J. Phys. Chem. 1982, 86, 1327-1332
the independent pair model is therefore an acceptable approximation to the diffusion and reaction in a system containing a few particles with initial Gaussian distributions. A similar idea underlies the model for the kinetics of charge recombination and scavenging in systems containing a number of isolated pairs proposed by Freeman and c o - ~ o r k e r s . ~ lThe - ~ ~ independent pair model described above extends the range of systems covered by showing how to deal with a few-particle system with stochastic methods and allowing a distribution of reaction times for each initial separation distance. 5. Conclusions
This paper describes the developent of a Monte Carlo study of reaction in a radiation-induced spur based on a model involving motion on a three-dimensional lattice. The model is a good approximation to the diffusive motion and reaction of neutral radicals for all times at which Fick's (31) Freeman, G. R.; Fayadh, J. M. J. Chem. Phys. 1965,43,86. (32) Freeman, G. R. J. Chem. Phys. 1965,43,93. (33) Freeman, G. R. J. Chem. Phys. 1967,46,2822.
1327
lam apply. These simulationsare necessary for the testing of analytical or partly analytical approximations of spur reactions. Comparison of the simulations with extant treatments based on prescribed diffusion shows that the latter are unable to reproduce any zero-time correlation between the radicals and also underestimate the rate at short times. The latter problem is alleviated by the use of time-dependent rate constanta although there is no exact theoreticaljustification for their use. The independent pair approximation, on the other hand, shows good agreement with the simulations for three- to six-particle spurs suggesting that it may be appropriate for the modeling of the majority of radiation-induced spurs, where the number of radicals per spur is generally34 less than 10. Important effecta which have not yet been examined are those arising from (i) different types of radical, (ii) reactive products, (iii) Coulomb interactions, and (iv) specific correlations arising from the mode of energy deposition. We are currently examining the first three effects by using both Monte Carlo simulations and the independent pair model.
-
(34) Magee, J. L.; Chatterjee, A. Radiat. Phys. Chem. 1980, 15, 125.
Interaction of Ethene, 2-Methyipropene, and Benzene with the Na+ Ion. 1. Quantum Chemical Study of Gas-Phase Complexes Joachlm Sauer and Detlef Deinlnger Cenbgl Institute of m y s h l Chemisby. Acedemy of SClences of the W ,DDR- 1199 &rlln-AdkKshof, German Democretic Republic, and N M Labatmy, Depertmnt of ~ y s l c s Karl , Merx University, DDR-701 Le@&, &man Lknocratic Republlc (Received:June 3, 1981)
The complexes of ethene, 2-methylpropene, and benzene with Na+ have been investigated by means of ab initio SCF calculations. For the hydrocarbon, the 4-31G basis set and, for the cation, a reoptimized STO-3G basis set have been used. The interaction energy equals -49, -60, and -78 kJ/mol, respectively. Discussion of the errors involved in the calculations and comparison with related experiments show that these values are too low by about 20%. The arrangement of the cation above the plane of the *-electron system is found to be the most stable one. This is the optimum structure for the electrostatic ion-quadrupole contribution to the interaction energy. The charge transfer to the cation proves to be very small and amounts to a few hundreths of an electron. These characteristicsare in agreement with what is known for the cation-n donor complexes. On the basis of the ab initio results, the capability of CNDO/2 with such complexes is assessed.
1. Introduction
The knowledge of the interaction between alkali ions and molecules is a prerequisite for understanding such important processes as separations using zeolites (molecular sieves),' heterogeneous catalysis on surfaces of solids: and ion complexing in biomole~ules.~Moreover, the comparison of affinities toward different cations on the one hand and with proton affinities on the other hand is of general chemical interest.4~~ Whereas only a few gas-phase complexes of Na+ (with Hz06 and with NH3') have been observed, the situation (1) Breck, D. W. 'Zeolite Molecular Sieves";Wiley New York, 1974. (2) Fomi, L.; Invemizzi, R. I d . Eng. Chem. Process Res. Dev. 1973, 12, 455. (3) Laszlo, P. Angew. Chem. 1978, 17, 254. (4) Staley, R K.; Eieauchamp, J. L. J. Am. Chem. SOC.1976,97,5920. (5) Kollman, P.; Rothenberg, St. J. Am. Chem. SOC.1977,99, 1333. (6) Woodin, R. L.; Eieauchamp, J. L. J. Am. Chem. SOC.1978,100,601.
