J . Phys. Chem. 1987, 91, 1440-1443
1440
the P-methyl-a-styryl radical, and this must reduce the rate markedly from the m - H case. In contrast, the ethynyl- and propynylcyclohexadienyl radical origin band yields were comparable as expected for H addition to the aromatic rings in each case. Replacing the ethynyl hydrogen with C H 3 and C2Hsgave a small red shift in the alkynylcyclohexadienyl radical electronic origin bands.14 Finally, these studies provide information on substituent effects in free radical addition to aromatic systems. In the case of ethylbenzene and benzene, the 3 17.3-nm ethylcyclohexadienyl radical origin was broader (fwhm = 260 cm-l) and stronger ( A = 0.21) than the 310.2-nm origin for cyclohexadienyl radical (fwhm 130 cm-', A = 0.05). Two noteworthy points arise from these observations. First, the H atom addition yield is substantially higher with ethylbenzene than benzene; this is surely due to the enhanced stability of the tertiary radical product with ethylbenzene (5) over the secondary cyclohexadienyl radical with benzene (l),
-
O
W
The ethyl substituent clearly stabilizes the cyclohexadienyl radical, but not as much as the electron-withdrawing -C=C-H group. Conclusions Reactions of H atoms from a blind discharge with phenylacetylene in argon gave two new free radical products with different photochemical behavior which were identified from matrix absorption spectra. The first, a-styryl radical, results from H addition to the P-carbon of the alkyne substituent, and the second, ethynylcyclohexadienyl radical, results from H addition to the aromatic ring. Deuterium substitution at all positions facilitates identification and vibronic assignment for the latter radical. The increasing yields of cyclohexadienyl radicals in benzene, ethylbenzene, and phenylacetylene experiments show that the strongly electron withdrawing ethynyl group stabilizes the cyclohexadienyl radical better than the ethyl group, which in turn gives a tertiary radical that is more stable than unsubstituted cyclohexadienyl. Finally, these studies are an important source of information on substituent effects in free radical addition to aromatic systems.
&+%
k S
which is consistent with rate factors from solution studies.33 Second, the increased line width for the ethylbenzene product may be due to a mixture of para and ortho tertiary radical isomers.
Acknowledgment. We gratefully acknowledge financial support for this research from the N.S.F. and helpful discussions with F. A. Carey on substituent effects and nomenclature. Registry No. 1, 15819-51-9;3, 34089-70-8; H, 12385-13-6;phenylacetylene, 536-74-3; styrene, 100-42-5; 1-phenylpropyne,673-32-5.
Ground- and Excited (3s13p1)-State Reactivity of Mg with HF: A Theoretical ab Initio SCF-CI Study Patrick Chaquin Laboratoire de Chimie Organique ThPorique, UniversitP Pierre-et- Marie- Curie, BLit, F, 75230 Paris Cedex 05, France (Received: December 30, 1985; In Final Form: September 29, 1986)
-
-
-
Model potential energy surfaces (PES'S) have been calculated (ab initio 631 G*and 631 G** + CI) for the following reactions of Mg (IS, 3P, and 'P) with HF: (1) Mg + H F MgF + H (Lo); (2) Mg HF MgH F (C-"); (3) Mg H F HMgF (Cs). Reaction 2 appears to be very unlikely, even from excited Mg. Triplet 3P Mg could yield (1) and (3) with a low efficiency; the singlet PES of (2), arising from 'P Mg, is attractive and exhibits a minimum. This path thus is presumably greatly favored. From the GS, the insertion reaction (3) is the most likely to occur. The various approaches and the topology of the PES are briefly discussed by using correlation and perturbation MO arguments.
Introduction The reactivity of metal atoms with small covalent molecules, either in the gas phase or in matrices a t low temperature, has stimulated many experimental and theoretical studies. The Mg + H2system has been recently studied by sophisticated meth0ds.l In a previous paper2 dealing with this system, we explored a complete set of model reaction paths (ab initio S C F CI) and we emphasized the easy C2, side-on approach of IP Mg, with formation of a 'B2 exciplex initially proposed by Jordan et al.lc We will now report the results of calculations relative to the Mg + H F system. This system, as far as we know, has not yet
+
(1) (a) Breckenridge, W. H.; Umemoto, H. J . Chem. Phys. 1981, 75,678. (b) Breckenridge, W. H.; Umemoto, H. J . Chem. Phys. 1981, 75,4153. (c) Blickensderfer R. P.; Jordan, K. D.; Adams, N.; Breckenridge,W. H. J. Phys. Chem. 1982, 86, 1930. (d) Adams, N.; Breckenridge, W. H.; Simons, J. Chem. Phys. 1981,56, 327. ( e ) Blickensderfer, R. P.; Breckenridge, W. H.; Moore, D. S. J . Chem. Phys. 1975, 63, 3681. (0 Breckenridge, W. H.; Umemoto, H. J . Chem. Phys. 1984, 80, 4168. (8) Breckenridge, W. H.; Stewart, J. J . Chem. Phys. 1982, 77,4469. (h) Kleiber, P. D.; Lyyra, A. M.; Sando, K. M.; Heneghan, S . P.; Stwalley, W. C. Phys. Rev. Lett. 1985, 54, 2003.
