J. Phys. Chem. 1991, 95, 1062-1066
1062
and the Kratzer functions are better suited to this purpose. The Kratzer functions have the additional advantage that all integrals may be computed analytically. Acknowledgment. The author acknowledges many useful
discussions with Bernard H. Chang and Robert E. Tuzun. This work was supported by a grant from the National Science Foundation, the donors of the Petroleum Research Fund, administered by the American Chemical Society, and the NCSA at the University of Illinois.
Dioxygen Complexes of 3d Transition-Metal Atoms: Formation Reactions in the Gas Phaset Carl E. Brown,: S.A. Mitchell,* and Peter A. Hackett Laser Chemistry Group, Division of Chemistry, National Research Council of Canada, 100 Sussex Drive, Ottawa, Ontario, Canada, K I A OR6 (Received: June 25, 1990)
Reactions of ground-state 3d transition-metal atoms including Ti, Mn, Co, Ni, and Cu with molecular oxygen in Ar buffer gas have been investigated in the pressure range 5-700 Torr at 296 K. Attention has been given to termolecular association reactions in which mono(dioxygen) complexes are formed. A pulsed laser photolysis-laser fluorescence technique is used where metal atoms are produced by visible multiphoton dissociation of a volatile organometallic precursor in a static pressure reaction cell, and reactions of metal atoms are monitored by resonance fluorescenceexcitation at variable time delay following the photolysis pulse. The present study completes a survey of the reactions of 3d transition-metal atoms with O2under room temperature conditions, from which it emerges that reactivity with respect to complex formation is correlated with a d"s' valence electron configuration of the metal atom. Simplified RRKM calculations have been used to interpret termolecular rate constants for the association reactions in terms of a trend in the binding energies of the dioxygen complexes.
Introduction It is known from matrix-isolation infrared' and ESR2,3spectroscopic studies that certain transition-metal (TM) atoms react with O2to form mono- and bis(dioxygen) complexes, T M ( 0 2 ) and TM(02)2. Very little is known about the formation of such complexes in the gas phase. Of the first-row (3d) TM atoms, only Sc, Ti, and V have exothermic 0-atom-transfer reactions with 02.4 Therefore, under moderate temperature conditions ground-state Cr, Mn, Fe, Co, Ni, and Cu atoms may only form an association complex with 02.Ritter and Weisshaar5 have reported rate constants for 0-atom-transfer reactions of Sc, Ti, and V atoms with O2 near room temperature in a flow reactor. The reaction Cu + O2+ Ar Cu(02) + Ar at room temperature and IO Torr total pressure has been investigated by Vinckier et a1.,6 who also used a flow reactor. We have previously described a pulsed laser photolysis-laser fluorescence technique for kinetic studies of Cr7 and Fes atoms under room temperature conditions and at total pressures to -760 Torr. This technique is based upon visible multiphoton dissociation (MPD) of a volatile organometallic compound for production of metal atoms. Whereas Cr atoms react rapidly with 02,7 Fe atoms were found to be unreactive with respect to O2 at room temperature.s We report here a survey of the reactivity of 3d TM atoms with respect to complex formation with O2in the gas phase under room temperature conditions. Together with previous work on S C ,Ti,5 ~ V,5 Cr,7 Fe,8 and Cu6 atoms, the present investigation of Mn, Co, and Ni atoms completes the survey of the 3d TM series. The present study also includes new measurements for the reactions of Ti and Cu atoms with 02.Our objective was to identify trends in reactivity across the 3d T M series and to seek correlations between reaction rate constants and molecular properties of the complexes. It emerges clearly that TM atoms with singly occupied valence s-orbitals are reactive with respect to complex formation with O2 at room temperature, and those with doubly occupied valence s-orbitals are not. A rationalization of this trend is given in terms of simple molecular orbital concepts. An attempt is made to correlate the magnitude of the termolecular rate constant for
-
-
the association reaction with the binding energy of the complex, using a simplified form of RRKM theory together with molecular parameters obtained &om experimental or theoretical investigations. This approach appears satisfactory for Cu O2but meets with difficulties for Ni + 02.It is suggested that the results for Ni + O2 point to the occurrence of reaction on more than one potential energy surface.
