Ab initio molecular orbital study of the electronic and geometric

J. Phys. Chem. 1993,97, 4064-4075

4064

-

Ab Initio Molecular Orbital Study of the Electronic and Geometric Structure of RhCH2+ and the Reaction Mechanism: RhCH2+ H2 Rh+ + CH4

+

Djamaladdin G. Musaev,+t*Nobuaki Koga, and Keiji Morokuma'y* Institute for Molecular Science, Myodaiji, Okazaki 444, Japan Received: October 20, 1992

-

By using CASSCF and MR-SDCI-CASSCF methods we have calculated electronic and geometric structures of RhCH2+, as well as the potential energy surfaces (PESs) of reaction: RhCH2+ H2 Rh+ CH4. The ground state of RhCH2+ is 'AI, and nearly degenerate 3A1and 3A2states lie about 4-5 kcal/mol higher. The calculated binding energy for RhCH,+('Al) Rh+(3F) CH2(3B1) is 78.3 kcal/mol vs experimental results of 91 f 5 kcal/mol. The PESs of the reaction, calculated for the ground 'Al and the excited 3Al states of RhCH2+, are very similar. In the first step, reactants give an ion-molecule complex, (H2)RhCH2+, with a stabilization energy of about 7 kcal/mol. Then the H-H bond activation takes place with a 16 kcal/mol barrier. The resultant complex HRhCH3+ probably does not exist but rearranges without barrier to the product complex RhCH4+(3A'), which is stable by about 17 kcal/mol relative to Rh+(3F) CH4.

+

-

+

+

+

I. Introduction Over the past decade, there have been extensive activities in studying gas-phase reactions of both transition-metal cations and their unsaturated carbene complexes MCH2+ with the molecule H2 and small alkanes, in order to provide insight into the mechanism of H-H, C-H, and C-C bond activation proces~es.l-~ In general, the following results have been obtained. a. For first-row transition-metal cations, dehydrogenationand demethanation are common processes. But there exists no example of facile, exothermic CH4 activation. The endothermic reaction

M+ + CH,

-

MCH,'

+ H,

has been observed only for early transition-metal ions SC+-C~+.'-~ b. Many second- and third-row transition-metal cations, such as Zr+, Ta+, Os+, Ir+, and Pt+ can dehydrogenate CH4 exothermically. c. Carbene complexes MCH2+ of the first-row transitionmetal cations, such as CoCH2+and FeCH2+,I4are less reactive with Hzandalkanesthan thoseof second- and third-rowtransitionmetal cations, such as RhCHz+,l5 IrCH2+,1°and TaCH2+.I0 d. The reactivity of these systemsdependson both the electronic configuration and the spin state.I6 Theoretical17-S9and experimenta11-9@investigations of structure and stability of both saturated L,MCRR' and unsaturated MCH2+ complexes also show that the M=C bond in these complexes is a double bond. But its character dramatically changes depending on the electronic states and chemical nature of atom M, as well as the ligand L and substituents R and R'. In a separate papers9 we have used an ab initio method and studied the structure and stability of CoCH2+, as well as the reaction mechanism: CoCH,'

+ H2

-

Co+

+ CH,

(1)

The following conclusions have been obtained. 1. The ground state of CoCH2+is nearly degenerate 3A2and 3AIstates. 2. The calculated binding energy BE, C O C H ~ + ( ~ A Co+~) (3F,ds)+ CHZ(~BI), is about 80.3 kcal/mol, in comparison with

-

~~

+ On leave from Institute of New Chemical Problems, Russian Academy of Sciences, Chernogolovka 142432, Moscow Region, Russia. Present address: Department of Chemistry, Emory University, Atlanta, GA 30322.

0022-365419312097-4064$04.00/0

the ion-beam experiment value of 77.5 f 2.3 kcal/moP and gas-phase photodissociation experiment value of 84 f 5 kcal/ mo1.62 3. The reactivity with H2 is very similar for low-lying 3A2and 3Al states of CoCH2+. 4. Reaction 1 is calculated to be exothermic by 27-29 kcal/ mol vs the experiment value of 25 f 7 k c a l / m ~ l . ~ ~ 5. The energetic barrier for activation of the H-H bond is calculated to be rather higher, 33.5 kcal/mol, suggesting that reaction 1 cannot take place at moderate conditions. 6. The complex HCoCH3+ does not exist. It rearranges without barrier into the ion-molecule complex CoCH4+, which is stable relative to the dissociation limit Coy3F) CH, by 21.4 kcallmol. The collision-induced experiment gives > 11 kcal/mol for the MCH4+complex of first-row transition meta1.63 7. The reaction Co+ CHI gives only one product, the CoCH4+ complex, in good agreement with experiment.63.64 In the present paper, we carry out a similar ab initio MO study on the structure and stability of the complex RhCH2+,as well as on the reaction mechanism:

