2278
J. Phys. Chem. 1991, 95, 2278-2282
energy potentials given by Williams’ potential and by MM3 force field are close to those given by the a b initio method, the carbon-carbon distances of the potential minima given by MM2 force field are shorter. The depths of the potentials of the dimers A and B obtained at the MP4(SDTQ)/6-31 lG(2d,2p) level are -0.128 and -0.274 kcal/mol, respectively. The calculated interaction energies at MP3/6-311G(3d,3p) for the same geometries are -0.152 and -0.336 kcal/mol, respectively. The depths of the potential of the dimers A and of B obtained by Williams’ potential are -0.168 and -0.398 kcal/mol, respectively. Those obtained by MM3 force field are -0.1 57 and -0.374 kcal/mol, respectively. These values are 3-1 1% larger than the values obtained at the MP3/6-311G(3d,3p) level calculation. The cause of the difference between the ab initio potentials and those obtained by Williams’ potential and by MM3 is not certain. There are a lot of possible reasons for this difference. The empirical potentials are optimized to various hydrocarbon molecules. Thus they can be different from the interaction potential of methane dimer. The crystal-derived potential could include many-body effect. The molecular mechanics potentials depend on the degree of molecular strain. The potential depths obtained by using MP3 level electron correlation correction might be 7-12’31 shallower than that obtained by using the MP4(SDTQ) correction. The BSSE given by the counterpoise method could be slightly larger than the real BSSE.4749 The intermolecular interaction potentials calculated by the MM2 force field have significantly deeper minima than those given by the former three types of calculations. The depths of the potentials of the dimers A and B given by MM2 are -0.293 and -0.806 kcal/mol, respectively. The depths of these potentials are (47) Schwenke, D. W.; Truhlar, D. G.J . Chem. Phys. 1985, 82, 2418. (48) Gutowski, M.;Lenthe, J. H. v.; Verbeek, J.; Duijneveldt, F. B. v.; Chalasinski, G. Chem. Phys. L t r . 1986, 124, 370. (49) Frisch, M.J.; Del Bene, J. E.;Binkley, J. S.;Shaefer 111, H.F. J . Chem. Phys. 1986,84, 2279.
larger than those obtained at the MP3/6-31 lG(3d.3~) level calculation as much as 93 and 140%. Recently, a lot of defects in the MM2 force field were found and the improved force field MM3 was p r o p o ~ e d Probably . ~ ~ ~ ~ the ~ ~overestimation ~~ of the attractive interaction energy of MM2 force field was a cause of the defects of this force field. The shape of the potential of the repulsive region of the dimer A given by MM2 force field is steeper than that obtained by MP4(SDTQ)/6-311G(2d,2p) level calculation. The potentials of this region given by Williams’ potential and by MM3 are close to the a b initio potential. The potential of the repulsive region of the dimer B given by MM3 is close to that from the same level ab initio calculation. The calculated potential of this repulsive region by Williams’ potential is steeper and that by MM2 force field is shallower than the a b initio potential. Conclusion The calculations of the intermolecular interaction energies of two orientations of methane dimers with electron correlation and BSSE correction using various levels basis sets showed that the calculated dispersions energies depended greatly on the basis set used. The calculations using a crude basis set underestimated the dispersion energies. The calculated intermolecular interaction potentials of the methane dimers obtained by the second- and third-order Maller-Plesset perturbation calculations were slightly shallower than those by the fourth-order (MP4(SDTQ)) calculation. The BSSE’s of the methane dimers estimated by the counterpoise method were about 30% of the calculated interaction energies even at the MP4(SDTQ)/6-311G(2d,2p) level for the dimers of the potential minima. The comparison of the MP4(SDTQ)/6-3 1IG(2d,2p) level intermolecular interaction potentials with those derived from empirical nonbonded potentials showed that the potentials from the ab initio calculations were much shallower than those derived from the MM2 force field but were close to those derived from Williams’ potential and from the recently reported MM3 force field.
