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J. Phys. Chem. 1980, 84, 2478-2481
(20) For example, see G. 8. Watts and K. U. Ingold in “Free Radicals”, Vol. 1, J. K. Kochi Ed., Wiley-Interscience, New York, 1973,p 557. (21) N. Jacobsen and K. Torssell, Liebigs Ann. Chem., 63,135 (1972). (22) V. A. Roginski and V. A. Belyakov, Dokl. Akad. Nauk SSSR, 237, 1404 (1977).
(23)T. Foster, K. S. Chen, and J. K. S. Wan, J. Organomet. Chem., 184, 113 (1960). (24) T. Kawamura and J. K. Kochi, J . Organomet. Chem., 30,c8 (1971); T. Kawamura, M. Ushio, T. Fujimoto, and T. Yonezawa, J. Am. Chem. Soc., 93,908 (1971).
EPR Spectrum of Cobalt Dinitrosyl Dicarbonylt J. R. Morton,” K.
F. Preston, and S. J. Stracht
Division of Chemistry, National Research Council of Canada, Ottawa, Canada K1A OR9 (Received: January 3, 1980)
An EPR spectrum observed during the photolysis of solutions of CO(CO)~NQ containing dissolved NO is ascribed to the free radical Co(N0)2(C0)2. Measurements on both liquid and frozen solutions of the free radical are interpreted in terms of a planar geometry (D2hsymmetry)for this species in which the unpaired electron occupies a blg orbital essentially confined to the nitrosyl ligands.
Introduction The recent discovery1 of the persistent free radical Fe(NO),CO, formed by photolysis of Fe(C0)5in the presence of NO, has prompted us to try to prepare its isoelectronic analogues. Our first attempt2led to the detection of Fe(NO),(CO)L trapped on y irradiation at 77 K in a single crystal of Fe(N0)2(C0)2.The unusual nature of the semioccupied molecular orbital (SOMO) of Fe(N0)3C0and Fe(N0)2(C0)2-led us to search for similar species among the nitrosyl carbonyls of other first-row transition metals. In our attempts to detect an equivalent manganese species from Mn2(CO)lophotolyzed in the presence of NO, we have succeeded only in obtaining the EPR spectrum of a manganese-containing n i t r ~ x i d e .The ~ photolysis of solutions of CO(CO)~NO containing dissolved NO has been more fruitful, however, and we discuss here a spectrum which a species isoelecwe believe to be that of CO(NO)~(CO),, tronic with the iron-centered radicals mentioned above. All three radicals possess one electron more than the eighteen-electron “krypton configuration”. Experimental Section Cobalt nitrosyl tricarbonyl CO(CO)~NO was prepared4 from CoS04.7H20 via KCO(CO)~.Carbon monoxide enriched to 90% in the isotope 13Cwas obtained from Merck Sharp and Dohme and used to prepare Co(CO),NO enriched in that isotope. Nitric oxide enriched to 99% in 15N (Prochem) was also used to prepare some samples. Approximately 5% solutions of Co(NO)(CO), in dried, degassed hydrocarbons were photolyzed under a pressure of 2-5 torr of NO with a Schoeffel 1000-W Hg-Xe lamp in the cavity of a Varian E12 EPR spectrometer. The magnetic field was measured with a Cyclotron Corp. Model 5300 proton gaussmeter, and the microwave frequency with a Systron-Donner Model 6057 frequency counter. The spectrometer was also equipped with variable temperature accessories which enabled the sample to be examined at any temperature between 4 and 400 K. Analysis of the EPR spectra of frozen solutions was facilitated by computer ~imulation.~ Results When CO(CO)~NO was dissolved in n-pentane and photolyzed at 195 K in the presence of dissolved NO, a ‘NRCC No. 18428. NRCC Research Associate 1977-1979. 0022-3654/60/2084-2478$01 .OO/O
TABLE I : EPR Spectral Parameters Used to Simulate the Spectrum of CO(’~NO),(CO),in Figure 3 g factor
’ 5Nhfia 59c0hfi
X
Y
1.9910 -5
1.9372 -5 10
io
z
1.9950 -78b
24
a Units are MHz; negative signs correspond t o a negative magnetogyric ratio for I5N. Divide by - 1.4 to obtain I4N hfi (56 MHz) shown in Figure 5.
