J . Phys. Chem. 1985, 89, 612-617
612
Substitution into (A-2) and (A-3) gives
+ 1/7g’]G~+ (1/7c’)Gc = iyHlM@B -[ac + ~ / T ~ ’ +] (I/TB’)GB G ~ = iyH,Mopc -[ag
(A-6) (A-7)
in which 1 A l/TB’ = l / S B - -= 7ABTBA
TA
l / s c ’ = 1/TC - -= TAC7CA
+7A
lBC
‘ACTBA
1
TA
7CB
7AB7CA
-+ -
1
k,’
Na-,Na+
+ Na+C,Na-
1 - = k-,
(‘4-9)
which for the case considered in this paper (pB= p c = 0.5) gives 79’ = 7C’ = 7. Derivation of the Exchange Rate for Mechanism I. Mechanism I consists of eq 7-9. Site C consists of Na- ion paired to two different cations, Na+ and Na+C. Therefore, for a step such as
+ Na+C,Na-
(A-14)
(‘4-8)
Equations A-6 and A-7 are identical in form to the two-site Bloch equations so that line shape analysis appropriate to the two-site case can be used. It may also be shown that 7B1/7C’ = P B / P C (A-IO)
Na+,Na-
The ratio give in braces is required because only this fraction of Na- is present in the ion pair Na+,Na-, so that the mean lifetime in site C, distributed between Na+,Na- and Na+C,Na-, is much longer than the mean lifetime of the ion pair Na+,Na-. Proceeding in this way, we obtain in addition to eq A- 12 and A-I3
(A-1 1)
in which Na- (site C) in the ion pair Na+,Na- exchanges with Na+ (site A) in the same ion pair, we have _1 -- 2ki[Na+C,Na-] (A-12)
(A-1 5)
7BA
1
2ki‘[Na+C,Na-]
lBC
K, [Cl
- = 2k2”[Na+,Na-] =
(A-16)
-1- - 2ki’[Na+C,Na-] TCB
(A-17)
1 + Kl[CI
With eq A-9 this gives (with k l [C] >> 2k,”[Na+C,Na-])
-1 -7
+ k2”][C] [Na+C,Na-] [ l + K,[C]](k,[C] + 2ki[Na+C,Na-]) 2k1[k,’
>> 1, and [Na+C,Na-] = [Na],/2, -1 - k-l(k2’ + k,”)[NaIo T k,[CI + b W a 1 0
Since K , [C] = P B / P A
Since k l [C]
we obtain
7AC
TCA
(A-19)
>> k2’[NaIo, this simplifies to (A-20)
and
_ I - 2ki[Na+C,Na-]
(A-18)
[Na+,Na-] [Na+,Na-]
+ [Na+C,Na-]
(A-13)
Equation A-8 gives the same result for 1 / to ~ within the approximation p A = 0. Registry No. Na, 7440-23-5.
Relationship between Structure and Reactivity for Metal Clusters Formed in Ion-Molecule Reactions in Decacarbonyldirhenlum Wilma K. Meckstroth,t D. P. Ridge,* Department of Chemistry, University of Delaware, Newark, Delaware 1971 6
and William D. Reents, Jr. AT& T Bell Laboratories, Murray Hill, New Jersey 07974 (Received: July 30, 1984)
Relative rate constants for ion-molecule reactions in Re2(CO),, are reported. Electron impact produced fragment ions react with the parent to form cluster ions containing three and four metal atoms. Subsequent sequential reactions lead to cluster ions containing as many as ten rhenium atoms. Rate constants for Re,(CO),+ ions decrease with increasing m. A correlation is found between the average electron deficiency per metal atom and the rate constant. An electron deficiency is assigned by using the 18-electron rule and assuming closed polyhedral structures for most of the ions. The relative rate constants increase rapidly with increasing electron deficiency until the deficiency reaches two electrons per rhenium atom. The rate constants then slowly approach a constant value close to the collision-limited rate. This is consistent with the notion that the rate constants are determined primarily by the degree of coordinative unsaturation of the metal atoms in the cluster ion reactant. This satisfactory structure-reactivity relationship also substantiates the structural assumptions made about the cluster ions in assigning electron deficiencies.
