J . Phys. Chem. 1984,88, 5225-5228
5225
used in this work was C2F6, for which ( A E ) d = 10 kcal/mol. However, an extrapolation of our results to N = 10 yields ( h E ) d = 13 kcal/mol. Although this value falls in the general trend presented by Carr, it is also higher than for C-C& CH3CF3,and CH2FCHzFwhich are molecules of the same or less complexity than TFC. In addition, for the less efficient colliders, our ( h E ) d values are higher (by a factor of -2) than those reported for CH3CF3and CHzFCH2F (see Table 111). In a study on chemically activated l,l-dichlorocyclopropane,I6the deactivation by CH2CC12and C3F8 resulted in values of 7.2 and 14.4 kcal/mol, respectively, which are closer to those for TFC*. Unfortunately, not much attention was given to the energy-transfer process in that work as it was mainly concerned with the chemical aspect. Most of the chemical activation studies on energy transfer are with excitation energies of about 100 kcal/mok5 however, for TFC, ( E ) = 87 kcal/mol. Even though the difference in energy is not large, a possible dependence of the energy-transfer process of ( E ) might be considered. Until recently, most of the data supported an independence of on ( E ) . 2 However, in a study on photoactivated azulene at two different excitation energies (50 and 87.4 kcal/mol), Barker et al. found a pronounced effect of ( E ) , with the large (&)d corresponding to the higher excitation energy.4a If this finding is confirmed, then the effect is just opposite to what one would need to explain the ( h E ) dvalues for TFC. However, azulene in a nonreactive system, and the question remains as to whether the energy-transfer process is also dependent on excitation above the critical energy for reaction or not, as pointed out by Barker. The opposite situation arises from other direct measurements on toluene and substituted cycloheptatrienes in which dependence of was not f o ~ n d . ~In~all , ~these works, ( m ) d values much smaller than expected were reported. Deciding if this is a consequence of the complexity of the molecule or of the experimental technique is speculative at present, and more experimental data seem desirable. However, it must be noted that the measurements of energy loss with these direct methods were performed with rather large excited molecules ( N = 15, 18, 21, and 24) and that the ( h E ) d values, low as they are, seem to fall
in the general trend of the plot given by Carr. Thus, it seems so far, that ( h E ) d depends not only on the bath gas but also, though to a lesser extent, on the nature of the activated molecule and, possibly, the critical energy for unimolecular reaction. This leads to the conclusion that the amount of energy transferred depends on the properties of the collisional complex, in accordance with the predictions of the quasi-statistical theories on energy t r a n ~ f e r . ~Common ,~ to these theories is the central idea of a finite lifetime of the complex, during which the energy is redistributed from the activated molecule into the transitional modes, subject to certain constraints. These theories have been successful in obtaining calculated values in agreement with experiment and predict a dependence of the energy-transfer probabilities with the density of states of the activated m ~ l e c u l e . ~The - ~ difference in the density of vibrational states was used to explain the behavior of CH2DCH2Clas compared with that of CHDzCD2Br,when deactivated by the same bath gas.8 The density of vibrational states of TFC at the average excitation energy is quite large (-9 X 10l2 states/cm-') when compared, for instance, with CF3CH3(-2 X 1Olo states/cm-I). On a statistical basis one would then expect that deactivation of TFC should be more difficult than CF3CH3, with the same collider, at variance with experiment. This reassures our idea that the energy-transfer process depends on the properties of the activated molecule in an indirect fashion through the properties of the collisional complex, which should also be dependent on the interaction potential. In conclusion, the properties of TFC responsible of its behavior in collisional energy transfer cannot be isolated, due to the lack of data on related molecules and to the various factors on which the deactivation process seems to depend, according to the present experimental evidence. We think, however, that the data reported here are valuable as they provide information on a different kind of molecule. Unfortunately, the theories on energy transfer at high levels of excitation are not enough developed, but even at their present state they may provide some insight into these processes. We postpone further considerations and modeling with these theories until the study with more complex gem-difluorocyclopropanes is completed.