+
Experimental Section The experimental setup has k e n described in detail previo~siy.~*~ Briefly, TM atoms are produced by visible MPD of volatile organometallic precursors in a static pressure reaction cell using the focused output of pulsed dye laser (photolysis laser). T M atoms are detected by saturated resonance fluorescence excitation using a second, independently triggered pulsed dye laser (probe laser). The photolysis and probe laser beams are aligned collinear and counterpropagating through the center of the reaction cell, with the photolysis beam focused in the fluorescence viewing zone at the center of the cell. Laser-induced fluorescence (LIF) is viewed through a 10 cm focal length monochromator by a gated photomultiplier tube. To obtain kinetic data, the interpulse delay is scanned in preset increments and the LIF signal from 50 to 200 shots averaged at each delay setting. The entire delay range was swept 4-6 times to allow monitoring of the sample stability during the data acquisition period. The repetition rate of the laser pulses was 20 Hz. Titanium atoms were produced by MPD of TiCI., at 445 nm, using a pulse energy of 2.5 mJ focused with a 25 cm focal length ( I ) (a) Moskovits, M.; Ozin, G. A. In Cryochemistry; Moskovits, M., Ozin, G. A., Eds.; Wiley: New York, 1976; Chapter 8, and references cited therein. (b) Huber, H.; Klotzbucher, W.; Ozin, G.A,; Vander Voet, A. Can.J. Chem. 1973, 51, 2722. (2) Kasai, P. H.; Jones, P. M. J . Phys. Chem. 1986, 90, 4239. (3) Howard, J. A.; Sutcliffe, R.; Mile, B. J . Phys. Chem. 1984,88, 4351. (4) For a compilation of bond energies for 3d transition metal oxide diatomic molecules, see: Merer, A. J. Annu. Reo. Phys. Chem. 1989, 40, 407. (5) Ritter, D.; Weisshaar, J. C. J . Phys. Chem. 1989, 93, 1576; 1990. 94, 49117.
(6) Vinckier, C.; Corthouts, J.; De Jaegere, S.J . Chem. Soc., Faraday Trans. 2 1988,84, 1951.
'Issued as NRCC No. 32289. t NRCC Research Associate 1989-present.
(7) Parnis, J. M.;Mitchell, S.A.; Hackett, P. A. J . Phys. Chem. 1990, 94, 8 152. (8) Mitchell, S . A.; Hackett, P. A. J. Chem. Phys. 1990, 93,7813,7822.
0022-3654/91/2095-1062%02.50/0 0 1991 American Chemical Society
The Journal of Physical Chemistry, Vol. 95, No. 3, I991 1063
Dioxygen Complexes of 3d Transition-Metal Atoms
lens. Ground-state (a3F2)Ti atoms were monitored by resonance fluorescence excitation at 363.55 nm (y3G03 a3F2)? Manganese atoms were produced by MPD of M I I ~ ( C O a) t~555 ~ nm, using a pulse energy of 0.5 mJ focused with a 25 cm focal length lens. Ground-state (a6S5/2) Mn atoms were monitored by resonance fluorescence excitation at 403.08 nm a6S5/2).10Cobalt atoms were produced by MPD of Co(CO),NO at 555 nm, using a pulse energy of 0.5 mJ focused with a 25 cm focal length lens. Ground-state (a4F9/2)Co atoms were monitored by resonance fluorescence excitation at 341.263 nm (z4D07/2 a4F9 2).'1 Nickel atoms were produced by MPD of nickelocene, Ni(CshS)2, 0 2 4 6 8 10 12 at 5 5 5 nm using a pulse energy of 0.5 mJ focused with a 50 cm Pressure O2 / Torr focal length lens. Nickel atoms in the first metastable excited state (a3D3), 204.8 cm-l above the ground state, were monitored Figure 1. Plot of pseudo-first-order rate constant for reaction of by resonance fluorescence excitation at 341.477 nm ( z 3 p 4 ground-state Ti atoms with O2against pressure of O2at 296 K. The pressure of Ar buffer gas was 20 Torr. Nonzero intercept is due to a3D3)." Copper atoms were produced by MPD of bis(hexafluoroacety1acetonato)copper dihydrate, C U ( C ~ H F ~ O ~ ) ~ . ~ H reaction ~ O , of Ti atoms with the precursor TiCll (4mTorr). at 552 nm, using a pulse energy of 0.5 mJ focused with a 50 cm focal length lens. Ground-state (a2SIl2)Cu atoms were monitored by resonance fluorescence excitation at 324.85 nm (a2P03/2 a2S1/2),12 using a KDP crystal to frequency double the output of the amplified probe dye laser. Bis(hexafluoroacety1acetonato)copper dihydrate was prepared and purified according to ref 13. TiCI4, Ni(C5Hs)2,and Co(CO),NO were supplied by Alpha Products. Mn2(CO)lowas supplied by Strem Chemicals. Research purity Ar and O2 were supplied by Matheson of Canada. All organometallics were extensively degassed by freeze-pumpthaw cycling before use. As in the work on Cr7 and Fe8 atoms, photolysis conditions were 0 20 40 60 Pressure O2 / Torr chosen to minimize