J . Phys. Chem. 1989, 93,4697-4698
The 23+ MeV electrons would radiate a large fraction of their energy as penetrating MeV X-rays ... (that would) be both detectable and lethal. 4. The muon-bound molecule would have an IC coefficient larger still by the fifth power of (207/10) ...”
4697
We appreciate the efforts of these reviewers and permission to quote their comments. Malcolm F. Nicol Mostafa A. El-Sayed
Electronic Structure of Palladium Clusters: Implications for Cold Fusion Lawrence L. Lohr Department of Chemistry, University of Michigan, Ann Arbor, Michigan 481 09 (Received: May 9, 1989)
Electronic structure calculations at the ab initio HF/STO-3G level are reported for the octahedral clusters Pd62-,pd612-, Pd6H-, and Pd6H2;these clusters serve as models for hydrogen (deuterium) in Pd metal. Electrostatic potentials, fields, and field gradients at various positions in the neighborhood of the octahedral hole are discussed. Forces sufficient to force two deuterium nuclei significantly closer than in diatomic D2 appear unlikely.
Introduction Recent reports1V2of the observation of the fusion of deuterium nuclei at ambient temperatures in condensed matter have led us to consider the electrostatic forces that are exerted upon deuterium nuclei imbedded in a host material such as elemental palladium. Since these forces may be computed from electronic wave functions, such as those calculable by ab initio procedures for molecular systems, we have chosen as a model an octahedral cluster of six Pd atoms having a Pd-Pd separation (2.74 A) equal to that in the fcc metallic structure. Several cluster variations were considered: the first was a cluster without explicit consideration of deuterium (hydrogen) atoms; this cluster was given a net charge of -2, corresponding to the extra electrons contributed from two D atoms. Other cluster variations include a fully charged cluster Pd6I2-, isoelectronic with Cd,, and the explicitly hydrogenated clusters Pd6H- and Pd6H2. Method Electronic energies and wave functions were obtained at the self-consistent field (HF) level for the Pd6 clusters by using the GAUSSIAN86 program3 and a minimal STO-3G basis set;4 thus we used 144 basis functions for Pd6Q-,145 for Pd6H-, and 146 for Pd6H2. The clusters Pd64- and Pd& were assumed to possess o h symmetry, while Pd6H2was assumed to possess D4* symmetry ( H atoms along (100) direction). From the H F wave function various electrostatic properties can be computed at any point in space; these include the electrostatic potential 9,the electric field F = -grad 9,and the field gradient tensor. Results and Discussion The cluster Pd62- was found to possess a totally symmetric charge distribution, with the highest occupied orbital being doubly degenerate (symmetry e ). The electrostatic potential is a local minimum at the center of the octahedron (the “octahedral hole”), with a value of -0.1707 au. This compares to a value of -0,5462 au which would arise from the total cluster char e of -2 taken to be spread over a spherical shell of radius 1.9375 (the distance from the center of the hole to each Pd nucleus). The gradient of the potential is zero at the hole center, with the potential rising gradually for increasing distance away from the center. We have
i
( 1 ) Fleischmann, M.; Pons, S. J . Electroanal. Chem. 1989, 261, 301. (2) Jones, S. E.; Palmer, E. P.; Czirr, J. B.; Decker, D. L.; Jensen, G. L.; Thorne, J. M.; Taylor, S.F.; Rafelski, J. Nature 1989, 338, 737. (3) Frisch, M. J.; Binkley, J. S.;Schlegel, H. B.; Raghavachad, K.; Melius, C. F.; Martin, R. L.; Stewart, J. J. P.; Bobrowicz, F. W.; Rohlfing, C. M.; Kahn, L. R.; DeFrees, D. J.; Sager, R.; Whiteside, R. A.; Fox, D. J.; Fluder, E. M.; Pople, J. A. GAUSSIANB~, Carnegie-Mellon Quantum Chemistry Publishing Unit: Pittsburgh, PA, 1986. (4) Sakai, Y.; Tatewaki, H.; Huzinaga, S. J . Compur. Chem. 1982 3, 6.