( 7 ) Castleman, A. W., Jr.; Holland, P. M.; Lindsay, D. M.; Peterson, K. I. J. Am. Chem. SOC.1978,100, 6039. 0022-365418212086-1327$01.25/0
with zeolites is very different: in recent years a lot of information about the interaction of Na+ with olefins and aromatics within zeolites has been gathered from various spectrocopic (IRand Raman,"'O NMFt,l1-I4UV15), neutron scattering,16and thermodynamic"J8 experiments. (8) FBrster, H.; Seelemann,R. J. Chem. SOC., Faraday Trans. I 1978, 74, 1435. (9) Carter, J. L.; Yates, D. J. C.; Lucchesy, P. J.; Elliott, J. J.; Kevorkian, V. J. Phys. Chem. 1966, 70, 1126. (10) Freeman, J. J.; Unland, M. L. J. Catal. 1978,54, 183. (11) Hoffmann, W.-D. 2.Phys. Chem. (Leipzig) 1976,257,315. (12) Lechert, H.; Wittern, K.-P. Ber. Bunsenges. Phys. Chem. 1978, 82,1054. (13) Michel, D.; Meiler, W.; Pfeifer, H. J. Mol. Catal. 1975, 1 , 85. (14) Pfeifer, H. Phys. Rep. 1976,26,293. (15) Unland, M. L.; Freeman, J. J. J. Phys. Chem. 1978, 82, 1036. (16) Wright, C. J.; Riekel, C. Mol. Phys. 1978, 36, 695. (17) Bezue, A. G.; Kiselev, A. V.; SedlaEek, Z.; Pham Quang Du Trans. Faraday SOC.1971,67,468. (18) Schirmer, W.; Tha", H.; Stach, H.; Lohae, U. Spec. Pub1.Chem. SOC. 1980, No. 33, 204.
0 1982 American Chemical Society
1328
The Jownal of Physial Chemk?ty,Vol. 86, No. 8, 1982
tz
d n3
2 -
-
Q
2 -
1 -
-1
1'
2 -
Flaw0 1. Structures tor complexes between Na+ and ethene, 2-
methylproperm, and benzene. For structures 1 and 3, r = R ; for structure 2, r = R '/p(C==c).
+
This has caused a need for theoretical information including the stabilization energy and the extent of charge transfer in the cation-hydrocarbon complexes. In particular, interest in the geometry of these complexes has arisen because interpretation of experimental findings often requires knowledge of the structure of sorption complexes. Two possible structures have been considered (Figure 1). In the first one,8JoJ1J6the cation is situated as in sandwich complexes above the ?r-electronsystem (1). This structure may be stabilized by ion-quadrupole interaction. In the second structure, 2, the cation is located within the molecular plane ('A plane). It has been suggestedu that thisstructure could be stabilized by induction f o r m since the polarizability is greater along the C-C axis than in the direction perpendicular to the molecular plane. Several attepts have been made to examine the various contributions to the ion-molecule binding energy by means of semiempirical quantum chemical The results obtained for the equilibrium geometry of such gas-phase complexes using different methods do not agree.= Moreover, semiempirical methods are known to fail badly for intermolecular interaction problems.26 Specifically they may yield values which are too large for the stabilization energy and the amount of charge transfer in interaction complexes. It is therefore necessary to check their applicability by comparison with reliable experimental and/or theoretical data. Nonempirical calculations have been reported only for complexes of ethene with Ag+ (ref 26) and Ni2+(ref 27) or for complexes of Na+ with the n donors H20%tBand (19) Geschke, D.; Hoffmann, W.-D.; Deininger, D. Surf. Sci. 1976,57, 559. (20) Deiniier, D.; Michel, D.; Heidrich, D. Surf. Sci. 1980,100,541. (21) Heidrich, D.;Deininger, D. Tetrahedron Lett. 1977, 42, 3751. (22) Lochmann, R.;Meiler, W. 2 . Phys. Chem. (Leipzig) 1977,258, 1059.
(23) Lochmann, R.;Meiler, W.; Miiller, K. 2. Phys. Chem. (Leipzig) 1980,261, 165. (24) D i l " b e t o v , E. E.; Kiselev, A V.; Lygin, .- V. I. Zh. Fiz. Khim. 1975,49,2984. (25) H o h , P.;Z a h r a d , R. "Weak Intermolecular Interactions in Chemistry and Biology"; Elsevier: Amsterdam, 1980. (26) Baech, H. J. Chem. Phys. 1972,56,441. (27) hermark, B.; Almemark, M.;AlmlBf, J.; Bhkvall, J.-E.; Roos, B.; Stogard, A. J. Am. Chem. Soc. 1977,99,4617. (28) Schuster, P.;Jakubetz, W.; Marius, W. Top. Curr. Chem. 1975, 60, 1. (29) Berthod, H.; Pullman, A. Chem. Phys. Lett. 1980, 70,434. (30) Sauer, J.; H o b , P. &had&, R.J. Phys. Chem. 1980,84,3318. (31) Pullman, A; Berthod,H.; Gresh, N. Znt. J. Quantum Chem. 1976, SlO, 59. (32) Boys, 5.F.;Bemardi, F. Mol. Phys. 1970, 19, 553.