the production of ions and excited-state metal atoms. For Co(CO),NO and Ni(C5HS)2,it was found necessary Figure 2. Plot of pseudo-first-order rate constant for reaction of to use relatively long photolysis wavelengths (>500 nm) in order ground-state Co atoms with O2against pressure of O2at 296 K. The to avoid single-photon photolysis of the precursor. Single-photon pressure of Ar buffer gas was 50 Torr. Nonzero intercept is due to photolysis was undesirable because it depleted the organometallic diffusion of Co atoms from the probe laser beam. in the static pressure reaction cell. (Multiphoton photolysis occurred only in the small focal region of the photolysis laser beam).' delay times, where the relaxation processes producing ground-state It sometimes happened that at high Ar buffer gas pressures metal atoms were no longer significant. Estimates of relative (-200-700 Torr) a nucleation process of the organometallic populations from fluorescence excitation spectra indicated that occurred in the reaction cell. This gave rise to a large background those metastables which were removed relatively slowly accounted signal due to scattering of the probe laser beam by particles. No for only a small fraction (3 mJ), Cu atoms continued to be produced after the end Results of the photolysis pulse (duration E IO ns). This was apparently Reactions of ground-state Ti, Mn, Co, Ni, and Cu atoms with due to a unimolecular decay process of a copper-containing moO2were studied under pseudo-first-order conditions in Ar buffer lecular fragment which was produced by the photolysis laser pulse. gas at 296 K. Total pressures were in the range 5-700 Torr, with From the decay traces, the half-life for the unimolecular decay partial pressures of O2in the range 0-50 Torr. The pressure of process which produced Cu atoms was estimated as = 10 ps. This the organometallic precursor was N 10 mTorr. Collisional reslow production of Cu atoms was not important for the pulse laxation of metastable excited-state metal atoms produced by the energies (-0.5 mJ) used for the Cu + O2 kinetic studies. photolysis laser was monitored by recording fluorescence excitation Titanium atoms were found to react rapidly with the precursor spectra at variable time delay between the photolysis and probe TiCI4,and relatively slowly with 02.A second-order rate constant laser pulses. I n addition, certain metastables were monitored of 8 X cm3 molecule-l s-' was estimated for the reaction with directly in the same manner as the ground-state atoms. By these T U 4 in Ar buffer gas at 296 K. Pseudo-first-order removal rates means it was confirmed that relaxation of metastables generally for ground-state Ti atoms are plotted against pressure of added occurred on a much faster time scale than chemical removal of O2 in Figure I . These data give a second-order rate constant ground-state metal atoms. Consistent with this, the decay traces of (2.3 f 0.3) X 10-l2 cm3 molecule-l s-' at 296 K. The uncerfor reaction of ground-state metal atoms with O2were generally tainty represents two standard deviations (20) obtained from linear of the form of simple exponentials. However, in some cases the regression. This result is in agreement with the value (1.7 f 0.5) decay traces for the lowest pressures of O2at low total pressures X reported by Ritter an WeisshaarS from a flow tube study showed a rounded-off appearance at the beginning of the decay, at 300 f 5 K, at total pressures of He buffer gas in the range due to a rclatively slow metastable relaxation process. In these 0.4-0.8 Torr. We found no significant dependence of the reaction cases t h e decay traces were fit to exponentials beginning at later rate on Ar pressure in the range 20-100 Torr. This is consistent with an 0-atom-transfer process forming Ti0 + 0, as observed (9) Wiese, W. L.; Fuhr, J. R. J . Phys. Chem. Ref. Data 1975, I, 263. by Ritter and Weisshaar5 and in beam-gas chemiluminescence (IO) Younger, S. M.; Fuhr, J. R.; Martin, G. A,; Wiese, W. L. J . Phys. experiments. l 4 Chem. Ref Data 1978, 7 . 495. Manganese atoms were unreactive with respect t o O2at 296 ( I 1) Fuhr, J . R.;Martin, G. A.; Wiese, W. L.; Younger, S. M. J . Phys. K. For IO Torr of added O2and a total pressure of 50 Torr, the Chem. ReJ. Data 1981, 10, 305. ( I t ) Moore, C. E. 'Atomic Energy Levels"; Natl. Bur. Stand. US.Circ.
