J . Phys. Chem. 1986, 90, 219-282
Theoretical Study on the CuH 4- H
279
Cu -t H, Reaction Pathway
-+
M. E. Ruiz, J. Garcia-Prieto, E. Poulain, Investigacidn Biisica de Procesos. Instituto Mexican0 de Petrdleo, 07730 MZxico D.F., Mexico
G. A. Ozin, R. A. Poirier, S. M. Matta, I. G. Czismadia, C. Gracie, Lash Miller Chemical Laboratory, University of Toronto, Toronto, Ontairo, Canada M5S 1AI
and 0. Novaro* Instituto de Fisica, Universidad Nacional Autdnoma de MZxico, 01 000 MZxico. D.F., Mexico (Received: August 28, 1985)
-
Quite recently, experimental results on the CuH + H Cu + H2thermal matrix phase reaction were reported, indicating that it proceeds with no activation barrier, and no evidence exists for an intermediate CuH2 species at 10-13 K. Here we present a theoretical study of this reaction using variational and perturbational configuration interaction calculations with a relativistic pseudopotential (PSHONDO-CIPSI) set of programs. The results confirm the lack of a barrier and provide an explanation as to why the CuH2 species may not be observed.
Introduction
Recently, it has been reported that the thermal reaction of CuH with H atoms trapped in Ar, Kr, and Xe matrices at 18-29 K produces high yields of Cu atoms with no detectable evidence of a copper dihydride species.’ In addition, no appreciable kinetic isotope effect was observed on going from CuH H to CUD D in the regeneration of Cu atoms on passing from Ar to Kr or to Xe. In the experiments it was also found that the extent and rate of the Cu atom recovery process were high and depended on the choice of Cu/H2/rare gas concentration conditions, the temperature of the matrix support, and the temperature at which CuH + H are photolytically generated.2 It should be mentioned that in ref 1 the reaction was interpreted in terms of a mechanism involving the abstraction of the H moiety of the copper hydride by a linear approach of the H atom. Here we present a series of theoretical calculations (with methods described in the following section) in order to determine the actual mechanism of the reaction by comparing the different possible reaction pathways, Although a rather comprehensive scan of the potential energy surface has been carried out and some results for random relative geometries and orientations for the approach of the CuH and H reactants shall be mentioned briefly, we shall concentrate in thtis study on two possible pathways. One involves a linear attack of the H atom on the Cu moiety of CuH to yield the Cu + H2 products. We shall refer to this as the “addition” mechanism ( H CuH) to distinguish it from the other pathway involving the linear attack of the H atom on the H moiety of the C u H molecule. The latter mechanism will be called the abstraction mechanism (CuH H). The choice between these two mechanisms (or perhaps an intermediate alternative) depends on how well they can account for the observed experimental evidence. Among the most relevant facts reported in ref 1 are the lack of detectable isotope effects, the fact that no activation energy is needed to reach the products, and particularly the nonexistence of a copper dihydride species as a detectable intermediate at any stage of the process. We must address these aspects if we want to relate our potential energy surface to the real chemical evolution of the matrix isolation experiments.’S2
+
+
+
+
Method Details of the method3 and basis sets used in the meudowtential configuration interaction (CI) study are given in re? 3-5. Briefly, (1) G. A. Ozin and C. Gracie, J . Phys. Chcm, 84, 643 (1984). (2) G. A. Ozin, J. Garcia-Prieto, and S. A. Michell, Angew. Chem., Int. Ed. Engl., Suppl., 785 (1982).
