J. Phys. Chem. 1981, 85, 3369-3371
inner lines being 140 f 10 Hz. In addition, resonance D for the CdLGly, species at pH 8.0 no longer appear as the well-resolved triplet in Figure l a but rather as a broadened featureless resonance of width 350-400 Hz. The multiplet structure for resonance E provides direct proof for its assignment to the CdILGly3- complex. Furthermore, at the higher pH values which is required for the observation of resonance E, the exchange rate of glycine ligand “in and our” of the Cd’I-GlyF and CdILGly2 complexes at -40 “C becomes comparable to J(’13Cd-15N). At lower pH (e.g., pH 7) resonance E cannot be observed even with a 10-fold excess of glycine. Obviously, the intermolecular exchange rate of ligands for solution I11 is slow enough on the l13Cd chemical shift scale (in our case -9700 Hz) at -40 “C to allow the detection of separate resonances D and E. Finally, our observation of the increasing ligand exchange rate for the Cd”-Gly2 and Cd”-Gly,- complexes with increasing pH may account for the rather broad D and E resonances observed at 22.09 MHz and -50 “C by the Ackerman’s (Figure 2, VI).8 In conclusion, l13Cd-16N spin-spin coupling constants appear promising for probing the aqueous solution-state structures of metal-amino acid complexes. In cases of rapid or intermediate exchange among labile complexes
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these parameters may be obtained from supercooled aqueous emulsions by 15N-labeledamino acids. This approach also proves useful in probing the environment and configuration of the metal binding site($ in studies of metal-peptide interactions and metalloproteins using specifically 15N-labeledpeptides/proteins. Furthermore, combining the results of such solution studies (e.g., for the Cd’I-glycine system) with solid-state l13Cd NMR investigations and X-ray crystal structure data should allow determination of any differences between the solution and solid-state structures of individual complexes. Finally, the structural role of water in the solution-state structures of metal complexes is often unknown. Such information may be derived from l13Cd NMR relaxation studies as has been recently demonstrated for Cd’I-EDTA.,
Acknowledgment. The authors gratefully acknowledge support of this research by the NATO Science Affairs Division, Brussels (Research Grant No. 1831),the Danish Natural Science Research Council (J. No. 11-2147), and the National Institute of Health (GM26295). The use of the facilities at the University of South Carolina Regional NMR Center, funded by the National Science Foundation (CHE78-18723), is acknowledged.
Ion-Pair Formation in Multiphoton Fragmentation N. Ohmlchi, J. Sllbersteln, and R. D. Levlne” The Fritz Haber Research Center for Molecular Dynamics, The Hebrew University, Jerusalem 9 1904, Israel (Recelved:August 11, 198 1)
Computational examples and physical considerations suggest that, in the statistical limit, ion-pair formation should be an important mechanism for the appearance of ions in the post-threshold region. This is particularly the case when the threshold energy for ion-pair formation is comparable or even lower than the first ionization potential. As the mean energy absorbed by the molecule increases, the ionization mechanism rapidly increases in importance. Deviations from the statistical limit are expected to favor the ionization pathway.
The formation of ionic fragments following multiphoton excitation (using lasers in the visible or UV spectral range) is currently thought to proceed via the parent molecular ion as an intermediate.14 The “two-color” e~perimentsl-~ and the dependence of the extent of fragmentation on the absorption cross section of the parent ion5 have lent considerable support to this mechanism. For many molecules the ionization potential is comparable to or even higher than the threshold energy for ion-pair formation. It is therefore reasonable to enquire whether ion pairs can be formed to any significant extent, as compared to ionization. We report computational results (and their interpretation) which show that in the statistical limit ion-pair formation is quite facile in the post-threshold region. Examples where essentially all ions in the threshold region are pro(1)U. Boesl, H.J. Neusser, and E. w. Schlag, J. Chem. Phys., 72,4327 (1980). (2) K.R.Newton, D. A. Lichtin, and R. B. Bernstein, J. Phys. Chem., 85,15 (1981). (3)D.M. Lubman, R. Naaman, and R. N. Zare, J. Chern. Phys., 72, 3034 (1980). (4)K.L. Kompa in “Lasers and Applications”, W. 0. N. Guimaraes, C. T.Lin, and A. Mooradian, Ed., Springer, Berlin, 1981,p 182. (5) D. H. Parker, R. B. Bernstein, and D. A. Lichtin, J. Chem. Phys., in press.
duced as pairs will be provided below. The importance of the ion-pair mechanism does, however, decline quite rapidly as the energy absorbed per molecule increases. Eventually, all ions are produced via the ionization pathway. I t is reasonable to expect a statistical approach to overestimate the branching ratio in favor of ion-pair formation. To see this consider the reasons why ion-pair formation may be disfavored. The first argument which is usually brought forward is that the ion-pair correlates with a particular electronic state of the parent. Hence, only excitation of that state will lead to ion pairs. This argument is, however, somewhat questionable even for single-photon excitation of diatomics, due to the extensive curve crossings between the ionic and covalent curves! The recent “alternative doorway state’’ test’ suggesta that, for multiphoton excitation of polyatomics, energy is indeed remarkably scrambled in the manner suggested by the statistical t h e ~ r y . ~That , ~ test, however, necessarily probes (6) M. B. Faist and R. D. Levine, J. Chem. Phys., 64,2953 (1976);J. J. Ewing, R. Milstein, and R. S. Berry, J. Chem. Phys., 54,1752(1971). (7)D.A. Lichtin, R. B. Bernstein, and K. R. Newton, J. Chem. Phys.,
in press. (8)J. Silberstein and R. D. Levine, Chern. Phys. Lett., 74,6 (1980).