spectrum was obtained at g = 1.9734 f 0,0001 (Figure 1). This spectrum was analyzed in terms of isotropic hyperfine interactions with two 14Nnuclei (I= 1,22.0 MHz) and one 5gC0nucleus (I= 7 / 2 , 26.0 MHz). The analysis was confirmed by computer simulation5 and by 15N (I = l / J substitution. Using Co(CO),NO and NO enriched to 99% in the isotope 15N reduced the number of resolved lines from 12 to 10 and revealed a 15Nhyperfine interaction of 31 MHz. However, spectra obtained from CO(CO)~NO enriched (90%) in 13Cwere identical with those containing I3C in natural abundance. A striking feature of the spectrum was the effect of change of temperature on the hyperfine interactions (Figure 2). Over the temperature range 120-200 K there was a modest increase (ca. 5 % ) in the 14Nhyperfine interaction, whereas over the same temperature range the 59C0interaction increased by almost 50%. The effect was detected in two solvents: n-pentane and n-propane. There was no significant (iO.0001) change in the g factor over the above temperature range. As in the case of Fe(NO),CO, additional information was obtained from the spectrum of a frozen solution of the free O was radical. A solution of C O ( C O ) ~ ~ ~inN isopentane photolyzed in the presence of 15N0 and then frozen by immersion in liquid NS. At 100 K, the spectrum shown in Figure 3a was observed. A computer simulation of this spectrum using the parameters given in Table I is shown in Figure 3b. Examination of the frozen solution at various temperatures down to 4 K revealed that the 59C0hyperfine interaction azzchanged dramatically with temperature, as can be seen from Figure 4. The azzcomponent of the “N hyperfine tensor, however, did not change significantly over the same temperature range.
Discussion Identification and Symmetry of the Radical. By analogy with our recent work1#2 on the radicals Fe(N0)3C0 and Fe(N0)2(C0)2-,it is tempting to identify the new 0 1980 American Chemical Society
EPR Spectrum of Cobalt Dinitrosyl Dicarbanyl
The Journal of Physical Chemistry, Vol, 84, No. 19, 1480 2479
GAUSS Figure 1. Isotropic spectrum of CO('~NO)~(CO)~ in n-pentane at 195
K.
14
+---
40 80 1 3 TEUPERAT L;RE/K Figure 4. Effect of temperature on 59C0a , hyperfine component. 0
*" I;'
Squares are experimental points; solid line is least-squares hypercotangent fit f( T ) = 15 -4- 2.9 coth (45/T); dashed line is the high-temperature asymptote f(T) = 15 2.9T/45.
+
a A" in C,
I
0
140 160 180 TEMPERATURE/K
200
Figure 2. Effect of temperature on the isotropic I4Nand 59C0hyperfine S o l i symbols: npropane. Open symbols: interactions in C@NO),(CO),. n-pentane.
b
8, in C,,
9.1.9372
Figure 5. Comparison of the proposed structure and semioccupied molecular orbitals of (a) Fe(NO),CO, (b) Fe(NO),(CO),-, and (c) Co(NO),(CO),.
Figure 3. (a) Spectrum of CO('~NO),(CO), in isopentane frozen to 100 K. (b) Computer silmulation of (a) using parameters in Table I.