Introduction Recently we reported relative rate constants for gas-phase anionic clustering reactions in pentacarbonyl iron.’ The relative rate constants were found to be related to the electron deficiencies of the reactant anions. Fe,(CO),- ions with large electron de+ Permanent address: Ohio State University-Newark, University Dr., Newark, OH 43055.
0022-3654/85/2089-0612$01.50/0
ficiencies reacted rapidly with Fe(CO)5 to form larger clusters. Reactant anions with small electron deficiencies reacted slowly, if at all. Electron deficiencies were determined by assuming that each metal atom in a given cluster required 18 electrons to satisfy its valency. The total number of valence electrons in the cluster divided by the number of iron atoms is the average number of ( 1 ) Wronka, J.; Ridge, D. P. J . Am. Chem. SOC.1984, 106, 67
0 1985 American Chemical Society
CO-Re Metal Clusters valence electrons available to each iron atom. The difference between 18 and this average number of valence electrons is the electron deficiency. Relative rate constants for clustering reactions dropped several orders of magnitude for clusters with electron deficiencies less than two. A cluster with an electron deficiency of two has on the average a vacancy for a two electron donor such as CO at each metal center. It is quite consistent with the general behavior of coordination compounds that reactivity should drop as these vacant sites fill and the electron deficiency decreases. For clusters with larger electron deficiencies the rate is approximately constant and within an order of magnitude of the collision rate.' If the correlation between electron deficiency and reaction rate constant proves to be general for metal carbonyls or for some class of metal carbonyls, it would be useful for several reasons. First, it would be helpful in designing schemes for generating clusters of varying size and composition for further studies. Second, it provides a means of characterizing the structure of the clusters. Each metal-metal bond in a metal cluster adds two valence electrons to the cluster. Thus the number of metal-metal bonds in a cluster might be deduced or at least limited from its reaction rate constant. In the present study relative rate constants for gas-phase positive ion clustering reactions in decacarbonyldirhenium were determined. This compound was chosen because each reaction step could potentially add two metal atoms to the cluster and large clusters2 could be made in relatively few steps. The strong Re-Re bond3 and the large neutral metal carbonyl clusters observed for third-row transition metals4 also suggested that the gas-phase ionic clustering reactions in decacarbonyldirhenium would be interesting. The Re2(CO),ois also thermally stable and sufficiently volatile that it is readily introduced into an ion cyclotron resonance mass spectrometer for ion-molecule reaction studies. Preliminary results confirmed that large clusters are formed in ion-molecule reactions occurring in Re2(CO)lo.5 Another interesting feature of Re2(CO)lois that it is the dimer of Re(CO), which is isolobal with a methyl radicaL6 That is, it has a singly occupied orbital that forms u bonds to a hydrogen atom, a halogen atom, or another isolobal species. Clusters made up of Re(CO), and Re(CO),+ would therefore be analogous in the isolobal sense to hydrocarbon ions. Experimental Section