Theoretical Study of the Bonding of Sc, Y, and La Singly Charged and Dipositive Ions to C2H2,C2H4,and CBHs Charles W. Bauschlicher, Jr.,* and Stephen R. Langhoff NASA Ames Research Center, Moffett Field, California 94035 (Received: March 19, 1990; In Final Form: July 10, 1990)
The interaction of the Sc and Y singly charged and dipositive ions with C2H2,C2H4, and C3Hs is studied using electronic structure calculations that include high levels of electron correlation. These results are compared with comparable calculations performed previously for La+ and La2+. For C2H2and CzH4, all three metal ions insert into the C-C r bond, making a three-membered ring. The optimal structures for the MC3H6+ions all involve rearrangement to make a four-membered ring. The strength of the metal-ligand bond for the singly charged ions follows the order La > Sc = Y. In contrast, the bonds involving the dipositive ions are electrostatic, so that the binding energy increases as the size of the ion decreases, leading to the trend Sc > Y > La.
Introduction The interaction of ligands with metal ions has become a very active area of research, in part due to the numerous experimental methods that have been developed to study ions in the gas phase.I-2 The determination of accurate experimental dissociation energies is leading to new insight into the nature of metal-ligand bonding. (1) (2)
Armentrout, P. B.; Georgiadis, R. Polyhedron 1988, 7, 1573. Buckner, S.W.; Freiser, B. S.Polyhedron 1988, 7 , 1583.
The singly charged ions of the transition metals on the left side of the row are interesting, not only because of the availability of experimental data but also because of the diverse reactions they undergo with hydrocarbon^.^.^ Since the second ionization potential (IP) of Sc, Y, and La is lower than the first IP of many (3) Sunderlin, L. S.; Aristov, N.; Armentrout, P. B. J . Am. Chem. Soc. 1987, 109, 78. (4) Sunderlin, L. S.; Armentrout, P. B. J . Am. Chem. SOC.1989, 1 1 1 , 3845.
This article not subject to US.Copyright. Published 1991 by the American Chemical Society
The Journal of Physical Chemistry, Vol. 95, No. 6, 1991 2279
Bonding of Sc, Y, and La Positive and Dipositive Ions
TABLE I: Comparison of Our Recommended Binding Energies (kcal/mol) with Those Derived from Experiment C2H2 metal ion sc+
Y+ La+ sc2+ Y2+ La2+
theorv 53 53 66 50 47 44
expt 77.9 f 2.3" 270.8" 265.0," 38 f 6d 33 i 6d
C2H4 theory 36 33 46 51 47 41
C3H6
expt 235.1 i 1.2," 40 i 5b 228.1," >33c 223.3," 233e
theory 41 43 51 64 54 48
expt
230: 63
* 6d
41 i 6 d
"Armentrout and co-workers, refs 3 and 4. bTolbert and Beauchamp, ref 9. CHuanget al., ref 8. dMacMahon and Freiser, ref 7.
hydrocarbons, the interaction of the latter with the dipositive ions is also of i n t e r e ~ t . A ~ previous study6 of La+ and La2+ bonding to C2H2, C2H4, and C3Hqshowed that the singly charged ions formed a chemical bond with the ligands, while the dipositive ion bound electrostatically. Thus by studying the singly charged and dipositive ions on the left side of the row, both chemical bonding in the singly charged ion and electrostatic bonding in the dipositive ion can be investigated for the same metal. Armentrout and co-workers3v4have studied the reactions of Sc', Y+, and La+ with C2H2and C2H4 and found binding energies that varied as Sc > Y > La. In contrast, the binding energies vary4 as Y > La > Sc for the process MH2+ M+ + 2H, where two metal-ligand bonds are broken, in analogy with reactions involving MC2H2+and MC2H4+ions. The experimental data3,4-7-9summarized in Table I indicate that in many cases only lower bounds to the binding energies have been established. For comparison our recommended values, based on correcting our calculated values for limitations in the theoretical treatment, are also included in Table I. The experimental binding energies of Armentrout and co-worker~~+~ tend to be over 40 kcal/mol larger for MC2H2+than for MC2H4+. Frieser and co-workers7**reported similar binding energies for LaC2H2+and LaC2H4+,but previous calculations6 suggested that their LaC2H2+value is too small. Binding energies for the dipositive ions have been measured' only for LaC2HZ2+ and LaC3Hs2+. In this work we study the interaction of the singly charged and dipositive ions of Sc and Y with C2H2,C2H+ and C3H6 (propylene). By combining this work with the previous study6 of La+ and La2+ with the same hydrocarbons, the trends for this column of the periodic table can be identified. The theoretical binding energies allow a critical assessment of the experimental data, as well as elucidating the trends in the binding energies.