0022-3654/86/2090-0279$01.50/0
the model potential method of Durand and Barthelat,3 parametrized as reported in ref 4,is used for the S C F calculations, and then through the CIPSI scheme a variational C I calculation of a reference state including approximately 100 determinants is used as a zeroth-order starting point of a second-order pertubation analysis where a much larger (up to nearly lo6 configurations) C I space is then taken into account through a Mdler-Plesset approach. The basis sets are of double-{quality with exponents and coefficients as given in ref 4,including a 3s, 2p, 5d set contracted to 2s, 2p, 2d for the Cu valence shell and 4s, 4p contracted to 2s, 2p for the H atoms. In order to supplement these calculations, a set of all-electron SCF-CI calculations were also carried out for a large portion of the reaction pathways. As shall be reported below, most of the all-electron results fit exactly the results of CIF‘SI. For the former results use was made of the MONSTERGAUSS program. MONSTERGAUSS is a modified and extensively updated version of Pople’s GAUSSIAN 80. The program uses a fully variational CI scheme. The basis sets used here were 14s, 9p, 5d of Wachters6 for Cu contracted to 6s, 3p, 2d. For the H atoms Pople’s 2s contracted basis set was used.’ Results
Energy Pathways. A substantial part of the potential energy surface for the CuH + H reaction was studied by using our CIPSI program, leading us to a minimal-energy pathway that is clearly localized in the region corresponding to the addition process described in the Introduction. This corresponds to the approach of the H atom toward the Cu moiety in copper hydride, maintaining a linear H - C u H geometry which energetically is the most favorable. Any shifts from this linear approach provoked energy destabilization. This was true whether the internal distance in the copper hydride was kept at its experimental value or optimized throughout the H approach. Before describing this pathway, however (for which, by the way, the results of the all-electron MONSTERGAUSS calculations faithfully reproduced the pseudopotential CIPSI results), let us report our calculations for the reaction pathway for the mechanism originally proposed in ref (3) J. C. Barthelat and Ph. Durand, Theor. Chim. Acta, 38, 283 (1975). (4) M. E. Ruiz, J. Garda-Prieto, and 0.Novaro, J . Chem. Phys., 80, 1529 ( 1 Q R A,,.) \-,-
( 5 ) J. Garcia-Prieto, M. E. Ruiz, E. Poulain, G. A. Ozin, and 0. Novaro, J . Chem. Phys., 81, 5920 (1984). ( 6 ) A. J. H. Wachters, J. Chem. Phys., 52, 1033 (1970); L. Ginoglio, R. Pavani, and E. Clementi, Gazz. Chim. Ital., 108, 181 (1978). (7) J. S. Brinkley, J. A. Pople, and W. J. Hehre, J. Am. Chem. SOC.,102, 939 (1980).
0 1986 American Chemical Society
280 The Journal of Physical Chemistry, Vol. 90, No. 2, 1986
Ruiz et al.
- -51 315a
/
0
>.
a -51325-
p: W
z W -1
4
c -51 335. 0 I-
iI -51 3601
1 IO
1 20
30
40 50 rICuH-H) d i s l a n c e
60
70
80
( a u
Figure 1. Energy curve for the CuH + H abstraction reaction pathway viewed as a linear approach of the H atom to the H moiety of the copper hydride molecule (for which the equilibrium distance of 2.76 a, is fixed
throughout).
1, i.e., the approach of the H atom toward the H moiety of copper hydride, also in a linear approach, which was called the abstraction process. Our pseudopotential CIPSI prediction for the abstraction mechanism has the form reported in Figure 1. A barrier of about 6.9 kcal/mol is obtained. The MONSTERGAUSS barrier is somewhat smaller. The sharp lowering of the energy for the shorter distances, after the barrier is surmounted, corresponds to the formation of an H 2 molecule perturbed by the presence of the Cu atom. This is borne by the analysis of the molecular orbitals at the minimum of the curve in Figure 1, but this shall be discussed in detail below. It may be argued that the barrier is not prohibitively high. However, at matrix isolation conditions even a smaller barrier, such as that of 2 . 