+

+

RhCH;

+ H,

-

Rh+

+ CH4

(2) E ~ p e r i m e n t a l l y lFourier ~ ~ ~ ~ transform mass spectrometry (FTMS) and HID exchangemethods have been used toinvestigate the structure and reactivity of the complex RhCH2+,which has been formed by reaction of laser-generated Rh+ with ethylene oxide. Rh+

+ O(CH,),

-

+

RhCH2+ CH,O

The electronic structure of RhCH2+ has theoretically been investigated by a density functional method.56 The following have been experimentally and theoretically found: 1. The most favorable structure is Rh+=CH2, methylene bound to Rh+. 2. The Rh+-CH* binding energy in RhCHZ+ is 91 f 5 kcal/ 11101.65

3. Reaction 2 is exothermic by about 20 kcallmol and can take place easily. 11. Methods of Calculations

In our calculations we use two sets of effective core potentials and basis functions. The first of them, called set I below, is the relativistic effective core potential (RECP) in which electrons in the outer 4d5s shells of Rh atom are explicitly considered66 and 0 1993 American Chemical Society

Electronic and Geometric Structure of RhCH2+

The Journal of Physical Chemistry, Vol. 97, No. 16, 1993 4065

TABLE I: Active Spaces Used for CASSCF and MR-SDCI-CASSCF Calculations of Rh+, Hz, CH2, and RhCHZ+' system

orbitals included

size

system

orbitals included

RhCH2+ H2, H*RhCH2+, and TS1 (H2 addition) HRhCH,+ and TS2 (CH4 elimination)*

RhCH2+ (10/8) = 3al lbl la2 2b2 4al 5al 6a1 2bl and HI (2/2) = 7a1 (H-H, bond) 3b2 (H-H, antibond) (Rh-H, bond) (Rh-C, bond) (C-H, bond) (Rh-H, antibond) (Rh-C, antibond) (C-H, antibond) + two (la2 2b2) lone-pair d orbitals + two (4al 5al) single occupied orbitals Rh+ (8/6) = bl(dxz) b2(dy,) a2(dXy)addxx-yy)a 1 ( d 2 ~ ~ - ~ ~ -and ~ ~CHI ) (4/4) = two C-H bonding and antibonding orbs

+

RhCHdtr

The (8/8) active space is obtained from (12/10) by excluding two lone-pair d orbitals. In case of TS2 (CH4 elimination) one lone-pair d orbital becomes involved in three-centered bonding between Rh, C, and H atoms. The (10/8) active space, used for geometry optimization of HRhCH,+ and TS2, is obtained from (12/ 10) by excluding C-H bonding and antibonding orbitals. The (8/6) active space, used for optimizing geometry of RhCH4+, includes only valence electrons and orbitals from Rh+. (I