0022-3654/81/2085-3369$01.2510 0 1981 American Chemical Society
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The Journal of Physical Chemistty, Vol. 85, No. 23, 1981
TABLE I: Threshold Energies (at 298 K) for the Lower Ionic Dissociation Channels in 0,,Cs,, HNO,, and CH,I channel A H , eV 0,' t 011.63 0,' + e12.69 0,' t 0 + e13.16 0,- + 0' 14.20 14.69 0' t 0, t eCs2+t e3.80 c s + t cs3.92 4.38 Cs' + Cs t eOH- t NO' 9.57 H N O , + t e10.98 O H t NO+ t e11.47 0,' t NH' (12.26) H- t NO,' 12.38 H' t NO,12.99 0- t HNO' 13.20 CH,' + I9.19 CH,I' + e9.62 CH,' t I(P,,,) t e12.25 CH,I+ t H t e(12.76) I'(P,) + CH, t e12.92
Letters 100 r
-
50t 4 l
O'
'
1
7
8
I
6
i
1
1
03 1
I
9
IO
I I
I
molecules with considerable excess energy. There has not been an appraisal of the statistical theory at lower energies, 8 just above the threshold for ionization. The detection of ( E ) /charge ( e V ) negative ions (e.g., in CH3X, X halogen) at low levels of excitation offers such a test. Figure 1. The fractions of negative (I-)and positive (I+) ions in 03, Cs2, and HNOpas a function of the mean energy per charge (cf. eq The second factor which may discriminate against ion- I-) of ionization processes. 4). Also shown is the fraction (I,I = pair formation is the disposal of excess energy. Any energy I = 0 corresponds to exclusive ion-pair formation (I+ = I-). The above threshold need be carried by the motion (whether computations were performed in the statistical limit and hence any vibration or translation) of the atoms, while for ionization constraints on the relative population of individual species which follow the excess energy can be carried away by the much lighter from mechanistic considerations need not be satisfied. electron. This dynamical constraint which is not imposed Here X = C,Xj is the total number of molecules and Qj in the present calculation, and which favors ionization, is is the partition function. a K + l j is the charge on species counteracted, however, on statistical grounds, in that the j and akj, It = 1, ..., K , is the number of atoms of type k much lighter electron has a much smaller volume in phase in species j . The program (available from us upon request) space (or, if you prefer, has a far smaller translational partition function). Hence again, statistics favor ion-pair determines the K + 1Lagrange parameters Yk and X . The formation. lowest energy at which computations could be carried out is governed by the finite accuracy of the program due to It is a result of the statistical theorf that the energy is the low fraction ( X j / X )of ions in the threshold region. It equipartitioned among all degrees of freedom. Negative is important to emphasize that the only constraints imions usually require only a small energy excess to detach posed in the computations are the ever-present onesEi9of their extra electron. Hence, when the energy per parent conservation of elements or of charge. Taking O3 as an molecule is increased and this energy is equipartitioned example we do not require (cf. Table I) that the number the fraction of negative ions will diminish while the fraction of 02+ions equals the number of 0- ions. This is as it of the corresponding neutral species and of free electrons should be since, in principle, 02+ is a product of a higher will increase. Taking O3 as an example (cf. Table I), as we increase the energy, the ion-pair pathway 02+ + 0- is ionization process and because 0- ions can detach an electron when their energy content is high. As with other expected, on statistical grounds, to be replaced by the statistical computation^^^^ the disregard of all mechanistic direct ionization pathways such as 02+ 0 + e- or 03++ constraints does imply, however, that the resulta for groups e-, etc. The computational results reported below show of ions are more reliable than for individual species. We this to be a general trend. In the statistical limit, ion-pair have therefore chosen to report only the relative fractions formation is an important mechanism only near its own of positive and negative ions. We also wish to reiterate threshold. At higher energies the ionization pathway inour earlier comment, that statistical computations need variably takes over. not necessarily agree with experiment. What they provide Computations were carried out by use of the statistical (maximal entropy) formalism as previously d e s ~ r i b e d . ~ ? ~ is a reference against which the observed results are to be compared. For each parent molecule, all possible ionic (both positive The computational results are shown in Figure 1,as the and negative) and neutral species were included (except fractions that species with very high heats of formation can safely be excluded for the lower energy computations). The I* = C * X j / ( C + + c-,xj (2) computation results in the number, Xj, of molecules of J j I species j of positive/negative ions. The superscript on the sumK+l mation sign indicates that the sum is only over positive xj = XQj eXp(- k = l Ykakj) (1) or only negative ions. The free electron is included in the computation as a distinct species but is not regarded as a "negative ion" for the purpose of eq 2. Such a nor(9) J. Silberstein and R. D. Levine, J. Chern. Phys., in press.
