifically benzyltrimethylsilane derivatives, has been the subject of numerous investigations in recent years. It has been found that the reaction can be initiated by both thermo- [1 – 3] and photo- [4 – 6] electron transfer with formation of benzyltrimethylsilane radical cation as a primary intermediate. The latter undergoes a fast Si –C bond cleavage (with nucleophilic assistance of the solvent [4,5,7]), giving benzyl radicals and the products derived therefrom. There are some controversial data about the Si – C bond cleavage under the direct photolysis. In early publications, benzyltrimethylsilane itself has been described as photochemically inert [8] or reacting with very low efficiency [9]. Negligible photoreactivity of benzyltrimethylsilane (compared to benzylsilacyclobutanes) has been corroborated * Corresponding author. Tel.: þ 7-96-517-1903; fax: þ7-96-514-3244. E-mail address: [email protected] (M.F. Budyka). 0166-1280/$ - see front matter q 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2003.08.121

recently [10], while application of aryl- and alkylsilanes, including benzylsilane, as photoinitiators and cross-linking agents assumes rather efficient Si – C bond cleavage under irradiation [11,12]. Hiratsuka et al. [13,14] carried out detailed investigations on the benzyltrimethylsilane photochemical behavior. They have found that both in methanol solution at room temperature and in ethanol glass at 77 K the Si –C bond photocleavage occurs in the excited singlet state, although the participation of higher triplet states at 77 K was not excluded. The photodissociation quantum yield ðwÞ at room temperature has been determined rather low, w ¼ 0:07 [14]. The reaction mechanism of the benzyl radical formation is assumed to be the Si – C bond cleavage in a nucleophilic reaction of the singlet-excited benzyltrimethylsilane with alcohols, the nature of this reaction is, however, not specified. They have also performed PM3 calculations and found a deformed (compared to the S0 and T1 states) structure of the excited singlet ðS1 Þ state, which has been

2

M.F. Budyka et al. / Journal of Molecular Structure (Theochem) 668 (2004) 1–11

Fig. 1. General structure of benzylsilane derivatives studied and atom numbering used.

tentatively named as the X state (see more detailed discussion below). Recently, interesting finding has been made as to the Si – C bond cleavage under the direct photolysis of benzyltrimethylsilane derivatives. Insertion of chromophore groups (anilino group or benzoyl one) on the para position of the benzyltrimethylsilane aromatic ring considerably enhances the ability of the compound for dissociation [15 –18]. For example, high photodissociation quantum yield ðw ¼ 0:9Þ has been found for 4-[diphenyl(trimethylsilyl)methyl]benzophenone (compound 7 in Fig. 1), while for the carbon analogue 4-PhCO-C6H4CPh2-CMe3 the yield is five times less ðw # 0:17Þ [19]. Both the Si – C and C – C bond dissociation in the above benzophenone derivatives has been proved to proceed in the lowest excited triplet ðT1 Þ state. In the present report we studied the structure and properties of the ground ðS0 Þ and lowest excited triplet ðT1 Þ states of p-benzoylbenzylsilane derivatives 1 – 7 (Fig. 1), paying attention to the Si – C heterobenzylic bond dissociation. To elucidate the role of the benzoyl (carbonyl) group, unsubstituted benzylsilane and model p-formylbenzylsilane were also investigated, and in order to clarify the possible specific effect of silicon, the properties of benzylsilane and p-benzoylbenzylsilane (concerning the Si –C bond dissociation) were compared with those of the carbon analogues ethylbenzene and p-benzoylethylbenzene. It is worth noting that the photodissociation of ethylbenzene (following 248 nm photoexcitation) has been recently found to take place mainly from the first triplet excited ðT1 Þ state [20,21], and thus can be directly compared to the photodissociation of the benzylsilane derivatives. Calculations were performed using PM3 method for all compounds studied and density functional theory (DFT) (B3LYP) with 6-31G** basis set for the simpler model compounds. The main effect predicted by all calculation methods used, consists in significant lowering of the photodissociation activation barrier of the heterobenzylic bond dissociation reaction in the triplet excited ðT1 Þ state on going from the carbon compounds to the silicon analogues. This is a specific ‘excited-state’ silicon effect since the C – Si bond dissociation energy (BDE) (a ground state parameter) does not practically change. The effect is explained in terms of energy gap between the aromatic pp orbital representing spectroscopic (local excited) configuration, and the antibonding spSi – C or

spC – C orbital representing reactive (dissociative) configuration. For the silicon compounds the energy gap is much less compared to the carbon analogues. As a result, the reaction barrier originating from the avoided crossing between the two potential energy surfaces corresponding to the two above configurations, is much less for the silicon compounds as compared to the carbon analogues. In turn, the relative position of the spSi – C or spC – C molecular orbitals (MOs) is determined by the nature of the bond forming atoms: silicon, being a third period element, has much higher lying atomic orbitals as compared to carbon, which is a second period element. Therefore, the spSi – C orbital by nature is always lower lying compared to the analogous spC – C one. The results of the calculations are in full accordance with the experimental data and explain the experimentally observed high photochemical activity of p-PhCOC6H4CPh2-SiMe3 compared to the carbon analogue p-PhCOC6H4CPh2-CMe3 and unsubstituted silanes PhCH2-SiMe3 and Ph3C-SiMe3.