0022-3654/89/2093-4697$01.50/0
calculated the electric field at a number of distances along (loo), (1 lo), and (1 11) directions; it rises in magnitude most steeply along (loo), reaching a value of -0.0994 au at a distance of 0.5 A, at which point the potential has risen to -0.1396 au, while the field is only -0.0229 and -0.0060 at this same distance along the (1 10) and ( 1 1 1 ) directions, respectively (the negative sign corresponds to a force on a positive charge in the direction of the hole center). Similar results and conclusions obtain for the fully charged cluster Pd612-,for which the potential at the center of the octahedral hole is -2.5933 au, rising to -2.5693 au at a distance of 0.5 A along (100); the field at this point has become -0.0707 au, somewhat less than the value for PdsZ-. The Pd6I2-potential value of -2.5933 au is somewhat smaller than the value of -3.2772 for the interior of a sphere of 1.9375 A radius with a charge of -12. The perturbation of the Pd cluster charge distribution by the presence of a positive charge has been roughly estimated by calculation of the wave function and electrostatic properties of the cluster Pd6H-, identical with Pd6’- except for an H nucleus, together with an STO-3G basis function, at the center of the octahedral hole. The electrostatic potential at this position is found to be -1.4546 au, considerably more negative than the value for Pds2- and reflecting transfer of charge (1.364 electron) into the H 1s orbital. The hydrogen nuclear charge does not contribute to this potential value, but does contribute to the potential at points nearby, where the potential is found to be positive out to 0.6 8, along (100) and out to 1.0 8, along (110) or (111). The above field values are all very small; by comparison, the field generated by a unit positive charge is 0.2800 au at a distance of 1 A. The electrostatic requirement for stabilizing a pair of positive charges at a separation of, say, 0.6 A, which is somewhat less than the equilibrium separation of 0.742 A in H2, is the presence of a field of 0.7769 au arising from the electronic charge distribution and all nuclei other than the other hydrogen; this field must, of course, also switch direction at the position of the other hydrogen nucleus, thus requiring a large field gradient as well. Our electrostatic results suggest that it is not likely that there are positions in the Pd cluster or in Pd metal at which there are strong electric forces capable of holding two deuterium nuclei significantly closer to each other than in a normal diatomic molecule. As an additional model, we considered Pd6H2with D4,,symmetry, the H 2 midpoint being at the octahedral hole center and the H atoms lying along the (100) axis. Whereas the equilibrium bond distance for an isolated H2 is 0.71 8, at this HF/STO-3G level, the equilibrium distance for H2within the Pd, cluster is found by energy minimization to be slightly greater than 0.90 A, corresponding to a Pd-H separation of 1.48 A. While other H2 orientations and cluster variants could be considered, as could computational improvements, little encouragement is found for a tightly confined hydrogen diatomic. The possibility remains 0 1989 American Chemical Society
4698
J . Phys. Chem. 1989, 93, 4698-4700
of a dynamically confined deuteron pair, particularly if deuterium (hydrogen) doped Pd behaves as a heavy-fermion metal in the manner5 of Pt alloys such as UPt3 and UAuPt,.
trostatic forces are not likely to exist in Pd metal of a nature sufficient to force two deuterium nuclei significantly closer together than the equilibrium separation in diatomic D2.
Summary
Electronic structure calculations at the HF/STO-3G level for the model cluster PdG2-and several variants suggest that elec-
Note Added in Proof: Further calculations for Pd6H- indicate an energy minh-" away from ok symmetry (hydrogen displaced at least 0.3 A from center of octahedron).
(5) Fisk, Z.; Hess, D. W.; Pethick, C . J.; Pines, D.; Smith, J. L.; Thompson, J . D.; Willis. J. 0. Science 1988, 239, 33.
Acknowledgment. The authors thanks the Computing Center of the University of Michigan for use of its IBM-3090 computer.
Stopped-Flow Study of the Reaction between CI(II1) and I- at Low pH' Woo M. Song, Kenneth Kustin,* and Irving R. Epstein* Department of Chemistry, Brandeis University, Waltham, Massachusetts 02254-91 10 (Received: February 21, 1989)
The initial reaction between chlorine(II1) and iodide ion has been studied by stopped-flow spectrophotometry at 2 5 OC and ionic strength 1.3 M (NaC104). At low pH (C1.75) and under conditions where the autocatalytic pathways are suppressed, the rate law is found to be d([12] + [I,-])/dt = (k,[H+] + k2[H+]2)[CI(III)][I-]/([H+] + K,) with k l = 4.6 f 0.7 M-2 s-l, k2 = 31 f 1 M-' s-l, and the dissociation constant of chlorous acid K, = (3.3 f 0.5) X M. The term second order in [H'] had not been observed in earlier studies at higher pH. It may have important consequences for understanding the complex nonlinear behavior of this reaction.