(2) Chaquin, P.; Sevin, A,; Yu, H. T. J . Phys. Chem. 1985, 89, 2813.
0022-3654/87/209 1- 1440$01.50/0
+
+
+
been investigated experimentally, and H F has been chosen as the simplest strongly dissymmetrical diatomic molecule. Our goal is to discuss the differences of reactivity brought about by this dissymmetry: for this purpose, we have limited ourselves to the three following model reactions, in the IS (ground state) and the 3P and IP excited states of the Mg atom:
+ F-H Mg + H-F Mg
Mg
+ H-F
-+
MgF
-
-+
MgH
+H
(C-,)
(1)
+F
(C-,)
(2)
(C,)
(3)
H-Mg-F
The potential energy surfaces (PES's) relative to reaction 1 in the ground state (GS) have been recently investigated by Paniagua et aL3 Moreover, Dykstra et al. studied the thermal insertion of Mg with HF and other related species such as C H 3 F and CH3CL4 Nevertheless, no theoretical study has been published concerning either the excited-state reactivity of Mg or the possible competition of reactions 1-3 in the GS, although (2) is unexpected (3) Paniagua, M.; Garcia de la Vega, J. M.; Alvarino, J. M.; Lagana, a. J . Mol. Struct. 1985, 120, 475. (4) Jasien, P. G.; Dykstra, C. D. J . Am. Chem. SOC.1985, 107, 1891.
0 1987 American Chemical Society
The Journal of Physical Chemistry, Vol. 91, No. 6,1987
Reactivity of Mg with H F
1441
TABLE I GS ref energies absolute, au relative, eV
Mi3 Mg
+ HF
-299.7873a -299.1905'
0.00 -0.08
-1.26
state energies: eV 'P, 2.71d
IS, 0.00 'E+,0.00
'E+, 2.53; 'II, 2.72
IZ+,0.00 l2+,0.00
'P,2.55' 'Z+,5.53; 311, 6.39 2n,
HMgF MgF + H MgH + F MgF
-299.8335" -299.1 164" -299.218 1'
22+, 0.00
MgH
-200.1695'
22+, 0.00
Mg...F.. .H (exciplex)
-299.6486" -299.6596
'P,4.35d IX+, 4.47; I l l , 4.60 l2+,4.35'
In, 6.97; ' 2 , 7.18
1.92 4.63 3.59 211, 3.45;' 2Z, 4.61e 211, 2.37 211, 2.38;' 2Zc, 4.80'
-0.708 -0.77h
"Method I1 (2'2+). bCalculated from experimental values (see text). CUnlessfurther indication: method 11, above GS of each species. dExperimental (Moore, C. E. Atomic Energy Levels; National Bureau of Standards: Washington, DC, 1949; Vol. I). CExperimental(ref 11). fMethod 111 (2IE+). gMethod 11, with respect to 2I2+ Mg + FH, C,, 4-A separation (exciplex stabilization). hMethod 111, with respect to 2IZ+ Mg + FH, C,, 4-A separation (exciplex stabilization). a priori for thermodynamic reasons.