2. Methods The structures, properties, and photodissociation reaction of benzylsilane derivatives 1– 7 were studied by means of the semiempirical quantum chemical method PM3 [22] (program package MOPAC 7.0). The structures of compounds in the ground and lowest excited triplet states were calculated with full optimization of the geometrical parameters. Three model compounds, benzylsilane, its carbon analogue ethylbenzene, and p-formylbenzylsilane were calculated using the DFT method (B3LYP) with 631G** basis set. The DFT calculations were performed using the GAUSSIAN -94 program package [23] on supercomputer RM600 at the computer center of IPCP RAS. Preliminary calculations of the triplet states of the benzylsilane derivatives and doublet states of the corresponding radicals using unrestricted Hartree – Fock (UHF) method showed contamination by higher spin states; for example, kS2 l was 2.28 for the T1 state of benzylsilane, and 0.77 and 1.21 for the radicals silyl (SiH3) and benzyl (PhCH2), respectively, formed through dissociation. Therefore, in further calculations we used the restricted open-shell HF (ROHF) method. The vertical excitation energy to the lowest singlet excited state DðS1v 2 S0 Þ was found

M.F. Budyka et al. / Journal of Molecular Structure (Theochem) 668 (2004) 1–11

3

˚ (Table 1); as a result ðrC4 – C5 Þ decreases from 1.39 to 1.34 A the para-disubstituted benzene ring accepts a para-quinoid structure. The bond length of the carbonyl group remains in ˚ . On going from S0 to T1 state the the range of 1.22 – 1.23 A ˚. Si1 –C2 bond length decreases slightly by 0.01 – 0.03 A Earlier it has been shown that one of the factors, which facilitates the dissociation of a benzylic s-bond, is its perpendicular arrangement in respect to the local excited pchromophore [25]. For compounds 1 – 6 the PM3 method predicts for both the S0 and T1 states an optimal (perpendicular) arrangement of the Si1 –C2 bond. Only for the per-phenylated compound 7 a deviation from this arrangement by 418 ðS1 Þ and 498 ðT1 Þ is calculated; obviously, in this case the deviation is the effect of the steric hindrance of the bulky trityl group. X-ray analysis of compounds 2 and 7 shows perpendicular arrangement in the ground state for the former and 208 deviation from the perpendicular arrangement for the latter [26]. In the S0 state the Si1 – C2 bond is highly polarized with large positive charge at the Si1 atom and negative charge at the C2 atom (Table 1). There exists also charge alternation in the disubstituted benzene ring of the benzophenone chromophore, which is observed for all series of the compounds studied. Upon consecutive substitution at C2 the electron density at this atom decreases gradually leading to a charge variation (S0 state) from 2 0.43e for 2 to 0.10e for 7. For the same series the positive charge at atom Si1 decreases slightly from 0.78 to 0.74 e. On excitation to T1 state distinctive charge redistribution takes place resulting in electron density shift from the C2 atom to the benzene ring and the carbonyl group (Table 1); at the same time, the charge at the Si1 atom remains practically unchanged. The geometry and charge changes on going from the S0 to T1 state can be easily explained by examining the structure of the frontier MOs of these states. As an example

as single-point calculation of S1 with the ground state optimized geometry. The activation energies ðEa Þ for the dissociation were obtained as the barrier maxima on the cross-sections of the T1 potential energy surface (PES), calculated using the corresponding Si – C or C –C distances as reaction coordinates. Thus located transition states coincided with those found using the keyword SADDLE, and their nature as the first-order saddle points having one imaginary frequency was confirmed by vibrational analysis (FORCE calculation).

3. Results and discussion 3.1. Structure In the ground state all benzylsilane derivatives have nearly the same geometry around the benzophenone group, whereas the main geometry changes are registered at the C2 atom where the various substituents are introduced (Fig. 1). From Table 1 one can see that every additional methyl or phenyl group elongates the Si1 – C2 bond by 0.02 or 0.03 – ˚ , respectively, and thus this bond changes from 1.92 0.04 A ˚ in the series 2– 7. In methylsilane the Si –C bond to 1.99 A ˚ [24]. length is 1.857 A The C2 –C3 bond is also slightly elongated in the same ˚ (from 1.47 to 1.50 A ˚ ). series by 0.03 A The same tendency, i.e. gradual elongation of the Si1 – C2 and C2 – C3 bonds with insertion of substituents at the benzylic carbon atom C2, is also observed in the lowest excited triplet state. In contrast to the ground-state, the T1 main geometry changes concern only the benzophenone chromophore group, namely the disubstituted benzene ring. For example, the C3 – C4 bond length ðrC3 – C4 Þ increases ˚ , whereas the C4 – C5 bond from 1.40 to 1.45 – 1.46 A

Table 1 Selected PM3-calculated geometrical parameters and charges for benzylsilane derivatives 1–7 in the ground ðS0 Þ and lowest excited triplet ðT1 Þ states Compound

State

rSi1– C2

rC2 – C3

rC3 – C4

rC4 – C5

zC2

zC3

zCO

PhCOC6H4CH2-SiH3

1

S0 T1

1.89 1.88

1.48 1.46

1.40 1.45

1.39 1.34

20.46 20.41

20.02 20.10

0.09 0.01

PhCOC6H4CH2-SiMe3

2

S0 T1

1.92 1.91

1.47 1.46

1.40 1.45

1.39 1.34

20.43 20.38

20.01 20.11

0.10 0.01

PhCOC6H4CHMe-SiMe3

3

S0 T1

1.94 1.92

1.48 1.46

1.40 1.46

1.39 1.34

20.33 20.27

20.01 20.12

0.10 0.01

PhCOC6H4CMe2-SiMe3

4

S0 T1

1.96 1.94

1.49 1.48

1.40 1.46

1.39 1.34

20.22 20.16

0.00 20.11

0.10 0.01

PhCOC6H4CHPh-SiMe3

5

S0 T1

1.95 1.93

1.49 1.47

1.40 1.46

1.39 1.34

20.28 20.23

20.01 20.10

0.10 0.01

PhCOC6H4CMePh-SiMe3

6

S0 T1

1.97 1.95

1.50 1.48

1.40 1.46

1.39 1.34

20.16 20.11

20.01 20.11

0.10 0.01

PhCOC6H4CPh2-SiMe3

7

S0 T1

1.99 1.96

1.50 1.50

1.40 1.46

1.39 1.34

20.10 20.09

20.02 20.08

0.09 0.01

Bond lengths in angstroms; charge in e.