Sauer and Deininger
NH329.H2C0 is the only *-electron molecule whose Na+ complex was the subject of a nonempirical calculation.% Thus, there is a lack of reliable theoretical data for complexes of Na+ with 'A-electron hydrocarbons. In this paper results of ab initio SCF calculations employing the 4-31G basis sets6are presented for the Na+ethene and Na+-2-methylpropene complexes. A preliminary report on similar calculationsfor complexes of ethene with Li+, Na+, and MgH is included in ref 30. Previously, this method was successfully applied for complexes of water with Na+, K+, Mg2+,and Ca2+(ref 31). A comprehensive comparison of proton and Li+ affinities5has been based on 4-31G calculations, too. Calculations using the STO-3G basis have also been performed in this study of the ethene- and 2-methylpropene-Na+ complexes in addition to the benzeneNa+ complex. The errors due to the basis set superposition effect32and poor representation of the molecular properties (quadrupole moment, polarizability) in the chosen basis sets are estimated. The equilibrium geometry and the stabilization energy obtained are discussed in terms of classical ion-quadrupole and induction forces.% Reference is also made to the experimental gas-phase binding energies for Li+ to propene, 2-methylpropene,and benzene. Comparison is made with the results of the semiempirical CNDO/2 and PCILO methods. We find that CND0/2 gives qualitatively correct answers. Therefore, in the second paper of this series,%CND0/2 is chosen as the method for the investigation of interactions of 'A hydrocarbons with Na+ ions attached to different clusters cut off from faujasite-type zeolites. At present such a system cannot be treated by nonempirical methods. From these calculations, conclusions concerning the influence of the surroundings on interactions of a hydrocarbons with cations at different sites in faujasites can be drawn. 2. Computational Methods The interaction energy is calculated as the difference between SCF energies of the complex and ita components (supermolecule approach)
AE = EscF(complex) - EscF(molecule) - PCF(Na+) (1) At this level of approximation, correlation contributions to the interaction energy involving, for example, the dispersion energy are neglected. A simple estimate of the latter, based on the well-known London formula and experimental values of the polarizability, yields about 3 and 10 kJ/mol for the Na+-ethene and Na+-benzene complexes, respectively. Thus, use of eq 1 seems justified considering the accuracy intended in this study (cf. paragraph 3.2). In the ab initio SCF calculations the minimum STO-3G and the split-valence 4-31G basis sets35have been employed. According to a proposal by Pullman, Berthod, and Gresh,3l the 4-31G basis for the hydrocarbons is combined with a reoptimized STO-3G basis for Na+. The 431G basis for Na is not presently available.3s For further information concerning the capability of various basis seta for cation(33) Buckingham, A. D.In "IntermolecularInteractions-From Diatomia, to Biopolymers";Bullman, B., Ed.; Wiley: New York, 1978; p l. (34) Sauer, J.; Deiniier, D. Zeolites In prese. (35) Hehre, W. J.; Lathan, W. A.; DitcWield, R.;Newton, M. D.; Pople, J. A. QCPE 1973,12, 236. (36) On completionof the calculationsfor thh paper, 3-21G and 6-21G basis seta for all atoms up to Ar became available." (37) Binkley, J. S.;Pople, J. A.; Hehre, W. J. J. Am. Chem. SOC.1980, 102,939. Gordon, M.S.;Binldey, J. S.; Pople, J. A.; Pietro, W. J.; Hehre, W. J. 'Self-Consistent Molecular Orbital Methode. Small Split Valence Basis Seta for Second-Row Elements",preprint.
Quantum Chemical Study of Gas-Phase Complexes
The Journal of Physical Chemlstty, Vol. 86, No. 8, 7982 1329
TABLE I: Interaction Energies, A E (kJ/mol), and Equilibrium Distances,” R (nm), for Complexes of Na+ with Ethene, 2-Methylpropene, and Benzene Obtained by Nonempirical4-31G and STO-3G Methods and the Semiempirical CNDOl2 Method complex of Na+ with etheneb
structurea
4-31G
STO-3G
CNDO/2
Ra AE R” AE Ra AE 0.265 -48.5 0.24 -71.4 0.32 -140 0.28 -13.6 0.27 2 -16.6 0.33 -103 2-methylpropene 1 0.26‘ -60.3 0.235d -80.8 0.32e -176e 2 0.27 -30.0 0.26 -31.2 0.325f -121f benzeneh 1 (0.235)8 (-78 F 0.21 -107.1 0.32 -202 2 (0.28)s (-20 F 0.28 -20.3 0.35 -126 Cf. Figure 1. 4-31G results for structure 3 (cf. Figure 1): R = 0.30 nm, A E = -8.6 kJ/mol. Distance a (cf. Figure 1)= 0.125 nm. Distance a (cf. Figure 1)= 0.104 nm. e Corresponding PCILO result” R = 0.37 nm, AE = -50.2 kJ/mol. f Corresponding PCILO result R = 0.34 nm, AE = -83.4 kJ/mol (R. Lochmann, Leipzig, personal communication). g Values extrapolated from STO-3G results; see text. STO-3G results for Na+ above a C-C bond of benzene (structure 1’;cf. Figure 1): R = 0.23 nm, A E = -84.2 kJ/mol. 1