Computational Details The calculations were performed in two steps. First, a model set of PES's was obtained at the 631G* S C F level, followed by the diagonalization of a set of about 100 selected configurations (method I). This way, the most realistic reaction paths were determined. Second, the crucial points of these surfaces (reactants, products, saddle point, exciplex) were treated at the 631 G** level with an extensive multireference CI: a set including up to 200 configurations was used to generate the perturbative set involved in the Mraller-Plesset technique (method 11). The basis set was taken from ref 5. A single d atomic orbital (AO) was used for Mg with an exponent of 0.165. In order to test the influence of this exponent15on the calculated energy, some crucial points have been calculated with an improved 3d set. According to Pople,16 we used a double d set with 0.33 and 0.0825 exponents (method 111). As it can be seen in Table I, the relative energetics are not strongly affected. The S C F step was achieved by using the MONSTERGAUS~series of programs; the closed-shell Roothaan' Hamiltonian was used, except for isolated M g H and MgF, calculated with the R H F Nesbet's Hamiltonian.6 All geometry optimizations were obtained at the S C F level with a full gradient algorithm. The CI's were performed with the CIPSI p r ~ g r a m . When ~ the Mraller-Plesset technique was used (method 11), the calculations were caried out in several steps, up to convergence on a threshold of lo4 au/particle. The total number of configurations ranged from 5 x IO5 to lo6 according to each case. In the first section, we will only report the calculated results, which will then be briefly discussed in the second section. Results A . Reactants and Products. The results relative to the G S and the first excited states, of the reactants and products involved in reactions 1-3 are given in Table I. The optipized geometries at SCF level are as follows: HF: H-F = 0.9016 A. HMgF: ( 5 ) Francl, M. M.; Pietro, W. J.; Hehre, W. J.; Binckley, J. S.; Gordon, M. S.; DeFrees, D. J.; Pople, J. A. J . Chem. Phys. 1982, 77, 3654. Gordon, M. S.; Binckley, J. S.; Pople, J. A.; Pietro, W. J. J . Am. Chem. SOC.1982, 204, 2797. Pietro, W. J.; Francl, M. M.; Hehre, W. J.; DeFrees, D. J.; Pople, J. A,; Binckley, J. S. J . Am. Chem. SOC.1982, 104, 5039. (6) This program is derived from the GAUSSIAN 80 series, written by J. S. Binckley, R. A. Whiteside, R. Krishnan, R. Seeger, D. J. DeFrees, H. B. Schlegel, S. Topiol, L. R. Kahn, and J. A. Pople, initially also from the GAUSSIAN 76, QCPE No. 368, Indiana University, Bloomington, IN. (7) Roothaan, C. C. J. Rev. Mod. Phys. 1951, 23, 69. (8) Nesbet, R. K. Rev. Mod. Phys. 1963, 35, 5 5 5 . (9) Huron, B.; Malrieu, J. P.; Rancurel, P. J. Chem. Phys. 1973, 58, 5745. Malrieu, J. P. Theor. Chim. Acta 1982, 62, 163. Evangelisti, S.; Daudey, J. P.; Malrieu, J. P. J . Chem. Phys. 1983, 75, 91. (10) M ~ l l e rC.; , Plesset, M. S. Phys. Rev. 1934, 46, 618.
lev
Figure 1. Calculated PES's for the C,. abstraction reaction (1) (central part).I2 The energies of the TS and exciplex structures are given in eV with respect to the same state of Mg FH at 3-A separation: (a) method I; (b) method 11.
+
Mg-F = 1.784 A; Mg-H = 1.694 A; H-Mg-G = 180' MgF: Mg-F = 1.781 A. MgH: Mg-H = 1.681 A (see ref 2 and references therein). The calculated parameters for H M g F are very close to those recently reported by Dykstra et al. B. C,, Abstraction Reaction: M g FH MgF H. The calculated model PES's of the crucial part of R C are shown in Figure 1. The Mg-F and H-F bond lengths have been varied in the ranges 2.0-1.75 and 0.9-1.65 A, which roughly correspond to the optimized reaction coordinates. The structures reported in the upper part of the figure have been optimized from 24 calculated points by using method I. Ground-State Reaction. The calculated endothermicity is 1.93 eV (method 11). N o transition state is found at S C F level, and using the limited CI of method I, we found a weak barrier of about 0.3 eV above endothermicity. The same qualitative result has been reported by Paniagua et aL3 Excited-State Reaction. The 3Z+ state, originating from the 3Pstate of Mg, is potentially reactive, although a 0.65-eV barrier is found along the corresponding PES. The 'E+state, from 'P Mg, is attractive and leads to an exciplex structure. Its presence
+
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+
Chaquin
1442 The Journal of Physical Chemistry, Vol. 91, No. 6. 1987
M L H - F
Mg-H
F
%Tx
2G
Figure 2. Calculated PES's for the C,, abstraction reaction (2) (central part of the reaction coordinate). 1.6'
----
---
3/
Figure 4. MO (upper part) and state (limited to the 2' species, lower
part) correlations of the abstraction reaction (1). The diabatic correlations are indicated by dotted lines. The electronic filling in the MO diagram refers to the GS of both reactants and products.