-
+-
+-
+ -
1952. No. 467, Vol. 11. (13) Belford, R. L.; Martell. A. E.;Calvin, M. J . Inorg. Nucl. Chem. 1956, 2, I ] .
(14) (a) Parson, J. M.; Geiger, L. C.; Conway, T. J. J . Chem. Phys. 1981, 74, 5595. (b) Dubois, L. H.; Cole, J. L. J . Chem. Phys. 1977, 66, 779.
Brown et al.
1064 The Journal of Physical Chemistry, Vol. 95, No. 3, 1991
1500
i I
I
/
0
0
2
4 Pressure
6
O2 /
6 Pressure Ar
Torr
Figure 3. Plots of pseudo-first-order rate constant for reaction of ground state Ni atoms with O2 against O2 pressure for Ar buffer gas pressures between IO and 160 Torr at 296 K. Nonzero intercepts are due to reaction of Ni atoms with the precursor Ni(C5H5)2(5 mTorr). Symbols: IO Torr; A, 20 Torr; A, 40 Torr; 0, 80 Torr; 0 , 160 Torr.
.,
"I
i"i E
'* s o
Figure 5. Plot of pseudo-second-order rate constant for reaction of ground-stateCu atoms with O2against pressure of Ar buffer gas at 296 K. The slope of the line gives the value of the termolecular rate constant. TABLE I: Pseudo-Second-Order Rate Constants for Reaction of cm3 Ground-State Ni and Cu Atoms with O2 at 296 K (in molecule-' s-')
argon/ Torr
range'
argon/ Torr
k(2)b
Ni
20
/ Torr
5 10 20 40
0-5 0-8 0-8 0-8
5.21 f 0.8 8.90 f 0.6 13.0 f 0.3 20;6 i 0.5
10 50 100
0-10 0-15 0-15
0.67 f 0.2 2.68 f 0.1 5.54 f 0.2
range'
k(2)b
80 160 320 640
0-8 0-8 0-1 0-1
36.0 f 0.5 68.5 f 2.9 120.0 f 5.5 171.0 f 2.3
300 500 700
0-15 0-15 0-15
18.6 f 0.5 32.1 i 0.5 46.6 f 1.4
+ O2
cu + 02 200
400
600
Pressure Ar / Torr Figure 4. Plot of psuedo-second-order rate constant for reaction of ground-state Ni atoms with O2against pressure of Ar buffer gas at 296 K. Solid curve represents the best fit of the data to the simplified falloff expression given in the text. Dashed line represents the fitted limiting high-pressure rate constant, k,. The slope of the line at low Ar pressure shows the value of the limiting low pressure, third-order rate constant.