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M.F. Budyka et al. / Journal of Molecular Structure (Theochem) 668 (2004) 1–11 Table 2 PM3-calculated heats of formation DHf (in kcal/mol) of benzylsilane derivatives 1– 7 and corresponding radicals Compound PhCOC6H4CH2-SiH3 PhCOC6H4CH2-SiMe3 PhCOC6H4CHMe-SiMe3 PhCOC6H4CMe2-SiMe3 PhCOC6H4CHPh-SiMe3 PhCOC6H4CMePh-SiMe3 PhCOC6H4CPh2-SiMe3

Fig. 2. Structure of the frontier molecular orbitals for p-benzoylbenzylsilane 1: the HOMO and the LUMO for S0 state; the lowest semioccupied MO (LSOMO) and the highest semioccupied MO (HSOMO) for T1 state.

1 2 3 4 5 6 7

DHf

Radical

DHf

15.27 234.64 239.43 244.18 24.62 27.07 28.10

SiH3 SiMe3 PhCOC6H4CH2 PhCOC6H4CHMe PhCOC6H4CMe2 PhCOC6H4CHPh PhCOC6H4CMePh PhCOC6H4CPh2

42.93 215.00 46.37 35.16 25.33 68.18 59.63 94.96

BDEðPhCOC6 H4 CR00 R000 2 SiR03 Þ ¼ DHf ðPhCOC6 H4 CR00 R000 Þ þ DHf ðSiR03 Þ

Fig. 2 shows the structure of the highest occupied MO (HOMO) and the lowest unoccupied MO (LUMO) of the S0 state and the lowest semioccupied MO (LSOMO) and the highest semioccupied MO (HSOMO) of the T1 state for 1. One can see that both HOMO and LUMO are localized to a large extent on the disubstituted benzene ring with partial contribution coming from the C2 atomic orbital (AO) in the case of the HOMO and from the carbonyl group AOs in the case of the LUMO. Upon excitation, electron transition from HOMO to LUMO converts in the T1 state these MOs to LSOMO and HSOMO, respectively. The electron transition results in the above charge changes and in elongation of the C3 – C4 bond with simultaneous shortening of the C4 –C5 bond. Since the excitation is localized on the benzoyl group, the variation of substituents at the benzylic (C2) carbon atom has little effect on the excitation energy and position of the T1 level (Table 3). It is note worthy that in the S0 state, the antibonding spSi1 – C2 orbital, which has to be filled as a pre-requisite for the Si1 –C2 bond dissociation, is LUMO þ 4 and lies by 0.9 eV higher than LUMO. In the T1 state, as a result of relaxation, the antibonding spSi1 – C2 orbital lowers and becomes LUMO, being the nearest orbital to HSOMO. This creates favourable conditions for mixing and repopulation of the two MOs upon the Si1 – C2 bond elongation and explains the efficiency of this bond photodissociation in the T1 state of benzylsilane derivatives as compared to the carbon analogous, see more detailed discussion below. 3.2. ‘DHr – BDE ’ relationship Heats of formation of the compounds 1 –7 and the corresponding radicals (which are formed upon the Si1 –C2 bond dissociation) in the ground state are listed in Table 2. On the basis of the calculated heats of formation, the BDE values of the Si1 – C2 bond (Table 3) were evaluated according to Eq. (1):

2 DHf ðPhCOC6 H4 CR00 R000 2 SiR03 Þ:

ð1Þ

One can see that PM3 predicts a BDE reduction by 8 kcal/mol on going from 1 to 2, the opposite effect of that observed on going from SiH3 – H to SiMe3 – H where the BDE values are 91.7 [27] and 94.9 kcal/mol [28], respectively, i.e. an increase by 3.2 kcal/mol. This can be explained by the fact that PM3 underestimates the heat of formation of SiMe3 radical (experimental value is 3.34 kcal/mol [29]), that results in underestimated BDE values for 2 compared to 1. Since the underestimation is the same for every compound in the series 2– 7, it does not affect the relative BDE values and their trends which is further discussed. One can see that the sequential insertion of methyl or phenyl groups at the C2 atom in the series 2 – 7 results in gradual reduction of the BDE, the effect of the first group (6.4 –8.2 kcal/mol) being slightly more than that of the second one (5.1 – 6.0 kcal/mol). Similar to earlier studied Nmethylaniline derivatives [30], the decrease in the BDE on going from 2 to 7 can be attributed entirely to the benzyltype radical stabilization effect due to delocalization of the unpaired electron.

