Ground- and Triplet Excited-State Properties Correlation: A

Article pubs.acs.org/JPCA

Ground- and Triplet Excited-State Properties Correlation: A Computational CASSCF/CASPT2 Approach Based on the Photodissociation of Allylsilanes Panayiotis C. Varras* and Antonios K. Zarkadis* Department of Chemistry, University of Ioannina, 451 10 Ioannina, Greece S Supporting Information *

ABSTRACT: Excited-state properties, although extremely useful, are hardly accessible. One indirect way would be to derive them from relationships to ground-state properties which are usually more readily available. Herewith, we present quantitative correlations between triplet excited-state (T1) properties (bond dissociation energy, D0T1, homolytic activation energy, EaT1, and rate constant, kr) and the ground-state bond dissociation energy (D0), taking as an example the photodissociation of the C−Si bond of simple substituted allylsilanes CH2 CHC(R1R2)-SiH3 (R1 and R2 = H, Me, and Et). By applying the complete-active-space self-consistent field CASSCF(6,6) and CASPT2(6,6) quantum chemical methodologies, we have found that the consecutive introduction of Me/Et groups has little effect on the geometry and energy of the T1 state; however, it reduces the magnitudes of D0, D0T1 and EaT1. Moreover, these energetic parameters have been plotted giving good linear correlations: D0T1 = α1 + β1· D0, EaT1 = α2 + β2 · D0T1, and EaT1 = α3 + β3 · D0 (α and β being constants), while kr correlates very well to EaT1. The key factor behind these useful correlations is the validity of the Evans−Polanyi−Semenov relation (second equation) and its extended form (third equation) applied for excited systems. Additionally, the unexpectedly high values obtained for EaT1 demonstrate a new application of the principle of nonperfect synchronization (PNS) in excited-state chemistry issues.

1. INTRODUCTION The bond-breaking and bond-forming process is central to chemical transformations. In regard to the fundamental bond homolysis of a carbon−carbon bond, considerable progress has been achieved in rationalizing the factors that govern the readiness of a molecule to undergo bond fission in the

relatively easily accessible ground-state property; for example, the bond dissociation energy (D0) which describes just the ground-state counterpart phenomenon. In our recent experimental work on the photodissociation of the C−N bond in substituted anilines6a,b and that of the C−Si bond in benzylsilanes (Scheme 1),6c−e we found that the dissociation

R1−R2 → R1• + R•2

Scheme 1.

1

ground-state. For example, it is impressive to see how phenylsubstitution drastically reduces the C−C bond strength while moving from ethane to “hexaphenylethane” (ca. 77 kcal·mol−1 reduction!), thus, accelerating enormously the C−C bond dissociation.1c,d,f,g,2 Substituent effects in photodissociations are even more complex due to the additional involvement of excited states, and predicting their influence still remains a challenge.3 A way to estimate the photodissociation efficiency and the extent of the concomitant formation of the corresponding radicals R1• and R2• would be of invaluable importance for both the mechanistic and applied photochemistry. The photodissociation ability of a material, for example, is crucial for many important processes and applications, either as a desirable property (e.g., photoinitiators,4 photodegradation of organic pollutants5) or, more frequently, as an unwanted one (e.g., photoimaging systems, photochromic materials, photosensitizers).4a One indirect way to address the complex problem of the photodissociation efficiency would be to relate it to some © 2011 American Chemical Society

efficiency (quantum yield) of the triplet excited state can be related to the D0 of the corresponding bond. Preliminary semiempirical calculations (PM3)7 supported these findings. Although the photodissociation as a fundamental key step in photochemical sciences was thoroughly studied,8 there is not much information in the literature regarding relations to the ground-state properties. Worth mentioning, however, are the detailed investigations by Allonas and co-workers9 regarding to Received: October 5, 2011 Revised: December 20, 2011 Published: December 30, 2011 1425

dx.doi.org/10.1021/jp209583z | J. Phys. Chem. A 2012, 116, 1425−1434

The Journal of Physical Chemistry A

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imaginary frequency. It is well-known that the CASSCF method, which has analytic first and second derivatives, provides a very good description of the topography of potential energy surfaces and gives very good molecular geometries. The CASSCF wave function (ΨCASSCF) includes the most important Configuration State Functions in the full CI wave function and thus all near degenerate configurations which describe static correlation effects, as for example in a bond breaking process, are included. Dynamic correlation effects are taken into account by applying perturbation theory to the CASSCF wave function. Because all the molecules under study have the common structure CC−C−Si, we select the orbitals σ, σ*, π, π* of the double bond, CC, and the orbitals σ and σ* of the C−Si bond as comprising the final active space with the corresponding six electrons. The resulting active space is referred to as CASSCF(6,6) or CAS(6,6), see Figure 1. All

the C−C photodissociation of the classical Norrish Type-I reaction of ketones, where they found that the bond dissociation energy (DC−C) does not control the outcome of the dissociation reaction whereas entropic and polar effects seem to be more important. On the other hand, Pincock et al.10a studying the photo-Claisen reaction of aryl ethers (ArO− CH2CHCH2), observed that to a considerable extent, the C−O photodissociation is dominated by the corresponding DC−O, disagreeing with earlier theoretical predictions by Grimme.10b It is also worth mentioning in this context, the work by Pearson11 who demonstrated the relation between ground-state bond strength (D0) and excitation energy of diatomic molecules, as well as the relevant basic description by Michl et al.12 and Plotnikov et al.13 In the present paper we investigate theoretically the photodissociation of the C−Si bond of allylsilanes 1−6 (Scheme 2), where letting the ethylene chromophore intact, Scheme 2.

we varied in a systematic way the ground-state bond dissociation energy (DC−Si) of the C−Si bond via successive methylation/ethylation of the allylic carbon. We chose this system because, (i) it constitutes the simplest possible π-system (ethylene) bearing a cleavable σ-bond (C−Si), (ii) it bears “photochemically inert” alkyl substituents, (iii) it is relevant to our experimental studies on benzylsilanes,6c−e,7b and (iv) as a small prototype system allows us to apply for the first time the powerful CASSCF/CASPT2 quantum chemical methodology which has been proved suitable for treating excited-states.15−19 We, thus, believe to have constructed a molecular system suitable to address the above formulated issues and to give reliable energetic (D0, D0T1, EaT1) and kinetic parameters (kr), enabling to test for useful correlations between ground- and excited-state properties. We restrict our study to the photodissociation of the T1 excited-state which leads adiabatically to ground-state radicals, as it was shown in the case of benzylsilanes,6c−e while the S1 state gives mainly 1,3-photorearrangement products.14