removal rate was not significantly greater than that due to diffusion of Mn atoms out of the probe laser beam. This places an upper cm3 molecule-' s-l on the value of the seclimit of N 1 X ond-order reaction rate constant. No evidence was found for reaction of Mn atoms with the precursor Mn2(CO)lo. Cobalt atoms reacted slowly with 02 at 296 K. Pseudo-firstorder removal rates for ground-state Co atoms are plotted against O2pressure in Figure 2, for a total pressure of 50 Torr (Ar). These data give a pseudo-second-order reaction rate constant ( f 2 4 , (1.9 cm3 molecule-' SI. The nonzero intercept in Figure f 0.2) X 2 is due to diffusion of Co atoms out of the probe laser beam. No evidence was found for reaction of Co atoms with the precursor CO(CO)~NO.It was not possible to obtain extensive data for the Co + O2 reaction at higher Ar buffer gas pressures due to nucleation and light scattering in the cell. Qualitatively, data obtained at 100 Torr showed an increase in the reaction rate, indicative of a termolecular association reaction of Co with 02. Under the assumption that the reaction was in its third-order kinetic regime at 50 Torr total pressure, the observed pseudosecond-order rate constant implies a third-order rate constant of I .2 x 10-32 cm6 molecule-2 s-l. Nickel and copper atoms reacted with 02.In both cases the pseudo-second-order rate constant showed a strong dependence on the Ar buffer gas pressure, consistent with the Occurrence of termolecular association reactions forming dioxygen complexes. Kinetic data are shown in Figures 3-5, and are summarized in Table 1 , The data for Ni were obtained by monitoring removal of the metastable state a3D3.204.8 cm-' above the ground state.I5 However, it was found that an equilibrium was rapidly established between thcsc states by collisions with Ar, so both states behaved similarly with rcspect to chemical removal by 02. The rate constant for transitions from the metastable state to the ground
'Oxygen pressure range in Torr. Pseudo-second-order rate constant. Error represents two standard deviations, obtained from linear regression. state induced by collisions with Ar was estimated as 6 X 10-l' cm3 molecule-' s-l. The Ar pressure dependence of the pseudo-second-order rate constant k(2)for reaction of Ni with O2was modeled by assuming a simple Lindemann-Hinshelwood mechanismI6
Here ko is the limiting low-pressure, third-order rate constant and k , is the limiting high-pressure, second-order rate constant. By fitting the data points shown in Figure 4 to eq 1, values of k , = cm6 molecule-2 s-I and k , = (3.3 f 0.4)X (1.7 f 0.3) X IO-'' cm3 molecule-' s-I were obtained. Uncertainties represent two standard deviations in the fitted values. Because of the approximate nature of eq 1, which neglects certain effects predicted by RRKM theory,16 the above value of k, derived by using eq 1 should be regarded as an approximate lower limit. (The inclusion in eq 1 of a term incorporating an assumed broadening factori6 resulted in a larger extrapolated value for k,, and a relatively small change in k o , ) The fitted curve, using eq I , is shown in Figure 4. Also shown is the value of k , and the limiting low Ar pressure slope, which gives the value of ko. Kinetic data for the Cu + O2 + Ar termolecular reaction are shown in Figure 5 and summarized in Table I . It is seen in Figure 5 that the reaction is in its third-order kinetic regime throughout the Ar pressure range investigated (linear dependence of removal rate on Ar pressure). The slope of the plot in Figure 5 gives the ) = (2.0 f 0.1) X cm6 termolecular rate constant ( 1 2 ~ ko molecule-2 s-I. This is significantly lower than the value (3.8 f 0.2) X reported by Vinckier et aL6 from a flow tube kinetic study. The reason for this disagreement is not known. Discussion In Table I I several properties of TM atoms and TM oxide diatomic molecules are summarized together with the third-order
( I 5 ) Corliss, C.; Sugar, J . J . Phys. Chem. Ref. Dam 1985. 14, Suppl. No.
2.