-
Computational Methods The Sc basis set is of the form (14s 1l p 6d 3f)/[8s 6p 4d If]. The f functions are based on a three-term fitlo to a Slater-type orbital with an exponent of 1.6. This basis set is described in more detail in ref 11. For Y we use the relativistic effective core potential (RECP) developed by Hay and Wadt.I2 In this RECP, the outermost core orbitals, the 4s and 4p, are in the valence shell. The valence electrons can thus be correlated, since the valence orbitals have the correct nodal structure.13 The supplemented valence basis sets described in ref 14 are employed, yielding a Y basis set of the form (6s 5p 5d)/[5s 4p 4d]. In the YH2+ calculations the (3f)/[ l f] polarization set from ref l l is added. For the LaH2+ calculations, we use the same La basis as used pre(5) Freiser, B. S. Private communication. (6) Rosi, M.; Bauschlicher, C. W. Chem. Phys. Lett. 1990, 166, 189. (7) MacMahon, T.; Freiser, B. S. Private communication. (8) Haung, Y.;Wise, M. B.; Jacobson, D. B.; Freiser, B. S . Organometallics 1987, 6, 346. (9) Tolbert, M. A.; Beauchamp, J. L. J. Am. Chem. Soc. 1984,106,8117. (IO) Stewart, R. F. J. Chem. Phys. 1970, 52, 431. (11) Bauschlicher, C. W.; Langhoff, S. R.; Partridge, H.; Barnes, L. A. J . Chem. Phys. 1989, 91, 2399. (12) Hay, P. J.; Wadt, W. R. J . Chem. Phys. 1985.82, 299. (13) Rohlfing, C. M.;Hay, P. J.; Martin, R. L. J. Chem. Phys. 1986,85, 1447. (14) Langhoff, S.R.; Pettersson, L.G. M.;Bauschlicher, C. W.; Partridge, H. J . Chem. Phys. 1987.86, 268.
TABLE 11: Equilibrium Structures for C2Hz,CzHa and CZHe AN0 Denotes That the AN0 Set Has Been Used" r(C-C) r(C-H) L(HCH) SCFb MCPF' MCPF(AN0) exptd
C2H2 1.20 1.24 1.21 1.203
1.05 1.08 1.06 1.061
SCF MCPF MCPF(AN0) exptd
C2H4 1.33 1.38 1.33 1.330
1.07 1.10 1.08 1.076
116.4 116.8 116.8 116.6
SCF MCPF exptd
1.54 1.57 1.53 1
1.08 1.11 1.096 r(C-C)
107.8 108.0 107.8 r(C-H)
C2H6
r( C=C)
C3H6
SCF exptC
1.33 1.318
1.51 1.501
1.07-1.08
"Bond lengths are in Angstroms and bond angles are in degrees. bGeometry optimized at the S C F level. cGeometry optimized at the MCPF level. Reference 24.
viously.6 Note that the treatments for Sc and Y are of approximately the same quality as the valence [4s 4p 3d If] contracted basis set in conjunction with the RECP treatment of La in a previous study.6 For C and H, we use both valence double-[, VDZ,and large atomic natural orbitalI5 (ANO) basis sets. The C and H VDZ basis sets are the (9s 5p)/[3s 2p] and (4s)/[2s] sets developed by Dunning and Hay16 from the primitive set of Huzinaga.17 The C and H A N 0 basis sets are the (13s 8p 6d 4f)/[5s 4p 2d I f ] and (8s 6p 4d)/[3s 2p Id] sets described in ref 18. For the MH2+ calculations the H basis set is improved to (8s 6p 4d)/[4s 2p Id]. Only the pure spherical harmonic components of the basis functions are included. All calculations used the modified coupled-pair functional method (MCPF),I9 which is based on a self-consistent-field (SCF) zeroth-order wave function. This provides an accurate treatment of electron correlation, because the S C F occupation is a good zeroth-order representation in all cases. In these calculations we correlate all of the electrons except the C 1s-like, the Y 4s- and 4p-like, and the Sc 1s through 3p-like electrons. For all of the MH2+ calculations including LaH2+ only four electrons are correlated. This is slightly different from previous work, where the La 5s and 5p electrons were also correlated because the La 5s and 5p orbitals mixed with the C 2s-like orbitals due to nearly equal orbital energies. However, this should not result in a significantly different level of treatment for La, as the 5s and 5p (15) Almlbf, J.; Taylor, P. R. J . Chem. Phys. 1987, 86, 4070. (16) Dunning, T. H.; Hay, P. J. In Methods of EIectronic Structure Theory; H. F., Schaefer, Ed.; Plenum Press: New York, 1977; pp 1-27. (17) Huzinaga, S.J. Chem. Phys. 1965, 42, 1293. (18) Bauschlicher, C. W.; Lannhoff, S.R.; Taylor, P. R. J. Chem. Phys. 1987, 87, 387. (19) Chong, D. P.; Langhoff, S. R. J . Chem. Phys. 1986,84, 5606. See also: Ahlrichs, R.; Scharf, P.; Ehrhardt, C. J. Chem. Phys. 1985. 82, 890.