TABLE III: Total and Relative Energy of Three Electronic the following split-valencebasis sets: ( 3 ~ 3 p 4 d / 2 ~ 2 ~ 2 d )(9s5p/ ~h,6~ States of Rh+, Calculated at Various Computational Levels 3s2p)~:~and (4s/2s)H.67 In the second set, called set 11, we use AE,,l, kcal/mol the RECP6*in which the Rh 4s4p4d5s electrons are explicitly -Etot,au 1D-3F SF-SF computational level 3F(d8) considered, with the following basis sets: triple-zeta (5s5p4d/ 3~3p3d)~ and h ~split-valence ~ polarizations ( 9 ~ 5 p l d / 4 ~ 2 p l d ) c ~ ~ HF/II 108.45726 58.5 36.2 (ad = 0.7Y9) and (4slp/2slp)H67(ap= l.0).69 Set IIa is set I1 CASSCF(8 /6) / I1 108.46064 28.1 38.3 CASSCF(8/8)/II 108.48914 32.8 41.9 supplemented with an fRh polarization function, and set IIb is MR-SDCI-CASSCF(8/6)/II 28.4 48.6 108.51653 supplemented with a double-zetafRh and dc and dH polarization MR-SDCI-CASSCF(8/8)/II 108.51812 29.0 46.2 functions, as will be detailed later. We also use other RECP and CASSCF(8/8)/II+f 108.46143 29.2 basis functions in some sections (sets I11 and IIIa). MR-SDCI-CASSCF(8/8)/II+f 108.55281 28.2 The geometric parameters of reactants, products, intermediates, e~pt'~ 23.3 55.4" and transition states of reaction 2 have been optimized by using Average over J. the CASSCF method with set I with the GAMESS package program.70 Their energies have been improved by the internally Such an active space is (8/8), which excludes two lone-pair d contracted single and double CI from the CASSCF reference orbitals from the (12/ 10) active space. functions, i.e., at the MR-SDCI-CASSCF level, with set I1 using For geometry optimization of HRhCH3+ and the transition the MOLPRO package program." state (TS2) for CH4 elimination, the (12/10) active space As shown in Tables I and 11, the complete active space (nlm), correlates one CH bond but not the other two CH bonds and is which includes all of the electronic configurations arising from not the most consistent. Thus, we used the (10/8) active space n electron in m active orbitals, used in these CASSCF and MRin which no CH bonds are correlated. For the same reason, we SDCI-CASSCFcalculations varies in a wide range and requires used for geometry optimization of the product complex Rh+CH4 some further explanation. For Rh+ two types of active space the (8/6) active space containing only valence orbitals and have been used. The first, (8/6), includes all valence electrons electrons from Rh+ but no CH bonds. When different active and orbitals of Rh+. The second, (8/8), includes the virtual spaces are used for geometry optimization of different species, orbitals corresponding to the doubly occupied orbitals, as well as one has to be sure to use the same active space and method for all valence electrons and orbitals. For H2, we use the (2/2) active energetic comparison of different species. We carried this out space consisting of ug and uu* molecular orbitals (MOs). For usingCASSCF( 12/10)/11 andCASSCF(8/8)/II, as wellasMRCH2, we include only 3al and lbl orbitals in the (2/2) active SDCI with either of the CASSCF reference functions. space and exclude orbitals and electrons of the two C-H bonds Below, we use notations such as CASSCF(n/m)/i, with i after that are not broken during the course of reaction 2. The (10/8) the slash denoting the RECP and basis set ( i = I and 11). active space for RhCH2+includes all (8/6) valence electrons and The binding energies for orbitals of Rh+ and (2/2) of CH2, again excluding the C-H bonds. The smaller (6/6) active space excludes the la2 and 2b2 RhCH: Rh+ CH, lone pairs on Rh+ and is used later in conjunction with the (8/8) calculation of the potential energy surfaces. As shown in Table 11, for calculation of the potential energy (H2)RhCH2+ H, RhCH; surfaces (PESs) of reaction 2, the consistent active space must be (12/10), consisting of all valence electrons and orbitals, including H-H, Rh-H, and C-H (excluding C-H bonds of the RhCH,' Rh+ CH, CH2 fragment) bonding and antibonding orbitals. At the dissociation limit, it becomes the RhCH2+ (10/8) and the H2 were calculated as energy differences between total energies of (2/2) active space. However, this active space is rather large and, to economize computer time and resources, we have also corresponding equilibrium structures and "supermolecules" Rh+-CH2, H2- ThCH2+, and Rh+-CH4, respectively. In used a smaller active space consistent along the reaction paths.

-

-

-

+

+

+

Musaev et al.

4066 The Journal of Physical Chemistry, Vol. 97, No. 16, 1993

TABLE I V Calculated Geometries and Energies for 'A1 and 3B1States of CH2 'AI calculation level and refs CASSCF(2/2)/1 CASSCF( 2/2)/11b MR-SDCI-CASSCF(2/2)/IIb CASSCF(2/2)/IIb

r(C-H), A 1.105

LHCH, deg 105.29

1.099

102.93

1.110

102.10

MR-SDCI-CASSCF(2/2)/IIbC Bauschlicher et al.75 e~pt'~

'BI

AE,u kcal/mol 23.2 18.1 12.4 13.6 1.5 9.1 9.02 0.01

*

r(C-H), A 1.073

LHCH, deg 130.37

1.071

129.57

1.079 1.077

133.70 133.40

EtOttau -38.91 360 -38.9244 1 -38.93080 -38.93221 -38.93946

Energy difference between the ground 'BI and the excited 'AI state. At CASSCF(2/2)/I geometry. At CASSCF(2/2)/IIb geometry.