Table 3 PM3-calculated vertical excitation energies DðS1v 2 S0 Þ; singlet–triplet energy gaps DðT1 2 S0 Þ; BDEs of the Si1–C2 bond in the S0 state, and heats of the Si1– C2 bond dissociation reaction DHr in the lowest excited triplet state T1 for the benzylsilane derivatives 1–7 (in kcal/mol) Compound PhCOC6H4CH2-SiH3 PhCOC6H4CH2-SiMe3 PhCOC6H4CHMe-SiMe3 PhCOC6H4CMe2-SiMe3 PhCOC6H4CHPh-SiMe3 PhCOC6H4CMePh-SiMe3 PhCOC6H4CPh2-SiMe3

1 2 3 4 5 6 7

DðS1v 2 S0 Þ

DðT1 2 S0 Þ

BDE

DHr

111.1 109.5 108.4 107.9 109.6 108.7 108.5

57.1 57.7 58.3 59.0 58.4 58.9 59.5

74.0 66.0 59.6 54.5 57.8 51.7 51.8

16.9 8.3 1.2 24.5 20.6 27.2 27.7

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Table 3 shows also calculated data for the excited states. The heats of formation of compounds in the lowest Franck – Condon excited state ðS1v Þ were calculated using equilibrium geometry of the ground ðS0 Þ state. Data for the lowest triplet excited state T1 were calculated with complete geometry optimization. One can see that the PM3 method predicts for all benzylsilane derivatives near the same vertical excitation energies DðS1v 2 S0 Þ: This indicates that the Franck – Condon transition S0 ! S1v is localized on the benzophenone chromophore being the same in all compounds. PM3 predicts also near the same energies for the lowest excited triplet states (values of the singlet –triplet gap DðT1 2 S0 Þ in Table 3). Comparison of the calculated data for 1– 7 with benzophenone’s experimental value (69 kcal/mol in nonpolar solvents [31]) indicates that PM3 underestimates the singlet – triplet energy gap by a constant value; the same tendency has been observed earlier for the T1 state of aniline derivatives [30]. Since the dissociation reaction of the compounds 1 –7, both in the S0 and in the T1 states, gives rise to the same radical products PhCOC6H4CR00 R000 and SiR30 , the heat of the Si1 – C2 bond dissociation reaction ðDHr Þ in the lowest excited triplet state can be calculated similar to the method used for the BDE’s DHr ¼ DHf ðPhCOC6 H4 CR00 R000 Þ þ DHf ðSiR03 Þ 2 DHf ðT1 ðPhCOC6 H4 CR00 R000 2 SiR03 ÞÞ;

ð2Þ

where DHf ðT1 (PhCOC6H4CR00 R000 -SiR30 )) is the heat of formation of the T1 state of 1 –7. The data obtained are listed in Table 3. Note that the heat of the dissociation reaction decreases with increased substitution, the effect of every substituent on the DHr value being slightly more than that on the BDE one. For example, insertion of the first methyl group (2 to 3) results in 7.1 kcal/mol reduction of the DHr as compared to the 6.4 kcal/mol reduction of the corresponding BDE; insertion of the second phenyl group (5 –7) gives rise to 7.1 kcal/mol reduction of the DHr as compared to 6.0 kcal/mol reduction of BDE. Recently, we found [30] for a homologous series of compounds having the same local chromophore (and therefore the same local triplet excited state) and the same dissociating bond, that the heat of the bond dissociation in the lowest excited triplet state DHr is in straight-line dependence to the BDE of that bond, Eq. (3) DHr ¼ BDE 2 DðT1 2 S0 Þ:

ð3Þ

Since the benzophenone derivatives 1– 7 represent a homologous series of compounds with the same local triplet excited state energy (average DðT1 2 S0 ) value for these compounds is 58.4 kcal/mol, see Table 3), Eq. (3) is converted to: DHr ¼ BDE 2 58:4 ðkcal=molÞ:

ð4Þ

5

Fig. 3. Correlation of PM3-calculated heat of the Si1–C2 bond dissociation reaction DHr in the triplet excited ðT1 Þ state vs. BDE in the ground ðS0 Þ state for benzylsilane derivatives 1–7 (correlation coefficient is 0.995).

The plot in Fig. 3 shows pictorially the relationship between the PM3-calculated values of BDE and DHr for 1 –7. Therefore, similar to the C –N bond photodissociation in aniline derivatives [32], one can expect straight-line dependence of the quantum yield of the Si – C bond photodissociation in benzylsilane derivatives on the BDE value for this bond. 3.3. The Si – C bond photodissociation reaction As was already mentioned in Section 1, the photodissociation of substituted benzylsilane derivatives proceeds in the triplet excited state. However, the (equilibrium) lowest triplet ðT1 Þ state of 1 –7 is in fact the ‘local’ excited state of the benzophenone chromophore, which is not dissociative in respect to the Si1 – C2 bond. In order dissociation to proceed, the pp benzophenone orbital involved in the excitation should interact with the antibonding spSi – C orbital representing the reactive configuration. This interaction can be evaluated by examining the frontier MOs structure along the reaction pathway. We investigated the PES of the triplet excited state of 1 in more detail considering the Si1 –C2 bond length as a reaction coordinate. During the calculations the distance between atoms Si1 and C2 was fixed and all other parameters were optimized. To elucidate the role of the benzoyl (carbonyl) group the unsubstituted benzylsilane 10 and the model derivative p-formylbenzylsilane 11 were investigated, while on the other hand to clarify a possible silicon-specific effect the properties of benzylsilane 10 and p-benzoylbenzylsilane 1 (concerning the Si – C bond dissociation) were compared with the carbon analogues ethylbenzene 8 and p-benzoylethylbenzene 9 (concerning the C – C bond dissociation). The atom numbering for

