11600
J. Phys. Chem. 1996, 100, 11600-11609
Molecular Orbital Study of the Reaction Mechanism of Sc+ with Methane. Comparison of the Reactivity of Early and Late First-Row Transition Metal Cations and Their Carbene Complexes Djamaladdin G. Musaev and Keiji Morokuma* Cherry L. Emerson Center for Scientific Computation and Department of Chemistry, Emory UniVersity, Atlanta, Georgia 30322 ReceiVed: February 13, 1996; In Final Form: May 3, 1996X
The reactions of Sc+ + CH4 and ScCH2+ + H2 have been studied with the CASSCF and MR-SDCI-CASSCF methods. The reaction of the ground state Sc+ with CH4 proceeds as Sc+(3D, s1d1) + CH4 f ScCH4+(3A′′) f TS2(1A′) f HScCH3+(1A′) f TS1 f (H2)ScCH2+(1A1) f ScCH2+(1A1) + H2 and is calculated to be endothermic by 24.8 kcal/mol. After formation of an ion-molecule complex ScCH4+, the reaction cannot proceed on the triplet surface because of a high barrier and has to cross over to singlet and reach the singlet transition state TS2 with a barrier of 28.6 kcal/mol. The insertion product HScCH3+, 4.9 kcal/mol more stable than the reactants Sc+ + CH4, produces most favorably an ion-molecule complex (H2)ScCH2+ with a barrier of 28kcal/mol, which can dissociate to give H2 and ScCH2+(1A1) with a small barrier of 3.2 kcal/ mol. At higher temperatures, production of ScH+ + CH3 and ScCH3+ + H from HScCH3+ will dominate. The reverse reaction ScCH2+(1A1) + H2 proceeds very easily and leads to HScCH3+(1A′), ScCH4+(3A′), and Sc+(1D or 3D) + CH4. Comparison of the results for Sc+ (and ScCH2+) with those for Fe+ and Co+ (and FeCH2+ and CoCH2+) shows the following. (a) Carbene complexes MCH2+ of early transition metal cations, M ) Sc, Ti, and V, should activate H-H/C-H bonds more easily than their late transition metal analogs and lead to hydridomethyl, HMCH3+, and ion-molecule M(CH4)+ complexes. For first-row late transition metals the hydridomethyl complex does not exist thermodynamically or kinetically. (b) The products of the reaction of early transition metal cations with methane at low temperatures should be MCH2+ and H2 as this channel (1) is less endothermic than MH+ + CH3 (2) and MCH3+ + H (3) channels. For late transition metals, though the endothermicities are similar between three channels, channel 1 requires a large H-H bond activation barrier and does not take place, whereas channels 2 and 3 should be possible at high temperatures. All these similarities and differences in the reactivity of early and late first-row transition metal cations and their carbene complexes are explained by using a molecular orbital picture.
I. Introduction The study of gas-phase activation of H-H, C-H, and C-C bonds of hydrogen molecules and saturated hydrocarbons, respectively, by bare transition metal cations and carbene complexes MCH2+ has been the subject of many experimental1-27 and theoretical28-34 papers in the last 10-15 years. Such studies provide thermochemistry of as well as insight into the mechanism and periodic trends of reactivity. Experimentally it has been shown that the interaction of methane with early first-row transition metal cations leads to the products of reaction 1 at low energies, while at higher energies reaction 2 is dominant.
M+ + CH4 f MCH2+ + H2
(1)
f MH+ + CH3
(2)
f MCH3+ + H
(3)
In contrast, for late first-row transition metal cations reaction 1 is a minor process compared to reaction 2. Some insight into this difference between early and late transition metal cations can be obtained by theoretical studies performed at the same level of theory for both systems. In our previous papers28-31 we have studied the mechanism of the interaction of M+ (M ) X
Abstract published in AdVance ACS Abstracts, July 1, 1996.
S0022-3654(96)00446-7 CCC: $12.00
Fe, Co, Rh, and Ir) with CH4 at the CASSCF and MR-SDCI levels of theory. This paper is a continuation of our previous studies and makes it a goal to study the reaction mechanism Sc+ + CH4 at the same level as in our previous papers, to compare the results with those for Fe+ and Co+, and to find trends in the reactivity of early and late first-row transition metal cations and their carbene complexes. The reaction of Sc+ with methane has been experimentally studied using the guided ion beam mass spectrometry35,36 and has been shown to proceed via oxidative addition, i.e. insertion of Sc+ into the C-H bond to form intermediate HScCH3+, which is estimated to lie 11 kcal/mol below the ground state reactants.36 From this intermediate the reaction proceeds via three different endothermic channels (1-3), among which channel 1 via a four-center transition state is predicted36 to be energetically most favorable. The structure and energetics of the products of reactions (13), ScH+, ScCH3+, and ScCH2+, have been the subject of several theoretical studies.37-42 The ground states are found to be 2∆ and 2E for ScH+and ScCH3+, respectively. The calculated Sc+-H and Sc+-CH3 binding energies are 56.040 and 52.441 vs 55.4 ( 2.043 and 57.6 ( 3.0 kcal/mol in experiment,43 respectively. The latest study of Ricca and Bauschlicher42c has shown that the energetically most favorable structure of ScCH2+ in the ground singlet state has Cs symmetry, where one of the H atoms of CH2 interacts with an empty dπ orbital of Sc+. The structure with C2V symmetry is only 1-2 kcal/mol higher. The © 1996 American Chemical Society
Reaction Mechanism of Sc+ with Methane
J. Phys. Chem., Vol. 100, No. 28, 1996 11601
TABLE 1: Active Spaces Used for CASSCF and MR-SDCI-CASSCF Calculations of the Reactants, Transition States, Intermediates, and Products of Reactions 1-3a system
orbitals included
size
Sc H2 CH2 ScCH2+ ScH+ and ScCH3+ H2ScCH2+ and TS1 HScCH3+ and TS2
b1(dxz)b2(dyz)a2(dxy)a1(dxx-yy)a1(d2zz-xx-yy)a1(s) σgσu* a1b1 5a12b11a23b26a17a18a13b1 σ(Sc-X, bond)σ*(Sc-X, antibond)δ (dxy)δ (dxx-yy)π(dxz)π(dyz)σ(sd2zz-xx-yy) ScCH2+(4/8) ) 5a12b11a23b26a17a18a13b1 and H2(2/2) ) 9a1(H-H bond)4b2(H-H antibond) (Sc-H, bond)(Sc-C, bond)(Sc-H, antibond)(Sc-C, antibond)1a22b24a15a1 (4/8) + (C-H, bond)(C-H, antibond) Sc+(2/6) ) b1(dxz)b2(dyz)a2(dxy)a1(dxx-yy)a1(d2zz-xx-yy)a1(s) (2/6) + two CH bond and antibond
(2/6) (2/2) (2/2) (4/8) (3/7) (6/10) (4/8) (6/10) (2/6) (6/10)
+
ScCH4+ a
The C2V notation is used throughout, except for H2, ScH+, and ScCH3+. The virtual orbitals are marked with an asterisk.