Figure 1. Six molecular orbitals of silane 4 comprising the final active space used in CASSCF(6,6)/6-31G(d) calculations.

calculations were performed with the Gaussian 03 software package.20

2. COMPUTATIONAL METHODS The structures, properties, and photodissociation reactions of substituted allyl silanes were studied by means of the ab initio CASSCF method15 and the 6-31G(d) basis set, while for a greater accuracy the energies were calculated by using the CASPT2/CASMP2 method.16−19 At the optimized equilibrium geometries we also performed single point energy calculations using the 6-31G(d,p) and 6-31+G(d) basis sets. Transition state structures for the dissociation of the Si−C bond in the first excited triplet state (T1#) were found by either stretching the C−Si bond initially to about 2.53 Å and using the Berny optimization algorithm or by performing a relaxed scan starting from the corresponding T1 minimum and considering the C−Si distance as the reaction coordinate. IRC calculations support the above results. Finally, vibrational analysis was used to characterize the corresponding points on the potential energy surfaces (PESs); T1# was confirmed through one and only one

3. RESULTS AND DISCUSSION 3.1. Structure of Ground (S0) and Triplet Excited-State (T1). Table 1 shows the geometric parameters of the groundstate (S0) and first excited triplet state (T1) of the allyl silanes 1−6 corresponding to fully optimized structures at the CASSCF level with the 6-31G(d) basis set. Each state preserves nearly the same geometry within the series and a tetrahedral arrangement around the C3 atom. Specifically, the results quoted above show for both electronic states a small increase in the length of the C3−Si bond as the number and size of the substistuents increases. A similar trend is observed for the C2− C3 bond, while the length of the C1−C2 bond remains practically unchanged. However, significant changes are observed if we compare S0 with T1, see the example in Figure 2. The S0 → T1 transition induces two main changes in the π-system, elongation (∼0.15 1426



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Table 1. Selected CASSCF(6,6)/6-31G(d) Geometrical Parameters and Mulliken Charges (q) for the Allyl Silane Derivatives 1−6 in the Ground- (S0) and Lowest Triplet Excited-State (T1)a comp.

state

rC3−Si

rC2−C3

rC1−C2

qSi

qC3

θC2C3Si

φHC1C2H

φC1C2C3Si

1

S0 T1 S0 T1 S0 T1 S0 T1 S0 T1 S0 T1

1.925 1.931 1.932 1.938 1.937 1.943 1.942 1.947 1.948 1.952 1.952 1.956

1.506 1.503 1.509 1.506 1.511 1.508 1.516 1.513 1.519 1.516 1.526 1.521

1.356 1.496 1.356 1.495 1.356 1.495 1.357 1.497 1.357 1.496 1.357 1.498

0.66 0.66 0.66 0.66 0.66 0.66 0.66 0.66 0.66 0.66 0.66 0.66

−0.61 −0.59 −0.43 −0.41 −0.43 −0.41 −0.26 −0.25 −0.26 −0.25 −0.26 −0.25

112.85 113.44 110.31 110.86 108.28 108.95 107.60 108.67 105.76 106.69 103.93 104.83

178.93 93.09 179.36 92.58 179.58 93.46 179.63 92.12 179.97 92.92 −179.08 91.26

108.58 82.17 107.43 80.13 106.46 81.61 110.52 77.37 111.71 79.21 116.34 73.94

2 3 4 5 6

Bond lengths r in angstroms (Å), θ and φ (dihedral) in degrees. The values are given according to the suggestions by Hoffmann, Schleyer, and Shaefer III.21 a

Scheme 3.

continuously for both electronic states due to delocalization toward the methyl/ethyl substituents. 3.2. Energetic Properties of the S0 and T1 States. The calculated CASSCF and CASPT2 adiabatic energy differences Δ(T1 − S0) between the S0 and T1 states are listed in Table 2. Table 2. CASSCF(6,6)/6-31G(d) and CASPT2(6,6)/631G(d)//CASSCF(6,6)/6-31G(d) Adiabatic Energy Differences Δ(T1 − S0)a between the Two Electronic States S0 and T1b

Figure 2. Characteristic geometrical parameters (bond lengths and dihedrals) of S0, T1, and T1‡ of allylsilane 4. The methyl substistuents on C3 have been omitted for the sake of clarity.

Å) of the C1−C2 bond, which acquires single bond character, and departure from planarity to a nearly orthogonal arrangement, as is seen by comparing the dihedral angle φHC1C2H in the S0 (∼0°) with that of the T1 (∼90°). The ∼90° internal rotation around the π-bond C1−C2 is the well-known twist that accompanies excitation and equilibration of T1 in alkenes as a result of the triplet electron repulsion. Scheme 3 shows the biradicaloid character of the optimized T1 structure confirmed through the spin densities (ρ) calculated using the unrestricted B3LYP/6-31G(d) method. Moreover, the parallel arrangement of the C−Si bond toward the single occupied p-orbital in C2 results in an effective stabilizing contribution of the β-silicon effect22 of the SiH3 group; radicals and carbenium ions are stabilized hyperconjugatively via β-silyl groups, as is portrayed by the resonance form (II). This leads to the bond length increase of C−Si in T1 as compared to S0 (Table 1). Another feature worth noting is the large polarization of the C3−Si bond, which is in accordance to the electronegativities of carbon and silicon. Upon consecutive substitution, though, the negative charge on C3 decreases

comp.