TABLE VI: Natural Orbital Occ ncies of Princi contigurntiollpl State Fmctiom a r m i r wei&+s Percent) for the Low-Lying IAl, 3 A ~3A2, , 3B1, and 3 B States ~ of RICH2+,Calculated at the CASsCF(10/8)/I Level'

ff

4= H

I

RhX

state

3a1

lbl

2bz

laz

4a1

5a1

2b1

6a1

wt

'A]

2 2 1 2 2 0

2 0 1 2 2 2

2 2 2 2 2 2

2 2 2 0 2 2

2 2 2 2 0 2

0 0 1 2 2 2

0 2 1 0 0 0

0 0 0 0 0 0

86.5 4.0 1.4 2.0 1.6 1.0

'AI

2 1 2

2 1 0

2 2 2

2 2 2

1 2 1

1 1 1

0 1 2

0 0 0

90.2 1.5 3.0

)A2

2 2 1 2

2 1 1 0

2 2 2 2

1 1 1 1

2 2 2 2

1 1 2 1

0 1 1 2

0 0 0 0

89.2 1.0 1.6 2.6

'Bi

2 2 2 2

2 1 1 2

1 2 1 1

1 2 1 1

2 2 2 2

2 1 2 1

0 2 1 0

0 77.1 0 7.5 0 5.4 1 3 . 3

2 2 2 1 2

2 2 1 1 0

1 2 1 1 1

2 1 2 2 2

2 1 2 2 2

1 1 1 2 1

0 1 1 1 2

0 8 1 . 6 0 1.8 0 1.6 0 2.3 0 4.0

Y

/

J

Figure 1. Coordinate system used for RhCH2+ and CH2.

Figure 2. Orbital correlation diagram for Rh+(d8,'F) RhCH2+('Ai).

+ CHz('B1)

-

TABLE V Geometric and her etic Parameters of Varieties of Electronic States of RbCHz+, fhlculated at the CASSCF( 10/8)/I Level state R(Rh-C), A r(C-H), A LHCH, den hE,,i, kcal/mol 'AI 3AI 'A2 3B~ 'B2

1.767 1.781b 1.870 1.870 2.107 1.901

1.OS0 1.078b 1.079 1.079 1.083 1.078

122.16 121.71b 116.50 116.59 111.71 118.33

0.00 11.4 9.6 39.0 29.9

Total energy is -60.92421 au. Optimized at the CASSCF( 10/8)/ IIb level.

calculationof supermoleculesthe distance between the dissociated fragments was taken to be 15.0 A. 111. Electronic Structures of Rh+, CH2, and RbCHz+

It is essential that our calculations can reproduce geometries, electronicstructure,and energies of reactant and product fragment molecules. Therefore, our discussion begins with Rh+ and CHI, followed by RhCH2+. Rh+. Experimentally the ground state of Rh+ is 3F(d*),with the ID(d8)and 5F(s1d7) states lying about 23.3 and 55.4 kcal/mol higher, re~pectively.~~ As seen from Table 111, where we give results of calculations for Rh+,the H F method cannot even give a correct order of the three lowest states. The full valence

Only configurations with weight of not less than 1.0% are shown.

TABLE M: Active Natural Orbital Occupancies and Rb and CHZContributions' to Them for Varieties of States of RhC&+, Calculated at the CASsCF(10/8)/I Level ~~

state

-

3a I 'Al, toal 1.921 Rh 0.959 CH2 0.962 'A!, total 1.935 Rh 0.907 CH2 1.028 'A2, total 1.934 Rh 0.904 CH2 1.030 )BI,total 1.957 Rh 0.590 CH2 1.367 'B2, total 1.925 Rh 1.071 CH2 0.854

1b1 1.862 1.25 1 0.61 1 1.878 1.464 0.414 1.882 1.474 0.408 1.866 1.712 0.154 1.835 1.406 0.429

2b2 1.990 1.959 0.03 1 1.989 1.982 0.007 1.996 1.98 1 0.015 1.093 1.088 0.005 1.047 1.036 0.011

~

la2 1.935 1.935 0.000 1.992 1.992 O.Oo0 1.002 1.002 0.000 1.094 1.094 0.000 1.950 1.950

4a I 1.996 1.978 0.018 1.005 0.995 0.010 1.995 1.988 0.007 1.996 1.974 0.022 1.962 1.868 0.OOO 0.094

5a I 0.126 0.079 0.047 1.028 0.792 0.236 1.025 0.784 0.241 1.898 1.669 0.229 1.045 0.729 0.316

2b1 6a I

0.148 0.059 0.089 0.132 0.044 0.088 0.123 0.039 0.084 0.058 0.013 0.045 0.198 0.064 0.134

0.023 0.01 1 0.012 0.042 0.023 0.019 0.041 0.022 0.019 0.039 0.022 0.017 0.039 0.021 0.018

Rh and CH2 contributionscalculated by Mulliken population analysis for each NO.