= lZ'
+
1
H
/
L'
\
H Mg
f
I
\
'\
I
'\
F
F
'I+
'-
1.26
Figure 3. Data relative to the insertion reaction (3). The energies are given in eV, with respect to the same state of Mg + HF. (a) Method I, reference triangular Mg + HF at a 3-A distance. (b) Method 11, reference linear Mg + FH at a 4-A distance.
is confirmed by using the extensive CI of method 11, at 0.70 eV below the energy of the same state of Mg HF at 4-A separation (see Figure 1). C. C,, Abstraction Reaction: Mg HF MgH + F. The model PES's are shown in Figure 2. All these surfaces are strongly repulsive, partly due (see Discussion) to the endothermicity of the reaction. This endothermicity is approximately 4.6 eV, calculated from experimental values of HF and M g H bond energies.l' The most reactive state, 2l2+, exhibits an energy barrier higher than 2 eV along the reaction coordinate. Moreover, the GS of the products (MgH F) lies slightly above the 'P Mg excited state (4.34 eV). D. C,Insertion Reaction: M g HF HMgF. Ground-State Reaction. The energetic parameters have been calculated by using method 11. The reaction is exothermic by 1.19 eV. The transition-state (TS) geometry, optimized at the SCF level, was used in the CI step (Figure 3). Its calculated energy is 1.35 eV (31
+
+
+
+
-
-
(1 1) Hmberg, G. Molecular Spectra andStructure; Van Nostrand: New 1950; Vol. 1 (1 2) One may note the important 311-32+ splittingin the starting structure,
York,
relative to the weak s litting of the corresponding singlet PES's. In fact, a crassing point of the 2 2* and I l l PES's is found nearby the starting structure, whereas it occurs later for the triplet ones. (13) The actual nature of the first '2' excited state of MgF is Rydberg to a great extent.
P
kcal mol-') above Mg HF. This value is close to that recently reported by Dykstra. Excited-State Reactivity. For an exploratory scan of the RC, only two degrees of freedom have been considered by keeping the distances Mg-F and Mg-H equal. The lowest triplet 3Af and singlet 2'A' PES's increase monotonously, though the thermal reaction is exothermic, due to the high energy of the low-lying states of H M g F (see Table I). We report (Figure 3) the energy (above the corresponding state of the reactants) of a structure close to the TS of the GS insertion as an index of feasibility of the reaction: if such a geometry is achieved, the system, upon deactivation, could "fall" either on the reactant side or on the product side. It can thus be seen that the reaction requires about 0.9 eV from the 3P state and 1.6 eV from the 'P state.
Discussion A . Compared Topology of the Abstraction Reactions ( 1 ) and ( 2 ) . It is worthy of note that the major features of these two reactions can be qualitatively interpreted by diabatic correlation considerations. Let us first consider reaction 1. The molecular orbital (MO) correlation diagram is shown in Figure 4 (upper part). The M O s that are of concern are schematically drawn, the size of each lobe symbolizing the importance of the coefficient of the corresponding are diabatically correlated AO. We can see that uFH and cMgF (dotted lines) since the major electron location remains on the F atom. Similarly, UHF and ISH, 3p,Mg and uM~H,and 3sMg and the s p type nonbonding M O of M g H are correlated. After taking into account the resulting M O avoided crossings, the actual correlations (full lines) are obtained. We are now able to build, on the same grounds, the state correlation diagram (lower part of Figure 4). The intended state correlations (dotted lines) are deduced from the corresponding diabatic MO correlations. We see that the GS and the low-lying excited states of both reactants and products are correlated with high-energy ionic states according to H+ + M g F (GS of both ions) Mg FH: GS
+
+
'q3Z+ (3s
MgF
+ H:
-- - + -- + +
's3GS
1Wl3
3p)
M g F (excited M g F )
H+
Mg+
FH- (GS of both ions)
H F (GS)
Mg+ (excited)
Taking into account the avoided state crossings, the actual correlation diagram (full lines) is obtained, showing (i) the possibility
The Journal of Physical Chemistry, Vol. 91, No. 6,1987
Reactivity of Mg with H F
2
3
1443
dA
Figure 6. MO's energy variation during the two C ,, approaches (left part) and total SCF energy for various C, approaches (right part). In