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benzylsilane and ethylbenzene corresponds to that depicted in Fig. 1 replacing, however, in the case of ethylbenzene atom Si1 with C1. To validate the applicability of the PM3 calculations three compounds, ethylbenzene, benzylsilane, and p-formylbenzylsilane were calculated also at B3LYP/631G** level. The results obtained, together with known experimental and literature data, are collected in Table 4. As an example, Fig. 4(a) shows the representative PM3calculated curves (minimal energy paths on the T1 energy surfaces) for the two analogues, benzylsilane 10 and ethylbenzene 8. The dissociation curve for ethylbenzene (Fig. 4(a), curve 1) shows a distinct maximum at ˚ (point B), FORCE calculation confirms rC1 – C2 ¼ 2.04 A that there is a transition state of the dissociation reaction (saddle point with one imaginary frequency, related to the breaking C1 – C2 bond). Compared to ethylbenzene, dissociation curve for benzylsilane (Fig. 4(a), curve 2) displays gradual ascending shape without global maximum but with local one at ˚ (point B0 ). The local maximum possesses rSi1 – C2 ¼ 2.32 A all characteristic features of the transition state: vibrational analysis gives one negative force constant ensuring that this is a first-order saddle point on the energy surface, and the negative mode corresponds to the reaction coordinate. Moreover, the same transition state was located using the SADDLE keyword and starting from both sides, the benzylsilane and the separated radicals. It is clear that through the minimization procedure the system ‘falls down’ ˚ , and then into the rather shallow local minimum at , 2.4 A rises to the transition state. The number of imaginary

frequency for the Si – C bond dissociation transition state (2 95 cm21), as compared to that for the C – C bond dissociation transition state (2 1320 cm21), characterizes the T1 PES for benzylsilane as being more flat compared to that for ethylbenzene (compare curvature of the curves 1 and 2 near points B and B0 , respectively, Fig. 4(a)). Obviously, the lack of global (barrier) maximum on the Si –C bond dissociation curve can be explained by the fact, that PM3 method underestimates the value of the singlet – triplet gap DðT1 2 S0 Þ for benzylsilane 10 (Table 4). Therefore, point A0 on the curve 2 (Fig. 4(a)) lies too low and also results in lowering of the barrier point B0 . The second consequence of the singlet – triplet gap underestimation is overestimation of the heat of reaction DHr ; as a result, at PM3 level the dissociation reaction is endothermic (Table 4). At the same time, calculations at B3LYP/631G** level reproduce precisely the position of the T1 level (82.1 kcal/mol) and confirm that the point B 0 at ˚ is a real barrier maximum, the dissociation rSi1 – C2 ¼ 2.32 A reaction being exothermic one (Table 4). The same relationship between PM3 and DFT calculated and experimental data is observed also for ethylbenzene 8: PM3 method underestimates the DðT1 2 S0 Þ value, whereas DFT reproduces it precisely (82.0 kcal/mol [31]). The examination of the MO’s structure confirms further the nature of the transition states involved in the photodissociation of the C – C and Si –C bonds. In the region of spectroscopic minima, for both ethylbenzene and benzylsilane (Fig. 5, points A and A0 , respectively) the semioccupied MOs are localized mainly on the benzene ring

Table 4 Triplet state ðT1 Þ comparative parameters (calculated and experimental) for benzylsilane and carbon analogues: the singlet–triplet energy gap DðT1 2 S0 Þ ˚ ) in the transition state; the activation energy Ea and the heat of the X1–C2 bond dissociation reaction (kcal/mol), the X1–C2 (X ¼ Si, C) bond length rTS (A DHr (kcal/mol) Compound

DðT1 2 S0 Þ

rTS

Ea

DHr

Method

PhCH2-CH3 (8)

58.4 81.0 86.8 82.0 82.0 [31]

2.04 2.07

36.7 19.0 20.8 19.6

14.5 212.0 27.7 210.8

PM3 B3LYP/6-31 þ G* [21] B3LYP/6-31G** B3LYP/6-31G** with ZPE correction Experimentala

57.5

2.06

37.4

15.6

13.3 7.5 6.3

13.3 215.8 216.9

p-PhCOC6H4CH2-CH3 (9) PhCH2-SiH3 (10)

60.2 85.6 82.1 82.1 [13]

p-HCOC6H4CH2-SiH3 (11)

57.1 68.5 65.8 72.0 [31]

p-PhCOC6H4CH2-SiH3 (1)

a b c

For toluene. See Section 3. For benzaldehyde.

57.1

b

2.32 2.32

2.47

17.3 16.9 15.7

17.3 0.38 21.51

16.9

16.9

PM3 PM3 B3LYP/6-31G** B3LYP/6-31G** with ZPE correction Experimental PM3 B3LYP/6-31G** B3LYP/6-31G** with ZPE correction Experimentalc PM3

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Fig. 4. PM3-calculated data for the dissociation of the C1 –C2 bond in ethylbenzene 8 and the Si1–C2 bond in benzylsilane 10 in the lowest excited triplet state ðT1 Þ (for the structure of molecular orbitals at points A, B, A0 , and B0 see Fig. 5). (a) PES cross-section calculated using the C1– C2 (curve 1) and Si1– C2 (curve 2) bond length as the reaction coordinate (minimal energy path); (b) variation of the bond order ðpÞ during elongation of the C1–C2 (curve 1) and Si1–C2 (curve 2) bonds.