Initial studies were done a t the University of Delaware on an ion cyclotron resonance spectrometer with a capacitance bridge detector which has been previously de~cribed.~Double resonance results were also obtained on this spectrometer. The high-resolution spectra, high-accuracy mass measurements, and kinetic data were obtained at Bell Laboratories on a Nicolet FT/MS-1000 (2) For examples of other methods of preparing large metal clusters, see: Leutwyler, S.; Hermann, A.; Woeste, L.; Schumacher, E. Chem. Phys. 1980, 48, 253. Powers, D. E.; Hansen, S. G.; Geusic, M. E.; Puiu, A. C.; Hopkins, J. B.; Dietz, T. G.; Duncan, M. A.; Langridge-Smith, P. R. R.; Smalley, R. E. J. Phys. Chem. 1982,86, 2556. Gole, J. L.; English, J. H.; Bondybey, U. E. Ibid. 1982,86, 2560. Barlak, T. M.; Wyatt, J. R.; Colton, R. J.; deCorpo, J. J.; Campana, J. E. J . Am. Chem. SOC.1982, 104, 1212. Lichtin, D. A.; Bernstein, R. B.; Vaida, V. Ibid. 1982, 104, 1831. (3) Freedman, A.; Bersohn, R. J . Am. Chem. SOC.1978,100,4116. Svec, H. J.; Junk, G. A. Ibid. 1967, 89, 2836. Hall, M. B. Ibid. 1975, 97, 2057. Poe, A. In "Reactivity of Metal-Metal Bonds"; Chisolm, M. H., Ed.; American Chemical Society, Washington, DC, 1981; ACS Symp. Ser. No. 155, p 135. Connor, J. A. Top. Curr. Chem. 1977, 71, 71. (4) For examples, see: Mason, R.; Thomas, K. M.; Mingos, D. M. P. J . Am. Chem. SOC.1973,95, 3802. Eady, C. R.; Johnson, B. F. G.; Lewis, J.; Reichert, B. E.; Sheldrick, G. M. J. Chem. SOC.,Chem. Commun. 1976, 271. (5) Meckstroth, W. K.; Ridge, D. P. Int. J. Mass Spectrom. Ion Processes 1984, 61, 149. (6) Elian, M.; Hoffman, R. Inorg. Chem. 1975.14, 1058. Elian, M.; Chen, M. M. L.; Mingos, D. M. P.; Hoffman, R. Ibid. 1976, 15, 1148. Schilling, B. E. R.; Hoffman, R.; Lichtenberger, D. L. J. Am. Chem. SOC.1979, 101, 585. Schilling, B. E. R.; Hoffman, R. Ibid. 1979, 101, 3456. Hoffman, R.; Schilling, B. E. R.; Bau, R.; Kaesz, H. D.; Mingos, D. M. P. Ibid. 1978, 100, 6088. Hoffman, R. Science (Washington, D.C.)1981, 211, 995. Halpern, J. Discuss. Faraday SOC.1968, 46, 7. Ellis, J. E. J. Chem. Educ. 1976, 53, 2 . Stone, F. G. A. Arc. Chem. Res. 1981, 14, 318. Hoffman, R. Angew Chem., Int. Ed. Engl. 1982, 21, 711. Stone, F. G. A. Ibid. 1984, 23, 89. (7) Wronka, J.; Ridge, D. P. Reu. Sci. Instrum. 1982, 53, 491. Wronka, J.; Ridge, D. P. Int. J . Mass Spectrom. Ion Processes 1982, 43, 23.
The Journal of Physical Chemistry, Vol. 89, No. 4, 1985 613 TABLE I: Relative Intensities of Positive Ions in the Mass Spectrum of RedCO)ln Obtained by 70-eV Electron Impact re1 int of largest isotope peak, % stoichiometry Re+ Re2' Re2Ct Re2(CO)' Re2(C0)2' Re2(C0)3' Re2(C0)4' Re2W)S' Re2(C0)6+ Re2(C0)7' Re2(C0)8+ Re2(C0)9' Re2(CO)10t Nominal mass.
m/zQ
measd
lit.b
187 372 384 400 428 456 484 512 540 568 596 624 652
48.7 30.9 7.3 14.3 25.1 25.0 34.4 34.6 41.2 100.0 6.9 16.2 42.0
11 43 15 24 32 27 41 35 44 1100 9 6 53
Reference 9.