Figure 1. Coordinate system and the orbital correlation diagram for Sc+(3D, s1d1) + CH2(3B1) f ScCH2+(1A1).
“best” calculated value of Sc+-CH2 binding energy is 85 ( 3 kcal/mol42c vs 96.9 ( 5.3 kcal/mol in experiment.43 In the second section we briefly describe the method. In the third section the calculated potential energy surface of the reaction of Sc+ with CH4 and the reverse reaction of ScCH2+ with H2 will be discussed. The present results will be compared with those for Fe+ and Co+ and FeCH2+ and CoCH2+, respectively, in the fourth section. In the final section we will make a few concluding remarks. II. Methods of Calculation We use two sets of basis functions. The basis set (BS) I consists of the standard (5s5p5d/3s3p3d) basis set for Sc with the effective core potentials (ECP)44 by Hay and Wadt, which explicitly considers the electrons in the 3s3p4s3d shells, and the split valence 6-31G basis sets for C and H atoms.45 The BSII is the BSI augmented with polarization fSc (R ) 1.335)46, dC (R ) 0.626),47 and pH (R ) 0.75)47 functions. The geometries of all the systems were optimized at the complete active space self-consistent-field (CASSCF) level of theory with the BSI by using GAMESS48 and MOLPRO49 programs. The energies of the stationary points were recalculated with MOLPRO using the BSII and the internally contracted configuration interaction method including all single and double excitations from the CASSCF reference wave function (MRSDCI-CASSCF) along with the Davidson correction for quadruple excitations (+DC).50 The CASSCF active spaces used for various species are summarized in Table 1, with the notation (m/n) denoting m
electrons and n orbitals in the active space, in the coordinate system defined in Figure 1. The (2/6) active space used for Sc+ includes all (4s and five 3d) valence orbitals and electrons, as shown in Figure 1. For both CH2 and H2, the (2/2) active space was used: 3a1 and 1b1 orbitals for CH2 and σg (or a1) and σu (or b1) for H2. For ScCH2+ we used the (4/8) active space, which consists of the (2/6) and (2/2) active spaces for Sc+ and CH2 fragments, respectively, at the dissociation limit. The PESs for reactions (1-3) are investigated by using the same procedure as in our previous papers.28-31 The local minima and transition states have been optimized by using a “chemically reasonable” active space. The nature of the stationary points has been identified positively by Hessian analysis at the same level of theory. MOs corresponding to those bonds that are well described at the single-determinant level of theory and are not directly involved in the current step of reaction were excluded from the active space. The (6/10) active space, constructed from the ScCH2+ (4/8) active space and the H2 (2/2) active space, was used for optimization of the geometry of the dihydrogen (H2)ScCH2+ complex, as well as the transition states TS1 corresponding to the H-H activation. The (4/8) active space, used for geometry optimization of the HScCH3+ complex and the transition state TS2 for the C-H insertion process, excludes from (6/10) the C-H bonding and antibonding orbitals and electrons to retain the symmetry of the CH3 group. Similarly, for geometry optimization of the ScCH4+ complex, the (2/6) active space including only the valence electrons of Sc+ was used. Once the stationary points on the PES were determined, the energy second derivatives are
11602 J. Phys. Chem., Vol. 100, No. 28, 1996
Musaev and Morokuma
calculated numerically at the CASSCF level and used for identification of the number of imaginary frequencies and the zero point energy correction (ZPC). The energetics was recalculated by using the contracted MR-SDCI-CASSCF method based on the CASSCF wave functions of the (6/10) active space, which includes at the dissociation limits the ScCH2+ (4/8) and the H2 (2/2), as well as the Sc+ (2/6) and the CH4 (4/4, including two bonding and antibonding orbitals for C-H bonds), active spaces. The geometries of ScH+ and ScCH3+ have been optimized by using the (3/7) active space, which includes all valence electrons and orbitals from Sc+, as well as Sc-H and Sc-C bonding and antibonding orbitals, respectively. This is consistent with the (4/8) active space for HScCH3+. The MR-SDCICASSCF calculations for the energies of the processes
HScCH3+ f ScH+ + CH3
(4)
HScCH3+ f ScCH3+ + H
(5)
have been carried out with the CASSCF(6/10) reference wave function, consisting of the (5/9) [)(3/7) + one C-H bonding and antibonding orbitals and electrons] and the (1/1) active spaces for ScH+ (or ScCH3+) and CH3 (or H), respectively, at the dissociation limit. The dissociation limits of the processes
ScCH2+ f Sc+ + CH2
(6)
(H2)ScCH2+ f H2+ScCH2+
(7)
ScCH4+ f Sc+ + CH4
(8)
as well as processes 4 and 5 were calculated using the “supermolecules”, Sc+--CH2, H2--ScCH2+, Sc+--CH4, HSc+-CH3, and H--ScCH3+, at the interfragment distance of 15.0 Å. One should note that similar approaches used in our previous papers28-31 have given qualitatively excellent agreement with the latest experiments,25 although quantitatively the calculated and measured energies are different up to several kcal/mol, especially for H-H bond activation barriers. The quantum chemical calculations and latest experiments have found the same trends for the reactivity of the complexes MCH2+ (M ) Fe, Co, and Rh) with molecular hydrogen. Therefore, we believe that the present calculations for M ) Sc also will provide good energetics and an equally good basis for comparison. The lowest point on the seam of crossing between two surfaces of different spin multiplicities was determined using the SEAM program,51 with the CASSCF gradient obtained by GAMESS. III. Potential Energy Surface for Reactions of Sc+ and ScCH2+ with Molecules CH4 and H2 We show the atomic energies of Sc+ in Table 2, the relative energies of the stationary points on the PES of reactions (1-3) in Tables 3-5, and their optimized geometries in Figure 2 and in Tables 4 and 5. Though the energies both with and without ZPC are given in Table 3, we use for discussion mainly the MR-SDCI+DC energies without ZPC for discussion, consistent with our previous papers.28-31 The final PESs, obtained at the higher level of theory, MR-SDCI-CASSCF(6/10) + DC/BSII, are shown also in Figure 3, and below, the energetics of the reaction will be discussed mainly at this level of theory. A. Sc+ + CH4. As seen in Table 2 the ground 3D(s1d1) and first excited 1D(s1d1) states of the reactant Sc+ are close in
TABLE 2: Total and Relative Energies of 3D(s1d1) and 1D(s1d1) States of Sc+ at Different Levels of Theorya method
3D(s1d1)
1D(s1d1)
∆Eb
CASSCF/BSI CASSCF/BSII MR-SDCI-CASSCF/BSI MR-SDCI-CASSCF/BSII experimentc
-45.752 208 -45.752 996 -45.753 631 -45.754 690
-45.738 916 -45.739 734 -45.743 000 -45.744 302
8.3 8.3 6.7 6.6 7.3
aD b ∞h symmetry was used in actual calculation. The energy (in kcal/ mol) of the singlet state relative to the triplet state. c Reference 52.