2280 The Journal of Physical Chemistry, Vol. 95, No. 6, 1991
Bauschlicher and Langhoff TABLE III: EgulUbrlum S t " for t k sspoly Charged llld D i p t t i v e Ions of Sc, Y,and La Interacw with C2H, .nd C2KU r(C-0 r(C-H) r(M-BMPb) H-bendc BE MCzHz+('AJ
sc SCFd MCPF' MCPF(AN0) Y SCF MCPF La MCPF
1.35 1.36 1.33
1.07 1.09 1.08
1.90 1.96 1.93
47.8 45.7 47.5
37.5 44.3
1.36 1.40
1.07 1.10
2.06 2.10
51.0 49.6
38.3
(1.09)
(2.26)
(50.1)
50.5
(1.36)
MC2HP(2B2)
sc MCPF
1.26 1.22
1.09 1.08
2.44 2.42
11.1 9.8
45.2 47.4
1.22 1.28
1.07 1.09
2.62 2.44
8.4 19.2
41.6
(1.27)
(1.08)
(2.63)
(24.4)
38.6
MCPF(AN0)
Y Figure 1. Optimal SCF geometry for Sc2+C2H,. The singly charged
species has a similar geometry, except that there are larger changes in the C2H4ligand geometry. electrons are not involved in the bonding. The MH2+systems are optimized at the MCPF level, as there are only two degrees of freedom. For the hydrocarbon species C2H2and C2H4, we determined the optimal geometries a t both the S C F and MCPF levels. We find that if we use a consistent set of ligand and metal-ligand geometries, the MCPF binding energies agree to better than 1 kcal/mol regardless of whether the equilibrium structures are taken from the SCF or MCPF levels of theory. For example, the MCPF binding energy for Y2+C2H4 is 41.7 kcal/mol using the MCPF geometries and 41.3 kcal/mol using the SCF geometries. Very similar results are obtained for Y2+C2H2. The ability to use the S C F geometry represents a significant saving in computer time, especially considering the highly efficient first- and second-derivative methods for SCF wave functions. For the MC3H6+and M2+C3H6systems, the structures were optimized at the SCF level and MCPF calculations were carried out at the optimal S C F geometries. The calculations were carried out by using the MOLECULES W E D E N and ~ ~ G R A D S C F ~program ~ systems at the NASA Ames Research Center central computing facility.