TABLE I 1 Relative Intensities of Positive Ions Formed by Ion-Molecule Reactions in Re*(CO)tn" re1 int of largest stoichiometry Re3(CO)11' Re3(C0)12+ Re3(C0)13C Re4(CO)7' Re4(CO)s' Re3(C0)lS' Re4(C0)9' Re4(CO)l~' %(CO)II' Re4(C0)12' RedCO) 13' RedC0)14' Re4(CO)I~' ReS(C0) Res(C0)16' ReS(C0)17+ RedCO) 18' ReS(CQ19' Re~(c0)20' RedC0)14' Re5(C0)2It Re6(CO)ist Re6(C0)16' Re6(C0)17+ RedCO)18' R~~(CO)I~' Re6(C0)20t RedC0)21' Re6(C0)22' ReS(C0)20+ RedC0)21+ Res(C0)22; ReS(C0)23 Re~(C0)2~' Res(CO)26+ Rel~(C0)29'
m/zb
isotope peak, %
867 895 923 940 970 979 998 1026 1054 1082 1110 1138 1166 1351 1379 1407 1435 1463 1491 1510 1519 1538 1566 1594 1622 1650 1678 1706 1734 2052 2078 2108 2136 2190 2220 2673
22.0 100.0 8.8 3.6 7.5 64.0 8.9 10.0 9.0 8.4 23.0 86.9 8.9 5.4 24.5 15.7 11.7 11.3 29.9 17.1 4.0 20.1 23.9 55.7 51.9 61.0 8.5 13.9 27.6 8.9 14.4 12.5 24.4 7.9 4.4 5.8
"Trapping time = 500 ms and pressure = 9.5 X torr. bNominal mass. Calculated for Re3 = 18sRe187Re2; Re4 = 18sRe'87Re3except for = 940, which is 1ssRe2187Re2; ReS = 18sRe2187Re,;Re6 = zge2187Re4; Re8 = 18sRe287Re6except for m / z = 2078 and 2190, which are 18sRe3187Res; Relo = 185Re4187Re6.
Fourier transform mass spectrometer with a 2-in. cubic cell. This instrument has also been described.* Re2(CO)lowas obtained from Strem Chemicals, Inc. and no impurities were found in the mass spectrum. The sample was heated to about 50 "C and admitted to the spectrometers through variable-leak valves. Under these circumstances pressures as high (8) Reents, Jr., W. D.; Mujsce, A. M. Int. J . Mass Spectrom. Ion Processes 1984, 59, 65.
Meckstroth et al.
The Journal of Physical Chemistry, Vol. 89, No. 4, 1985
614
TABLE I V Isotope Peak Intensities of Re6(C0),9+
re1 int, % Re4(C nm
-15
isotope' peaks in Re6(C0)19+ 18'Re6 185Re 187Re 185Re4 1 8 72 ~ ~ 185Re31 8 73 ~ ~
I
I8Qe
2 1 8 74 ~ ~
18sRe187Re Ig7Re6
calcd
measd
0.85 8.5 35.7 19.7 100.0 67.0 18.7
6.6 30.1 76.0 100.0 64.1 15.5
"37.4% 184.9530 amu and 62.6% 186.9560 amu
0 IO00
1800
1400 MASS
IN
2200
2600
A.M.U.
Figure 1. Positive ion mass spectrum of ion-molecule reaction products of reactions between Re2(CO)loand its electron impact produced fragtorr. ment ions. Trapping time = 500 ms and pressure = 9.5 X TABLE 111 Precise Mass of Some Representative Re,(CO),+ Clusters mlra
stoichiometry calcd '85Re'87Rez(C0)15t 978.788 185Re187Re3(CO)15t 1165.744 1490.672
1 8 52 1~. 9~ 7 3(CO)20t ~ ~
'8sRe2187Re4(C0)22t 1733.617 185Re3187Re5(C0)25t2189.51 1 1 8 54 1~ 8 ~ 76(CO)29' ~ ~ 2673.400
measd
error, ppm
978.771 1165.684 1490.608 1733.478 2189.544 2673.395
17 51 43 80 -1 5 2
Precise mass. as 3 X lod torr of sample could be obtained in the spectrometer, and there was very little evidence of sample decomposition. The pressures reported are nominal pressures measured with standard ionization gauges.