species as CO(NO)~(CO)~. A comparison of the important spectral parameters of the three radicals is shown in Figure 5. Because of the close similarity between the three sets of data it is highly probable that we are dealing with a
group of isoelectronic species. For example, (1) each radical possesses two equivalent nitrogen atoms whose I4N principal hyperfine values are approximately 60, 0, and 0 MHz, and (2) each g tensor has axial symmetry, with the unique principal value being significantly less than the free-spin value. The number of ligands associated with the radicals is of great importance since it determines our description of the point group describing their symmetry and hence the representation of their electronic ground state. In the case of Fe(NO),CO, the presence of all four ligands has been
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The Journal of Physical Chemistry, Vol. 84, No. 19, 1980
confirmed by analysis of their hyperfine interactions. Both 14Nand 15N data were used to verify the analysis of the powder spectrum of Fe(NO),CO, and we have recently detected an isotropic hyperfine interaction of 5 MHz from the 13Cnucleus in a sample enriched to 90% in that isotopea6 In the case of the other two species, we have not yet established by 13Csubstitution the presence of two CO ligands, but the similarity of their EPR data to those of Fe(NO),CO leaves us in little doubt of their presence. In Figure 5, a and b, respectively, the radicals Fe(NO)3C0 and Fe(N0)2(CO)2-are shown in a nonplanar configuration. This is because, on the one hand (Fe(NO),CO), the principal directions of the g and 14Nhyperfine tensors were noncoincident in the xz plane; on the other hand (Fe(NO)z(CO)z-),the principal directions of the two 14N hyperfine tensors in the y z plane were inclined 25’ to each other. For CO(NO)~(CO)~ this was not the case: within experimental error (f5”) the g, 59C0,and 14N hyperfine tensors were coaxial, and the unique directions of the two 14Nhyperfine tensors were parallel. There was, therefore, no reason for us to suggest a lower symmetry than DZhfor Co(N0)2(C0)2. Semioccupied Orbital. The semioccupied molecular orbital (SOMO) in CO(NO)~(CO)~ is essentially confined to 2p, orbitals on the two nitrogen atoms. Since the principal values axxand a, of the 14Nhyperfine interaction are small and of indeterminate sign, a rough estimate of the N(2p,) contribution of the SOMO is obtained by comparing l/,aZ2(19 MHz) with estimates of 0.4g/3yN(r-,),, from Hartree-Fock-Slater wave functions (56 MHz).~Spin density in each N(2p2) atomic orbital is therefore approximately 0.33. By contrast, the unpaired spin density in each N(2s) atomic orbital is estimated to be only -0.01. The residual spin density is distributed over the nitrosyl oxygen atoms and the cobalt atom (3d,,), since the symmetry of the b%orbital (Figure 2c) of planar CO(NO)~(CO)~ does not permit any contribution from C(2p) atomic orbitals. This requirement is consistent with the lack of a resolvable isotropic 13Chyperfine interaction (i.e., less than 2.0 MHz) in a sample prepared from CO(CO)~NO enriched to 90% in the isotope 13C. Spin density in these orbitals is only permitted (by symmetry) in the nonplanar analogues such as Fe(NO),CO and Fe(N0)2(C0)z-. In considering the Co atomic orbital contributions to the SOMO, it is important to use the 59C0hyperfine interactions extrapolated to 0 K, since they are clearly subject (Figures 2 and 4) to considerable vibrational modulation. If the temperature dependences shown in Figures 2 and 4 are due to a single, intramolecular vibration, extrapolations of the high-temperature asymptotes to 0 K should give approximate values of the hyperfine parameters for a hypothetical, “vibrationless” molecule. In the case of the isotropic 59C0hyperfine interaction (Figure 21, extrapolation to 0 K gives 2 f 1MHz, a value indicating virtually zero Co s-orbital participation in the SOMO, and conground state. sistent with a 2B3g The variation with temperature of the jgCo hyperfine interaction is one to two orders of magnitude greater than that usually encountered. For example, in the ethyl radical (l3CHzCH3)the isotropic 13C hyperfine interaction increased by only 1.8% over the temperature range 200-300 K.9 Again, the isotropic 35Clhyperfine interaction in ClF6 decreased by 1.0% over the range 50-100 K.l0 Thus, changes of ca. 2% over a 100 K temperature range are typical. In contrast, the magnitude of the isotropic j9Co hyperfine interaction in CO(NO)~(CO)~ increased by over 30% between 150 and 200 K, and the z component increased by 25% between 10 and 100 K. In the case of the
Morton et al.