Results and Discussion The free ligand geometries for C2H2,C2H4, C&, and C3H6 are summarized in Table 11. While we do not consider the interaction of metal ions with C2H6, it is included as a representative C-C single bond length. Inclusion of electron correlation increases the bond lengths, while basis set improvements decrease them. Overall the agreement with experiment is very good. In Table I11 we summarize' the equilibrium geometries and binding energies for the singly charged and dipositive ions of Sc, Y, and La interacting with C2H2and C2H4. The most stable structures of MC2H2+and MC2H4+involve metal insertion into a ligand ?r bond to give a three-membered ring. Both molecules have C , symmetry and a IA, ground state. The MC2H4+structure is illustrated in Figure 1. The metal-bond midpoint distance varies from the different metals, but the ligand geometries are quite similar. Rearrangement to form other structures is found to be unfavorable; for example, Sc==C=CH2 is about 20 kcal/mol above the equilibrium structure. Our results are consistent with the study of ScC2H4+by Sarasa et a1.,22who also find the most stable structure to involve approach of Sc+ along the bond midpoint of the C-C bond. The C-C bond distance in MC2H2+ and MC2H4+increases relative to C2H2and C2H4, respectively, reflecting the reduced C-C bond order. For example, the C-C bond (20) MOLECULE-SWEDEN is an electronic structure program system written by J. Almlbf, C. W.Bauschlicher, M. R. A. Blomberg, 'D. P. Chong, A. Heiberg, S.R. Langhoff, P.-A, Malmqvist, A. P. Rendell, B. 0. Roos, P. E. M. Siegbahn. and P. R. Taylor. (2 I ) GRADSCF is a vectorized SCF first- and second-derivative code written by A. Komornicki and H. King. (22) Sarasa, J. P.; Poblet, J. M.; Anglada, J.; Caballol, R. Chem. Phys. Lett. 1990, 167, 421.
SCF MCPF La MCPF
r(C-C) r(C-H)
1.49 1.53 1.48
1.08 1.10 1.09
111.2 111.6 112.3
1.97 2.03 1.98
35.2 34.0 34.1
20.9 24.9
1.52 1.56
1.08 1.11
110.2 110.8
2.11 2.15
39.6 40.5
18.3
1.54
1.11
118.5
2.30
19.6
30.7
MC2Hd2+('B2)
sc MCPF MCPF(AN0) Y SCF MCPF La MCPF
H-bend BE
MCZH~+('AI)
sc SCF MCPF MCPF(AN0) Y SCF MCPF La MCPF
L(HCH) r(M-BMP)
1.40 1.36
1.10 1.09
116.0 117.2
2.54 2.50
11.3 8.1
46.3 47.8
1.36 1.41
1.08 1.10
117.0 115.7
2.72 2.6 1
11.7 14.9
41.7
1.41
1.10
121.1
2.96
6.8
36.4
Bond lengths are in angstroms, bond angles are in degrees, and binding energies (BE) are in kcal/mol. A N 0 denotes that the A N 0 basis sets have been used for C and H and that f functions have been added to Sc. * BMP is the bond midpoint of the C C bond. (H-bend is the angle for H bending away from the metal. dGeometry optimized at the SCF level. CGeometry optimized at the MCPF level.
distance in MC2H2+is consistent with a double bond, as can be seen by comparing with the C-C distance in C2H4-see Table 11. The C-C-H bond angles change to reflect the rehybridization of the C to make the three-membered ring. The C-C-H angle in MC2H2+is consistent with sp2 hybridization for carbon. The similar ligand geometries reflect a common bonding mechanism for all three metals. The theoretical metal-ligand binding energies increase in the order La > Sc Y, whereas experiment4 shows a Sc > Y > La trend. Neither the theoretical nor the experimental trend is consistent with the general observation,l*" that the second-row transition-metal atoms form stronger bonds than the first-row transition-metal ions. The experimental binding energies4 for process MH2+ M+ + 2H follows the order Y > La > Sc. For this process, we compute De values of 112.7, 127.2, and 126.4 kcal/mol, for Sc, Y, and La, respectively, at the MCPF level. This is reasonably consistent with the experimental Do values4 of 114.6 f 3.0, 126.4 f 1.6, and 122.7 f 1.8 kcal/mol. However, the theoretical trend for MH2+ is different from that found for MC2H2+. In MH2+the metal is sd hybridized leading to an H M H angle of about 1 l o o . However, in MC2H2+the C M C angle is about 35O, and therefore the bonding contains much more d2 character. The La+ ground state is derived from the dZoccupation, while the lowest state derived from this occupation is 13.9 and 24.1 kcal/mol above the ground state for Sc+ and Y+, respectively. We find that reducing the angle in MH2+ to that in MC2H2+ destabilizes ScH2+, YH2+, and LaH2+ by 16.9, 29.8, and 19.5