molecule complexes, the reader is referred to ref 25 and 28. 3. Results and Discussion 3.1. Nonempirical Results. The most reliable interaction energies and equilibrium distances obtained in this study for the gas-phase complexes are listed in Table I under the heading “4-31G”. For the hydrocarbons experimental geometries have been used. The values for the benzene-Na+ complex have not been determined directly on the 4-31G level but obtained by extrapolation from STO-3G values. The comparison between 4-31G and STO-3G results for the ethene-Na+ and the 2-methylpropene-Na+ complexes shows that, for structure 2, STO-3G yields almost the same results as 4-31G but, for structure 1, STO-3G largely exaggerates the interaction energy and yields equilibrium distances too short by 0.025 nm. Thus, for structure 2 of the benzene-Na+ complex, the STO-3G values have been directly used whereas the energy of structure 1 has been extrapolated by means of eq 2. Details are given below (cf. paragraph 3.2). The equilibrium distance was obtained by adding 0.025 nm to the STO-3G value. The 431G results clearly favor structure 1 compared to structure 2, while the stabilization for structure 3 (in case of ethene) is still smaller than for structure 2. For benzene, structure 1’ (cf. Figure 1)in which the Na+ approaches a C-C bond directly from above is leas favored than structure 1. 3.2. Reliability of Nonempirical Results. Basis Set Superposition Error (BSSE). This error is due to the possibility that, in the complex, any subsystem can make use of the basii set of another subsystem. Table II contains estimates of the BSSE obtained by the Boys-Bernardi counterpoise methodF2 A4A) is the extra stabilization which is gained if the atomic orbitals at the other subsystem are added to subsystem A. Table II shows that the 4-31G basis together with a reoptimized STO-3G basis for the cation is a reasonable combination because the BSSE is of comparable magnitude for both subsystems. The difference in Ae between the two structures 1 and 2 is negligible when compared with the difference in the total interaction energy. Similar results can be expected for 2-methylpropene. In the case of the more restricted STO-3G basis, the BSSE will be generally larger (Table 11). It is particularly large for structure 1. This can be ascribed to the lack of flexibility of STO-3G wave functions. Consequently,the hydrocarbon makes extensive use of unoccupied orbitals at Na+ to lower ita energy. This is also connected with an artificially high charge transfer from the hydrocarbon to Na+ for structure 1 (Table V, cf. paragraph 3.4).
TABLE 11: Boys-Bernardi Estimate, A e (kJ/mol), of the Basis Set Superposition Errof 4-31G structureb (Na’) (hc)C
STO-3G (Na’) (hc)C ethene 1 -2.0 -2.5 -2.9 -38.5 -1.9 -2.2 2 -2.3 -0.2 2-methyl1 -3.0 -36.7 propene 2 -2.3 -2.6 benzene 1 -5.8 -48.3 1 -3.8 -39.0 2 -2.6 -2.5 a See ref 32. a e ( A ) denotes the energy lowering for the subsystem A if the functions of the other subsystem are added to the basis set of A. Cf. Figure 1. Hydrocarbon. complex
The use of Ae for correcting the interaction energy has been proposed: 98 hE,,(A,B)
AE(A,B) - f[Ae(A) + Ae(B)I
(2) Taking the 4-31G results for ethene and 2-methylpropene as reference data, eq 2 can be exploited for extrapolating the interaction energy for structure 1of the benzene-Na+ complex. A value off = 0.54 is obtained, which yields AE = -78 kJ/mol. For structure 2 the Ac values are of reasonable magnitude even with the STO-3G method and the STO-3G energy is therefore adopted for this structure with the benzene-Na+ complex. From Table I1 it can be concluded that the 4-31G interaction energies given in Table I are overestimated by 10-20% on account of BSSE. Molecular Properties. In the framework of a classical approach, complexes of ethene and benzene with cations will be mainly stabilized by the ion-quadrupole interaction, Ei,, and the induction term, Eind(ion-induced dipole interaction): 33 Ei-q
= qiQ,zM/(2@)
Eind
= -q?azzM/(2fl)
(3)
where qi is the charge of the ion, QzzMand aZzM are the components of the quadrupole and the dipole polarizability tensors along the line connecting the ion and the center of gravity of the molecule, and r is the distance of the ion to the center of gravity. Hence, the reliability of the results will largely depend on the quality of the quadrupole moment and the polarizability in the basis set chosen. For ethene the following results for the quadrupole moment have been obtained by 4-31G calculations (cf. Figure 1): Q,, = -2.38, Qyy = 1.29, and Q,, = 1.08 au.39 (38) Johameen, A.; Kollman, P.; Rothenberg, S. Theor. Chim. Acta 1973, 29, 167. (39) 1 au of quadrupole moment = eaez N 4.48616 X
lo4 C m*.