anisotropic hyperfine interaction uzz,the data fitted very well (Figure 4) a hypercotangent function of inverse temperature8i9and lead to a frequency of 60 f 10 cm-l for the internal motion responsible for the temperature dependence. The magnitude of the change in the 59C0hyperfine interaction is such that one is forced to contemplate CO(4s) admixture into the ground state via a vibration of appropriate symmetry. Moreover, very small changes in co(4s) character translate into quite substantial changes in the isotropic 59Cahyperfine interaction because of the large value of the Fermi contact term (ca. 6000 MHz7) per unit electron in co(4s). In these circumstances it is natural to think first of the out-of-plane motion of the central atom. However, such motion only lowers the symmetry from to Czu,and the Bsgrepresentation correlates with Bz in C2”, not A, required for co(4s) admixture. Regarded as a pentaatomic species, nonplanarity permits admixture not of co(4s) but of C(2py),as we saw earlier. In fact, to permit admixture of co(4s) the symmetry must be lowered to C,, retaining the yz plane as a plane of symmetry. A vibration which destroys the linearity of the ONCoNO axis (e.g., NO “wagging” in the yz plane) is required. Excitement of such a vibration would permit admixture into the ground state not only of co(4s) but also of Co(3dzz)character. The latter would appear to be suggested by the results shown in Figure 4. Extrapolation of the isotropic 59C0hyperfine interaction (Figure 2) indicates that it falls to zero as the temperature is lowered to 0 K. Its z component, however, extrapolates asymptotically to 15 MHz at absolute zero (Figure 4). This residual hyperfine interaction, which appears to be positive in sign, corresponds to a spin density of approximately 0.01 in a Co(3d) orbital, and probably represents the effect of bond polarization by the spin in N(2p,) orbitals. An induced spin density of 0.01 is entirely reasonable in magnitude for a polarization phenomenon, but it could of course be either positive or negative in sign depending on whether the induced spin enters Co(3d2z)or Co(3d,,). g Factor of C O ( N O ) ~ ( C O )It~ ,is apparent from the principal values (Table I) of the g tensor of CO(NO)~(CO)~ that there is considerable unquenched orbital angular = -0.065). The spinmomentum about the y axis (AgYy orbit interaction mixes excited states of other symmetries into the ground state via the orbital angular momentum operator. The latter has the properties of a rotation, and since R, transforms as B, in D%, the excited state belongs to the representation B, An appropriate bl, orbital would be an out-of-phase combnation of N(2px) atomic orbitals (Figure 5c). In brief, the large Ag, tells us there is a low-lying excited ?E$, state. If the spin-density distribution in the excited state is similar to that in the ground state (Le,, in each N(2p) orbital and ‘/6 in each O(2p) orbital), then the excitation energy AE 4 0 ~ / 3+ A0/6)/&yy where XN and Xo are the spin-orbit interaction constants of nitrogen and oxygen, respectively. Using the valuedl AN = 76 cm-l, A 0 = 151 cm-l, one obtains AE 3000 cm-l. The analogy with NZ-,l2which we mentioned in connection with Fe(NO),CO, is even more striking with Co(NO),(CO),. In both cases the maximum 14Nhyperfine interaction is -60 MHz, and the maximum g shift occurs when Ho is parallel to the N-N direction. The fact that than for Fe(NO),CO the g shift is greater for CO(NO)~(CO)~ is probably due to the linearity of the ONCoNO axis imposed by the higher symmetry. Fe(NO),CO is known to be nonplanar, and the two Fe-N bonds may therefore not be parallel, which would tend to quench orbital angular
248 1
J. Phys. Chem. 1980, 84, 2481-2484
momentum about the N-N direction. Note Added in Proof: We have recently observed the spectrum of the radical anion of Mn(NO)&O by sodium reduction of Mn(NO)3C0 in THF at 200 K: g = 1.9968, ~ p ~ (= 3 )16.5 IMHz, uMn = 33.0 MHz.
References amd Notes (1) N. M. Atherton, J. R. Morton, K. F. Preston, and M. J. Vuolle, Chem. Phys. Lett., 70, 4 (1980). (2) C. Couture, J. R. Morton, and K. F. Preston, J. Magn. Reson., to be submitted for publication. (3) g = 2.0061, aN(2)= 50.5 MHz, ah = 13.5 MHz, a+ ,', = 24.3 MHz.