energy, with the difference calculated to be 6.6-6.7 kcal/mol at the MR-SDCI-CASSCF+DC level with either basis set I or II, which is in reasonable agreement with the experimental 7.3 kcal/mol.52 Since they are close in energy, we will study the reactions of both triplet and singlet states of Sc+ with CH4. At first, the reactants, Sc+ and CH4, form a methane complex Sc(CH4)+. As seen in Figure 2, the bidentate structure I with C2V symmetry is a real minimum for the singlet Sc(CH4)+, while the triplet Sc(CH4)+ has the tridentate structure II with C3V as a real minimum. However, as seen in Table 3, the energy difference between structures I and II is less than 1 kcal/mol. Therefore, one can conclude that Sc(CH4)+ is a structurally nonrigid system, where Sc+ can nearly freely rotate around the CH4 molecule by the pathway (C2V) T (C3V, TS) T (C2V) T ... and (C3V) T (C2V, TS) T (C3V) T ... for singlet and triplet state, respectively. In our previous papers28,29 we have shown that the monodentate structure of the M(CH4)+ complex, where the CH4 molecule coordinates to M by one of its hydrogen atoms, is about 10-15 kcal/mol less favorable than structures I and II. Thus, we did not study the monodentate structure for M ) Sc. As seen in Table 3 and Figure 3, the stabilization energy for Sc+ + CH4 f Sc(CH4)+ is calculated to be 13.3 and 15.1 kcal/mol for the 1A′ and 3A′′ states, respectively. The next step of the reaction is insertion of Sc+ into the C-H bond of methane. As seen in Figure 3, the potential energy surfaces of reaction from Sc(CH4)+ to the (H2)ScCH2+ are very different between triplet and singlet states. For the triplet 3A′′ state the reaction proceeds directly, without formation of the inserted product HScCH3+, and leads to (H2)ScCH2+ complex via the four-center transition state TS1, VI, in Figure 2. It is highly endothermic, 47.3 kcal/mol, and proceeds with a large barrier, 60.6 kcal/mol, relative to the Sc(CH4)+(3A′′) complex. Thus, this process is not likely to take place under normal conditions. For the singlet 1A′ state, however, Sc+ inserts into the C-H bond of methane with a relatively small barrier, 20.0 kcal/mol, at TS2, III, relative to the Sc(CH4)+(1A′) complex and leads to insertion product HScCH3+(1A′) IV, which is only 1.6 kcal/mol higher than Sc(CH4)+(1A′). The HScCH3+(1A′) complex IV lies 11.7 and 4.9 kcal/mol lower than the singlet and triplet reactants, respectively. Thus, the reactivity of the singlet excited Sc+ is expected to be much larger than the triplet ground state. As seen from Figure 3, the PESs of reaction for singlet and triplet states cross between the Sc(CH4)+ complex and the HScCH3+(1A′) complex. The lowest point XM on the seam of crossing between two potential surfaces has been located at structure V in Figure 2. Structure V has C2V symmetry and has a structure tighter than the triplet ion-molecule Sc(CH4)+ I but with the CH bond not as stretched as in TS2, III, somewhere between the two. The energy of V at the CASSCF level is about 10 kcal/mol above the ion-molecule complex Sc(CH4)+(3A′′) II but is still 13 kcal/mol below the TS2, III. At the MR-SDCI+DC level, the energy of the 3A′′ state at this CASSCF-determined XM point is about 2.3 kcal/mol higher
Reaction Mechanism of Sc+ with Methane
J. Phys. Chem., Vol. 100, No. 28, 1996 11603
TABLE 3: Relative Energies of Stationary Points on the Potential Energy Surfaces of Reactions 1-3a structure Sc+ + CH4 ScCH4+ TS2(C-H activation) HScCH3+ XM TS1(H-H addition) (H2)ScCH2+ H2 + ScCH2+ HSc+ + CH3 H + ScCH3+ Sc+ + CH4 ScCH4+ XM TS1(H-H addition) (H2)ScCH2+ H2 + ScCH2+
MR-SDCI CASSCF
CASSCF 1A′
-85.968 552/7.9 -9.0/-1.1 -8.1/-0.2 13.8/21.7 -6.4/1.5 0.6/8.5 20.8/28.7 18.4/26.3 19.2/25.5 21.1/29.0 37.6/45.5 34.8/42.7
I II III IV V VI VII VIII
I II V VI VII VIII
MR-SDCI CASSCF+DC+ZPC
State -85.998 088/6.6 -13.2/-6.6
-85.998 550/6.8 -13.3/-6.5
7.9/14.5 -10.9/-4.3 1.6/8.2 16.3/22.9 14.9/21.5
6.7/13.5 -11.7/-4.9 1.8/8.6 16.3/23.1 14.8/21.6
9.8/16.6 -8.4/-1.6
18.1/24.7 36.6/43.2 37.6/44.3
18.0/24.8 35.8/42.6 37.1/43.9
26.8/33.6 42.7/49.6 43.8/50.6
-6.8/-86.009 387
-6.8/0.0
3A′′
State -6.6/-86.008 606
-7.9/-85.981 142 -26.2/-18.3 -26.9/-19.0 0.6/8.5 42.9/50.8 24.8/32.7 24.0/31.9 27.9/35.8
MR-SDCI CASSCF+DC
0.0/6.8 -15.3/-8.5
21.9/28.7 21.3/28.1
-21.9/-15.3 3.7/10.3 39.0/45.6 25.5/32.1
-21.9/-15.1 4.1/10.9 38.7/45.5 25.4/32.2
-24.2/-21.9
29.0/35.6
28.9/35.7
36.7/43.5
45.6/52.4 32.5/39.3
a
Total energies (in italics, in hartrees) are given only for reference structures, and energies (in kcal/mol) for other structures are relative to the reference structures. The numbers after slash are relative energies with respect to the 3A′′ state of the reactants.
TABLE 4: Geometries of Different Electronic States of the ScCH2+ Complex Optimized at the CASSCF(4/8)/BSI Level and the Energetics at Various Levels at the CASSCF(4/8)/BSI Optimized Geometries, Compared with Other Theoretical and Experimental Results states
singly occupied orbitals
1
A1
3A
1
3B 1 3 A2 3 B2
b1(CH2)b1*(dSc) b1(CH2)a1(dSc) b1(CH2)b2(dSc) b1(CH2)a2(dSc)
R(Sc-C) (Å)
r(C-H) (Å)
∠HCH (deg)
1.991 1.997 1.973 1.841
1.087 (1.075)c (1.080)
111.12 112.0 109.4 112.3
2.235 2.263 2.169 2.164 2.167
1.097 (1.075) 1.084 1.084 1.084
109.83 111.36 110.29 110.19 110.24
CASSCF/I
relative energiesa CASSCF/II MR-CI/II
-84.777 48
-84.787 01
32.4
29.7 24.7 7.0 6.8 6.9
10.5 10.1 9.9
-84.807 13
+DC
Deb
ref
-84.807 41
79.3 68.0 81.7 85 ( 3 96.9 ( 5.3
this work 39 42b 42cd expt 43 this work 39 this work this work this work
29.6 25.7 11.7 10.9 11.2
29.6 11.7 10.9 11.2
a The energies (in kcal/mol) relative to the reference state, for which the total energy (italics, in hartrees) is given. b BE is the energy of reaction for ScCH2+(1A1) f Sc+(3D) + CH2(3B1). The present results are at the MR-SDCI-CASSCF/BSII level. c The numbers in parentheses are fixed. The calculations in refs 39 and 42b have been performed at the CI-MCSCF and ICACPF//MCPF levels, respectively, with the C2V symmetry constraint. d This calculation has been perfomed by using the B3LYP method without the C2V symmetry constraint. The C-H bond lengths are calculated to be 1.089 and 1.125 Å.