Δ(T1 − S0)e casscf

Δ(T1 − S0)0 casscf

Δ(T1 − S0)e caspt2

Δ(T1 − S0)0 caspt2

1 2 3 4 5 6

70.79 70.68 70.60 70.38 70.28 69.56

67.62 67.51 67.45 67.08 66.96 66.40

72.87 72.56 72.18 72.20 72.00 71.44

69.69 69.40 69.03 68.89 68.68 68.28

In kcal·mol−1. bΔ(T1 − S0)e: CASSCF energy; Δ(T1 − S0)0: CASSCF energy including zero point vibrational energy (ZPE); Δ(T1 − S0)caspt2 and Δ(T1 − S0)0,caspt2 are the CASPT2 energies without and with ZPE, respectively. Absolute energies of S0 and T1 in hartrees are collected in Table S1 (see Supporting Information). a

They are almost constant for all derivatives 1−6. The mean CASSCF and CASPT2 values of Δ(T1 − S0) are about 67 and 69 kcal·mol−1, respectively, and because substitution produces no significant changes in the geometry and energy values, we conclude that the excitation produces a local excited ethylenic group that is very similar for the whole series. For the triplet excited state of ethylene itself, the experimental values of the adiabatic energy difference are 1427



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reported as 58 ± 3,24 65,25b and 78.827 kcal·mol−1, with the first and especially the last value having a significant difference from recently computed theoretical values (including ZPEs), which fluctuate between 65.623 and 66 kcal·mol−1.28a On the other hand, our CAS(4,4), CAS(16,12), and CASPT2(4,4) calculations with the 6-31G(d) basis set give for ethylene Δ(T1 − S0) = 66.98, 66.87, and 68.86 kcal·mol−1 at 0 K, respectively. These energies are close to the transition state energies for thermal cis−trans isomerization of 1,2-dideuterioethylene (65 kcal·mol−1)28b and 2-butene (66.2 kcal·mol−1).28c 3.3. Photodissociation Reaction of the C−Si Bond in the S0 and T1 States. During the second part of the work we investigated the PESs of the ground (S0) and the first excited triplet (T1) state of compounds 1−6 by considering the rC−Si bond distance as the reaction coordinate. The dissociation starts from the minima of the S0 and T1 states and proceeds uphill through a transition state the structure of which for T1‡ was fully optimized, as it was shown previously in Figure 2 for compound 4. Relaxed scans were performed for the corresponding states until complete dissociation to the respective radicals occurred. As an example we consider here the dissociation of 4 in the S0 and T1 states (Figure 3).

distance of Si to the electronegative atom C3 increases considerably. The transition state T1‡ is linked smoothly to the reactant and products, as was additionally confirmed by performing IRC CASSCF/6-31G(d) quantum mechanical calculations. Activation energies (Ea), heats of reactions (ΔHr) corresponding to the T1 states and the bond dissociation energies (D0) from the ground-state (S0) were calculated by means of eqs 1−3 at T = 0 K,

Ea T1 = E0 T1 ‡ − E0,min T1

(1)

T1 ΔHr = D0 T1 = ΣΕ0(radicals) − Ε0,min

(2)

S

0 D0 = ΣΕ0(radicals) − Ε0,min

(3)

where is the triplet energy (see Δ(T1 − S0)0 in Table 2). ΔHr is equivalent to the bond dissociation energy of the T1 state, which we designated as D0T1 (eq 2). Absolute energies of S0, T1, T1‡ and ΣE0(rad) in hartrees are collected in Tables S1 and S2 (see Supporting Information). The results of the calculations obtained for compounds 1−6 are gathered in Table 3. Based on the same optimized T1 E0,min

Table 3. Bond Dissociation Energies, D0 and D0T1, Corresponding to the S0 and T1 States, respectively, and Activation Energies EaT1 in the T1 State Calculated Using CASSCF(6,6)/6-31G(d) at 0 K in kcal·mol−1a 1 2 3 4 5 6

D0T1

D0

comp. 58.84 54.78 53.87 51.40 49.61 45.25

(69.17) (65.59) (65.43) (63.33) (62.11) (58.86)

30

−8.73 (−0.26) −12.68 (−3.83) −13.55 (−3.59) −15.68 (−5.49) −17.31 (−6.55) −21.15 (−9.41)

EaT1 19.59 18.12 18.07 16.96 16.84 16.34

(24.95) (23.59) (24.16) (22.62) (22.84) (22.55)

a

The corresponding values using CASPT2(6,6) /6-31G(d)// CASSCF(6,6)/6-31G(d) are shown in parentheses.

Figure 3. CASSCF(6,6) /6-31G(d) potential energy curves for the dissociation of the C−Si bond of compound 4 in the two electronic states S0 (blue) and T1 (red). De, DeT1, EeT1 and EaT1 are CASSCF electronic energies (see text).

geometries, we performed additional single point calculations (i) using the basis sets 6-31+G(d) and 6-31G(d,p), see Table S3 in the Supporting Information, and (ii) at the CASPT2(6,6) level of theory using all the three above-mentioned basis sets (Table 3 and Table S4 in Supporting Information). It is worth noting by looking at Tables 3, S2, and S3 that, as the number and size of the substituents increases, the heat of the dissociation reaction from the triplet state (ΔHr = D0T1) becomes more negative, that is, the exothermicity of the reaction increases and at the same time the magnitude of the activation energy (EaT1) decreases as well. A corresponding decrease is observed in the bond dissociation energy (D0) of the ground-state. The same trend holds for both methods (CASSCF and CASPT2) and for all basis sets used in the present study. The D0, D0T1, and EaT1 values derived by CASPT2, although considered more reliable, may be overestimated due to the well-known tendency of CASPT2 to overestimate dissociation and activation energies.31 3.4. Correlations Among the Quantities D0, D0T1, and T1 Ea of the Photodissociation Reaction. While from a chemical point of view one would expect a decrease in the quantities D0, D0T1, and EaT1 with increasing substitution, our interest in this work was focused on finding functional relationships among these quantities. In an attempt to explore this possibility we used the results quoted in Table 3 and

Calculations of bond orders using the NBO method29 and spin densities using the unrestricted B3LYP/6-31G(d), indicate that the formed products were derived either from the T1 state or the S0 state and are the separated radicals allyl• and •SiH3. In both potential energy curves we see the existence of the two minima (S0,min and T1,min) corresponding to the values reported in Table 2, while in the T1 surface we find also a distinct maximum point which corresponds to the transition state T1‡. The associated frequency is −569.4 cm−1 and corresponds to the C−Si bond stretching. At the transition state, the equilibrium C−Si bond length is equal to 2.517 Å, indicating 30% C−Si bond breaking. The bond order is equal to 0.33, while the σ*CSi antibonding orbital is occupied by only 0.1 electrons. As the dissociation continues this orbital becomes populated, and at complete dissociation, silicon’s pπ orbital is now occupied by 1e. The dihedral angle φC1C2C3Si = 87.29° corresponds to an almost perpendicular arrangement of the silyl group (SiH3), which is preserved throughout the dissociation process. This follows the stabilizing action of the β-silicon effect which is maximized at 90° (see Scheme 3). The polarization of the C−Si bond in the transition state decreases since the 1428