both cases, the HF bond length has been optimized on each point. Excited Singlet State 'Pof Mg. In this case, the abstraction reaction (l), yielding MgF H , is greatly favored over the other two, since the corresponding PES is attractive, with formation of an exciplex whose geometry is very close to the TS of the GS Figure 5. MO (upper part) and state (limited to the 2' species, lower reaction. part) correlations of the abstraction reaction (2). The diabatic correlaC. Compared Behavior of HF and H2: Qualitative Intertions are indicated by dotted lines. The electronic filling refers to the pretation and Experimental Consequences. The differences in GS's of both reactants and products. behavior of H2 and H F relative to Mg can be qualitatively interpreted by M O perturbation considerations. We see in Figure of a minimum (exciplex) on the 2l2' PES and (ii) the presence 6 (left part) the energy variation of the relevant MO's of the Mg of a barrier along the GS and the 3 X + PES'S. If we now examine H F system in both C,, approaches. In the M g F - H approach, the other abstraction reaction (2), M O and state correlations are the 2sF, uFH, and 2p, orbitals are strongly stabilized by mixing easy to assess, giving the two diagrams of Figure 5 . The GS and with the 3s and 3p AO's of suitable symmetry of Mg. Concomthe first singlet and triplet states of Mg HF are correlated to itantly, we note a destabilization of 3sMgand 3pMg, moderated, ionic excited states of much higher energy than in the preceding especially for the latter, by the presence of a higher empty u * ~ ~ case. uHFis no longer diabatically correlated to the uMgH MO; thus, each configuration of the reactants involving an empty u * ~ ~level. These effects nearly cancel out in the M g - H - F approach, and an intermediate situation is encountered in the side-on C, M O intentionally leads to an empty uMgH M O in the M g H + F approaches. We thus can understand that the linear Mg-F-H system. This fact, in addition to the larger endothermicity of the approach is favored in the GS (see right part of Figure 6) and reaction, "erases" the possibility of a minimum on the 2l2' PES. even more so in the 3s-3p excited state. For the Mg + H 2 system, The reaction, compared with reaction 1, appears to be quite there is no longer an evident stabilization in the C,, geometry. unlikely, from the GS as well as from the low-lying excited states. Nevertheless, this geometry is found to be slightly favored in the The preceding discussion is the translation into the quantum G S 2 In contrast, the C , geometry is the most stable in the excited language of the chemical intuition which tells us that the easiest 'P state, as one 3p A 0 (B,) interacts only with the u* M O of H2 reaction is that which requires the weakest changes in electron and thus is stabilized. Indeed, as was stated in the Introduction, density, other things being equal. the existence of a 'B2 exciplex is confirmed by a b initio calculaB. General Survey of Reactivity. GS. The feasibility of tions. An experimental consequence is that MgH is mainly reaction 2, yielding M g H F, can be ruled out due to its enproduced from a side-on attack and thus with a high rotational dothermicity (4.6 eV). the exothermic formation of HMgF, with number.lb Following far wing absorption experiments and sian energy barrier of 1.35 eV, is greatly favored over the other multaneous measurements of reactive and nonreactive channels, abstraction reaction (l), the activation energy of which is about and in order to test this reaction scheme, the study of a dynamic 2.2 eV. model is in p r 0 g r e ~ s . l ~The opposite situation in encountered in Excited Triplet State 3P of Mg. Here again reaction 2 can the Mg FH system. As a matter of fact, because of the linear be discarded, since the initial excitation energy is lower than the geometry of the '2' exciplex, this channel would be favored and GS of the products. Regarding the other two reactions, we note thus MgF is expected to be produced with a low rotational that, along the triplet PES, a 0.65-eV activation energy must be quantum number. overcome (reaction 1). An additional energy of about 0.9 eV (reaction 3) is necessary for reaching a reactive region, Le., a Acknowledgment. The author is greatly indebted to Dr. Alain geometry close to that of the GS transition state. Taking into Sevin for discussions and help. These calculations have been account the exploratory character of the calculation, these two achieved using the computing facilities of the CIRCE center values remain of comparable magnitude, and the competition (CNRS, Orsay). between both paths is possible. Nevertheless, the reactions should be rather unefficient and dependent upon temperature. On the Registry No. Mg, 7439-95-4; HF, 1664-39-3. other hand, as the starting 3Pstate lies 1.35 eV above the TS of reaction 3, this reaction could occur, upon deactivation, via a "hot" (14) Kleiber, P. D., private communication. GS. Reaction 1 is also energetically possible in the same way, (1 5 ) As suggested by one reviewer. although rather unfavored, for the excess of excitation energy (16) Frisch, M. J.; Pople, J. A,; Binckley, J. S . J. Chem. Phys. 1984, 80, 3265. above the TS is only 0.5 eV.
+
+
+
+
+