TABLE 5: Calculated Geometries of the ScCH3+ and ScH+ Molecules and Binding Energies of the Sc+-CH3, HSc+-CH3, Sc+-H, and H-ScCH3+ Bondsa ScH+(2∆)
ScCH3+(2E) property R(Sc-X) (Å) r(C-H) (Å) ∠ScCH (deg) BE (kcal/mol) Sc+-CH3e HSc+-CH3f Sc+-H CH3Sc+-H
this work 2.199 1.098 111.83 44.2/51.0/51.8 44.0/47.5/47.5
other work b
this work 1.796
2.200 1.095b 111.4b
other work 1.829c
52.4b [57.5 ( 3.0]d 50.6/52.9/53.0 41.2/48.6/48.8
54.0c [55.3 ( 2.0]d
a Geometries of ScH+ and ScCH3+ calculated at the CASSCF (3/7)/I level. b Reference 41. c Reference 40. d Numbers in brackets are experimental values taken from reference 43. e The binding energies separated by slashes are calculated at the CASSCF(3/7)/II, MR-SDCI-CASSCF(3/7)/II, and MR-SDCI-CASSCF(3/7)/II)+DC levels, respectively. f The binding energies separated by slashes are calculated at the CASSCF(6/10)/II, MRSDCI-CASSCF(6/10)/II, and MR-SDCI-CASSCF(6/10)/II + DC levels, respectively.
than the 1A′ state, suggesting that the crossing seam minimum will be shifted slightly toward complexes I and II. Therefore, the energetically favorable mechanism of reaction of the triplet ground state 3D(s1d1) of Sc+ with CH4 would at first yield a triplet methane complex Sc(CH4)+(3A′′), then make
an intersystem crossing to the singlet state at the seam minimum XM, V, and go over the singlet TS2 to reach the singlet hydridomethyl complex, HScCH3+(1A′) IV. Because of intersystem crossing, this process may not be efficient but is still energetically accessible at low temperature. Energetically the
11604 J. Phys. Chem., Vol. 100, No. 28, 1996
Musaev and Morokuma
Figure 2. Geometries (distances in angstroms and angles in degrees) of intermediates and transition states (TS) for 1A′ and 3A′′ (in parentheses) states of the reaction ScCH2+ + H2, calculated at the CASSCF/BSI level. Nimag is the number of imaginary frequencies, with their values shown explicitly for nimag * 0. Arrows indicate the reaction coordinate vector for the 1A′ state at the transition state geometry.
barrier separating the triplet ion-molecule complex Sc(CH4)+ from the singlet intermediate HScCH3 is the singlet state transition state TS2, III, at 28.6 kcal/mol. The calculated exothermicity of 4.9 kcal/mol for Sc+(3D) + CH4 f HScCH3+(1A′) is in reasonable agreement with the experimental value of 10.8 kcal/mol.36 From the HScCH3+(1A′) complex IV the reaction may split into three different channels corresponding to eqs 1, 2, and 3. Although all three channels are endothermic, by 24.8, 42.6, and 43.9 kcal/mol, respectively, channel 1 is thermodynamically the most favorable, in good agreement with experiment.36 It proceeds via the four-center transition state TS1, VI, in the singlet state, shown in Figure 2. At TS1 the H-H bond is 1.031 Å, e.g. 0.30 Å longer than in the free H2 molecule, the C-H2 bond is much longer than in the CH3 fragment, and the Sc-H1 bond is close to that for the ScH+ molecule in Table 5. According to these geometric parameters, the transition state TS1, VI, is a late transition state. The barrier height corresponding to this transition state is calculated to be 28.0 and
23.1 kcal/mol relative to the HScCH3+(1A′) complex IV and the ground state reactants, Sc+(3D) + CH4, respectively. After overcoming the transition state VI, it reaches the molecular hydrogen complex, (H2)ScCH2+(1A′) VII, where H2 and CH2 moieties are perpendicular to each other. The triplet state also has a complex of very similar structure. Structure VIII with the coplanar conformation in either state has one imaginary frequency that corresponds to a 0.8 kcal/mol barrier to rotation of H2 around the Sc-X axis, X being the center of the H-H bond. In the complex VII, the H-H distance is 0.75 Å in both states, about 0.01 Å longer than that in free H2. The complex VII, (H2)ScCH2+(1A′), in the singlet lies 26.5 kcal/ mol higher than the hydridomethyl complex IV and is stable only by 3.2 kcal/mol relative to the dissociation limit H2 + ScCH2+(1A1). The calculated endothermicity of the entire reaction 1, 24.8 kcal/mol, is about twice as large as the experimentally estimated value, 11-12 kcal/mol.36 The reason for this discrepancy between experiment and theory probably is in the description of the Sc+dCH2 bond. As seen in Table
Reaction Mechanism of Sc+ with Methane
J. Phys. Chem., Vol. 100, No. 28, 1996 11605 TABLE 6: Natural Orbital Occupancies of Principal Configurational State Functions and Their Weights (in %) for the Low-Lying 1A1, 3A1, 3A2, 3B1, and 3B2 States of ScCH2+, Calculated at the CASSCF(4/8)/BSI Levela state
3a1
1b1
1a2
2b2
4a1
5a1
2b1
6a1
weight
1A
2 2 1 2 2 2 2 2 2 2 2 2 2
2 0 1 1 1 0 1 1 0 1 0 1 0
0 0 0 0 0 0 0 0 0 1 1 0 0
0 0 0 0 0 0 0 0 0 0 0 1 1
0 0 0 0 1 0 0 0 1 0 0 0 0
0 0 1 0 0 0 1 0 0 0 0 0 0
0 2 1 1 0 1 0 0 1 0 1 0 1
0 0 0 0 0 1 0 1 0 0 0 0 0
88.4 7.8 1.7;1.1 98.0 43.6 7.3 2.7 30.3 9.0 80.7 10.2 82.3 8.6
1
3A
1 3B 1
3B 2 3A
a
Figure 3. Potential energy profiles of the reaction ScCH2+ + H2 calculated at the MR-SDCI-CASSCF(6/10)/BSII+DC level.