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plotted the following pairs D0T1/D0, EaT1/D0T1, and EaT1/D0, as shown in Figure 4. From these graphs, the following linear

ΕaT1 = α3 + β3·D0

with α and β being constants representing the intercept and slope, respectively. All constants are shown collectively in Table 4. Equation 4 describes the linear dependence between the bond dissociation energy D0 in the ground-state and that corresponding to the first excited triplet state, D0T1; it shows an excellent correlation coefficient (R) for both CASSCF and CASPT2 and for all basis sets (Table 4), indicating essentially the “local” character of the excited ethylenic system or, in other words, the essentially nonperturbing nature of the Me/Et substituents. Next we consider the linear relationship between the activation energy EaT1 and the bond dissociation D0T1 depicted in Figure 4b. This correlation (5) is a Evans− Polanyi−Semenov25,35 equation corresponding to the T1 adiabatic excited state potential energy hypersurface (see Figure 3). Although this equation seemed to apply for reactions taking place in the ground-state, we found it to be equally valid for reactions occurring in excited-states. The correlation coefficient is here less good and it comes as a surprise the fact that it deteriorates further at the CASPT2 level (Table 4).32 The activation energy EaT1 is thus connected through eq 5 linearly to the corresponding bond energy D0T1, and this opens the way to directly corelate EaT1, an excited-state property, to the groundstate bond dissociation energy D0. This is shown in Figure 4c and expressed via eq 6, which represents an extended Evans− Polanyi-Semenov relation (Table 4). Equation 6 indicates that the activation energy and hence possibly the rate constant and quantum yield of a photodissociation reaction can be determined and controlled by a fundamental and easily accessible ground-state property such as the bond dissociation energy, D0. This underlines the fact that ground-state properties are reflected in the behavior of excited states; corroborative hereupon is the work by Pearson11 who showed that excitation energies and bond strengths of diatomic molecules are linearly correlated among themselves. 3.5. Kinetics of the Photodissociation Reaction. As a logical outgrowth of the foregoing discussion, we now consider

Figure 4. Linear graphs between the variables D0, D0T1, and EaT1 according to the values listed in Table 3 [CASSCF(6,6)/6-31G(d)]. R is the correlation coefficient of the corresponding plot.

relations were deduced,

D0T1 = α1 + β1· D0

(4)

ΕaT1 = α 2 + β2 ·D0T1

(5)

(6)

Table 4. Constants α and β and Correlation Coefficients R Resulted by Plotting the Energetic Parameters D0, D0T1, and EaT1 (Tables 3, S2, S3)a D0T1 = α1 + β1 · D0; eq 4 method CASSF

α1

β1

R

α2

β2

R

α3

β3

R

b

−62.39 −62.59 −62.30 −61.18 −58.36 −62.74

0.91 0.91 0.91 0.88 0.85 0.90

0.999 0.999 0.999 0.999 0.997 0.998

21.63 21.79 21.64 24.83 25.16 25.13

0.27 0.29 0.27 0.28 0.32 0.30

0.964 0.966 0.964 0.913 0.822 0.906

4.93 4.47 4.79 7.53 5.83 6.64

0.24 0.25 0.25 0.25 0.28 0.27

0.960 0.963 0.959 0.905 0.837 0.889

d b c d

a

EaT1 = α3 + β3 · D0; eq 6

basis set c

CASPT2

EaT1 = α2 + β2 · D0T1; eq 5

The values of α are in kcal·mol−1. b6-31G(d). c6-31+G(d). d6-31G(d,p). 1429



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reaction (−15 kcal·mol−1). The activation entropy ΔS‡ (and the pre-exponential factor A) is very small, a fact that can easily be deduced by looking at Figures 2 and S1 in Supporting Information; It is obvious that, except for the lengthening of the C−Si bond, the changes in the molecular geometry during the transition from T1 to T1‡ are almost negligible. The 180-fold increase of kr as the substitution progresses reflects the corresponding lowering of the activation energy and the simultaneous increase in the exothermicity (Table 3). The increase in the rate constants is attributed entirely to the energetic part exp(EaT1/RT) of Eyring’s eq 9, with the entropic contribution exp(ΔS‡/R) being negligible. More precisely, ΔS‡ decreases slightly down the series and counteracts the positive contribution of the energetic part, causing, however, a minor attenuation of the kr values. This is nicely illustrated on the one hand by the excellent linear correlation between ln(kr) and the values of EaT1 (see Figure 5) and with the failure on the other to

the kinetics of the C−Si bond dissociation of silanes 1−6 in the T1 state. Usually, the motion from one local minimum to another on the potential energy hypersurface is described quite well by Eyring’s transition state theory of chemical reactions with corrections for quantum mechanical tunneling contributions. In its simple form, the rate constant kr, of an adiabatic reaction is given by the following expression:33−37

k T k r = κ B · exp( − ΔG‡/RT ) (7) h where κ is the transmission coefficient (≈1), kB is Boltzmann’s constant, h is Planck’s constant, T is the absolute temperature, and ΔG‡ is the free energy of activation. Quite often, the Arrhenius equation is used: k r = A · exp( − Ea /RT ) (8) where A is the frequency or pre-exponential factor (in s−1) with typical values for unimolecular reactions ranging from 1012 to 1015 s−1 and Ea is the activation energy. Because ΔG‡ = ΔH‡ − TΔS‡ and ΔH‡ = Ea − RT for a unimolecular reaction, it follows that we can write eq 7, with κ = 1, as ‡ ⎞ ⎛ k T k r = ⎜e B · eΔS / R ⎟e−Ea / R ⎝ h ⎠ ‡

(9)

‡

with ΔH and ΔS denoting the activation enthalpy and entropy, respectively. Comparing eqs 8 and 9, we see that ‡ k T A = e B · eΔS / R (10) h The two equations show that the rate constant (kr) depends not only on ΔH‡ (or Ea), but also on ΔS‡. In Table 5 we give the values of the dissociation rate constants (kr), pre-exponential factors (A), activation free

Figure 5. Linear plot between ln(kr) and EaT1 according to the values listed in Table 3 and 5 (CASSCF(6,6)/6-31G(d)). R is the correlation coefficient of the plot.

correlate with ΔS‡ (Figure S2, Supporting Information). Additionally, we find good linear correlations of ln(kr) to D0 (R = 0.957; Figure S3) and to D0T1 (R = 0.951; Figure S4) as one would expect from the aforementioned eqs 4−6 relating the quantities D0, D0T1, and EaT1 (section 3.4).