4 kcal/mol predicted at the all-electron level (which probably stems from the much smaller configuration space that MONSTERGAUSS takes into account as compared with the lo6 configurations included in CIPSI), would be hard to overcome by the system. For the addition reaction the CIPSI total energy variation of the H CuH system as a function of the H to CuH distances is shown in Figure 2. Here the CuH moiety was fixed at 2.76 ao, which corresponds to the copper hydride equilibrium distance of the isolated m o l e c ~ l e .A~ similar curve was found when the distance was fixed at 2.84 ao, corresponding to the equilbrium Cu-H distance of the symmetrical-linear HCuH m~lecule.~ These results show that the H atoms will react with the CuH molecules without any activation barrier to give a symmetrical-linear copper dihydride molecule. We calculated the CuH equilibrium distances to be 2.84 a, using CIPSI and 2.75 a,, using MONSTERGAUSS. For initially nonlinear reactive encounters between the H and CuH species, we obtain small barriers when we reorient the reactants with respect to one another in forming the copper dihydride molecule. A detailed analysis of the copper dihydride molecule which results from the H + CuH addition reaction shows an interesting mechanism whereby the reductive elimination of the H2 molecule from the HCuH complex is feasible and may also explain why the CuH2 species is not observed experimentally. In the ClL symmetry the lowest lying energy states of the HCuH molecule that correlate with Cu('S) H,, C U ( ~ D+ ) H2, and Cu('P) + H2 at the dissociation limit are 'A, and two 'B2 states, respectively. The analysis of the ground 2A, and the lower excited 2B2states was carried out by first fixing the CuH distance to 2.84 au and varying the angle between the two branches of the HCuH molecule
+
+
-51 3 5 5 ' 16
I
32
24
48
40
5 6
72
64
00
r (H-CuH) distance (a u 1 Figure 2. Energy curve for the H + CuH addition reaction pathway taken as a linear array where now the H atom approaches the Cu moiety of CuH. 1
lot
3' . . . . . . .. - . . .... .-.t..
....1
1'567
.
1. _ .......... I 1 --... I-...
~~
469 425
554
I
cs
~
Cu:H
C2"
254
,4aa
~CUlZSi+H2
-
,
H'
Figure 3. Addition reaction (similar to that of Figure 2 but now using an optimized 2.84 a, for the equilibrium distance) represented on the left-hand side-identified as having C, symmetry- and supplemented on the right-hand side by the description of the dissociation of the HCuH intermediate in the C, portion of the figure. On the right-hand side the HCuH complex leaves its linear form, passing through another minimum and going to the Cu + H2 products by allowing the H moieties to approach each other while keeping their common Cu-H separation fixed at its optimal 2.84-a, value, thus maintaining a C, symmetry throughout. Furthermore, the *A, ground state of the HCuH complex is shown to interact with its ,B2 first excited state through a Herzberg-Teller coupling tfat lowers the barriers (see text), thus allowing the intermediate complex HCuH to dissociate into the final products Cu + H,.
until the H-H distance corresponds to that of the H 2 molecule (H-H bond length of 1.4 au and H-Cu-H angle of 28.6'). Subsequently, the Cu to H2 molecular center distance was increased to finally form the Cu H2 products. Figure 3 depicts this H-Cu-H angular dependence of the total energy for the 2B2and 'A, electronic states. Starting from the linear geometric configuration, we can see that for the 2A, state, which correlates with the C U ( ~ S+ ) H2 products, the system has an energy barrier of 66 kcal/mol in going from 180 to 28.6'. The 'B2 state shows an absolute minimum when the H moieties approach each other; the H-Cu-H angle reaches 11 1.5' and af-
+
CuH
+H
-
Cu
+ H2 Reaction Pathway
The Journal of Physical Chemistry, Vol. 90, No. 2, 1986 281
TABLE I: Main Atomic Orbital Contributions for the Occupied I: Molecular Orbitals of the CuH Ha-H Internuclear Separation B
R,a, 6.7 4.9 3.1 2.2 1.8 1.5 1.3
Cu s +0.07 +0.09 +0.09 +0.09
2, d,z
s*
+0.63 +0.63 +0.60 +0.47 +0.36 +0.28 +0.24
+0.24 +0.24 +0.27 +0.35 +0.39 +0.42 +0.43
pp +0.05
+ H Abstraction Reaction as a Function of the