CASSCF(8/6) is not adequate either. Methods which also take some d-d* correlationinto account, CASSCF(8/8), MR-SDCICASSCF(8/6), and MR-SDCI-CASSCF(8/8), however, give acceptable agreement with experiment. Inclusion of the f polarization function (a = 0.3573)to the Rh basis set probably is not necessary for energetic parameters of Rh+. As seen in Table 111, the f function changes the 3F-ID energy difference very little, 3.6 and 0.8 kcal/mol at the CASSCF(8/8) and MR-


Electronic and Geometric Structure of RhCH2+ -1.00

-O.IO

-2.40

0.80

2.40

-4.00

-2.40

-0.80

0.60

2.40

-4.00

1

I

b

-2.40

0.60

-0.60

2.40

C

i

i

8

1

t8

8

i

l---L--

9,

9 -4.00

I -4.00

-2.40

I

I

,

-0.80

'

I

I

I

I

2.40

0.60

-2.40

-0.80

X -4.00

-2.40

-0.60 I

I

0.60 I

I

I

2.40

0.60

2.40

Y

2.40 t

0.80

-4.00

I

-2.40

-0.80

f

d 8

0

I

n

71 4

0

0

9

9 -4.00

-2.40

0.80

-0.00

I

2.40

-4.00

,

I

-0.80

-2.40

-2.40

2.40

0.60

-0.60 I

I

I

,

2.40

0.80

,

,

!

-4.00

-2.40

,

~~, , ,

,

I

,

0

I

1: 0

9

9

I

-4.00

X

X -4.00

I

I

-2.40

0.80

-0.80

2.40

Y

-0.80

2.40

0.80

,

h

9

I

-4.00

-2.40

I

,

-0.80

,

x

,

0.80

,

,

2.40

,

tI 8C I

si

~

- 1 I

I

-4.00

I

I

-2.40

I

I

I

-0.80

I

0.80

I

I

2.40

9

I

Y

Figure 3. Natural orbitals in the active space for 'A,state of RhCHI+ at the CASSCF(10/8)/1level. Note the difference in the projection plane fo;each orbital.

SDCI-CASSCF(8/8) levels, respectively. Since the results of MR-SDCI-CASSCF(8/6) and MR-SDCI-CMSCF(I/B) methods are similar, one can use the less expensive MR-SDCICASSCF(8/8) method. CH2. This molecule has been studied e x t e n ~ i v e l y . ~The ~?~~ ground state is 3Bl,with the singlet 'AI state lying experimentally 9.02 f 0.01 kcal/m01~~ above, to be compared with an elaborate ab initio result of 9.11 kcal/m01.~5 As seen in Table IV, our modest correlation calculation gives at the CASSCF(2/2)/II level a 3BI-IA1 energy splitting of 18.1 kcal/mol, which is improved to 12.4kcal/mol upon inclusion of dynamic correlation effects at the MR-SDCI-CASSCF(2/2)/11 level. RhCH*+. According to e ~ p e r i m e n t land ~ , ~density ~ functional c a l c ~ l a t i o nthe , ~ ~most favorable structure of complex RhCH2+ is Rh+=CH2, methylene bound to Rh+. The orbital correlation diagram for RhCH2+ is shown in Figure 2. Considering the fact that la2, 2b2, and 4al are essentially lone-pair orbitals on Rh+ and that Sal is not very high in energy, one can expect that a

closed shell IAI and several open shell triplet 3Al,3A2,3B1,and 3B2states may be low-lying states. We have optimized the geometries of these states at the CASSCF(10/8)/I level under the C2"constraint. As seen in Table V, at this level of calculation, the ground state is the singlet 'A1, and the next low-lying states are 3A2and 3 A ~with , 3B2and 3B1states lying much higher in energy. The analysis of wave functions for various electronic states at their respective optimized geometries at the CASSCF( 10/8)/I 1evelshowsinTableVIthat,asexpected, thelAlstateisin principle the closed shell state shown in Figure 2, with some dynamic correlation contributions from the covalent lbl(?r) and 3al(u) orbitals between Rh+ and CH2, as well as from 4al and la2lone pairs. The 3AIand 3A2states are states where 4al and la2 lone pairs, respectively, are singly excited into the low-lying Sal orbital and can be described essentially by a single configuration. The 3B2state is also i Jingly excited state involving 2b2 5al but

-

Musaev et al.