Table 5. CASSCF(6,6)/6-31G(d) Dissociation Rate Constants (kr), Pre-exponential Factors (A), Activation Entropies ΔS‡ (cal·mol−1·K−1) and Activation Free Energies ΔG‡ (kcal·mol−1) for the Photodissociation of Silanes 1−6 in the Triplet State (at T = 298.15 K) comp.

kr/s−1

A/s−1 × 1013

ΔS‡

ΔG‡

1 2 3 4 5 6

0.06 0.61 0.69 4.37a 5.41 10.99

5.01 4.49 4.43 4.70 4.53 3.69

2.16 1.94 1.92 2.04 1.96 1.55

19.14 17.75 17.67 16.58 16.45 16.03

4. DISCUSSION AND CONCLUSIONS Summarizing, CASSCF and CASPT2 quantum chemical calculations with the basis sets 6-31G(d), 6-31+G(d) and 631G(d,p) were performed for the ground (S0) and lowest excited triplet states (T1) of alkyl-substituted allyl silanes 1−6, CH2CHC(R1R2)SiH3 (R1 and R2 = H, Me, and Et). It was shown that the consecutive introduction of Me and Et groups has little effect on the geometry (Table 1, Figure 2) and energy (Table 2) of the T1. The relaxed T1 state is characterized by (i) a nearly 90° twisted π-system (Figure 2), (ii) an elongated C1− C2 bond becoming almost single (bond order pC1C2 ≈ 1.03), and (iii) energies of about 67 or 69 kcal·mol−1 using CASSCF or CASPT2, respectively (Table 2). However, as the number and size of the substituents increases, the homolytic bond dissociation energy of the C−Si bond in the S0 state (D0) and that corresponding to the T1 state (D0T1) were found to decrease, with the whole variation spanning about 13 kcal·mol−1 (Table 3). Thus, silanes 1−6 constitute a well-defined model of closely related derivatives that possess very similar T1 states in all respects except that of the C−Si bond strength D0T1. In other words, the system can be described in terms of two interacting subunits; the first is the ethylenic π-system that acts as the “local” antenna chromophore, which funnels about 68 kcal·mol−1 of excitation energy to the second part, namely,

We have calculated kr = 4.33 s−1 using the molecular partition functions for the triplet minimum T1 and the transition state T1‡.

a

energies ΔG‡, and entropies ΔS‡ calculated at the CASSCF (6,6)/6-31G level of theory for the photodissociation reactions (T1). The full list of the G‡ and S‡ values is given in Table S5 (see Supporting Information). Consideration of the results shows two main features. The first one relates to the generally small values of the rate constants (kr),38 and the second is their increase on going down the series 1−6, which spans 2 orders of magnitude with respect to the number and size of the introduced substituents. The small values of kr reflect mainly the relatively large values of the activation energies EaT1 reported previously in Table 3 (17 kcal·mol−1 on the average, CASSCF values) and are in contrast to the large exothermicity of the 1430



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from the calculation of kinetic parameters such as the dissociation rate constants (kr), pre-exponential factors (A), activation entropies ΔS‡ and activation free energies ΔG‡ (Table 5). The results show small values for the rate constants kr but considerable differentiation on going down the series 1− 6 spanning 2 orders of magnitude. The small kr values reflect essentially the relatively large values of the activation energy (EaT1) because the contribution of the activation entropy ΔS‡ is almost negligible, a fact that agrees with the excellent linear correlation between ln(kr) and EaT1 shown in Figure 5. Experimental data concerning the allylsilanes 1−6 are not available; however, as reported in the Introduction, we have found such correlations studying the photodissociation of the C−N bond in substituted anilines6a,b and that of the C−Si bond in benzylsilanes (Scheme 1).6c−e The importance of coefficients α2 and β2 deserves some special comment. According to Leffler and Grunwald,37 β2 varies between 0 and 1, denoting the position of the transition state along the reaction coordinate.39 Values close to zero denote transition states structurally similar to reactants, while those approaching one were considered to show product-like transition states. In the photodissociation of silanes 1−6 we found β2 = 0.26 (Table 4) showing rather earlier occurring transition states in line with the calculated exothermicities. This agrees perfectly with Hammond’s postulate25,26,36,37,40 and its various modifications summarized by the acronym Bema Hapothle.40b This is qualitatively portrayed in Figure 6 taking,