(16) Troe, J. Ber. Bunsen-Ges. Phys. Chem. 1983, 87, 161
The Journal of Physical Chemistry, Vol. 95, No. 3, 1991
Dioxygen Complexes of 3d Transition-Metal Atoms
1065
TABLE 11: Prowties of Transition-Metal Atoms and Rate Constants for Termolecular Association Reactions with 0, at 296 K ~
~~~~~
&,Qk e
TM"
IPb/eV
Do(TMO)c/eV
AE(s')d/eV
Sc(d1s2)2D Ti(d2s2)'F
Fe(d6s2)5D Co(d7s2)4F Ni(d8s2) )F
6.56 6.82 6.74 6.77 1.43 7.90 7.86 7.64
7.01 f 0.12 6.92 f 0.1 6.44 f 0.2 4.41 f 0.3 3.83 f 0.08 4. I7 f 0.08 3.94 f 0.14 3.91 f 0.17
1.43 0.8 1 0.25 0 2.15 0.87 0.42 -0.03
Cu(dlos') 2S
7.73
2.75 A 0.2
47Fs
V(d'f! Cr(d s )
Mn(dss2) 6S
(DoVM021)
kOCxPt/
AT AT AT 0.7 (113)
0.03 (40) 0.1 (60) 0.25'(80) 0.05 (1 5) 0.11 (20)
0
6.5 NR NR -0.001 0.17 0.02
"Transition-metal atom and ground-state electronic configuration. Ionization potential from ref 15. e Dissociation energy of TM oxide diatomic molecule from ref 4. dExcitation energy of ground-state atom to lowest state with SI configuration, using average term energies for multiplets. cm6 molecule-2 s-l, and assumed dissociation energy for TM-02 complex in units of kcal cCalculated termolecular rate constant in units of cm6 molecule-2s-', for Ar buffer gas. AT means atom-transfer mol-' in parentheses (see text). /Observed termolecular rate constant in units of reaction hnd N R means no reaction.
+ +
-
rate constants for TM O2 Ar TM(0,) + Ar association reactions at 296 K. Among the TM atoms for which 0-atom transfer is not feasible (Cr, Mn, Fe, Co, Ni, and Cu), it is seen that those which are reactive with respect to complex formation with 0, have ground state or very low lying S I valence electron configurations, and those which are not reactive have s2 configof their population in urations. Note that Ni atoms have ~ 2 2 % an excited S I configuration at room temperature. Cobalt appears to lie in an intermediate position with respect to both reactivity and electronic configuration. Thus the reactivity of Co is low but observable, and although the configuration of the ground state is s2, there exists a relatively low lying si excited state, lying lower in energy than the SI excited states of the unreactive atoms (Table 11). Note in Table I I that the reactivities do not appear to be correlated with either the ionization potentials of the TM atoms or the bond strengths of the corresponding TM oxide diatomic molecules. The correlation between reactivity and electronic configuration may be understood in terms of simple molecular orbital concepts. Consider the approach of a TM atom to 0, in the least symmetrical arrangement (C,symmetry). The nature of the potential in the region of the onset of orbital overlap effects will be determined by the interaction between the s-orbital of the TM atom (which has a larger spatial extent than the d-orbitals)" and the in-plane x*-antibonding orbital of 02, both of which are singly occupied. For a T M atom with an S I configuration, an electron pair bond may be formed from the overlap of these orbitals, as in a radical-radical recombination process. In the case of an s2 configuration, one of the s-electrons occupies the antibonding molecular orbital between the TM atom and O,,which destabilizes the complex and leads to a less attractive or a repulsive potential. It should be noted here that the nature of the bonding in the final complex may be different from the simple electron pair bond described, and bound dioxygen complexes may exist for those TM atoms which are designated as unreactive in Table 11. For example, there is evidence that a complex may be formed between Fe and O2,I8but we have previously shown that the rate constant for formation of such a complex under room temperature conditions is negligibly small.* The point of the argument given above is that the initial interaction potential may be expected to be attractive in the case of a TM atom in an s' configuration, which therefore facilitates the formation of the complex. The range of the termolecular rate constants for TM + O2 reactions given in Table I I is very large. This contrasts with the situation for the association reactions of Li,I9 Na,20and K2' atoms (17) Walch, S. P.; Bauschlicher, C. W. Jr. I n Comparison of Ab lnitio Quantum Chemistry with Experiment for Small Molecules; Bartlett, R. J. Ed.; Reidel: Dordrecht, 1985; p 17. (18) (a) Chang, S.; Blyholder, G.;Fernandez, J. Inorg. Chem. 1981,20, 2813. (b) Abramowitr, S.: Acquista, N.; Levin, I. W . Chem. Phys. Lett. 1977, 50, 423. (19) Plane, J. M . C.; Rajasekhar, B. J . Phys. Chem. 1988, 92, 3884.