(in the case of the p-benzoyl benzylsilane derivatives SOMOs are localized mainly on the benzophenone chromophore, see Fig. 2 and discussion above). It is note worthy that in the T1 PES minimum, the antibonding spC1 – C2 orbital in ethylbenzene is LUMO þ 5 and lies by 6.47 eV higher than HSOMO, whereas the antibonding spSi1 – C2 orbital in benzylsilane is LUMO and lies by 3.45 eV higher than HSOMO. However, as the dissociating C –C or Si – C bond is lengthened, the contribution of the sp MO to the HSOMO gradually increases, and in the transition state HSOMO represents mainly (with some contribution by the aromatic p-orbital) the spC1 – C2 orbital in the case of ethylbenzene dissociation (Fig. 5, point B), or the spSi1 – C2 orbital in the case of benzylsilane dissociation (Fig. 5, point B0 ). After bond breaking, the singly occupied orbitals are in fact those of the separated radicals. Re-population of orbitals upon bond elongation is clearly indicated by the dependence of the bond order on the distance between C1 (or Si1) and C2 atoms (Fig. 4(b)). One can see that in line with above observations on the orbital structure, the main changes of the bond order along the reaction pathway take place in the region of the transition ˚ for ethylbenzene and at state, i.e. at rC1 – C2 , 1.8 – 2.2 A ˚ rSi1 – C2 , 1.9 – 2.5 A for benzylsilane; there the antibonding sp orbitals mixes strongly with the aromatic pp MOs. Table 4 summarizes the data for benzylsilane and derivatives and carbon analogues in the lowest excited triplet state: the singlet – triplet energy gap DðT1 2 S0 Þ; the X1 – C2 (X ¼ Si, C) bond length rTS in the transition state, the activation energy Ea and the heat of the X1 –C2 bond dissociation DHr ; calculated by different methods. From these one can evaluate (i) the effect of the para-substituent (H atom or carbonyl group), and (ii) the specific role of the dissociating bond (C– C or Si – C) on the dissociation reaction. Comparison of the PM3-calculated data allows us to conclude that in general energetic parameters for the simpler model compounds 8 and 10 are close to

the parameters of the benzophenone derivatives 9 and 1, respectively. Thus, for both carbon analogues (compounds 8 and 9), the heat of the C –C bond dissociation reaction and the activation energy (in the T1 state) are near 15 and 37 kcal/mol, respectively. For the silicon analogues (compounds 10, 11 and 1), insertion of the carbonyl group (formyl in 11 and benzoyl in 1) results in increase of the heat of the Si –C bond dissociation reaction from 13 to 17 kcal/mol, exactly the same changes (13 –17 kcal/mol)

Fig. 5. Structure of the lowest (LSOMO) and highest (HSOMO) semioccupied MOs at characteristic points A, B, A0 , and B0 (Fig. 4) along the reaction coordinates of the dissociation of ethylbenzene 8 (points A and B) and benzylsilane 10 (points A0 and B0 ) in the lowest excited triplet state ˚ (at point A); (B) rC1 – C2 ¼ 2.04 A ˚ (at point B); ðT1 Þ : (A) rC1 – C2 ¼ 1.52 A ˚ (at point A0 ); (B0 ) rSi1 – C2 ¼ 2.32 A ˚ (at point B0 ). (A0 ) rSi1 – C2 ¼ 1.87 A

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come out also for the activation energy (in all cases there are gradually ascending dissociation curves without global maxima at PM3 level). Therefore, according to PM3 (i) insertion of parabenzoyl group has little influence on the photoinduced C –C bond cleavage and increases slightly the heat of the Si –C bond dissociation, and (ii) replacement of carbon by silicon results in considerable barrier lowering, from 37 to 13 kcal/mol for the unsubstituted compounds (8 and 10, respectively) and to 17 kcal/mol for the para-substituted analogues (9 and 1). To check the reliability of the PM3 calculations, higherlevel B3LYP/6-31G** calculations were performed on the model compounds 8, 10, and 11. In Table 4 are shown the data obtained in this work as well as data from earlier calculations on ethylbenzene 8 at B3LYP/6-31 þ G* level [21]. One can see that, compared to PM3, DFT predicts both the C – C and Si –C bond dissociations in the T1 state to be exothermic processes (the reason why PM3 overestimates DHr values is discussed above). At the same time, in agreement with PM3, DFT also predicts an increase in the heat and the barrier height of the Si –C bond dissociation reaction if a carbonyl (formyl) group is introduced; on the same time we note a decrease in the reaction exothermicity on going from 10 to 11. The reaction modeling at the B3LYP/6-31G** level confirms also the main conclusion of the PM3 calculations: the activation barrier for the C –C bond dissociation reaction in ethylbenzene 8 (19.6 kcal/mol at B3LYP/6-31G** with ZPE correction) is much higher than that for the Si – C bond dissociation in benzylsilane 10 (6.3 kcal/mol at the same level). Obviously, this significant barrier lowering can be ascribed to a specific silicon effect. It is note worthy here to mention some specific effects of silicon in the ground-state chemistry. There is the wellestablished b-effect consisting in the ability of silicon to stabilize positive charge (carbenium ion centre) in bposition, R3Si –CH2 –CHþ 2 [33,34]. The effect reveals itself in an acceleration (compared with carbon-analogue) of reactions which lead to the development of positive charge on a b carbon atom, and in marked dependence of the reaction rate constant upon the Si – C –C – X dihedral angle (X ¼ leaving group) [33,35,36] and the elongation of the C – X bond [37,38]. The mechanism of the b-effect has been clarified to be a s –sp ‘hyperconjugative-like’ (vertical) interaction between the sSi – C orbital and the antibonding spC – X orbital or s – p (s –p) hyperconjugation between the sSi – C orbital and the empty p orbital of positively charged b-carbon atom. Ab initio calculations at different levels of theory corroborated the stabilizing effect of silicon in carbenium ions (for bisected conformation), the effect being reduced on going from primary to secondary and to tertiary cations [39 – 41]. Another known effect of silicon, the a-effect, embodies its ability to stabilize an adjacent negative charge. The effect is disclosed in an anomalously reduced basicity of