TABLE MII: Atomic Charge Q and Overlap Population II from the M W e n Population for Various Electronic States of RhCH2+,Calculated at the CASSCF(10/8)/I Level

Q state 'Ai 'AI 'A2

'BI 'B2

n

Rh

C

H

Rh-C

C-H

+0.715 +0.821 +0.811 +0.838

-0.205 -0.330 -0.324 -0.345 -0.388

+0.245 +0.254 +0.257 +0.253 +0.269

0.674 0.729 0.728 0.570 0.709

0.740 0.734 0.730 0.687 0.717

+0.850

H'

H4

dihedral angle (H',Rh,C,H4) = 116.89

17.74 66.42

dihedral angle (H,,Rh,C,H3) = 122.03

98.81 C1-> C,

C2"

Figure 4. Geometrical parameters (distances in angstroms and angles indegrees) of ] A land 3Al (inparentheses) statesofion-moleculecomplex (H2)RhCH2+, optimized at CASSCF(l2/lO)/I level.

3A'

Figure 6. Geometric parameters (distances in angstroms and angles in degrees) of 'A' (C,) and 3A' (C,) state of hydridomethyl complex HRhCH,+, optimized at the CASSCF(10/8)/1 level.

TS1

H'

J"'

4 19c

)...

, ==.

dihedral angle

,H'

& '

105.01

/1.083

/

dihedral angles:

(H2,C,Rh,H4)

1660 (1.637)

134.45 '.,, (139.98) ',,,, 1.527 ',/(l ,573)

96.06 (97.79)

1 075

C,

CS

(Rh,H',C,H4) = 148.96

H3

'A

9 , = 870 i cm.'

3, = 1657 i cm.' for 'A'

v,= 1479 I cm"

for

3~

Figure 5. Geometric parameters (distances in angstroms and angles in degrees) of 'A' and 'A' (in parentheses) states of transition state (TSI) for H2 oxidative addition, optimized at the CASSCF( 12/1O)/I level. Arrows indicate the reaction coordinate vector for the ]A' state.

-

-

contains varieties of open shell configurations. The 3B1state is a doubly excited state involving la2 4al and 2b2 Sal. As shown in Table VII, each active natural orbital (NO) is qualitatively similar among all states calculated except for the 3BI state. Therefore, we show in Figure 3 only those for the 'AI state. The 3al is the nearly homopolar Rh-C u-bonding orbital consisting mainly of d,, (and s) atomic orbitals ( A O ) of Rh and al(u) MO of CH2. The lbl is the Rh-C *-bonding orbital, polarized like Rh--C+, made of Rh d,, A 0 and CH2 bl(*) MO. The la2,2b2, and 4al are lone-pair d,, d,,, and dxxWyy A 0 of Rh, respectively. The orbitals Sal and 2bl are, respectively, Rh-C u*- and **-antibonding orbitals. The 6al MO is dominantly 5s A 0 of Rh. Thus, for 3Al, 3A2. and 3B2 states, all having one electron in the Sal Rh-C(u*) orbital, the Rh-C bond distance is about 0.10-0.13 A longer than in the 'Al state, which has no electron in Sal, as seen in Table V. Mulliken population analysis in Table VI11 shows that 3A1, 3A2, and 3B2 states are similar to each other in atomic charges

(H',Rh,C,H3) = 122.14

1.939 97.95

c1--> c, 3A' 9, = 343 i cm.' Figure 7. Geometric parameters (distances in angstroms and angles in degrees) of ]A (Cl) and 'A' (C,)transition states (TS2) for CH4 elimination, optimized at the CASSCF( 10/8)/I level.

and overlap population and have more electrons on C than the 'A1 state. Responsible for this is excitation of one electron from lone-pair 4al, la2, and 2b2 orbitals, respectively, to the Rh-C a-antibonding Sal, thus transferring electron from Rh to C. However, unexpectedlythesestates have even larger Rh-C overlap population than 'Al. Since the minimum basis set calculation gives expected bond population, we may blame the Mulliken population analysis, which is known to be unreliable for extented basis sets. The first entry line of Table IX shows that the relative energies of various states change substantially by the use of set 11, a 17electron RECP for Rh, in comparison with the results in Table V using set I, a 9-electron Rh RECP, though the ordering of