1330
Saver and Delninger
The Jownal of Physlcal Chemistry, Vol. 66,No. 6, 1962
TABLE 111: Classical Ion-Quadrupole and Induction Energy (kJ/mol) (eq 3) of the Ethene-Na' Complex at the Equilibrium Distancea Compared with 4-31GResults
1 (zIb 2 (YIb 3 (XIb -49.7 12.0 15.9 -57.3 13.5 19.0 -57.5 f f -10.4 -26.3 sv -27.1 -26.8 -29.0 -29.0 -25.8 -34.1 -47.8 -8.6 A E (4-31G) -48.5 -13.6 a The 4-31Gvalues have been used thorougly (cf. Table Cf. Figure 1 for structure of the complex and direcI). tion of approach of the cation. Quadrupole moment obtained in this study. Quadrupole moment obtained by ab initio calculations using a double-f + polarization bask4" e Experimental value for the quadrupole moment.* No accurate values known. The data published recently4' are in error by 25%, and several assumptions had to be made. g Polarizability (sum-over-statesformula) obtained by a split-valence basis.@ Polarizability (sumover-states formula) obtained by a double-r + polarization basis.40 Experimental values for the polarizability. energy
Ei-q, 4-31GbasisC Ei-q, Dr + P basisd Ei-q, experimente Eind, basisg Eind, Df + P basish Eind, experiment'
The values are 13%, 11%, and 16% smaller than the results obtained by using a polarized basis set,40-2.74,1.45, and 1.29 au, respectively (experimentalvalue Q,, = -1/2(Qxt + Q), = -2.75 au). Because the deviations are fairly small and of similar magnitude in both the z and y directions, the relative stability of structures 1 and 2 will be correctly described by 4-31G calculations. With the induction term the situation is more complicated. First, the 4-31G data for the dipole polarizability is not available. We may expect, however, that the 4-31G basis would yield results similar to the split-valence basis employed by Mulder et aL40 The comparison with polarized basis sets and experimental values shows that fairly reasonable results are obtained even at the split-valence level for the components along the x and y axes (i.e., within the molecular plane; cf. Figure l), but the value in the z direction is far too low. That means that the interaction energy will become significantly more negative only for structure 1 when better basis sets are used (cf. Table 111). Hence, the preference of structure 1 will not be changed. A quantitative assessment of the error is difficult, however, because the description of the polarizability may be improved in the complex due to the presence of the atomic orbitals of Na+ which will diminish the basis set dependence of the induction term. Moreover, the numerical values are changed if, instead of sum-over-state formulas, another procedure is used for determining the polarizability.40 Table I11 shows the energy contribution calculated (eq 3) by means of accurate values for the molecular properties taken either from experiments or from fairly extended calculations. They confirm the relative stability of structures 1-3 for the etheneNa+ complex found by 4-31G calculations. The only effect that using the 4-31G basis has on these classical terms is by way of the equilibrium distance. A detailed analysis shows that the ion-quadrupole term is the largest factor favoring the stability of structure 1over structure 2. Moreover, the induction term favors structure 1, too. The effect of the larger polarizability in the y direction is outweighed by the shorter distance r for structure 1 compared with that for structure 2 (cf. Figure
TABLE IV: Classical Ion-Quadrupole and Induction Energy (kJ/mol) (Eq 3 ) of the Benzene-Na+ Complex at the Equilibrium Distancea energy lb 2b Ei-q, double-r basisC -203 20.3 Ei-g, experimentd -182 18.2 Eind, double-r basise -129 -28.7 Eind, experimentf -137 -28.8 Cf. Table I. Cf.Figure 1 for structure of the complex. Quadrupole moment obtained by ab initio calculations using a double-r basis set.42 Experimental value of the quadrupole e Polarizability calculated by using a double-r basis set.42 f Experimental values of the polari~ability.~~
*
Table IV shows similar results for the Na+-benzene complex. Again structure 1 is preferred to structure 2 not only through the ion-quadrupole term but also through the induction term in agreement with the results given in Table I. In the case of 2-methylpropene, a dipole moment exists in the direction of the C=C bond, due to the methyl groups. Thus, the stability of structure 2 depends upon the degree to which the dipole moment is accurately predicted. A dipole moment of 0.46 D was found by using the 4-31G basis and 0.40 D by using the STO-3G basis. Both of these correspond satisfactorilyto the experimental value of 0.50 D.43 Concluding Remarks. The analysis of BSSE and the quality of molecular properties within the basis sets used show the following: (1)The preference of structure 1 to structure 2 is not expected to change when extending basis sets. Rather, the energy difference found between both structures will be larger because of a larger quadrupole moment and a considerably larger polarizability perpendicular to the molecular plane. (2) A quantitative assessment of the errors connected with the quadrupole moment and the polarizability is difficult. From experience with similar complexes, from the discussion above, and taking into consideration BSSE, we estimate that the 4-31G interaction energies (cf. Table I) for structure 1may be too low by up to 20%. 3.3. Comparison with Results of Related Experiments and Calculations. As already mentioned, no gas-phase enthalpies4 are available for a direct comparison with the interaction energies calculated. Some use can be made, however, of the enthalpies4 for the binding of Li+ to propene (about -95 kJ/mol), to 2-methylpropene (about -115 kJ/mol), and to benzene (-155 kJ/mol). The values for propene and 2-methylpropene have been derived from the diagram contained in ref 4. The accuracy of these values is lt8 kJ/mol. From these data a value of about -75 kJ/mol was extrapolated for the Li+-ethene complex, which compares well with the 431G result of -63 kJ/mol.30 Expression 3 for the ion-quadrupole term suggests that the ratio of Li+ and Na+ binding enthalpies is approximately proportional to the ratio [r(Li+)+ r(C)IS/[r(Na+)+ r(C)I3 N 0.70 involving the ionic radii and the carbon van der Waals radius. If the Li+ binding enthalpies are reduced by this ratio, we arrive at values of about -80 and -110 kJ/mol
1).