a-silylalkylamines [42], in the stabilization of a-silyl carbanions [43], in lowering activity of silylamides (stabilization of the nitrogen anion) [44], in increasing electron affinity of a-silyl radicals [45], in unexpected spectroscopic properties [46]. Some mechanisms have been proposed to explain the a-effect: (i) formation of threemembered ring with one weak donor-acceptor bond in the system Si – X –N (X ¼ C, O), (ii) interaction of the nitrogen lone pair with the silicon empty d-orbital (the lp(N) – d(Si) homoconjugation), (iii) s(CX) – d(Si) hyperconjugation between the filled sC – X orbital of the C – X bond and the empty d-orbital of silicon in Si –CH2 – X fragment (X ¼ H, Cl, N), or (without involving any d-orbital participation) the negative lp(N) – sp(SiX) hyperconjugation between the nitrogen lone pair and antibonding spSiX orbital in the N –CH2 –SiX fragment (X ¼ H, F, Cl), etc. Ab initio calculations have revealed that, contrary to earlier assumptions, silicon d-orbitals are not important for describing the a-effect, however, depending on every particular case one or another type of the above interactions can contribute to electron delocalization [47 –49]. In contrast to the above findings, silicon seems to have negligible effect on BDEs, for instance the experimental BDEs of the C– C and Si – C bonds in CH3 – CH3 and SiH3 – CH3 are practically similar, 89.9 and 89.2 kcal/mol, respectively, [24]. PM3 calculations predict also the lack of the effect on the BDE of the benzoyl derivatives in the ground state ðS0 Þ; the BDEs for the silicon compound 1 and the carbon analogue 9 are 74.0 and 73.1 kcal/mol, respectively. However, all calculation methods used predict significant decrease of DHr and especially of Ea for the dissociation reaction in the triplet excited state ðT1 Þ on going from the carbon compounds to the silicon analogues, that means there is a specific excited-state silicon effect. To understand the reason of the Ea decrease in the case of the Si – C bond dissociation in the T1 state, one should consider the nature of the barrier origin. In the case of simple compounds, when excitation results in direct population of the dissociative term (for example, electron transition from bonding s orbital to antibonding sp one) a barrierless dissociation takes place (the relation between chemical bonding and electronic spectra for the s ! sp excitation has been discussed by Michl [50]). In the case of ethylbenzene and benzylsilane (and derivatives), as already stated above, excitation is localized on the aromatic pp orbitals and does not affect the antibonding spC – C or spSi – C orbitals. So the configuration of the T1 spectroscopic minimum is not the reactive one. As the dissociating bond lengthens the aromatic pp orbital mixes with the antibonding sp orbital, and a barrier results from the avoided crossing between the two PESs corresponding to the bound spectroscopic (local excited) and reactive (dissociative) configurations. The larger the energy gap between the two mixing orbitals (between the two configurations), the higher is the arising barrier.

M.F. Budyka et al. / Journal of Molecular Structure (Theochem) 668 (2004) 1–11

In ethylbenzene the antibonding spC1 – C2 orbital, being LUMO þ 5, lies by 6.47 eV higher than HSOMO (T1 state), whereas in benzylsilane the antibonding spSi1 – C2 orbital, being LUMO, i.e. next to HSOMO, lies just 3.45 eV higher than HSOMO, i.e. much lower (by near 3 eV) than in ethylbenzene. The smaller energy gap between HSOMO and sp orbital for benzylsilane provides favourable conditions for orbital mixing and results in a much lower barrier for the Si –C bond dissociation. The same situation regarding the orbital energies is observed also for the p-benzoyl derivatives in the T1 state. In p-benzoylbenzylsilane 1, the spSi1 – C2 orbital is LUMO and lies only 3.56 eV higher than HSOMO, the latter being a pp benzophenone MO, see Fig. 2. In the carbon analogue 9, the spC1 – C2 orbital is LUMO þ 11 and lies much higher (6.82 eV) than HSOMO. In view of the above orbital considerations, the experimental high photochemical activity observed for pPhCOC6H4CPh2-SiMe3 7 (dissociation quantum yield w ¼ 0:9 [16,19]) compared to the carbon analogue ðw # 0:17 [19]) and to the unsubstituted trimethylsilanes PhCH2SiMe3 ðw ¼ 0:07 [13]) and Ph3C-SiMe3 ðw ¼ 0:16 [19]), can be interpreted as follows: (i)

insertion of the benzoyl group to the para-position of benzyltrimethylsilane molecule leads to a new chromophoric system, the benzophenone chromophore which is characterized by increased rate constant of the S1 2 T1 intersystem crossing ðkisc ¼ 1011 s21 and wisc ¼ 1 for benzophenone, for PhCH 2-SiMe 3 kisc #2 £ 107 s21 [13]), thus the T1 state where the dissociation takes place is achieved more easily in the case of the p-benzoyl derivatives; (ii) replacement of the carbon by silicon leads to reduction of the barrier height on the T1 PES that facilitates the Si – C bond dissociation reaction; (iii) phenyl substitution at the benzylic carbon atom (C2) leads to the Si –C bond weakening and reduces the heat of dissociation reaction in the T1 state; this, due to correlation between DHr and Ea [30], further reduces the barrier height and facilitates the dissociation. Obviously, the relative position of the antibonding spC – C and spSi – C MOs (as well as the corresponding bonding ones) are defined by the nature of the bond forming atoms. The silicon being a third period element has much higher lying atomic orbitals as compared to the carbon (a second period element), a fact indicated by the ionization potentials which are for Si and C 8.15 and 11.26 eV, respectively [51]. Therefore, the C – C bond formation results in rather low-lying bonding sC – C MO and high-lying antibonding spC – C MO; in CH3 –CH3, the energies of these MOs are 2 13.80 and 3.89 eV, respectively, with an energy gap DE ¼ 17.69 eV (PM3 data). Due to higher initial silicon AOs the Si –C bond corresponds to