The Mass Spectrum of Re2(CO)ro Table I gives the relative intensities of the peaks in an Re2(CO)io torr pressure and short mass spectrum obtained at 1 X trapping time so that there are no ion-molecule reactions. The ionizing electron energy was 70 eV. The agreement with a previously published spectrumg is satisfactory except for an intensity difference for the Re+ peaks. A possible explanation is that metastable ions decompose to give Re' on the ion cyclotron resonance time scale (several milliseconds) but are observed as stable ions on the conventional mass spectrometric time scale (several microseconds) I
Ion-Molecule Reaction Products Figure 1 shows a spectrum of Re2(CO),* at 500-ms trapping time, 1 X l V 7 torr pressure, and 70-eV ionizing energy. A number of ion-molecule reaction products have appeared which are identified on the spectrum. The stoichiometries and relative abundances of the various product species in the spectrum are listed in Table 11. The ion-molecule reaction products were identified by their masses and by the relative abundance of the isotopic variants of each ion. Measured and calculated precise masses for representative ions are given in Table 111. The mass calibration was constructed by using several peaks, whose stoichiometry was quite certain, as mass standards. All the measured masses were accurate to within 100 ppm and most were more accurate than that. Due to the limited combination of elements possible (Re, C, and 0) this was sufficient accuracy to assign elemental compositions unequivocally. (9) Lewis, J.; Manning, A. R.; Miller, J. R.; Wilson, J. M. J . Chew. Soc. A 1966, 1663.
1
0.4
1.2
0.8
I .6
2.0
2.4
2.8
Time
Figure 2. Time dependence of relative concentrations of Re6(CO),+ torr of Re2(CO)lo. For clarity the various curves species in 9.5 X have been displaced so that they do not intersect. While this affects relative intensities,it does not affect the relative rate constants implied by the curves.
Table IV indicates the relative intensities of the peaks in a typical isotopic cluster. The agreement between the observed relative intensities and those calculated from the natural abundances of lssRe and lS7Reconfirms the assigned stoichiometry. The variation of ion abundances with time for Re,(CO),+ ions are shown in Figure 2. Typically an ion abundance increases to a maximum and then levels off or diminishes depending on its reactivity. Since the neutral concentration is much larger than the ion concentration, the kinetics of all the reactions are pseudo first order. Rate constants for reactions of those that are reactive can be determined from the decay portion of the curve. An upper limit on the rate constants for less reactive ions can be derived from the flat or slowly increasing part of the curve. The decay portions of the curves are found to give satisfactorily linear logarithmic plots. The pseudo-first-order rate constants derived from these plots are given in Table V. The rate constants for species other than those containing six Re atoms can be similarly derived and are also given in Table V. The pseudo-first-order rate constants all correspond to the same neutral pressure so that the numbers are in proportion to the bimolecular rate constants. In other words, the numbers represent relative bimolecular rate constants multiplied by a constant neutral number density. The nominal pressure was 1 X lo-' torr which would correspond to a number density of 3 X 1O9 molecules at 298 K. It was not possible to generate a pressure of Re2(CO)lohigh enough that it could be measured with an absolute pressure gauge such as a capacitance manometer. The sensitivity of an ion gauge to
-
The Journal of Physical Chemistry, Vol. 89, No. 4, 1985 615
CO-Re Metal Clusters
TABLE V Electron Deficiencies and Relative Rate Constants for Reactions of Re,(CO),+ Ions with Re2(CO)lo stoichiometry re1 rate constant' structure metal-metal bonds 3 0 triangle Re3(C0)II+ 2.1 f 0.2 3 0 triangle Re3(C0) 12'