+
~~
Letters
The Journal of Physical Chemistty, Vol. 85, No. 23, 198 1 3371
-
malization convention has the advantage that when ioni1, while for exclusive ion-pair zation dominates, If formation I+ = I- = 0.5. The overall conservation of charge implies that the fraction of dissociations which proceed via ionization is given by I = I+ - I(3) The abscissa in Figure 1is the mean energy per charge, defined by @)/charge = (C’X;H;/C’XJ - (H1/2) I
I
(4)
where the summation in eq 4 is over all charged species, including the electron. H . is the standard heat of formation of species j while H1is the standard heat of formation of the neutral parent. Heats of formation and other thermochemical data are all from standard sources.loJ1 The threshold energies, at 298 K, for the lower ionic dissociation channels are given in Table I. The two entries in parentheses are somewhat uncertain. The summation in eq 4 does include the electron for the following reason. At the lowest energies of interest, each possible process gives rise to two charged species. By averaging the heat of formation over all charged species and multiplying by two we have the average heat of formation of the products. Subtracting the heat of formation of the parent leads to the average heat of reaction. In other words, the mean energy per charge is, at the lowest energies, one-half the required energy for dissociation into ionic products. Ozone is unusual among the several molecules studied in that ionization persists down to the lowest energies that could be reached, Figure 1. In Csz, ion-pair formation has been observed12 in a resonant, two-photon process at wavelengths shorter than 600 nm. In the present, statistical computations ion-pair formation dominates in the threshold region. In HN02, the several possible lower energy ion-pair processes, Table I, lead to a significant interval over which ion-pair formation dominates over ionization. In all molecules, there is extensive dissociation into neutral fragments at the lower energies. Indeed, in the post-threshold region the fraction of molecules which follow the ionic dissociation pathway is quite low. It is therefore not surprising that for infrared multiphoton (IO) H. M. Rosenstock, K. Draxl, B. W. Steiner, and J. T. Herron, J. Phys. Chem. Ref. Data, 6, Suppl. 1 (1977). (11) D. R. Stull and H. Prophet, Eds., “JANAF Thermochemical Tables”. National Bureau of Standards. Washington. DC. 1970. (12) M.Klewer, M. J. M. Beerlage, J.’Los, and-M. J. V& der Wiel, J . Phys. B, 10, 2809 (1977).
pumping (e.g., of CH3N0213),ion formation is thought to occur primarily via secondary collisional processes. Ion pair formation in methyl halides has been observed14 in a resonant, one-photon process, and assigned15as responsible for discontinuities in ionization efficiency curves measured in electron impact excitation. The present results for all CH3X molecules are qualitatively similar to those for Csz. Ion-pair formation dominates at threshold, but the multitude of possible low energy ionization processes rapidly take over. (HN02is thus an exception as typically there will not be so many pathways for ion-pair formation.) At the energies used for comparisongwith the experimental7 fragmentation patterns in CH31, ion-pair formation is already unimportant. Resonant ion-pair formation in I2 has been proposed16 and very recently 0bserved.l’ In conclusion, because of the low ionization potential of negative ions, they can make an appearance, in the statistical theory, only when the energy up-take per molecule is comparatively low. Since the statistical theory does impose the conservation of charge, negative ions can appear only due to ion-pair formation. When the threshold energy for ion-pair formation is comparable to the ionization potential of the parent, the branching fraction for negative ion formation can be significant in the postthreshold region. It will, however, rapidly decline as the mean excitation energy per molecule is increased. Detection of negative ions following nonresonant18excitation is thus a test of the statistical theory8pgin the threshold region, where the paucity of decay processes makes alternative tests less clear cut.
Acknowledgment. We thank Professor K. H. Welge for pointing out the low threshold for ion-pair formation in CH31and Professor C. Lifshitz for discussions. N.O. is indebted to the Kranzberg Fund for financial support. The Fritz Haber Research Center is supported by the Minerva Gesellschaft fur die Forschung, mbH, Munchen, BRD. This work was supported by the Office of Naval Research and by the US.-Israel Binational Science Foundation. (13) P. Avouris, I. Y. Chan, and M. M. T. Loy, J. Chen. Phys., 72, 3522 (1980). (14) J. Berkowitz, “Photoabsorption, Photoionization and Photoelectron Spectroscopy”, Academic Press, New York, 1979, p 17. (15) S. Tsuda, C. E. Melton, and W. H. Hamill, J. Chem. Phys., 41, 689 (1964). (16) F. W. Dalby, G. Petty-Sil, M. H. Pryce, and C. Tal, Can. J. Phys., 55, 1033 (1977). (17) M. S. DeVries, N. J. A. Van Veen, T. Baller, and A. E. De Vries, Chem. Phys., 56, 157 (1981). (18) The excitation may, however, be resonance enhanced provided
only that the intermediate state does not asymptotically correlate with an ion pair.