-
Bonding of Sc, Y, and La Positive and Dipositive Ions
The Journal of Physical Chemistry, Vol. 95, No. 6,1991 2281 9
TABLE I V Geometrical Parameters for Selected Structures of MCfit and M 2 + C A a
Structure a Sc
Y La
r12 r23 1.79 2.31 1.95 2.49 2.09 2.68
r34
1.41 1.41 1.41
43,2,5) 64.0 59.4 54.9
43,4,5) 120.4 121.9 122.8
~ ( 4 ~ 3 ~ rd(3,2,5) 2) 78.4 60.0 79.3 69.9 79.8 78.5
Structure b: Three Carbons and Metal Are in a Plane rI2
rZ3 42,1,4)
Sc 2.09 1.59
Y
2.25
1.59
La 2.41 1.59
78.8 72.8 66.9
L(1,2,3) 84.3 86.3 89.0
b
Ibl
L(2,3,4) 112.5 113.8 113.6
Structure c: Singly Charged Ions Sc
Y La
r12
r13
r23
r34
2.18 2.28 2.51
2.07 2.21 2.43
1.46
1.53 1.53 1.53
r12
r13
1.50 1.46
Sc 17.9 Y 23.1 La 28.6
Structure c: Dipositive Ions Sc 3.27 2.41
Y
3.40 2.58
La 2.89 2.89
rZ3
9 4
1.39 1.38 1.40
1.49 1.49 1.52
rI2
rz3
rj4
2.27
1.35 1.36 1.36
Sc 2.14 2.11
Y
2.31
La 2.46 2.43
L(1,2,3) 114.1 108.9 105.8
L(2,3,4) 121.5 121.1 120.5
Structure e: Three Carbons and Metal Are in a Plane r12
r23
r24
1.52
1.55 1.55 1.54
Sc 1.89 1.51
Y
2.03
La 2.17 1.52
41,2,3) 151.0 147.6 139.2
43,2,4) 113.9 113.6 114.4
Structure f: Three Carbons and Metal Are in a Plane r12
r23
Sc 1.79 2.07
Y La
1.95 2.24 2.10 2.39
r34
1.36 1.36 1.36
r4,
1.51 1.51 1.51
~(1~2~3) 114.8 110.1 108.3
“bond distances in angstroms and angles in degrees. Atoms are labeled as in Figure 2.
kcal/mol, respectively. Thus at this small CMC bond angle, the relative binding energies are La > S c = Y, which is consistent with the trend observed for MC2Hz+. Therefore, the unexpected trend in the MC2H2,+ binding energies can be attributed to the very small CMC angle. By comparing the energy required (computed at the MCPF level) to dissociate C2H2,to two CH, fragments, we deduce that it requires 28 kcal/mol more to break the ?r bond in CzH4 than C2H2. Therefore the MC2H4+binding energy is expected to be about 28 kcal/mol less than that for MC2H2+. However, the MCPF binding energies for MCzH4+ are only 16.6 to 20.0 kcal/mol less than that for MC2H2+,because of the extra strain for MC2H2+arising from the shorter C-C bond length and the larger geometry changes associated with rehybridization (sp to sp2 for MC2H2+as compared with sp2 to sp3 for MC2H4+). In Table IV we summarize the most important geometrical parameters for the six structures of MC3H6+depicted in Figure 2. For brevity the C-H bond lengths are not given, since they vary only over a narrow range (1.08 f 0.01 A). Also, bond angles with carbon at the apex are not given when they are very near that expected on the basis of the type of carbon sp hybridization. For example, the M-C-C angle in structure d is very close to 12O0-see Table IV. Two different four-membered rings are found. The allyl-like structure (structure a in Figure 2) is the most stable for Y+and La+, while structure b is the most stable for Sc+. Both of the four-membered rings reduce the strain and the binding energies of MC3H6+are larger than those for MC2H4+, even though a double bond is broken in both ligands. Also note that the reduction in strain leads to Y being more strongly bound than Sc. The two four-membered rings differ in the location of one hydrogen: it is bound to the metal and central carbon in
6
Id)
IC)
Structure d
4 La 20.8
v
le)
LS
19.9
b
If1
Figure 2. Structures and binding energies (kcal/mol) of the MC3Hst ions. Results for the dipositive ion are given in parentheses. Structures
are drawn to scale and ordered for the La+ ions.