22
CU
Sb
+0.07 +0.19 +0.26 +0.32 +0.35
S
+0.36 +0.34 +0.24 +0.13 +0.09 +0.08 +0.07
PI
dz2
+0.11 +0.10 +0.07
-0.28 -0.28 -0.35 -0.58 -0.60 -0.65 -0.66
x3
sb
CU s
+0.12 +0.21 +0.24 +0.22 +0.20 +0.18
+0.05 +0.16 +0.38 +0.52 +0.61 +0.67 +0.70
sa
+0.33 +0.32 $0.27 +0.19 $0.14 +0.11 +0.09
pr
dz2
sa
sb
-0.65 -0.65 -0.57 -0.46 -0.39 -0.32 -0.26
+0.09 +0.11 f0.08
-0.09 -0.14 -0.14 -0.14 -0.13
-0.07
‘Due to the double-{ nature of the basis set, two coefficients exist for each atomic orbital; only the most important one is reported. TABLE I1 Main Atomic Orbital Coefficients for the Z: MOs of the H Separation R’
+ CuH Addition Reaction as a Function of the Cu-H
21
R’,a,, 6.5 5.25 4.0 2.76 2.5
Cu s
+0.06 +0.16 +0.17
22
pr
dzz
Sa
+0.05 +0.05
+0.64 +0.63 +0.59 +0.52 +0.51
+0.24 +0.25 +0.29 +0.24 +0.20
sb
CU s
pz
d2z
+0.35 +0.34 +0.35
+0.18 +0.06
-0.28 -0.28 -0.30
+0.08 +0.07
+0.24 +0.30
terward crosses the 2A, curve at 155 and 54O, and it has a saddle point at 180’. At the lowest level of approximation the ,Bzand the ZA,surfaces are expected to cross.s However, a Herzberg-Teller vibronic couples both electronic states and leads to an avoided crossing. According to Herzberg and Tellerg the normal vibrational mode coupling of these two states is of b2 symmetry which corresponds to the nonsymmetrical stretching mode of the triatomic molecule. This avoided crossing is represented by the dashed curves in Figure 3. As a consequence of this coupling, we have a minimum-energy pathway for the CuH + H Cu Hz reaction, where the original energy barrier of 66 kcal/mol is reduced to two small barriers of 14 and 27 kcal/mol according to our CIPSI results, as is shown in Figure 3. Figure 3 consequently represents a schematic description, albeit with full details, of the whole CuH + H Cu Hz reaction coordinate. According to our CIPSI (and confirmed by MONSTERGAUSS) results there is no activation barrier for the addition mechanism, where the formation of linear copper dihydride molecule results for the H + C u H reaction. Both pseudopotential and all-electron computations show that this reaction is 38 kcal/mol exothermic as is confirmed experimentally. Consequently, after the addition reaction the HCuH intermediates can easily overcome the two low-energy barriers, yielding as a net result the Cu H2 products. These results demonstrate that the permanent formation of copper dihydride from the H C u H addition reaction pathway is improbable even if it is the intermediate species in this reaction pathway. Molecular Orbitals. The molecular orbital analyses of the CuH, systems as it undergoes the geometrical changes corresponding to the abstraction and addition reactions discussed above (whose energy pathways are given in Figures 1 and 2, respectively) are reported in Tables I and 11. Only those molecular orbitals (MO) which correspond to B symmetry are reported because the MOs with K and A symmetry are by definition nonbonding within the z axis of the linear CuH, geometries. In Tables I and I1 the rows represent the MOs main contributions at each internuclear distance between the incoming H atom and the H and Cu moieties in copper hydride, respectively. In each table the three occupied Z MOs are given. Table I11 reports MOs of the isolated copper hydride system as a reference in order to see the changes that the second incoming H induces in each reaction. We see that CuH has two Z MOs: one deep in energy representing the Cu d2 atomic orbital which interacts with the H sa orbital, and a second which
-
+
-
+
+
+
(8) R. G.Pearson, ‘Symmetry Rules for Chemical Reactions”, Wiley, New York, 1976. (9) G. Herzberg and E. Teller, 2.Phys. Chem., Abf. B, 21, 410 (193).
Sa
Sb
+0.32 +0.29 +0.19 +0.39 +0.44
+0.10 +0.16 +0.25 -0.39 -0.35
CU
S
+0.09 +0.12 +0.39 +0.40
pz
+o. 12
+0.18 +0.19
Internuclear
E3 dZ2
-0.10 -0.19 -0.42 -0.42
sa
sb
+0.17 +0.27 +0.14 +0.09
-0.60 -0.51 -0.37 +0.14 +0.15
TABLE I11 Main Atomic Orbital Coefficients for the Occupied Z MOs of the Isolated Copper Hydride Molecule 22
Z:l
Cus
D,
d,* +0.65
Hs +0.24
Cus +0.36
D.
d?