4, the calculated Sc+dCH2 binding energy in this paper, 79.3 kcal/mol, is not far from the best theoretically estimated value of 85 ( 3 kcal/mol,42c but is 17.6 ( 5.3 kcal/mol smaller than the experimentally estimated value, 96.9 ( 5.3 kcal/mol.43 Therefore, the experimental value of the endothermicity of reaction 1, seems to be overestimated by 10 ( 5 kcal/mol. Reactions 2 and 3 are simply uphill from the hydridomethyl intermediate HScCH3+(1A′) IV and are endothermic by 42.6 and 43.9 kcal/mol, respectively. As seen from Table 5 the binding energies of ScH+ and ScCH3+ calculated at the MRSDCI-CASSCF(3/7)+DC level are 53.0 and 51.8 kcal/mol, respectively, which are in good agreement with previous calculations40,41 and experiment.43 The energies of dissociation of H and CH3 groups from HScCH3+(1A′) are 48.8 and 47.5 kcal/mol, respectively, calculated at the MR-SDCICASSCF(6/10)+DC level. One also notes that the products of reactions 2 and 3 can be reached also by dissociation on the triplet potential surface. As discussed above, in the triplet state, the hydridomethyl complex does not exist as a stable intermediate. However, from the ground state reactants Sc+(3D, s1d1) + CH4 and the triplet ionmolecule complex Sc(CH4)+(3A′′), one can simply (without transferring to the singlet) climb up the triplet potential surface through the vicinity of the hydridomethyl complex all the way to the dissociation products ScH++ CH3 or ScCH3+ + H. Without the intersystem crossing, this may be more efficient than the path via the singlet intermediate HScCH3+(1A′) IV discussed above. B. ScCH2+ + H2. Now we will examine the reverse reaction processes:
ScCH2+ + H2 f Sc+ + CH4
(1′)
f ScH+ + CH3
(2′)
f ScCH3+ + H
(3′)
It is worth starting our discussions with the reactant, the ScCH2+ complex, which has been the subject of several studies.39,42 Recently Ricca and Bauschlicher,42c by using the B3LYP and CCSD(T) methods with large basis sets including double-ζ contracted polarization functions, have shown for ScCH2+ that
2
Only configurations with weight of not less than 1.0% are shown.
the structure in Cs symmetry with Sc--H agostic interaction is 1-2 kcal/mol more stable than the structure with C2V symmetry. The energy being so small, the existence/nonexistence of agostic interaction should not change the chemistry of the reaction. At the CASSCF/BSI level used in the present work, the C2V structure is a real minimum. The theoretically “best estimated” Sc+dCH2 bonding energy is 85 ( 3 kcal/mol42c for the ground singlet electronic state 1A1 of ScCH2+ vs 96.9 ( 5.3 kcal/mol in experiment.43 The ground state 1A1 of this complex is a result of interaction of Sc+(3D, s1d1) with CH2(3B1). As seen in Table 6, the 3B1, 3B2, and 3A2 states are results of one-electron excitation from the π-bonding b1 orbital to nonbonding a1(dxx-yy), a2(dxy), and b2(dyz) orbitals, respectively, and are clustered in the range of 11-12 kcal/mol relative to 1A1, as shown in Table 4. The 3A1 state, with one-electron excitation from the π-bonding b1 orbital to the π* antibonding b1 orbital, is about 30 kcal/mol higher than 1A1. The Sc-C bond distances increase in the order 1A1 < 3B1 ∼ 3B2 ∼ 3A2 < 3A1, reflecting the nature of the excitation. As seen in Figure 3, the PESs of reaction 1′ for triplet and singlet electronic states of ScCH2+ behave quite similarly at the beginning. At first both the singlet and triplet reactants yield the ion-molecule complex (H2)ScCH2+ VII with stabilization energies of 3.2 and 3.5 kcal/mol; then activation of the H-H bond takes place with a 1.5 and 13.3 kcal/mol barrier relative to the singlet and triplet (H2)ScCH2+ complex, respectively. One should note that the transition state TS1 VI, corresponding to the H-H activation on the singlet surface, is 1.7 kcal/mol lower than the reactants; therefore the activation of the H-H bond by the ground singlet state ScCH2+ should occur easily in the gas phase. After the cleavage of the H-H bond the PESs of the singlet and triplet states become very different. For the triplet state the H-H bond cleavage directly leads to Sc(CH4)+ II without formation of the intermediate, HScCH3+. The singlet state forms the hydridomethyl complex, HScCH3+ IV, which lies 29.7 kcal/mol lower than the reactants and with a 18.4 kcal/mol barrier rearranges into the ion-molecule complex, Sc(CH4)+ I. The PES of reaction for the singlet crosses with the triplet PES at the seam minimum XM, structure V, between the HScCH3+(1A′) and Sc(CH4)+ complexes. Some trajectories will produce adiabatically the excited singlet state of the complex Sc(CH4)+ I, and some others will make intersystem crossing into the triplet state to produce the triplet ground state of the complex Sc(CH4)+ II. In either case, the barrier from the hydridomethyl complex IV is determined by the singlet state transition state TS2, III, which is calculated to be 18.4 kcal/
11606 J. Phys. Chem., Vol. 100, No. 28, 1996
Musaev and Morokuma
Figure 4. Potential energy profiles of the reaction FeCH2+ + H2 calculated at the MR-SDCI-CASSCF(9/9)/BSII+DC level (see ref 31 for details).
Figure 5. Potential energy profiles of the reaction CoCH2+ + H2 calculated at the MR-SDCI-CASSCF(8/8)/BSII level (see ref 30 for details).
mol relative to the HScCH3+(1A′) complex. All the calculated intermediates and transition states in the ground state are lower in energy than the ground state reactants, and therefore one can conclude that the reaction of the ground singlet state ScCH2+(1A1) + H2 should occur very easily and lead to HScCH3+(1A′) and Sc(CH4)+ (both 1A′ and 3A′′) complexes, which will dissociate to Sc+(1D and 3D, s1d1, respectively) and CH4. The entire reaction (1′) from the ground state ScCH2+(1A1) + H2 is exothermic by 18.0 and 24.8 kcal/mol for the singlet and triplet state products, Sc+(1D and 3D, s1d1, respectively) and CH4. The mechanisms of reactions 2′ and 3′ should follow the same path from the reactants up to the formation of HScCH3+(1A′) for the singlet and to the vicinity of the nonstationary hydridomethylscandinum structure for the triplet, where three channels should split. No barrier exists for either dissociation path.