(16) Eichler, K.; Heydtmann, H. Int. J . Chem. Kinet. 1981, 13, 1107. (17) Setser, D. W.; Rabinovitch, B. S.; Simons, J. W. J . Chem. Phys. 1964, 40, 1751. (18) Kohlmaier, G. H.; Rabinovitch, B. S.J . Chem. Phys. 1963, 38, 1692.
Acknowledgment. This work was partially supported by CONICET (Argentina) through INFIQC. Registry No. 1,1,2,2-Tetrafluorocyclopropane,3899-7 1-6.
Molecular Structure of CuOH and Cu(OH),-.
An Ab Initio Study
F. Illas,* J. Rubio, Department Quimica Fhica, Facultat de Q u h i c a de Tarragona, Tarragona, Spain
F. Centellas, and J. Virgili Department Quimica Fhica, Facultat de Quimica de Barcelona, Barcelona-28, Spain (Received: April 17, 1984) The geometries of CuOH and CU(OH)~have been optimized at the SCF level with a basis of double { quality. The C, geometry of CuOH is more stable than C ,,, and a C2geometry is predicted for CU(OH)~-; this geometry is like that for H 2 0 2but with the Cu atom lying in the middle of the 0-0 bond. Dissociation energies have been calculated at the SCF and CI levels. While the SCF dissociation of CuOH only accounts for 60% of the experimental value, good agreement between calculated and experimental data is found at the CI level. Introduction Copper(1) hydroxide seems to play an important role in several industrial processes,i-3 as well as in the process of inhibiting
formaldehyde c~ndensation.~Likewise, both CuOH and Cu(0H), (referred to as I and 11) have been postulated as intermediates in the anodic formation of Cu,O. From an electrochemical viewpoint, and depending on the particular technique used, the
(1) Rogic, M. M.; Demmin, T. R. Aspects Mech. Organomel. Chem., [Proc. Symp.] 1978, 141. ( 2 ) Shenai, V. A.; Sharma, K. K. J . Appl. Polym. Sci. 1976, 20, 377.
(3) Takeda, T.; Matsumoto, K.; Nogata, M. Japanese Patent 77 96, 531; C.A. 88/81834s, 1978. (4) Morozov, A. A. Kinet. Katal. 1973, 14, 193.
0022-3654/84/2088-5225$01.50/0
0 1984 American Chemical Society
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The Journal of Physical Chemistry, Vol. 88, No. 22, 1984
mechanism of CuzO formation is interpreted on the basis of species I or I1 inde~endently.~-~ However, recent works suggested that both species must simultaneously exist in that proces~es.~-'~ On the other hand, the dissociation energy of I has been determined by Belyaer et al.I3 using flame spectrophotometry, and a value of 62 f 3 kcal/mol has been reported. These authors suggeste! a C,, symmetry, and values of 1.75and 0.97 8,for the Cu-0 and 0-H distances were proposed. A calculation of I by the extended Hiickel method, assuming linear geometry and a Cu-0 distance of 2.2 8,,has also been reported. l 4 In the view of the above-mentioned results and of the technical and electrochemical interest in I and I1 a detailed study of the structure of both compounds seems necessary. In this paper, ab initio techniques are used to find the fully optimized geometries of I and 11. Relative stabilities according to the dissociation processes CuOH Cu(OH),
-
-
+ OH CuOH + OH: Cu
Illas et al. TABLE I: Valence Gaussian Basis Set
orbital S
0.654 0.1102 0.037 6
P
0.191 4 0.077 6 0.03 1 6
0.379 9 0.508 5 0.221 9
d
28.87 7.727 3 2.355 0.656 9 0.12
0.069 8 0.296 5 0.479 4 0.433 7 0.1298
(10) Centellas, F.; Garrido, J. A. Perez, E.; Virgili, J. An. Quim., in press. (1 1) Castro de Luna Medina, A. M.; Marchiano, S . L.; Arvia, A. J. J . Appl. Electrochem. 1978, 8, 121. (12) Burstein, G. T.; Newman, A. C. J . Electrochem. SOC.1981, 128, 2270. (13) Belyaer, V. N. Izu. Vyssh. Uchebn. Zaved. Khim. Khim. Tekhnol. 1978. 21. 1968. (14) Opitz, C. H.; Dunken, H. H. Z . Phys. Chem. 1972, 249, 154. (15) Pseudopotential adaptation by J. P. Daudey and 6d 5d recombi-
-
nation by M. Pelissier and J. P. Daudey, Laboratoire de Physique Quantique, Universite Paul Sabatier, 3 1062 Toulouse Cedex, France. (16) Dupuis, M.; Rys, J.; King, H. F. QCPE, 338. (17) Durand, PH.; Barthelat, J. C. Theor. Chim. Acta 1975, 38, 283. (18) Pelissier, M., Durand, Ph Theor. Chim. Acta 1980, 55, 43.