9

higher-lying bonding sSi – C MO and lower-lying antibonding spSi – C MO; in SiH3 – CH3, the energies of these MOs are 2 11.44 and 0.70 eV, respectively, corresponding to reduced energy gap DE ¼ 12.14 eV (in SiH3 – SiH3 the energy gap reduces further to 8.65 eV). Therefore, the bonding sSi – C orbital by nature is always higher lying compared to the analogous sC – C one, but the antibonding spSi – C orbital is always lower lying compared to the analogous spC – C one. It is noteworthy to compare the results obtained here with earlier theoretical considerations. Hiratsuka et al. [13,14] have performed PM3 calculations of the ground ðS0 Þ and lowest excited singlet ðS1 Þ and triplet ðT1 Þ states of benzyltrimethylsilane with similar results. The calculated molecular structure of the S1 state has been found to be, however, quite different from that of the S0 or T1 state: the silicon atom is located near the ortho carbon and ipso carbon atoms (see Fig. 1, atoms C4 and C3, respectively) and is ˚ . This above the plane of the benzyl group by ca. 2 A deformed state is not the fluorescing state because a good mirror-image relationship with little Stockes shift is observed between the absorption and fluorescence spectra, indicating that the geometry of the fluorescing state is similar to that of the ground state. The calculated deformed excited singlet state has been tentatively named as the X state. It has been assigned to the 1La state generated by the HOMO–LUMO transition, while the fluorescing state has been assigned to the 1 Lb state [14]. However, a variance arises in this case, since (for the most organic compounds) the fluorescing state is the lowest excited singlet state and corresponds therefore to the lowest HOMO–LUMO transition. We found also on the PM3-calculated T1 PES for benzylsilane and its benzophenone derivatives additional minima with molecular geometries similar to that of the Xstate (with the silyl group rearranged to the ipso and ortho carbon atoms). But calculation at B3LYP/6-31G** level corrected the PES structure and located the rearranged compound as a by-product possessing higher activation barrier and larger heat of reaction as compared to dissociation. Thus, at least on the T1 PES, rearrangement is a side reaction channel and is not discussed further. We suppose the above findings are related to the limitations of the PM3 method used (see also special paper [52] dealing with some difficulties encountered with AM1 and PM3 calculations). Evidently, it is necessary to perform additional higher-level calculations to clarify the structure of the S1 PES for benzylsilane, since the rearrangement is known experimentally to be one of the reaction channels in photochemistry of these compounds and takes place most probably only in the S1 state [9,14,19,26].

4. Conclusions PM3 calculations performed on the structure and properties of the ground ðS0 Þ and lowest excited triplet

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ðT1 Þ states of benzylsilanes p-PhCOC6H4CH22nRn-SiX3, where n ¼ 0 – 2; R ¼ Me, Ph, and X ¼ H, Me result in the following conclusions. The lowest excited states of the compounds studied correspond to local excitation of benzophenone chromophore group. Upon excitation, MO localized on the benzophenone group is occupied; this is accompanied by the characteristic geometry change and charge transfer within this group. The variation of substituents at the aliphatic carbon atom has little effect on the position of the lowest excited triplet state ðT1 Þ level. The BDE of the heterobenzylic Si –C bond in the S0 state and the heat of the bond dissociation reaction ðDHr Þ in the T1 state decreases with increasing substitution at silicon and/or at the benzylic carbon atom. There exists a straight-line dependence between the BDE and DHr values, which can be expressed by the equation DHr ¼ BDE 2 DðT1 2 S0 Þ; where DðT1 2 S0 Þ is the triplet – singlet gap. This equation is valid since the benzylsilane derivatives studied represent a homologous series of compounds having the same local chromophore and the same dissociating bond [30]. The properties of some model compounds: unsubstituted benzylsilane, p-formylbenzylsilane, and ethylbenzene, were calculated at B3LYP level with 6-31G** basis set. Comparison of the semiempirical and DFT data for the silicon compounds and the carbon analogues revealed the role of the benzoyl (carbonyl) group and the specific effect of silicon on the dissociation reaction. The main effect observed, which is predicted by all calculation methods used, consists in significant decrease of DHr and especially Ea for the dissociation reaction in the triplet excited ðT1 Þ state on going from the carbon to silicon. This is a specific excited-state silicon effect, since the C – Si BDE (a ground state parameter) does not practically change. The effect is explained by the magnitude of the energy gap between aromatic pp orbital, representing the spectroscopic (local excited) configuration and antibonding spSi – C or spC – C orbital, representing the reactive (dissociative) configuration. For the silicon compounds the energy gap is much less compared to the carbon analogues. As a result, the reaction barrier, originating from the avoided crossing between the two PESs corresponding to the two above configurations is much less for the silicon compounds as compared to the carbon analogues. In turn, the relative position of the spSi – C or spC – C MOs is determined by the nature of the bond forming atoms: the silicon, a third period element, has much higher lying atomic orbitals as compared to carbon which is a second period element. Therefore, spSi – C orbital by nature is always lower lying compared to the analogous spC – C one. The results of calculations are in full accordance with experimental data and explain the high observed photochemical activity of p-PhCOC6H4CPh2-SiMe3 (dissociation quantum yield w ¼ 0:9Þ compared to the carbon analogue

ðw # 0:17Þ and to the unsubstituted silanes PhCH2-SiMe3 ðw ¼ 0:07Þ and Ph3C-SiMe3 ðw ¼ 0:16Þ:

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