(42) Mulder, F.; van Dijk, G.;Huiszoon, C. Mol. Phys. 1979,38,567. (43) Nelson, R. D., Jr.; Lide, D. R.; Maryott, A. A. Natl. Stand. Ref. Natl. Bur. Stand.) 1967, No. 10. Data Ser. (US.,
(40) Mulder, F.; van Hemert, M.; Wormer, P. E. S.; van der Avoird, A. Theor. Chim. Acta 1977.46. 39. (41)Gray, C. C.; Gubbins, K. E.; Dogg, I. R.; Read, L. A. A. Chem. Phys. Lett. 1980, 73, 278.
(44)Although it is well-knownfrom thermodynamics that enthalpies and energies of interaction are not identical, a comparison of them yields useful fmt information. Interaction enthalpies are usually leas negative quantities than interaction energies because of zero point vibrations of the intermolecular degrees of freedom.
Quantum Chemical Study of Gas-Phase Complexes
TABLE V: Charge Transfer in Na+-Hydrocarbon Complexes Obtained by Different Methods change in electron population at Na+ (in e ) strue STOcomplex turea 4-31Gb 3Gb CND0/2d Na+-ethene 1 0.024 0.103 0.131 1 0.023 0.106 0.161 Na+-2-methylpropene 1 0.145 0.104 Na+-benzene Na+-ethene 2 0.009 0.025 0.109 Na+-2-methyl2 0.011 0.030 0.125c propene Na+-benzene 2 0.029 0.112 a Cf. Figure 1. Mulliken gross atomic opulation. Corresponding PCILO result: 0.172. Electron density.
B
for the Na+-2-methylpropene and Na+-benzene complexes, respectively.& The calculated values in Table I amount to 75% and 71% of these estimates. Thus, the indirect comparison with Li+ binding enthalpies leads to the same conclusions as those which have been drawn in the previous paragraph. On the other hand, the binding enthalpies for the h y d " with Na+ sites in zeolites (heats of adsorption) may be used. Because the electrical field created by the cation is reduced within the zeolite," the heats of adsorption should form lower limits (in absolute values) for the gas-phase interaction energies. The relevant values are -37 and -80 kJ/mol for ethene" and benzene,'8 respectively, supporting the view that the 4-31G values in Table I are underestimated. Finally, the preference of structure 1 has been found to be in agreement with spectroscopic results8Jo-12J6for 7r hydrocarbons adsorbed in zeolites. This is not due to the zeolite environment, as will be shown in the forthcoming paper.% Our conclusion that the structure of the Na+ complexes with the 7r donors ethene, 2-methylpropene, and benzene is determined by the electrostatic ion-quadrupole contribution to the interaction energy fits in with the results previously obtained for Li+ complexes of other 7r donors, Nzls and HzC0.28 The linear structure of the Li+-N2 complexMand the arrangement of Li+ coaxial to the C-O bond in H2CO-Li+ (ref 28) are the structures optimal for stabilization by ion-quadrupole and ion-dipole interactions, respectively. Generally, the results reflect the role of electrostatic contributions (see, e.g., ref 4 and 5) in the interaction of alkali ions with molecules. 3.4. Applicability of CNDOIB and PCILO to the Complexes under Study. The comparison with the nonempirical reference data (4-31G-level results) shows the CNDO/2 method to be qualitatively correct for the cation-molecule complexes investigated4' (cf. Table I). Although both the equilibrium distances and the absolute values of the interaction energies are far too large, all trends are properly reproduced. Structure 1 is clearly preferred to structure 2, which is also reflected by shorter interaction distances for structure 1. Even the energy (45) The ratio of the binding enthalpies of Li+ and Na+ withiin X-type zeolite~l'ie 0.73. (46)Staemmler, V. Chem. Phvs. 1975. 7. 17. (47) The attempt to use the &proved INDO parameter set proposed by Gordon" failed badly. With the Na+-ethene complex, interaction energies of 864 kJ/mol (R = 0.18 nm)and 632 kJ/mol (R = 0.185 nm) have resulted for structures 1 and 2, respectively. (48)Gordon, M. S.; Bjorke, M. D.; Marsh, F. J.; Korth, M.S. J. Am. Chem. Soe. 1978,100, 2670.