(4) F. Seel, 2.Anorg. Allg. Chem., 269, 40 (1952). (5) R. Lefebvre and J. Maruani, J . Chem. Phys., 42, 1480 (1965). (6) We thank Dr. P. J. Krusic for a sample of Fe(CO), enriched to 90% in the isotope "C. (7) J. R. Morton and K. F. Preston, J. Magn. Reson., 30, 577 (1978). (8) A. R. Boate, J. R. Morton, and K. F. Preston, J . Magn. Reson., 29, 243 (1978). (9) D. Griller, P. R. Marriott, and K. F. Preston, J. Chem. Phys., 71, 3703 (1979). (10) A. R. Boate, J. R. Morton, K. F. Preston, and S. J. Strach, J. Chem. Phys., 71, 388 (1979). (11) A. Carrington and A. D. McLachian, "Introduction to Magnetic Resonance", Harper and Row, New York, 1967, p 138. (12) J. R. Brailsford, J. R. Morton, and L. E. Vannotti, J . Chem. Phys., 50, 1051 (1969).
Mass Transport and Chemical Reaction in Cylindrical and Annular Flow Tubes Henry S. Judelkls Chemistry and Physics Laboratory, The Ivan A. Getting Laboratories, The Aerospace Corporation, €1 Segundo, California 90009 (Received: October 22, 1979; In h a / Form: April 16, 1980)
Solutions of the mass transport equations, including axial and radial diffusion, are presented for cylindrical and annular flow systems. The solutions include first-order gas-phase and wall reactions, at either wall or both walls in the annular case. The solutions are applicable at large distances from the entry to the flow tube, Le., where pure exponential decay of the reacting species is observed. The solutions, which are in the form of infinite series, can be used to calculate both axial and radial concentration gradients under these conditions or, given experimentally measured gradients, to extract kinetic information on gas-phase and wall reaction rates.
Introduction The extensivle use of cylindrical flow tubes in the study of fast gas-phase reactions has led to a number of discussions on their limitations (e.g., ref 1 and 2). These limitations frequently are based upon the fact that solutions of the mass-transport equations applicable to flow systems generally cannot be obtained in closed form, necessitating laborious numerical integration of the equations. To circumvent the latter difficulty, one usually chooses experimental conditions such that certain terms can be neglected and approximate closed-form solutions obtained. Indeed, under ideal conditions, particularly simple approximations can be used (ref 1and 2). One such condition is the situation where mass transport by axial diffusion is negligible compared to mass transport by flow. In selected gas-phase studies, and especially in the study of wall reactions, it is not always possible to work under conditions where the simpler approximations can be utilized. In these cases, alternate approximations are desirable. Presented here are solutions to thle mass-transport equations, including first-order gas-phase and wall reactions, that are valid a t large distances from the entry to the flow tube. Solutions applicable to flow through a cylindrical tube are discussed, as well as those for flow through the annular space between concentric cylinders. Discussion A. Single-Tube Solutions. Under conditions of constant temperature and pressure, the steady-state concentration of a trace reacting species ( C ) in a tube with fully developed Poiseuille flow is described by eq 1,3-7 where D is the
0022-3654/80/2084-2481$01 .OO/O
diffusion coefficient, k is the (first-order) gas-phase reaction rate constant, r and z are the radial and axial dimensions, and V, is given by eq 2. In eq 2, V,, is the
average volume flow velocity and R is the radius of the flow tube. In many cases axial diffusion, Dd2C/dz2, can be neglected. Solutions of eq 1for these conditions have been d e ~ c r i b e d .Analogous ~~ solutions for related heat-transfer problems have also been given.&13 When axial diffusion cannot be neglected, the method of Graetz'* and others15is generally employed. This method involves substitution of m
C = C fi(r)e-biz i=l
(3)
into eq 1, where m
fi(r) =
C uimrm m=O
(4)
This results in an infinite set of ordinary differential equations that, when coupled with the appropriate boundary conditions, can be solved for the aimcoefficients and the pi eigenvalues. Walker3 has described these solutions for a single tube including gas-phase and wall reactions. At sufficiently large distances from the entry to the flow tube (ref 3-71, only the first term (i = 1) of eq 3 is important in the solution of eq 1. Under these conditions, a single ordinary differential equation is obtained. In such cases, analysis of data from flow-tube experiments is greatly simplified. Derivation of a model for wall reactions only (k = 0) under such conditions is given in ref 16. 0 1980 American Chemical Society