TABLE I X Energetic Parameters of Various Electronic States of RhCH?+. Calculated at Different Computational Levels' sets for energy//geometryb WII Ila//I llb//I IIb//IIb III//I IIIa//I

-147.461661-147.54657 -1 47.472421-1 41.59186 -1 47.460121-1 47.6870 1 -147.4635 11-147.69321 -148,047941-148.13589 -148.053691-148.18460

3.114.9 6.013.9 4.212.5 4.912.9

2.514.5

24.1123.6

17.8119.5

47.9162.3 54.0f 71.7 57.1114.8 58.4178.3 53.6f67.1 56.0174.3

All energies are relative energies (in kcallmol) with respect to the ground 'A] state, for which the total energy (in au) is given. Values before and after a slash are those at the CASSCF( 1018) and MR-SDCI-CASSCF( 1018) levels, respectively. Numbers before and after double slash represent the ECP and basis set used for energy and geometry, respectively.



-

‘i’

1.081 (1.076)

C

C2”

C3”

Figure 8. Geometric parameters (distances in angstroms and angles in degrees) of C2,. and Cj, structures of ‘ A Iand ’A1 (in parentheses) states of ion-molecule complex Rh+CH4, optimized at the CASSCF(8/6)/1 level.

these states does not change. Inclusion of dynamic correlation effects with the MR-SDCI-CASSCF( 10/8) method does not change CASSCF( 10/8) resultsvery much, except for the binding energy (BE), which we will discuss separately. According to our final MR-SDCI-CASSCF( 10/8)/11 results including dynamic correlation, the ground state of RhCH2+ is ’AI, and the next low-lying states are nearly degenerate 3Aland ~ Astates, z which lie only 4-5 kcal/mol higher in energy. The 3B2and 3 B states ~ are 19.5 and 23.6 kcal/mol, respectively, higher than ]Al. Binding Energy: BqRhCH*+.(’AI) Rh+(’F) + CH~(’BI)]. As seen from Table IX, the binding energy, BE[RhCHz+(’Al)

-.

+

Rh+(3F) CH2(3BI)],calculated at the CASSCF(lO/B)/II level is 47.9 kcal/mol, and inclusionof dynamiccorrelation effects at the MR-SDCI-CASSCF(lO/8)/II level increases it to 62.3 kcal/mol. The latter result is still about 27 kcal/mol less than the experimental value, 91 f 5 kcal/mol, obtained by the gasphase photodissociation method.6s To improve the agreement with experiment, we have used large basis sets and other methods of calculation. The results are also shown in Table IX. First, to check the ability of the Hay-Wadt (HW) ECP to describe the energetic parameters of RhCHZ+, we carried out calculation for IAl and 3Alstates and BE[Rh+(3F) + CH*(jBl)] by using the Stevens-Krauss-Basch-Jasien (SKBJ) ECP and corresponding (8s8p5d/4s4p3d) basis set for Rh atom76and the standard 6-311G** basis sets for C and H atoms77(named set 111) at the CASSCF( 10/8)/1 geometry. As seen from Table IX, sets I1 (HW-ECP) and III(SKBJ-ECP) givequalitatively similar results. The BE obtained with set I11 is 5-6 kcal/mol larger than that with set 11. Second, we improved the basis sets by adding to sets I1 and I11 a singlezeta polarizationflq = 0.3S73)function on Rh (named sets IIa and IIIa, respectively). As seen from Table IX, this function increases the BE by 5-10 kcal/mol to give 71.7 and 74.3 kcal/mol at the MR-SDCI-CASSCF(10/8) level by using HWand SKBJ-ECP, respectively. These results show that the polarization f function is very important for calculation of BE. The effect of this polarization function is more important for dynamic correlation, i.e., for MR-SDCI than for CASSCF calculation.