The Journal of Physical Chemlstty, Vol. 86,No. 8, 7982 1331
difference between the two structures is of the right order of magnitude. Additionally,the increase in the interaction energy in the series ethene, 2-methylpropene, benzene is fairly well reflected. This fits in with the previous findings which showed that CNDOI2 is capable of reproducing small energy differences between u and 7r complexes of protonated benzene. Moreover, it correctly describes the different modes of approach toward benzene for protons, on the one hand," and for the Li+ and Na+ cations, on the other hand.21 In the neighboring field of cation-n donor interaction, CNDOI2 has also proved to be for qualitative purposes, provided that certain structural restrictions are imposed. In contrast to CNDO/2 and the nonempirical reference data, PCILO prefers structure 2 to structure 1 for the 2-methylpropene complex. While the energy for structure 1 is of the right order of magnitude (-50 kJ/ mol),23that for structure 2 is largely overestimated (-83 kJ/mol). The equilibrium distances (0.37 and 0.34 nm) are too large. Similar observations hold for 1-butene,where the energy difference found between structures 1 and 2 is only 4 kJ/moLZ3 Preliminary PCILO calculations for the interaction of Li+, Na+, and Mg2+with H20have not been encouraging either.60 Whereas the Li+-H20 complex is well described, the method fails with Na+ and Mg2+. Such difficulties of PCILO with systems involving small distances between atoms with lone pairs and atoms with vacant orbitals have recently been pointed In summary, CNDOI2 is considered to be an appropriate method for investigating the interaction between hydrocarbon molecules and cationic binding sites, e.g., in zeolites.34 However, one must not expect quantitatively correct answers but rather relative estimates. 3.5. Charge Transfer in Cation-7r Hydrocarbon Complexes. Although the charge transfer within a complex cannot directly be related to an observable quantity, it is widely discussed in qualitative approaches in theoretical chemistry. Table V shows the amount of charge transfer in terms of Mulliken's gross atomic population52obtained by the different methods for the systems investigated. The 4-31G values in Table V indicate a very small charge transfer to the cation. As expected, it is larger for structure 1 than for structure 2. The STO-3G results for structure 2 are of the right order of magnitude, but for structure 1 the charge transfer is exaggerated because of the different magnitude of the BSSE for both structures. Quite similar observations have previously been made for complexes of cations with n-donor molecules.28 CNDO/2 exaggerates the amount of charge transfer by up to 1 order of magnitude. PCILO gives even poorer results23(see also ref 51). This failure of semiempirical methods is obviously connected with their tendency to simulate chemical bonds even in nonbonded complexes. Consequently, the charge transfer in cation-7r hydrocarbon complexes is expected to be very small, and caution is necessary with minimum basis or semiempirical results.52
Note Added in Proof. The recent study of Sunner et al. on benzene-K+ gas-phase complexes (Sunner, J.; Nishizawa, K.; Kebarle, P. J.Phys. Chem. 1981,85,1814) (49) Heidrich, D.; Grimmer, M. Znt. J. Quantum Chem. 1975,9,923. (50) Sauer, J., unpublished results. (51) Lochmann, R.; Deininger, D. J . Comput. Chem., submitted for publication. (52) Our conclusions are not affected by referring to Mulliken's definition of charges. If the charge transfer in cation-water complexes is analyzed by means of integrating the electron density distribution over subspaces, it is found to be even smaller." (53) Battaglia, M. R.; Buckingham, A. D.; Williams, J. H. Chem. Phys. Lett. 1981, 78, 421.
1332
J. Phys. Chem. 1082, 86, 1332-1333
involves STOdG calculations on different structures of benzene-Na+ complexes, the results and conclusions being in full agreement with those of this paper. Acknowledgment. We are indebted to Professor W.
Schirmer (Berlin) for continuous support and interest in this work. Dr. M. Urban (Bratislava)has kindly performed the quadrupole mome_ntcalculations. We are grateful to Professor R. Zahradnik (Prag) for substantial improvements to the manuscript.