-0.189 0.623 1
.o
Oxygen S
5.799 125 1.298 338 0.547 297 0.226 132
-0.137 734 0.292 953 0.531 222 1
P
12.655 163 2.953 693 0.886 188 0.259 961
0.068 201
are also calculated by both S C F and C I procedures.
(5) Dignam, M. J.; Gibbs, D. B. Can. J . Chem. 1970, 48, 1242. (6) Ambrose, J.; Barradas, R. G.; Shoesmith, D. W. J. Electroanal. Chem. Interfacial Electrochem. 1973, 47, 47. (7) Ashworth, V.; Fairhurst, D. J. Electrochem. SOC. 1977, 124, 506. (8) Miller, B. J. Electrochem. SOC.1969, 116, 1675. (9) Droog, J. M. M.; Alderliesten, C. A.; Alderliesten, P. T. Bootsma, G. A. J. Electroanal. Chem. Interfacial Electrochem. 1969, 61, 111.
coeff
Copper
(a)
Method of Calculation Calculations at the S C F level were carried out with the PSHONDO program,15a version of the HONDO program16which includes the adaptation of the general ab initio pseudopotentials of Durand and Barthelat.'7s18 This method deals only explicitly with valence shell electrons and permits the use of a more extended basis for valence electrons than those used in all-electron calculations. It must be pointed out that in all-electron calculations, inner electrons are often treated with a minimal basis, leading to a poor description of the inner shells, and, more important, to unbalanced basis sets when using extended basis in the valence shell, which produce basis effects in the inner ones. This is not the case when using psedopotentials which are determined from extended all-electron atomic calculations. Final geometries were determined by using a double {quality basis set on all atoms, except the d electrons of copper which were treated at the single level because the d shell is completely filled in the 2S ground state of Cu; a single p function was added to account for polarization (and later angular correlation effects) of the s electron. The Gaussian valence basis set is described in Table I. Pseudopotentials were utilized in copper and oxygen atoms (see Table 11). Minimization of trial geometries was carried out by optimizing independently each of the geometrical parameters without imposing any symmetry restriction. The process was cycled until distances and angles no longer change within a precision of 0.015 8, and 3 O , respectively. Once the final structures were found, the total energy was calculated again by using a more extended basis, to explicitly
exponent
.o
0.274 403 0.482 324 1
.o
Hydrogen S
13.247 9 2.003 13 0.458 67 0.124 695
0.019 255 0.134 420 0.469 565 1.o
account for polarization effects. Thus, a p function (exp = 0.8) was added to the hydrogen basis set and a d function (exp = 1.25) to the oxygen set. On the copper basis set, a 4,l procedure was applied to the d shell, and a p function (exp = 0.012)was added to the p shell,Ig with the four Gaussian primitives contracted through a 3,l procedure. Hereafter we will refer to these basis sets as basis 1 and basis 2, respectively. In order to properly describe the dissociation energies, correlation effects were accounted for in the calculations at the final geometries using an improved version of CIPSI algorithm,2°,21as suggested by Pelissier on diatomic Cu2.19 The method uses a multireference set S of determinants which is constructed iteratively. From an initial guess of configurations, an initial space S is constructed, and the matrix representation in S is diagonalized. Furthermore, all