with O,,for which the corresponding rate constants vary by less than a factor of ~ 3 . We ' have carried out simplified RRKM calculations of the termolecular rate constants for Cu and Ni atom association reactions with 0, at 296 K, using the formalism of Similar calculations for Cr + 0, have been described elsewhere.' The principal assumptions underlying the application of such calculations to these reactions are the following: (1) no activation energy barrier for the association reaction; (2) unit efficiency for stabilization of collision complexes by Ar buffer gas (strong collisions); and (3) reaction on a single potential energy surface corresponding to the ground electronic state of the TM(0,) complex. In addition, the calculations incorporate several assumptions and approximations which have been discussed by Troe.22,23The molecular structures, vibrational frequencies, and ground-state spin multiplicities for Cu(0,) and Ni(0,) complexes were taken from the results of matrix-isolation infrared' and ESR2g3 spectroscopic studies, and from ab initio electronic structure calculations for CU(O,),~and Ni(02).25 Since the dissociation energies of the complexes are not known, these were taken as parameters which were varied to obtain approximate agreement between calculated and observed termolecular rate constants. The calculated rate constants are proportional to the density of vibrational states at the dissociation limit of the complexZ2and therefore show a steep dependence on the assumed dissociation energy. Details of the calculations are given in the Appendix, and the results are given in Table TI, which also includes results for the Cr 0, reaction.' No attempt was made to compare calculated and observed rate constants for Co 0,. The very small value of the experimental rate constant for this case (Table 11) suggests that the reaction has a significant activation energy barrier, so the simplified RRKM calculations used here are not applicable according to the first assumption noted above. The presence of an activation energy for formation of a Co(0,) complex would be consistent with the rationalization of the reactivity trend given above in terms of electronic configurations. Thus a collision complex involving Co in the ground state (s2 configuration) would have to overcome a repulsive interaction in order to form a bound complex. In this interpretation the bound state is associated with the excited s1 configuration of Co. In Table 11, calculated rate constants for Ni + 0, and Cu 0, are given for several assumed dissociation energies. For Cu + O,, a dissociation energy of 15 kcal mol-' gives reasonable agreement with experiment. For Cr + 0,. it is not clear whether
+
+
+
(20) Plane, J. M. C.; Rajasekhar, B. J . Phys. Chem. 1989, 93, 3135. (21) Husain, D.; Lee, Y. H.; Marshall, P.Combust. Flame 1987, 68, 143. (22) Troe. J. J. Chem. Phys. 1977, 66. 4158. (23) Troe, J . J . Phys. Chem. 1979, 83, 114. (24) Mochizuki, Y.; Nagashima, U.;Yamamoto, S . ; Kashiwagi, H. Chem. Phys. Lett. 1989, 164, 225. (25) Blomberg, M. R. A.; Siegbahn, P. E. M.; Strich, A. Chem. Phys. 1985, 97, 287.
1066 The Journal of Physical Chemistry, Vol. 95, No. 3, 1991
the product is the bent dioxide species 0-Cr-0 known from .~ matrix-isolation studies26or a dioxygen complex C T ( O ~ )The calculated rate constant in Table I1 applies for the dioxide model, for which the dissociation energy (relative to Cr 0,) is as 1 13 f I 1 kcal mol-’. Regardless of the structure of the Cr O2 complex, it is seen that the striking disparity in the termolecular rate constants for Cr O2 and Cu O2 (differing by a factor of = 300) may be interpreted in terms of widely differing dissociation energies. The nature of the Cu(02) complex is well established from matrix-isolation ESR ~ t u d i e s and ~ . ~ ab initio
+
+
+
+
The reaction between Ni and 0, is subject to a severe restriction according to assumption 3 above. Whereas the complex Ni(02) has a singlet ground electronic state25with unit degeneracy, the reactants Ni + 0, have an effective degeneracy of 34.8 (product of electronic partition functions). The factor 1/34.8 must therefore be included in the expression for the rate constant. The corresponding factor for Cu + 0,is 1/3. If Ni + O2 combines on excited-state potential surfaces as well as on the ground-state surface, then the simple treatment used here is inadequate, and the calculated termolecular rate constant is too low. An indication that this is the case is provided by the value estimated for the limiting high-pressure rate constant (cm3 molecule-’ s-l), k , 3.3 X IO-” (see above). This follows because if reaction occurs only on the ground-state surface, then an upper limit for k , may be estimated as 1 34.8 multiplied by a hard-sphere collision rate, or k , N 1 X lo-’ , which is smaller than the lower limit estimated for the experimental value. It seems likely, therefore, that the Ni O2 reaction may occur both on the ground-state and on excited-state potential surfaces. These considerations suggest an explanation for the finding that unreasonably large values must be used for the Ni(02) dissociation energy (-80 kcal mol-’) in order to obtain agreement between calculated and observed rate constants (Table 11). A dissociation energy of 18 kcal mol-’ has been derived for Ni(02) from ab initio calc~lations.~~ According to the results in Table 11, if the dissociation energy of Ni(02) is -40 kcal mol-’, then association on the ground-state potential energy surface accounts for only 18% of the observed rate. Detailed information on the low-lying electronic states of Ni(02) is required in order to further interpret these results.