the C−SiH3 group, which contains the relatively weak C−Si bond (D0 = 45−59 kcal·mol−1). We, thus, believe that this simple prototype π-system is suitable for testing for possible correlations between groundand excited-state properties regarding the photodissociation of the σC−Si bond. Moreover, the small size of the system allows us to use the powerful CASSCF/CASPT2 quantum chemical methodology. Hence, the potential energy curves in the S0 and T1 states of the 1−6 derivatives have been calculated with relaxed scans (Figure 3) until complete dissociation to the separated radicals allyl• + •SiH3 was accomplished. The system follows the concept of an insulating chromophore with a local triplet excited state described qualitatively by Michl, BonacicKoutecky, and Klessinger;12 they pointed out that the photocleavage of a σ-bond needs to overcome a barrier (EaT1), which arises by the crossing of the T1 local excited state (spectroscopic) with the 3(σσ*) dissociative (reactive) triplet state of the bond to be broken. See Figure 3 for such a representative example. Next we followed our main target to plot the energy values of D0, D0T1, and EaT1 listed in Table 3 in order to test for possible correlations. The first plot between the bond dissociation energy in the ground- (D0) and excited-state (D0T1) is expressed in Figure 4a, giving an excellent linear correlation D0T1 = α1 + β1 · D0, eq 4; this is actually expected since both dissociations lead to the same radicals in the dissociation limit (see Figure 3) and indicates additionally the “local” character of the excited ethylenic system, which is essentially unaffected by the “photochemical inert” substituents Me and Et. Plotting the next two excited state quantities D0T1 and EaT1, we observe a good linear correlation EaT1 = α2 + β2 · D0T1, eq 5, reminiscent of the Evans−Polanyi−Semenov relation,25,26,35−37 well-known in ground-state chemistry. The present case demonstrates for the first time, as far as we are aware, its application in excited-state chemistry.7c Generally, such simple relations are reliable only for essentially homolytic mechanisms and are apt to break down for reactions in which there is considerable charge development in the transition state;35,36 in latter cases, a multiparametric relation is probably needed.36b Indeed, in our case, there is little charge development on going from T1 to T1‡ (Table 6). Finally, the activation energy EaT1 is plotted against Table 6. Selected Geometrical Parameters, NBO Bond Orders (pAB), Mulliken Charges (q), and Spin Densities (ρ) for T1‡ and T1,min of Compound 4a rC1C2

rC2C3

rC3Si

qC3

T1‡ T1,min

1.502 1.497 pC1C2

1.396 1.513 pC2C3

2.517 1.947 pC3Si

−0.11 −0.25 ρC1

0.44 0.66 ρC2

qSi

T1‡ T1,min

1.01 1.03

1.42 1.02

0.33 0.71

1.05 1.02

0.52 0.91

φHC1C2H

φC1C2C3Si

84.92 93.12 ρC3

87.29 77.37 ρSi

−0.02 −0.17

Figure 6. Qualitative comparison of the T1 potential energy curves for the dissociation of silanes 1 and 6 (CASSCF values), where 1‡ and 6‡ denote the respective transition states (T1‡).

0.60 0.07

a

Bond lengths (r) are in Å, and angles (θ) and dihedral angle (φ) are in degrees (°).

for example, the two extreme cases, namely, the derivatives 1 and 6. The dissociation of compound 6 is much more exothermic than that corresponding to 1 (D0T1), consequently, the potential curve concerning 6 is shifted to the left and the activation energy is lowered (EaT1). The parameter α2 corresponds to the intrinsic barrier (α2 = Eai ) defined as the activation energy required to form or break a bond whose bond strength D0 is zero.41,42 Marcus42 defined the intrinsic barrier (Eai ) using a modified form of his equation:

the ground-state bond dissociation energy D0 and the linear equation EaT1 = α3 + β3 · D0 (6) is deduced (Figure 4c). Relation 6 indicates that the activation energy and, hence, possibly the rate constant and quantum yield of a photodissociation reaction can be controlled by the bond strength, D0. In other words, ground-state properties are in some way reflected in the behavior of excited-states. All correlations are collected and presented in Table 4. Confirmation of the above findings comes 1431



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Scheme 4.

Ea T1 = Ea i + D0 T1/2 + (D0 T1)2 /16Ea i

about 68 kcal·mol−1 of excitation energy, which makes the dissociation of allylsilanes 1−6 strongly exorthemic (∼−15 kcal·mol−1), the cleavage process occurs with low rate constants due to the high activation energy barriers, which are derived from the inherent triplet electron repulsion of the excited ethylenic chromophore. Unfortunately, no experimental results are available for comparison. An indirect comparison can be made30 to the thermal ground-state dissociation of the C−Si bond of the trimethyl derivative CH2CHCH2−SiMe3.48 Concluding, and as chemical intuition suggests, the present work has shown that the ground-state C−Si bond strength D0 of silanes 1−6 determines through linear correlations the triplet excited-state bond strength (D0T1), as well as the energy barrier (EaT1) and the rate constant (kr) of the corresponding photodissociation reaction. The crucial point behind these correlations is the validity of the Evans−Polanyi−Semenov eq 5 and its extended form (eq 6) for excited-states, which function as a bridge between ground- and excited-state chemical behavior. This conclusion is in line with our experimental work done in more complex systems (anilines, benzyl silanes)6 and has prompted us to analyze literature data reported by Zewail and co-workers49 concerning the photoinduced Norrish Type-I cleavage of ketones as well as data reported by Plotnikov et al.13 concerning the photodissociation of C−H bonds; we found a good correlation between EaS1 and D0 (see Figure S5, Supporting Information) in the former case and excellent correlation between kr and D0 in the latter (see Figure S6). Thus, at least in principle and in a system of closely related derivatives, knowledge of the bond strength D0 would be of high importance in predicting important photodissociation properties of materials.

(11)

If we apply eq 11 using the CASSCF (CASPT2) data of EaT1 and D0T1 from Table 3, we find Eai = 24.5 ± 0.7 (25.8 ± 0.7) kcal·mol−1 as the intrinsic barrier for the dissociation of the C− Si bond in the T1 state, while a similar value of 21.7 ± 0.1 (24.0 ± 0.2) kcal·mol−1 is derived from the simple Evans−Polanyi− Semenov eq 5, setting α2 = Eai . These high energy barriers and low rate constants (kr) are in striking contrast to the large exothermicities (−15 kcal·mol−1 on the average, CASSCF) and the 50% reduction of the bond order p in the transition state. For comparison, we consider the ground state decarboxylations R−COO• → R• + CO2, which have similar exothermicities, yet they show low activation energies and high rate constants (kr ∼ 108 s−1).43 Undoubtedly, we face here the everlasting question concerning the factors that control reaction barriers and reactivities,35−37,39−42,44 this time, however, in a new context involving triplet excited electronic configurations (T1). In an attempt to address the question of these high energy barriers, the principle of nonperfect synchronization (PNS) formulated by Bernasconi45 seems to be relevant. As we showed above and summarize in Scheme 4, the minimum of the triplet electronic configuration T1,min adopts an orthogonal twisted geometry of the ethylenic moiety12,46 as a response to relief from the inherent triplet electron repulsion and that this distortion remains intact along the way to the transition state T1‡, and albeit the 50% reduction in the bond order. Hence, at the ‡ transition state T1 , the allylic part of the system cannot achieve planarity and the energetic benefit which would result from resonance stabilization is lost. Return to planarity takes place later during the formation of radicals all the way down to the dissociation limit. The resonance stabilization which for the allyl radical is about 15 kcal·mol−1,47 constitutes a large part of the energy released from the transition state down to the separated radicals (Figures 3 and 6). We get the impression that the high energy barriers and particularly the high intrinsic barrier (Eai ≈ 25 kcal·mol−1) demonstrate the operation of the PNS that states that “high intrinsic barriers are typically associated with a lack of synchronization between concurrent reaction events such as bond formation/cleavage, solvation/ desolvation, development (loss) of resonance, etc.”.45a In the present case, the C−Si bond cleavage is progressed by about 30% at the transition state, judging from the extent of the bond elongation, accompanied by a 50% decrease in bond order and a 50% increase in the spin density at the silicon atom (Scheme 4, Table 6, and Figure 2); however, the resonance that is involved as an essential product (allyl radical) stabilizing factor develops later in the bond cleavage process, so that the transition state itself does not profit energetically hereof (the gain in planarity is less than 10%). Thus, in spite of funneling of