single and double excitations of determinants belonging to S are generated. The contribution to the wave function of each determinant interacting with S is calculated according to the Epstein-Nesbet definition of the unperturbed Hamiltonian22up to first order. If the contribution of a generated determinant at this level is greater than a certain threshold, the determinant is added to S leading to an improved unperturbed wave function. This process is repeated until there are no significant contributions. In the present study a threshold value of 0.02 was used. While the selection procedure is carried out according to the Epstein-Nesbet definition, the second-order energy contribution is calculated within the barycentric Moller-Plesset definition of the unperturbed Hamiltonian in the framework of the many body perturbation theory (MBPT).23 This definition does not suffer the artifact of the Epstein-Nesbet theory when the molecular basis set is delocalized. The S space is taken as the zeroth-order wave function. Thus, the energy correlation has clearly two contributions, one arising from diagonalization of the matrix representation in S, which is the zeroth-value of the energy and is variational, and the other from the perturbation of S up to second order. (19) (20) 5145. (21) (22)
Pelissier, M. J . Chem. Phys. 1981, 75, 775. Huron, B.; Malrieu, J. P.; Rancurel, P. J. Chem. Phys. 1973, 58,
Pelissier, M. Thesis, Toulouse, 1980. Epstein, P. S. Phys. Rev. 1926, 28, Nesbet, R. K. Proc. R . SOC. London, Ser. A 1955, 312, 922. (23) Moller, C.; Plesset, M. S. Phys. Reu. 1934, 46, 618.
The Journal of Physical Chemistry, Vola88, No. 22, 1984 5227
Molecular Structure of CuOH and C u ( 0 H ) T
TABLE II: Pseudopotential Parameters for Copper and Oxygen W , ( g ) = exp(-ar2)Cic& 1 0
1 2 0
1
a
nl
n2
Cl
c2
2.696 56 0.596 40 1.465 46
-1 -2 -2
13.6183 0.12938 -0.835 37
0 -1 -1
Copper -24.624 7.869 4 -3.220 6
10.373 87 25.320 09
-1
1.647 68 -1.790 73
0
Oxygen 45.078 28
0
n3
c3
n4
c4
2 0 1
71.246 -2.9146 6.7931
2
-5.5701
TABLE 111: Optimal Geometrical Parameters for CuOH and Cu(OHbcomud CuOH CU(OH)2-
symmetry group
c-" c s c 2
distance, 8, Cu-0 0-H 0.952 1.788 0.960 1.818 0.966 1.883
CuOH angle, deg 180.0 131.9 116.1
As in the MBPT the formal cancellation of size inconsistent terms, appearing in the Rayleigh-Schrodinger perturbation series, is carried out explicitly, the CIPSI method appears to be size consi~tent.~~,~~ The largest calculation uses a multireference zeroth-order wave function which consists of 17 determinants and involve perturbative contribution of 1 01 1 422 determinants. Finally, let us say that Cu, OH, and OH- have been studied with the same procedure above described in order to calculate the dissociation energies of processes (a) and (b).
a
Figure 1. Optimized geometries of (a) CuOH and (b) &(OH), TABLE I V Dissociation Energies of Processes a and b dissociation energy, kcal/mol Process a SCF basis 1 33.4 SCF basis 2 34.6 SCF + CI basis 1 52.7 SCF CI basis 2 59.1 exptl value 62 f 3
Results and Discussion Geometries. To have a correct descritpion of the dissociation processes (a) and (b), the internuclear distance of O H and OHwas optimized with basis 1 . The final results are 0.9789 and + 0.9915 A, compared to experimental values of 0.9696 and 0.97 A, respectively,26 so the error at this level is