TABLE V Summary of Metal Net Populations for the Singly Charged and Dipositive MC2Hh MCIH4, and M C A Systems at the MCPF Level. For MCJ+,+, the Notation a-f Denotes the Six Structures Depicted in Figure 2
metal (M) sc
MC2Hz+ M2+C2Hz MC2H4+ M2+C2H4 1.11 1.25 1.24
Y La M
Sc
Y La
a 0.98 1.20 1.11
b 1.17 1.36 1.24
1.63 1.72 1.77
MCqHn+ c d 1.05 1.20 1.09
1.33 1.52 1.38
1.16 1.30 1.27
1.62 1.73 1.74
e
f
1.11
1.15 1.31 1.19
1.18 1.04
M2+C3H6 1.65 1.71 1.67
structures a and b, respectively. As expected, structure c, where the metal ion has inserted into the 7~ bond to form a three-membered ring, has a comparable binding energy to MC2H4+. The C(2)-C(3) bond length has increased to =1.50 A, similar to that for MCzH4+and close to a typical C-C single bond length as expected. Insertion of the metal ion into a C-C or C-H bond, structures d and f, results in less strain than the three-membered ring but requires that a C-C single or C-H bond must be broken. As with the four-membered rings, the reduction in strain leads to Y being more strongly bound than Sc for these two structures. As both the C-C single and C-H bonds are stronger than a C-C a bond, structures d and f a r e less favorable than the four-membered rings where the strain is reduced, without the requirement of breaking these strong u bonds. The fact that structure e is slightly asymmetric may be an artifact of the level of correlation treatment. In any case, the formation of a M-C double bond as in structure e is very unfavorable, especially for ScC3H6+and YCSHs+. To obtain some insight into how the relative stability of the six MC3&+ structures depicted in Figure 2 varies with metal, consider the Mulliken net metal populations derived from the MCPF wave
2282 The Journal of Physical Chemistry, Vol. 95, No. 6,1991 functions in Table V. The populations indicate that the charge donation decreases in the order Y > La > Sc. For the singly charged ions, charge donation is from the metal to the ligand, whereas the converse is true for the dipositive ions. Overall, however, the populations indicate a similar bonding mechanism for all three metals. The most significant difference in the populations is the slightly smaller net charge on Sc due to its higher ionization potential. Although we are unable to find a simple explanation for the different order of the structures for the various metal ions, it is probably a result of the combined differences in the order of states of the ions, ring strain, and the strength of bonds involving the 3d, 4d, and 5d orbitals. For the dipositive ions we studied both the symmetric (C,) and asymmetric (C,)structures for Y2+C2H4. In the symmetric structure, the metal ion approaches the ligand T bond along the bond midpoint just as in the singly charged ion, while in the asymmetric structure the metal ion approaches one end of the molecule such that the C-C-M angle is about 1 2 0 O . At the SCF level the asymmetric structure is 1.1 kcal/mol lower in energy, but at the MCPF level the symmetric structure is 1.7 kcal/mol more stable. Because of this small difference in the binding energies, we consider only the higher symmetry C , case for the other M2+C2H4systems and for all of the M2+C2Hzsystems. For M2+C3H6,the most stable structure found at the S C F level has the M2+ ion approaching the T bond, although the metal is not at the midpoint. However, it is unclear whether this asymmetry is real. We expect that interaction with the T bond is a true minimum, since it is energetically more favorable to interact with the a bond than another portion of propylene. This is consistent with the fact that Sc2+ is 8 kcal/mol more strongly bound to C2H4 than to C2H6.23 The bonding in the dipositive ions is dominantly electrostatic for all three metals, thus the ligand geometries are changed by less from their free ligand values than in the singly charged ions where a ligand bond is broken. For example, the C=C bond length in M2+C2H4and M2+C3H6is increased by only about of the difference between typical C-C and C-C bond lengths. Another consequence of the electrostatic bonding is that the bond strength is not significantly affected by the differing ability of the 3d, 4d, and 5d orbitals to form bonds. The bond strength depends almost exclusively on the metal ligand distance and hence on the radial extent of M2+. Thus the bond strengths vary as Sc > Y > La and the metal-ligand bond distances vary in the inverse order (La > Y > Sc). To facilitate comparison with experiment, we have attempted to estimate the errors in the theoretical binding energies. The importance of expanding the one-particle basis set was assessed by carrying out calibration calculations using the larger (ANO) sets for C and H and by expanding the Sc basis set by adding a (3f)/[ lfl polarization set. This increases the binding energy by a maximum of about 7 kcal/mol for the singly charged ion where there is covalent bonding but by only 2 kcal/mol for the dipositive ion where the bonding is electrostatic. Uncontracting the f polarization set increases the binding energy by an additional 0.8 kcal/mol for ScC2H2+. Further, basis set expansions are (23) Hill, Y . D.; Freiser, B. S.;Bauschlicher, C. W. J.'Am. Chem. Soc., in press. (24) Pople, J. A. In Applications of Electronic Structure Theory;H. H. F. Schaefer, ed.;Plenum Press: New York,1977; pp 1-27 and references therein.