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ASSOCIATED CONTENT

S Supporting Information *

Absolute energies of the S0, T1, and T1‡ states and ΣE0(radicals) in hartrees (CASSCF and CASPT2), the values of the energies D0, D0T1, EaT1 using basis sets 6-31+G(d) and 6-31G(d,p), the full list of the G‡ and S‡ values, a figure comparing T1 and T1‡ states, and plots of ln(kr) versus ΔS‡, ln(kr) versus D0, ln(kr) versus D0T1, and EaS1 versus D0. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Fax: (+30)-26510-08799. E-mail: [email protected] (A.K.Z.); [email protected] (P.C.V.).

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ACKNOWLEDGMENTS This manuscript is part of the Ph.D. thesis of P.C.V., University of Ioannina (GR), 2010. We thank Nick Goudas for his useful 1432



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(14) The ground-state (S0) thermal 1,3-silyl shiftof allylsilane was studied by Takahashi, M.; Kira, M. J. Am. Chem. Soc. 1999, 121, 8597. (15) Roos, B. O. Adv. Chem. Phys. 1987, 69, 399. (16) McDoual, J. J. W.; Reasley, K.; Robb, M. A. Chem. Phys. Lett. 1988, 148, 183. Anderson, K.; Malmqvist, P. A.; Roos, B. O.; Sadlej, A. J.; Wolinski, K. J. Phys. Chem. 1990, 94, 583. (17) Computational Photochemistry; Olivucci, M., Ed.; Elsevier: Amsterdam, 2005; Computational Methods in Photochemistry; Kutateladze, A. G., Ed.; Taylor & Francis: London, 2005. (18) Gagliardy, L.; Roos, B. O. Chem. Soc. Rev. 2007, 36, 893. (19) Anderson, K.; Malmqvist, P.; Roos, B. O. J. Chem. Phys. 1992, 96, 1219. (20) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, Revision B.03; Gaussian, Inc.: Pittsburgh, PA, U.S.A., 2003. (21) Hoffmann, R.; Schleyer, P. von R.; Shaefer, H. F. III Angew. Chem., Int. Ed. 2008, 47, 7164. (22) Brook, M. A. Silicon in Organic, Organometallic, and Polymer Chemistry; Wiley: NY, U.S.A., 2000; Chapter 14, p 480; Lambert, J. B.; Zhao, Y.; Emblidge, R. W.; Salvador, L. A.; Liu, X.; So, J.-H.; Chelius, E. C. Acc. Chem. Res. 1999, 32, 183. (23) Nguyen, M. T.; Matus, M. H.; Lester, W. A. Jr.; Dixon, D. A. J. Phys. Chem. A 2008, 112, 2082. (24) Qi, F.; Sorkhabi, O.; Suits, A. G. J. Chem. Phys. 2000, 112, 10707. (25) (a) Evans, M. G.; Polanyi, M. Trans. Faraday Soc. 1938, 34, 11. (b) Dewar, M. J. S.; Dougherty, R. C. The PMO Theory of Organic Chemistry; Plenum/Rosetta: NY, U.S.A., 1975; (c) Saeys, M.; Reyniers, M.-F.; Van Speybroeck, V.; Waroquier, M.; Marin, G. B. ChemPhysChem 2006, 7, 188. (26) Lowry, T. H.; Richardson, K. S. Mechanism and Theory in Organic Chemistry; Harper and Row: New York, U.S.A., 1976. (27) Mirbach, M. F.; Mirbach, M. J.; Saus, A. Chem. Rev. 1982, 82, 59−76. (28) (a) Anderson, A. G.; Goddard, W. A. III J. Chem. Phys. 2010, 132, 164110. (b) Rabinovitch, B. S.; Looney, F. S. J. Chem. Phys. 1955, 23, 2439. (c) Jeffers, P. M. J. Phys. Chem. 1974, 78, 1469. (29) Glendening, E. D.; Reed, A. E.; Carpenter, J. E.; Weinhold, F. Gaussian NBO version 3.1, Gaussian 03, Revision B.03; Gaussian, Inc.: Pittsburgh, PA, U.S.A., 2003 (30) The calculated CASPT2 bond dissociation energy DC−Si = 69.17 kcal·mol−1 (silane 1: CH2CHCH2-SiH3) compares well to the experimental value of 73 kcal·mol−1 of the trimethylsilyl derivative (CH2CHCH2-SiMe3);48b the introduction of three methyl groups strengthen the C−Si bond by 3.1 kcal·mol−1 as we have found by calculating the bond dissociation energies DC−Si of CH2CHCH2SiH3 (62.4 kcal·mol−1) and CH2CHCH2-SiMe3 (65.5 kcal·mol−1) using DFT [B3LYP/6-31G(d)]. This strengthening seems reasonable in view of the difference of 4.6 kcal·mol−1 in the experimental values of H3Si-Me (89.6 ± 1.0 4.6 kcal·mol−1) and Me3Si-Me (94.2 ± 2.0 kcal·mol−1) (Becerra, R.; Walsh, R. The Chemistry of Organic Silicon Compounds; Rappoport, Z., Apeloig, Y., Eds.; Wiley: NY, U.S.A., 1998; Vol. 2, p153). A value of DC−Si = 70 kcal·mol−1 has been reported for 1 by applying CCSD(T)/6-311+G(2d,p) (Carra, C.; Ghigo, G.;

remarks on improving the language style of the manuscript, and Prof. Ioannis Dimitropoulos for helpful discussion.