+0.17
-0.28
Hs
___
+0.34
is of essentially bonding s character from both the Cu and H moieties, but with an antibonding interference by the Cu dg orbital. When following the abstraction reaction in Table I, we first see that at a long H-.HCu separation of 6.7 a. the lowest two Z MOs are essentially those of CuH and a third I: state, higher in energy, is the s b function of the incoming H atom. In the region around the maximum of Figure 1, Le., near 4.9 a,, this situation still holds. However, when the H-H distance gradually reaches the 1.4-a, separation, the ordering of the Z levels is interchanged. First the second I: MO begins to gather some contribution of the incoming H sb function, and at 3.1 a, it already begins to resemble an internal H2(I:) bond. At 2.2 a, it actually becomes the lowest in energy of the three Z MOs of the CuH, system, displacing the one that had essentially a Cu dZ2character which now interacts with both of the H moieties s functions, and the other B MO of essentially Cu s character, now playing no role in the CuH, bonding, is now the highest in energy of the occupied states. Looking carefully to the bonding situation in the last stages of the CuH H abstraction reactions (Le., with the H-H separation around 1.4 ao), we see the justification of the statement given above, that at the minimum of Figure 1 we had essentially an H2 molecule perturbed by the presence of a Cu atom. As concerns the results of Table I1 for the addition process, the changes are not so drastic. The lowest Z MO is always the same Cu d,z function which at first interacts with the sa orbital as in isolated copper hydride and at shorter distances begins to gradually add the s b orbital of the other incoming H atom. At the minimum of Figure 2 (-2.8 ao), in fact, the d,z orbital overlaps equally with both H s orbitals forming a three-center bond. The new Z MO, which at the beginning is highest in energy as also was the case in Table I, originally consists of sb from the incoming H atom; it however begins to interact by establishing an antibonding relation with s, which is of no great consequence because of the interposed Cu atom between the two H moieties. In fact, a small contribution of the p1 function in Cu serves to give this Z MO a nominally bonding character. This third 2 MO eventually displaces the second B MO which as mentioned above contains Cu s and d,2 contributions of opposite signs interacting with sa and, later, also with sb. The above-mentioned molecular orbital structure gives us some insight of how the bonding situation is established for the Cu-H-H and H-Cu-H complexes. The question is whether the extensive
+
J . Phys. Chem. 1986, 90, 282-287
282
configuration interaction allowed by CIPSI introduces substantial modifications to this S C F picture. This is, in fact, not the case because the most important configurations of our C I space are basically transitions from the closed d shell of Cu, Le., essentially d-shell relaxation, which allows for a more direct participation of the dzz orbital in a manner that would reinforce rather than contradict the conclusions derived from Tables I and 11.
Conclusions From these theoretical results we can now explain the experH Cu H2 thermally imental observation of the CuH induced matrix phase reaction. The computations show that the linear attack of the H atom on the Cu moiety of the copper hydride molecule is energetically completely downhill (see Figure 2) and in complete agreement with the experimental results of Ozin et a1.I This addition of an H atom would form a HCuH complex with a bent structure, although the linear complex is only marginally higher in energy (see Figure 3). By exothermicity considerations the excess energy does not allow for the permanent existence of these species, which explains why they are not detected experimentally.’ To dissociate the HCuH species, only two relative small barriers exist that can easily be surmounted, as is shown in Figure 3 . The reverse reaction is endothermic and has an activation barrier of 28 kcal/mol according to our CIPSI calculations. This last result is in close agreement with the observedI0
+
-
+
heat of dissociative chemisorption of hydrogen on copper surfaces. Regarding the abstraction pathway originally proposed in ref 1, our theoretical results show that there is an energy barrier of several kcal/mol (see Figure 1). At this point the CIPSI results definitely predict that the abstraction is less probable than the addition mechanism discussed above, due to the existence of this nonnegligible barrier for the former while none is present for the latter. Considering however that the rare gas solid matrix cage might conceivably induce an effective lowering of the abstraction barrier, we perhaps should not rule out this alternative pathway altogether. The study of such effects induced by the rare gas matrices implies a completely new approach for theoretical calculations. A pseudopotential perturbative SCF-CI method is being developed for the purpose of evaluating the changes in energy when the surrounding media are taken into account.“ In any case the explanation of the experimental results of ref 1 is quite clear. The potential energy surface shows an optimal energy pathway that corresponds to our so-called addition reaction, and this mechanism allows to justify theoretically all the observations of Ozin and Gracie.’ Registry No. CuH, 13517-00-5: H2, 1333-74-0; H, 12385-13-6 (10) A. Clark, “The Chemisorptive Bond”, Academic Press, New York, 1974. (1 1) Work in progress.