Gas-Phase Chemistry of Atomic Metal Cations with Metal Carbonyls. A Novel Route to MlxebMetal Clusters Manfred M. Kappos'. and Ralph H. Slaley*'b h p m n t of chemisay, Massachusetts Institute of T e ~ h n o b ~Catnbr&lge, y, Massachusetts 02139 (Received: June 17, 1981)
Ion cyclotron resonance spectroscopy with a pulsed-laser volatilization-ionization source of atomic metal cations is used to investigate the gas-phase chemistry of various atomic metal cations, M+, with Cr(CO)6and Ni(CO)& The initial products are typically bimetallic-carbonyl cations, MM'(CO),+ with n = 4-5 for M' = Cr and n = 2-3 for M' = Ni. These react further with Cr(CO)6or Ni(C0)4by condensation with loss of carbonyls to give small mixed-metal-cluster-cation species. Reactivity of the bimetallic carbonyl cations resembles that of metal carbonyl cations rather than atomic metal cations. Carbon monoxide is readily displaced by a variety of organic molecules that are more basic ligands than CO.
Introduction Transition metal clusters play an important, though poorly understood, role in heterogeneous catalysis and are currently the subject of intensive investigatiom2 An interesting class of clusters are those that contain two different transition metals. These mixed-metal clusters are particularly interesting because of the role one metal can play in modifying the reactivity of the other. Studies of mixed-metal clusters have been hampered by a lack of general procedures for the preparation of specific clusters. The reaction of atomic metal cations with metal carbonyls in the gas phase affords a facile route to the designed synthesis of small mixed-metal-cluster-cation species. This paper is the first report of such reactions. Studies of the reactions of various transition-metal cations with Cr(CO)6 and Ni(CO)4 are reported along with studies of the ion chemistries of the mixed-metal-carbonyl-cation products with various molecules. Experimental Section Experiments were carried out with ion cyclotron resonance (ICR) instrumentation and techniques which have been previously described.*' Various metal targets are mounted in the end plate of the ICR cell. The output of a pulsed YAG laser is focussed onto a selected target to produce atomic metal cations. For each metal studied, the mass spectrum for the source with no added gases shows the naturally occurring isotope abundance ratios. Chem(1) (a) Institute for Inorganic and Physical Chemistry, University of Bern, CH-3012 Bern, Switzerland. (b) Central Research Department, Experimental Station, Du-Pont Company, Wilmington, DE 19898. (2) For a review, see Gladfelter, W. L.; Geoffroy, G. L. Adu. Organometal. Chem. 1980,18,207-73. A h ,a novel method for laser production of supersonic metal cluster beams has recently been reported: Dietz, T. G.; Duncan, M. A.; Powers, D. E.; Smdey, R. E. J. Chem. Phys. 1981, 74, 6511-2. (3) Uppal, J. S.; Staley, R. H. J. Am. Chem. SOC.Submitted for publication. (4) Uppal, J. S.; Staley, R. H. J. Am. Chem. SOC.Submitted for publication. (5) Jones, R. W.; Staley, R. H. J. Am. Chem. SOC.1980,102,3794-8. (6) Uppal, J. S.; Staley, R. H. J. Am. Chem. SOC.1980,102,4144-9. (7) Jones, R. W.; Staley, R. H. J . Am. Chem. SOC.Submitted for publication.
TABLE I: First-Step Reactions of Various with Cr(CO),a Atomic-Transition-Metal Cations, M +, MCr(CO),+ MCr(CO),+ M+ + co + 2co other products Ti+ 1 99 V+ 60 40 Cr 30 10 60% Cr,(CO),+ Mn 0 20 80% MnCr(CO),+ Fe 5 95 co 0 70 20%Cr(CO),+ + Co(CO), 10% Cr(CO),+ + Co(C0) Ni+ 1 19 60% NiCr(CO),+ -I.3CO 20%Cr(CO),+ + Ni Product distributions are given as percentages, ~~
~
+
+
+
+
icals used were from commercial sources. Ni(C0)4 and Cr(CO)6were purchased from Alfa Products. Ni(C0)4was purified by vacuum distillation. All other chemicals were degassed by repeated freeze-pump-thaw cycles before use.
Results and Discussion The first-step reactions of atomic transition-metal cations, M+, with Ni(C0)4 and Cr(C0)6 are similar. Production of MNi(CO)3+and MNi(C0I2+is seen exclusively, reactions 1and 2, when Ni(C0)4reacts with Ti+ (100, 0 ) ,
Cr+, (70,30),Mn+ (95, 5), Co+ (90, lo), Ni+ (70,30),and Cu+ (100,O)where product distributions for reactions 1 and 2, respectively, are given in parentheses as percentages for each atomic metal cation reactant. Condensation with loss of one or two carbon monoxide molecules is also a commonly observed first-step reaction of atomic metal cations with Cr(C0)6(Table I). Other reactions observed with Cr(CO)6 are condensation with loss of three co's for Ni+, condensation with fragmentation giving two metalcontaining products for Co+, and direct condensation (no neutral product) for Cr+ and Mn+ (Table I). An apparent charge-transfer process is also observed for Ni+, but the relative ionization potentials for Ni (7.64 eV) and Cr(CO)6 (8.14 eVI8 suggest that some other mechanism such as 0 1982 American Chemical Society