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Tonachini, G. J. Org. Chem. 2003, 68, 6083−6095), while Zavitsas and coworkers have estimated 77.2 kcal·mol−1 (Matsunaga, N.; Rogers, D. W.; Zavitsas, A. A. J. Org. Chem. 2003, 68, 3158). (31) Bachrach, S. M. Computational Organic Chemistry; Wiley Interscience: NJ, U.S.A., 2007; pp 223−225, 228; Anderson, K. Theor. Chim. Acta 1995, 91, 31. (32) The tendency of CASPT2 to overestimate dissociation and activation energies is well-known.31 However, the energetic differences between the CASSCF and CASPT2 values do not affect the values of the crucial parameters α and β in the correlations 4−6, as is shown in Table 4. The deterioration of the correlation coefficient R with the CASPT2 values reflects probably a less uniform treatment of the dynamical correlation of the transition states of the successive member molecules 1−6. (33) Steinfeld, J. I.; Francisco, J. S.; Hase, W. L. Chemical Kinetics and Analysis; Pentice Hall: NJ, U.S.A., 1989; Computational Thermochemistry; Irikura, K. K., Frurip, D. J., Eds.; ACS Symposium Series; American Chemical Society: Washington, DC, 1998. (34) Lewars, E. Computational Chemistry; Kluwer Academic Publishers: Boston, MA, 2003. (35) Laidler, K. J. Chemical Kinetics; Harper & Row: NY, U.S.A., 1987; p 74. (36) (a) Marston, G.; Monks, P. S.; Wayne, R. P. General Aspects of the Chemistry of Radicals; Alfassi, Z. B., Ed.; John Wiley & Sons Ltd.: NY, U.S.A., 1999; p 429. (b) Roberts, B. P.; Steel, A. J. J. Chem. Soc., Perkin Trans. 2 1994, 2155. (37) Leffler, J. E.; Grunwald, E. Rates and Equilibria of Organic Reactions; John Wiley: NY, U.S.A., 1963; p 157. (38) The calculated kr values are much too small to compete with the decay from alkene’s twisted triplet states (lifetime in the ns time scale),38a that is, the calculations predict that compounds 1−6 will be photochemically inert with respect to C−Si bond dissociation. We thank a reviewer for this comment. (a) Unett, D. J.; Caldwell, R. A. Res. Chem. Intermed. 1995, 21, 665. (39) See, however, exceptions and discussion: Pross, A. J. Org. Chem. 1984, 49, 1811. Pross, A.; Shaik, S. S. New J. Chem. 1989, 13, 427 and literature cited therein. (40) (a) Hammond, G. S. J. Am. Chem. Soc. 1955, 77, 334. (b) Jencks, W. P. Chem. Rev. 1985, 85, 512. (41) Huang, X. L.; Dannenberg, J. J. J. Org. Chem. 1991, 56, 6367. (42) Marcus, R. A. J. Am. Chem. Soc. 1969, 91, 7224. (43) Abel, B.; Assmann, J.; Botschwina, P.; Buback, M.; Kling, M.; Oswald, R.; Schmatz, S.; Schroeder, J.; Witte, T. J. Phys. Chem. A 2003, 107, 5157. Abel, B.; Assmann, J.; Buback, M.; Grimm, C.; Kling, M.; Schmatz, S.; Schroeder, J.; Witte, T. J. Phys. Chem. A 2003, 107, 9499; see energy barriers of other exorthemic reactionsin ref 36b.. (44) Carpenter, B. K. Science 2011, 332, 1269. Schreiner, P. R.; Reisenauer, H.-P.; Ley, D.; Gerbig, D.; Wu, C.-H.; Allen, W. D. Science 2011, 332, 1300. Isborn, C.; Hrovat, D. A.; Borden, W. T.; Mayer, J. M.; Carpenter, B. K. J. Am. Chem. Soc. 2005, 127, 5794. Zavitsas, A. J. Am. Chem. Soc. 1998, 120, 6578. Shaik, S.; Shurki, A. Angew. Chem., Int. Ed. 1999, 38, 586. Donahue, N. M. Chem. Rev. 2003, 103, 4593. (45) (a) Bernasconi, C. F. Acc. Chem. Res. 1987, 20, 301. (b) Bernasconi, C. F. Adv. Phys. Org. Chem. 2010, 44, 223. (46) (a) This triplet electron repulsion causing the twist of the planar ethylenic system46b is to be distinguished from the triplet repulsion introduced by Zavitsas et al. in an effort to describe activation barriers involved in radical H-atom abstractions (e.g., R-H + •X → [R↑···↓ H···↑X]‡ → R• + HX): Zavitsas, A. A. J. Phys. Chem. A 2010, 114, 5113. See also Denisov, E. T. Russ. Chem. Rev. 2000, 69, 153. (b) Woeller, W; Grimme, S.; Peyerimhoff, S. D.; Danovich, D.; Filatov, M.; Shaik, S. J. Phys. Chem. A 2000, 104, 5366. (47) Pasto, D. J. J. Phys. Org. Chem. 1997, 10, 475. (48) (a) NIST Chemistry WebBook, NIST Standard Reference Database Number 69; Linstrom, P. J., Mallard, W. G., Eds.; National Institute of Standards and Technology: Gaithersburg, MD, U.S.A., 2011; p 20899; http://webbook.nist.gov (retrieved September 6, 2011); (b) Barton, T. J.; Burns, S. A.; Davidson, M. T.; IjadiMaghsoodi, S.; Wood, I. T. J. Am. Chem. Soc. 1984, 106, 6367: Here is

reported the activation energy of the C−Si ground state dissociation of CH2CHCH2-SiMe3, which we assumed equal to the corresponding bond dissociation energy DC−Si = Ea = 73 kcal·mol−1. (49) Diau, E. W.-G.; Kötting, C.; Zewail, A. H. ChemPhysChem 2001, 2, 273.

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Ground- and Triplet Excited-State Properties Correlation: A

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