Introduction
The chlorite-iodide reaction was among the first systematically designed chemical oscillators2 and displays a number of other unusual dynamical phenomena such as spatial wave propagation3 and stirring rate ~ensitivity.~Chemical oscillators derived from this reaction, in particular the coupled bromate-chlorite-iodide system, show a wide variety of complex dynamical b e h a ~ i o r . ~ Mechanistic studies of the chlorite-iodide reaction6q7 have yielded encouraging results, but some discrepancies between the experimentally observed and computer simulated behavior exist. One possible source of error lies in the kinetics of the initial stage of the oxidation of iodide by chlorite, specifically in the pH dependence of the reaction rate.' The known kinetics were determined at low acidity (pH 4-8),*-1° while the oscillatory behavior and other dynamical phenomena of interest occur in the pH range 0-4. In the pH range 4-8 the rate law for this reaction was found to consist of three terms, the last two of which are autocatalytic:
where [XI21 = [I21 + [I,-]. However, at higher acidity (PH C-2) (1) Part 54 in the series Systematic Design of Chemical Oscillators. Part 53: Simoyi, R. H.; Kustin, K.; Epstein, I. R. J . Phys. Chem. 1989, 93, 1689. (2) Orbfin, M,; Dateo, c, E,; De Kepper, p,; Epstein, I, R , J , Am, Chem, SOC.1982, 104, 591 1, (3) Weitz, D. M.; Epstein, I. R. J . Phys. Chem. 1984, 88, 5300. (4) Roux, J. C.; De Kepper, P.; Boissonade, J. f'hys. Lett. 1983.97A3168. (5) (a) Alamgir, M.; Epstein, I. R. J . Am. Chem. SOC.1983, 105, 2500. (b) Alamgir, M.; Epstein, I. R. J . Phys. Chem. 1984, 88, 2848. (c) Maselko, J.; Alamgir, M.; Epstein, I. R. Physica D 1986, 19, 153. ( 6 ) Epstein, I. R.; Kustin, K. J . Phys. Chem. 1985, 89, 2275. (7) Citri, 0.; Epstein, I. R. J . Phys. Chem. 1987, 91, 6034. ( 8 ) de Meeus, J.; Sigalla, J. J . Chim. Phys. Phys.-Chim. Eiol. 1966, 63,
TABLE I: Apparent Pseudo-First-Order Rate Constants with [CI(III)I= 1.0 x 10-3 M
0.0200 0.0560 0.07 10 0.0739 0.0887 0.0923 0.103 0.121
0.142 0.213 0.284 0.355 0.426 0.497 0.568 0.788 0.888 0.994
0.300 0.300 0.1044 0.179 0.179 0.1044 0.179 0.1044 0.1044 0.1044 0.1044 0.1044 0.1044 0.1044 0.1044 0.1044 0.1044 0.1044
1.24 1.64 0.632 1.25 1.31 0.768 1.39 0.795 0.861 1.19 1.55 1.48 1.63 2.16 2.18 2.90 3.44 3.64
4.13 5.50 6.06 6.98 7.3 1 7.36 7.76 7.65 8.24 10.30 14.8 14.2 15.6 20.7 20.9 27.8 32.9 34.8
a kinetics study of the analogous chlorite-bromide reaction revealed a rate law that contains a complex [H+] dependence:]' rate = k[Br-] [Cl(III)] [H+]'/([H'] + K , ) (2) where [ ~ ~ ( I I I=) ][c102-] + [ H C ~ O ~and I , K , is the equilibrium constant for the dissociation of chlorous acid. Citri and Epstein7 suggested that a similar term might exist in the rate law for the chlorite-iodide reaction. Such a term would be observed only at low pH. The present study was undertaken to test this hypothesis. ~
~ section
~
~
~
i
Materials. NaC102 (Fisher) was purified by recrystallization. Reagent grade NaC10, (Fisher), NaI (Fisher), and HClO,
453.
(9) Kern, D. M.; Kim, C. H. J . Am. Chem. SOC.1965, 87, 5309. ( I O ) Indelli, A. J . Phys. Chem. 1964, 68, 3027.
0022-3654/89/2093-4698!$01.50/0
( 1 1) Valdes-Aguilera, 0.;Boyd, D. W.; Epstein, I. R.; Kustin, K. J . Phys. Chem. 1986, 90, 6072.
0 1989 American Chemical Society
~