SURFACE SCIENCE, CLUSTERS, MICELLES, AND INTERFACES Water Activity in Reversed Sodium Bis(2-ethylhexyl) Sulfosuccinate Micelles Mario J. Politi* and Hernan Chaimovich Department of Biochemistry, Chemistry Institute, University of Siio Paulo, 01 498 Siio Paulo, SP, Brazil (Received: October 25, 1984; In Final Form: August 30, 1985) The rate of proton dissociation from the first excited singlet state of aromatic alcohols (8-hydroxypyrene-1,3,6-trisulfonate, ~-naphthol-6,8-disulfonate,@-naphthol-6-sulfonate,and &naphthol) was measured by steady-state fluorimetry in AOT reversed micelles as a function of H 2 0 content. Acid dissociation rate constants (kerf*) of the alcohols were related with apparent water activity (a,’) by comparison with koff*’smeasured in salt solutions of known water activity (uw). The a,’ in the reversed micelles estimated by this procedure depends on the probe positioning in the water pool. The data are consistent with the existence of two types of water in the water pools of reversed micelles.
Introduction Reversed micelles, stable isotropic solutions of the oil/surfactant/water system in the L2 domain, are powerful models that have found several applications ranging from biological cornpartmentalization analysis to chemical catalysis.’s2 Among the surfactants that form reverse micelles the best characterized are the systems derjvd from bis(2-ethy]hexy])sulfosuccinate(AOT).l-S (1) Fendler, J. H. In “Membrane Mimetic Chemistry”: Wiley: New York, 1982. (2) Mittal, K. L., Lindman, B., Eds. “Surfactants in Solution”; Plenum Press: New York, 1984: Vol. 3. (3) (a) Zulauf, M.; Eicke, H.-F. J . Phys. Chem. 1979,83, 85. (b) Eicke, H.-F. Top. Curr. Chem. 1980, 87, 85. (4) Mittal, K. L., Ed. ‘Solution Chemistry of Surfactants”; Plenum Press: New York, 1982; Vol. 2. (5) Douzou, P.; Keh, E.; Balny, C. Proc. Natl. Acad. Sci. U.S.A.1979, 76, 681.
0022-3654/86/2090-0282.$01.50/0
AOT reversed micelles can dissolve large amounts of water which remain compartmentalized in the organic media as bubbles (water Pools Or droplets) surrounded by the surfactant. Several reports demonstrate that these water pools are spherical with low (size) po1ydispersity.3’6-8 Several features of these systems remain to be solved. One of them pertains to the very debated question of water structure close to the interface9-I4 and the related questions of water activity ( 6 ) Eicke, H.-F.; Kubik, R.; Hammerich, H. J. Colloid Interface Sci. 1982, 90, 27. (7) Magid, L. J.: Daus, K. A,; Butler, P. D.; Quincy, R. B. J . Phys. Chem.
1983,87, 5412.
(8) Eicke, H.-F.; Hilfiker, R.; Holz, M . Helu. Chim. Acta 1954, 67, 361. (9) Wong, M.: Thomas, J. K.; Nowak, T. J . Am. Chem. SOC.1977, 99, 4730. (IO) Wong, M.; Thomas, J. K.; Gratzel, M. J . Am. Chem. SOC.1976, 98, 2391.
0 1986 American Chemical Society