intersystem crossing, one expects that the excited (4F, d7) state of Fe+ is more reactive with CH4 than the ground (6D, s1d6) state. (3) As seen in Figure 4, the form of potential energy surface of the reaction of FeCH2+ with H2 is qualitatively similar in the ground 4B2 and excited 2A1 states. The reaction pathway for the ground state process FeCH2+(4B2) + H2 f (H2)FeCH2+(4B2) f [TS1, 4A′′] f FeCH4+(6A2) f Fe+(6D, s1d6) + CH4 is estimated to be exothermic by 29.3 ( 5 kcal/ mol.31 In the first step, the reactants yield an ion-molecule complex (H2)FeCH2+, with a stabilization energy of 6 kcal/ mol. Then the H-H bond is activated through a four-centered transition state with a barrier of 24 and 18 kcal/mol relative to the (H2)FeCH2+(4B2) complex and the ground state reactants, respectively. The resulting complex, HFeCH3+, is not an intermediate (a local minimum at the CASSCF level, but its energy is higher than TS2 at the MR-SDCI level) and rearranges without barrier to an ion-molecule complex, FeCH4+. The ground state of the FeCH4+ complex is the sextet 6A2 state derived from the interaction of Fe+(6D, s1d6) with CH4 and can be reached via a seam of crossing between sextet and quartet PESs. The excited 4A2 state derived from interaction of Fe+(4F, d7) with CH4 lies 13 kcal/mol higher. The sextet FeCH4+ complex is stable relative to the dissociation limit Fe+(6D, s1d6) + CH4 by 15.5 kcal/mol vs the experimental value of 13.7 ( 0.8 kcal/mol.53 (4) As seen in Figure 5, the reactivity of CoCH2+ with H2 is very similar for low-lying 3A2 and 3A1 states. The reaction CoCH2+ + H2 f Co+ + CH4 (1′) is exothermic by 20 kcal/ mol. In the first step, reactants yield an ion-molecule complex (H2)CoCH2+, with a stabilization energy 8-9 kcal/mol. Then the H-H bond is activated through a four-centered transition state with a barrier of 34 kcal/mol. The resultant complex, HCoCH3+, does not exist (a local minimum at the CASSCF level, but its energy is higher than TS2 at the MR-SDCI level) and rearranges without barrier to the ion-molecule complex CoCH4+, which is stable relative to the dissociation limit Co+(3F, d8) + CH4 by 21-22 kcal/mol vs the experimental value of 22.9 ( 0.7 kcal/mol.54 (5) The mechanisms of reactions 1′-3′ should follow the same path from the reactants MCH2+ + H2 up to formation of HMCH3+, for both M ) Fe and Co. Though HMCH3+ is not an intermediate, it is likely that the system passes through the
IV. Comparison of PESs of Reactions 1-3 for Early (Sc+) and Late (Fe+ and Co+) Transition Metal Cations In this section we will compare the above discussed results for the Sc++CH4/ScCH2++H2 reaction system with those for the Fe++CH4/FeCH2++H2 and Co++CH4/ CoCH2++H2 systems calculated earlier29-31 at essentially the same level of theory, MR-SDCI-CASSCF/BSII (without ZPC) at the CASSCF/ BSI optimized geometries. While the calculation for the Fe and Sc systems includes the DC, that for Co does not, which would cause differences in energy of a few kcal/mol but would not affect qualitative conclusions of the comparison. The potential energy surfaces for the Fe and Co systems are shown in Figures 4 and 5, respectively, where the same energy scale as in Figure 3 is used. At first, it is useful to recall the main conclusions of the previous papers. (1) The ground states of FeCH2+ and CoCH2+ are nearly degenerate (4B2, 4B1) and (3A1, 3A2) pairs, respectively. (2) The reaction M+ + CH4 for Fe and Co at moderate temperatures can give only one stable product, the ion-molecule complex MCH4+. Though the endothermicities of reactions 1-3 are similar, reaction 1 requires a large activation barrier and is not likely to take place, whereas reactions 2 and 3 should be possible at elevated temperatures. Also since the Fe+(6D, s1d6) f Fe+(4F, d7) excitation makes reactions 1-3 by a few kcal/mol less endothermic and does not require unfavorable
Reaction Mechanism of Sc+ with Methane neighborhood of HMCH3+ and dissociates into MH+ + CH3 or MCH3+ + H. These reactions are more exothermic for M ) Fe than for M ) Co. Comparison of PESs of reactions 1-3, as well as 1′-3′ between M ) Sc, Fe, and Co given in Figures 3-5 shows some significant differences in the reactivity between early (Sc) and late (Fe and Co) first-row transition metal cations and carbene complexes. The insertion product HMCH3 is both thermodynamically and kinetically stable relative to the ground state dissociation limit M+ + CH4 for M ) Sc, while it is neither thermodynamically nor kinetically stable (i.e. not a local minimum) on the PES for M ) Fe and Co. In other words, Sc+ reacts with methane in an indirect manner with formation of the hydridomethyl complex HScCH3+, while Fe+ and Co+ react with methane in a direct manner without formation of the HMCH3+ complex. The ground state insertion reaction M+ + CH4 f HMCH3+ is exothermic by 5 kcal/mol for M ) Sc but is endothermic by 17 and 7 kcal/mol for M ) Fe and Co, respectively. This trend in the thermodynamic stability of insertion products can be understood by the following two factors. (1) In the HMCH3+ complex the s1dn+1 state of the cation is the dominating bonding state; it can form two covalent bonds and lowers the spin of the system by two. For Sc+ and Fe+ the s1dn+1 state (3D(s1d1) and 6D(s1d6), respectively) is actually the ground state and can directly form bonds to give HMCH3+ in the 1A′ and 4A′′ state, respectively. However, for Co+ the 3F(s0d8) state is the ground state. To form bonds, one has to imagine that Co+ is promoted to the excited state 5F(s1d7) with the promotion energy of 10.1 kcal/mol52 (4.4 kcal/mol at the present calculation), which can form bonds to give triplet HMCH3+. (2) Upon formation of M-H and M-CH3 bonds, which stabilize the system, the loss of exchange energy takes place and counteracts the stabilization. The exchange energy loss increases with the increasing number of unpaired electrons. This loss upon formation of a transition metal-ligand bond has been mentioned in many previous studies34b,55 and tabulated for transition metal cations by Carter and Goddard.55 According to this table,55 the exchange energy loss for formation of two covalent bonds to an s1dn-1 state is calculated to be 4.2, 41.4, and 29.3 kcal/mol for Sc+(3D, s1d1), Fe+(6D, s1d6), and Co+(5F, s1d7), respectively. For the ground state of Co+, adding the promotion energy from factor (1), this increases to 39.4 kcal/mol.30 Thus, the decrease in the thermodynamic stability of HMCH3+ relative to M+ + CH4 in the order M ) Sc > Co ∼ Fe is well correlated with the increase in exchange and promotion energy loss. As the exchange and promotion costs for formation of two bonds increase via Sc+ (4) < Ti+ (14) < V+ (34) < Cr+ (73) and then decreases via Mn+ (52) > Ni+ (42) ∼ Fe+ (41) > Co+ (39) (in kcal/mol),55 we expect the thermodynamic stability of the insertion product to decrease via M ) Sc+ > Ti+ > V+ > Cr+ and increase via Mn+ < Ni+ ∼ Fe+ < Co+. The kinetic stability of the inserted product, HMCH3+, for Sc+ compared with Fe+ and Co+ also can be explained by mentioning two factors. (1) The first factor is the endothermicity of the reaction MCH4+ f HMCH3+. The large endothermicity of reaction reduces the barrier for the reverse reaction, HMCH3+ f MCH4+.56 As seen from Figures 3-5, the adiabatic potential profile within the low-spin state for the reaction MCH4+ f HMCH3+ is endothermic by 2, 19, and 30 kcal/mol for M ) Sc, Fe, and Co, respectively. (2) The second is the electronic factors controlling the strength of interaction between reactants M+ + CH4. It is well-known that upon oxidative addition of a C-H/H-H σ bond to the transition metal center a charge transfer takes place from the C-H/H-H σ