Bauschlicher and Langhoff expected to increase the binding energy only slightly. However, an improved treatment of electron correlation will probably increase the binding energies by about as much as the basis set improvement. Therefore, we estimate that the binding energies obtained in the small basis set at the MCPF level are probably 5 and 15 kcal/mol too small for the dipositive and singly charged ions, respectively. If we add 15 kcal/mol to our MCPF binding energies (in the small basis), we obtain binding energies of 53,53, and 66 kcal/mol for ScC2H2+.YC2H2+,and LaC2H2+,respectively. While the estimated binding energy is in excellent agreement with the experimental value of Sunderlin and Armentrout4 for LaC2H2+,the estimated values for ScC2H2+and YC2H2+are about 20 kcal/mol smaller than the corresponding experimental value^.^ The experimentaP binding energies for ScC2H2+and ScC2H4+differ by much more than the difference in the a-bond strength in C2H2 and C2H4. A consideration of other structures for ScC2H2+ indicates that rearrangement is an unlikely cause for this discrepancy. It is therefore likely that the experimental values for ScC2H2+and YC2H2+are incorrect. Our best theoretical estimates for the binding energies of MC2H4+are 36, 33, and 46 kcal/mol for Sc through La, respectively. As can be seen from Table I, our values for ScC2H4+and YC2H4+agree with experiment, but our theoretical value for LaC2H4+is much larger than the experimental lower bound. For MC3H6+our best estimates for the M-C binding energies are 41, 43, and 51 kcal/mol for Sc, Y, and La, respectively. The previous result6 for Lac&+ is consistent with the lower bounds of Huang et ale8but about 6 kcal/mol below the lower bound of MacMahon and F r e i ~ e r . ~ For the dipositive ions, the binding energies have been measured only for La2+C2H2and La2+C3H6. We agree with the experimental binding energy of La2+C3H6,but our results suggest that the experimental value7 for La2+C2H2is too small. Conclusions
The nature of the bonding is very similar for the Sc, Y, and La metals. The singly charged ions insert into a C-C a bond forming a three-membered ring. In MC3H6+ there is rearrangement to form a four-membered ring to reduce the strain. We find that the singly charged ion binding energies increase in the order La > Sc i= Y for all three ligands. This is different from the MH2+systems where Y is more strongly bound than Sc. The different trend in MC2Hh+ is due to the much smaller CMC bond angles, which results in a larger contribution from d2 in the wave function. This destabilizes Y+, because it has a larger promotion energy to reach d2 than either Sc+ or La+. The experimental binding energies for ScC2H2+and YC2H2+ are probably incorrect, as they are well outside the uncertainty of the theoretical calculation. The experimental lower bound for LaC2H4+is much too small. For the dipositive ions the bonding is predominantly electrostatic in origin, and the binding energies vary as Sc > Y > La, which is inversely related to the radical extent of the ions. More accurate experimental determinations of the binding energies are required to test the trends and bonding mechanisms proposed in this work.
Acknowledgment. We would like to thank Ben Freiser for many helpful discussions. Registry No. Sc', 22537-29-7; Y+,22537-40-2; La', 14175-57-6; Sc2+, 14336-96-0; Yz+,14995-74-5; LaZ+,17643-88-8; CZHZ,74-86-2; C2H4, 74-85-1 ; C,H6, 1 15-07- 1 .