-
i
+
-
(26) Almond, M. J.; Hahne, M. J . Chem. SOC.Dalton Trans. 1988, 2255. (27) JANAF Thermochemical Tables, 3rd ed.: Dow Chemical Company: Midland, MI; J . Phys. Chem. ReJ Data 1985, 14. Suppl. No. 1,
Brown et al. Notwithstanding the difficulties noted above, we suggest that the simple approach used here is useful for identifying trends in binding energies. Thus the data in Table I1 indicate Do[Cr-02] >> Do[Ni-02] > Do[Cu-02], which is similar to the trend in the bond energies for the corresponding TM oxide diatomic molecules (Table 11). Conclusions
The trend in the reactivities of 3d transition-metal atoms with respect to complex formation with O2 at room temperature may be understood in terms of simple considerations of molecular orbitals. Mn and Fe atoms are unreactive and Co atoms are only slightly reactive because of unfavorable ground-state electronic configurations. Simplified RRKM calculations are useful for interpreting the magnitudes of the termolecular rate constants, although difficulties arise for Ni 02.These difficulties may arise because the association reaction proceeds on more than one potential energy surface. Large differences in the magnitudes of the termolecular rate constants reflect widely differing binding energies for the TM-02 complexes.
+
Acknowledgment. We thank Dr. Hubert van den Bergh and Daniel Braichotte of Institut de Chimie-Physique, Ecole Polytechnique FidErale, Lausanne, Switzerland, for the preparation and purification of the C U ( C ~ H F , ~ ~ ) ~ .sample. ~H,O Appendix
For Ni(02), with ground electronic state ’A, in C, symmetry, we used R ( N i a 2 ) = 1.74 A and R(O-0) = 1.40 A from ab initio calculation^.^^ Vibrational frequencies wI = 966 cm-’ and w2 = 504 cm-’ were taken from matrix-isolation studies.lb The value of w 3 320 cm-’ was estimated. In the notation of Troe,22*23 we used zLJ = 7.6 X lo-” cm3 moIecu!e-l s-’ and Fan,,= 1.78 (for s = 3, m = 2). For a dissociation energy of Eo = 40 kcal mol-’, we found p(Eo) = 248 (kcal mol-1)-’, FE = 1.03, I + / I = 39.4, u = 1.2044, C, = 5.052 X cm-I, and Fro, = 28.8. This gave kscrec,O= 2.7 X IOw3, cm6 molecule-2 s-l. For Cu(02),with ground electronic state 2A” in C, we used R(Cu-0,) = 1.91 A, R(O-0) = 1.34 A, w1 = 1161 cm-I, w2 = 535 cm-l, and w 3 = 220 cm-I from ab initio calculation^.^^ For this case we used ZLJ= 7.5 X cm3 molecule-’ s-I and = 1.78 (s = 3, m = 2). For a dissociation energy Eo = 15 kcal mol-’, we found p(Eo) = 48.6 (kcal mol-1)-’, FE = 1.07, I + / I = 13.8, u = 1.1408, C, = 1.719 X 10-2cm-1,and Fro,= 9.5. This gave kscrec,O = 5.0 X cm6 molecule-2 SKI.
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