J. Phys. Chem., Vol. 100, No. 28, 1996 11607 orbitals to the metal (donation) and from the metal π orbitals to the σ* antibonding orbital of the C-H/H-H bond (backdonation). These interactions are efficient when the metal center has empty (or partially empty) σ-type s and dσ orbitals and occupied dπ orbitals. Fe+ and Co+ have occupied dπ orbitals, but Sc+ has none, favoring late transition metals over early ones. It is also well-known that states of atoms or cations with less s population activate the H-H and C-H σ bonds with less barrier.9,34 The s0dn+2 state is the ground state for Co+, but lies 6 and 37 kcal/mol higher than s1dn+1 states for Fe+ and Sc+, respectively. These two electronic factors thus should result in stronger interaction for M ) Fe and Co than for Sc and therefore in the lack of transition state for the former. On the basis of these comparisons, we can predict that all early first-row transition metal cations (Sc+, Ti+, and V+) which have empty s or d orbitals with a1 symmetry can easily activate C-H σ bonds as well as O-H and N-H bonds in the gas phase. ScCH2+ is much more reactive to H2 than its Fe+ and Co+ analogs. The energy of the transition state for H-H activation, relative to the ground state reactant MCH2+, increases in the order Sc(-1.7 kcal/mol) < Fe(18 kcal/mol) < Co(26 kcal/mol), e.g. with the increasing number of electrons in the transition metal cations. The easiest activation of the H-H bond by ScCH2+ compared with late transition metal complexes FeCH2+ and CoCH2+ can be explained by analyzing the ground state of the reactant, MCH2. As was mentioned above, the ground state of ScCH2+ is 1A1 with doubly occupied [a1(σ bond)]2 and [b1(π bond)]2 and unoccupied a1(dxx-yy), a1(dzz), a2(dxy), and b2(dyz) orbitals. All these unoccupied orbitals are metal-localized d orbitals and are nearly degenerate. Thus, the empty a1 orbitals of Sc+ can easily accept electrons from the H-H σ-bonding orbital. On the other hand, in the ground states of FeCH2+ and CoCH2+, 4B2 (or 4B1) and 3A2 (or 3A1), respectively, all these molecular orbitals are singly or doubly occupied:
[a1(σ bond)]2[b1(π bond)]2[a2(dxy)]2[a1(dxx-yy)]1 [a1(dzz)]1[b2(dyz)]1: 4B2, FeCH2+ and
[a1(σ bond)]2[b1(π bond)]2[a2(dxy)]1[a1(dxx-yy)]2 [a1(dzz)]1[b2(dyz)]2: 3A2, CoCH2+ Therefore, the donation of the electrons from the H-H σ bond to the metal center is energetically difficult. From these observations and discussions, we can predict also that the activation of H-H (or C-H) bonds should take place more easily with early transition metal carbene cations than with their late transition metal analogs. V. Conclusions The following key points may be drawn from the calculations presented here. (1) The ground state of ScCH2+ is 1A1, a result of the interaction of Sc+(3D, s1d1) with CH2(3B1). The 3B1, 3B2, and 3A states, results of one-electron excitation from the π-bonding 2 b1 orbital to nonbonding a1(dxx-yy), a2(dxy), and b2(dyz) orbitals, respectively, are clustered in the range 11-12 kcal/mol, relative to 1A1. The structure of ScCH2+ with C2V symmetry is calculated to be a real minimum at the present level of theory. The dissociation energy for ScCH2+(1A1) f Sc+(3D, s1d1) + CH2(3B1) is calculated to be 79.3 kcal/mol. This is in good agreement with previous calculations, 85 ( 3 kcal/mol,42c and
11608 J. Phys. Chem., Vol. 100, No. 28, 1996 is 17.6 ( 5.3 kcal/mol smaller than the experimental value, 96.9 ( 5.3 kcal/mol, which seems to be overestimated.43 (2) The reaction of the ground state (3D, s1d1) of Sc+ with CH4 proceeds via the pathway Sc+(3D, s1d1) + CH4 f ScCH4+(3A′′) f TS2 f HScCH3+(1A′) f TS1 f (H2)ScCH2+(1A1) f ScCH2+(1A1) + H2 and is calculated to be endothermic by 24.8 kcal/mol vs the experimentally estimated value of 11-12 kcal/mol,36 which seems to be underestimated by 10 ( 5 kcal/mol due to the overestimation discussed in (1). In the first step, the reactants yield an ion-molecule complex, Sc(CH4)+, with a stabilization energy of 15.1 kcal/mol. The insertion of Sc+ into the C-H bond of CH4 cannot take place on the triplet potential surface. It has to make an intersystem crossing to the singlet surface and proceed over an insertion barrier of 28.6 kcal/mol. The reaction of the first excited state 1D(s1d1) should take place much more easily, because of extra initial electronic energy and because it is not necessary to make inefficient intersystem crossing. The insertion product, HScCH3+, exists on the PES of the reaction in the singlet state and lies 4.9 kcal/mol lower than ground state reactants Sc+(3D, s1d1) + CH4. From the complex HScCH3+, the reaction may split into three different channels, ScCH2+ + H2 (1), ScH+ + CH3 (2), and ScCH3+ + H (3). Among these, channel 1 is energetically and kinetically more favorable and proceeds through a fourcenter transition state, TS1, and the ion-molecule complex, (H2)ScCH2+(1A1). The energetic barrier for this process is calculated to be 28 kcal/mol. The calculated energy of the decomposition of (H2)ScCH2+(1A1) into H2 and ScCH2+(1A1) fragments, which takes place without barrier, is 3.2 kcal/mol. Reactions 2 and 3 may also take place directly via the triplet surface, without going through the singlet intermediate HScCH3+. The H-ScCH3+ and HSc+-CH3 bonding energies are calculated to be 48.8 and 47.5 kcal/mol, and reactions 2 and 3 are endothermic by 42.6 and 43.9 kcal/mol, respectively. Thus, the reaction of methane with Sc+ should proceed via channel 1 at low temperatures, while at higher temperatures channels 2 and 3 may dominate. This conclusion is in good agreement with the available experiments.35,36 (3) The reverse reaction ScCH2+ + H2 should proceed very easily and lead to the products HScCH3+(1A′), ScCH4+(1A′ and 3A′), and Sc+(1D and 3D) + CH at low temperatures. 4 (4) A comparison of calculated results in this paper for early first-row transition metal Sc+ (or ScCH2+) with those in our previous papers29-31 for late first-row transition metals Fe+ and Co+ (or FeCH2+ and CoCH2+) has shown the following. (a) The main products of the reaction of early first-row transition metal cations, such as Sc+, Ti+, and V+, with CH4 at low temperatures should be MCH2+ and H2 because of channel 1 is less endothermic than channels 2 and 3. The hydridomethylmetal complex HMCH3+ is thermodynamically and kinetically stable and should be observed. For late first-row transition metals, the endothermicity of channels 1-3 is similar; reaction 1 requires a large H-H bond activation barrier and is not likely to take place, whereas reactions 2 and 3 should be possible at elevated temperatures. The hydridomethylmetal complex does not exist thermodynamically or kinetically and cannot be observed. This conclusion is in good agreement with available experiments.35,36 (b) The carbene complex of early transition metal cations, such as ScCH2+, TiCH2+, and VCH2+, should more easily activate H-H or C-H σ bonds than their late firstrow transition metal analogs. While the main products of this reaction are expected to be M+ + CH4, the hydridomethylmetal complex HMCH3+ along with the ion-molecule complex M(CH4)+ can be observed. The reaction of the carbene complex of late first-row transition metal cations should be more difficult.
Musaev and Morokuma Acknowledgment. The authors express their gratitude to C. Haynes and Prof. P. B. Armentrout for providing experimental results concerning the reaction FeCH2+ + H2 before publication. Acknowledgment is made to Qiang Cui for his assistance in searching the crossing seam minimum. The present research is in part supported by a grant (CHE-9409020) from the National Science Foundation. References and Notes (1) Structure/ReactiVity and Thermochemistry of Ions; Ausloos, P., Lias, S. G., Eds.; Reidel: Dordrecht, The Netherlands, 1987. (2) In Gas Phase Inorganic Chemistry; Russell, D. H., Ed.; Plenum: New York, 1989. (3) SelectiVe Hydrocarbon ActiVation: Principles and Progress; Davies, J. A.; Watson, P. L., Liebman, J. F., Greenberg, A., Eds.; VCH: New York, 1990. (4) Eller, K.; Schwarz, H. Chem. ReV. 1991, 91, 1121. (5) Gas-Phase Metal Reactions; Fontijn, A., Ed.; Elsevier: Amsterdam, 1992. (6) Weisshaar, J. C. In AdVances in Chemal Physics; Ng, C., Ed.; Wiley-Interscience: New York, 1992; Vol. 81. (7) Transition Metal Hydrides; Dedieu, A.; Ed.; VCH: New York, 1992. (8) Bonding Energetics in Organometallic Compounds; Marks, T. J., Ed.; ACS Symposium Series 428; American Chemical Society: Washington, DC, 1990; p 55. (9) Armentrout, P. B. In Gas Phase Inorganic Chemistry; Russell, D. H., Ed.; Plenum: New York; 1989, p 1. (10) Armentrout, P. B.; Beauchamp, J. L. Acc. Chem. Res. 1989, 22, 315. (11) Armentrout, P. B. Science 1991, 251, 175. (12) Roth, L. M.; Freiser, B. S. Mass Spectrom. ReV. 1991, 10, 303. (13) Weisshaar, J. C. Acc. Chem. Res. 1993, 26, 213. (14) Irikura, K. K.; Beauchamp, J. L. J. Am. Chem. Soc. 1989, 111, 75. (15) Irikura, K. K.; Beauchamp, J. L. J. Phys. Chem. 1991, 95, 8344. (16) Irikura, K. K.; Beauchamp, J. L. J. Am. Chem. Soc. 1991, 113, 2769. (17) Armentrout, P. B.; Georgiadis, R. Polyhedron 1988, 7, 1573. (18) Elkind, J. L.; Armentrout, P. B. J. Phys. Chem. 1986, 90, 5736. (19) Gord, J. R.; Freiser B. S. J. Chem. Phys. 1989, 91, 7530. (20) Bucker, S. W.; MacMahon, T. J.; Byrd, G. D.; Freiser, B. S. Inorg. Chem. 1989, 28, 3511. (21) Roth, L. M.; Freiser, B. S. Mass Spectrom. ReV. 1991, 10, 303. (22) (a) Hettich, R. L.; Freiser, B. S. J. Am. Chem. Soc. 1986, 108, 2537. (b) Hettich, R. L.; Freiser, B. S. J. Am. Chem. Soc. 1986, 109, 3543. (c) Jacobson, D. B.; Freiser, B. S. J. Am. Chem. Soc. 1985, 107, 67. (d) Jacobson, D. B.; Freiser, B. S. J. Am. Chem. Soc. 1985, 107, 2605. (e) Jacobson, D. B.; Freiser, B. S. J. Am. Chem. Soc. 1985, 107, 4374. (f) Jacobson, D. B.; Freiser, B. S. J. Am. Chem. Soc. 1985, 107, 5870. (23) Tonkyn, R.; Ronan, M.; Weisshaar, J. C. J. Phys. Chem. 1988, 92, 92. (24) Schroder, D.; Schwarz, H. Angew. Chem., Int. Ed. Engl. 1995, 34, 1973, and references therein. (25) (a) Haynes, C. L.; Chen, Y. M.; Armentrout, P. B. J. Phys. Chem. 1995, 99, 9110. (b) Haynes, C. L.; Armentrout, P. B. J. Phys. Chem., in press. (c) Chen, Y. M.; Armentrout, P. B. J. Phys. Chem. 1995, 99, 10775. (26) (a) Bushnell, J. E.; Kemper, P. R.; Maitre, P.; Bowers, M. T. J. Am. Chem. Soc. 1994, 116, 9710. (b) van Koppen, P. A. M.; Kemper, P. R.; Bushnell, J. E.; Bowers, M. T. J. Am. Chem. Soc. 1995, 117, 2098. (27) (a) Guo, B. C.; Castleman, A. W., Jr. J. Am. Chem. Soc. 1992, 114, 6152. (b) Guo, B. C.; Kerns, K. P.; Castleman, Jr. A. W. J. Phys. Chem. 1992, 96, 4879. (28) Musaev, D. G.; Koga, N.; Morokuma, K. J. Phys. Chem. 1993, 97, 4064. (29) Musaev, D. G.; Morokuma, K. Isr. J. Chem. 1993, 33, 307. (30) Musaev, D. G.; Morokuma, K.; Koga, N.; Nguyen, K. A.; Gordon, M. S.; Cundari T. R. J. Phys. Chem. 1993, 97, 11435. (31) Musaev, D. G.; Morokuma, K. J. Chem. Phys. 1994, 101, 10697. (32) Perry, J. K.; Ohanessian, G.; Goddard, W. A., III. J. Phys. Chem. 1993, 97, 5238. (33) Perry, J. K.; Ohanessian, G.; Goddard, W. A., III. Organometallics 1994, 13, 1870. (34) (a) Blomberg, M. R. A.; Siegbahn, P. E. M.; Svensson, M. J. Phys. Chem. 1994, 98, 2062. (b) Siegbahn, P. E. M.; Blomberg, M. R. A.; Svensson, M. J. Am. Chem. Soc. 1993, 115, 4191. (35) Tolbert, M. A.; Beauchamp, J. L. J. Am. Chem. Soc. 1984, 106, 8117. (36) Sunderlin, L. S.; Armentrout, P. B. J. Am. Chem. Soc. 1989, 111, 3845. (37) Alvarado-Swaisgood, A. E.; Allison, J.; Harrison, J. F. J. Phys. Chem. 1985, 89, 2517.
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