TABLE X Calculated Frequencies (in cm-I) and Normal Modes for the Transition State (TS1) in the ‘A‘ State at the CASSCF(12IlO)II Level atom, coordsymm Rh, X Y

z c,x Y

z

HI, X Y

Z H2,X Y

Z H3,X Y

Z H4, X Y

Z

1657i a’

265 a”

485 a’

615 a”

716 a‘

956 a”

1056 a’

1479 a’

1520 a’

1653 a’

0.00

0.00 0.00

0.01 0.05

0.00 0.00

0.01 -0.01

0.00 0.02 -0.15

0.00

0.00 0.00 0.00

0.00 0.00

0.00 -0.00

0.00 0.06 -0.25 0.00 -0.06 -0.60 0.00 -0.03 -0.16 0.01 -0.03 -0.16 -0.01

0.02 0.00 0.00 0.60 0.00 0.00 -0.41 -0.12 -0.41 -0.21 0.12 0.41 -0.21

0.00 0.00 0.00 -0.12 -0.06 0.00 -0.19 0.08 0.00 -0.08 -0.02 0.00 0.59 0.14 0.02 0.59 0.14 -0.02

0.00 0.00

0.00

0.00 0.00 0.00 0.00 0.00 -0.10 0.00 0.00 0.53 0.00 0.00 -0.08 -0.31 0.40 0.17 0.31 -0.40 0.17

0.00 0.00 0.06 0.03

0.00 -0.57 0.64 0.00 -0.19 -0.40 0.00 -0.08 0.03 0.02 -0.08 0.03 -0.02

0.00 0.00 0.09 0.00 0.00 0.15 0.00 0.00 -0.60 0.42 0.22 0.17 -0.42 -0.22 0.17

0.00 -0.07 0.18 0.00 0.02 -0.40 0.00 -0.08 -0.56 0.00 0.00 0.18 -0.01 0.00 0.17 0.00

0.00 -0.03 -0.03

0.00 0.70 0.49 0.00 0.03 -0.25 0.00 -0.03 0.26 0.15 -0.03 0.26 -0.15

0.04 -0.08 0.00 -0.29 -0.28 0.00 -0.03 0.14 0.00 -0.15 0.47 0.33 -0.15 0.47 -0.33

0.00

-0.01 0.00 0.00 -0.17 0.05 0.00 0.96 -0.16 0.00 0.02 0.02 0.00 0.02 0.02 0.00

3298 a’

0.00 0.00 0.00 0.01 -0.06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.08 0.33 -0.61 -0.08 0.33 0.61

3447 a” 0.00

0.00 0.00 0.00 0.00 -0.10 0.00 0.00 0.00 0.00 0.00 0.00 0.07 -0.33 0.57 -0.07 0.33 0.57

TABLE XI: Calculated Frequencies (in cm-I) and Normal Modes for the Transition State (TS1)in the 3A‘ State at the CASSCF(lZ/lO)/I Level atom, coordsymm

1479i a’

390 a”

47 1 a’

557 a‘

655 a”

848 a’

Rh, X Y

0.00 0.00 0.00 -0.07 -0.01 0.00 0.58 -0.63 0.00 0.17 0.38 0.00 0.13 0.00 0.00 0.13 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.08 0.00 0.00 0.80 -0.36 -0.17 -0.09 0.36 0.17 -0.09

0.01 0.00 0.00 -0.10 0.09 0.00 -0.03 -0.35 0.00 -0.10 -0.74 0.00 0.11 0.12 0.01 0.11 0.12 -0.01

0.00 0.04 0.00 0.00 -0.22 0.00 0.08 -0.13 0.00 -0.03 -0.38 0.00 -0.06 -0.22 0.00 -0.06 -0.22 0.00

0.00 0.00

0.00 0.00 0.00 -0.09 -0.07 0.00 -0.22 0.23 0.00 -0.03 0.14 0.00 0.59 0.08 0.08 0.59 0.08 -0.08

z

c, x Y

z

HI, X

Y

z H2, X Y

z

HI,X Y

z H4, X Y

z

0.00

0.00 0.00 0.06 0.00 0.00 0.49 0.00 0.00 -0.38 -0.08 -0.47 -0.22 0.08 0.47 -0.22

986 a’’

1465 a’

1580 a’

1787 a’

0.00

0.00 0.00

0.00

0.00

0.00

0.00 0.00

0.00

0.00

0.00 0.00 0.00 0.00 0.32 0.10 0.00 -0.94 0.09 0.00 0.00 0.01 0.00 0.00 -0.01 0.00

0.00 0.00 -0.06 0.00 0.01

0.00

0.00 0.00 0.00 -0.08 0.00 0.00 0.62 0.00 0.00 -0.18 -0.34 0.34 0.12 0.34 -0.34 0.12

0.00 0.01 -0.08 0.00 0.26 0.13 0.00 0.08 -0.08 0.00 -0.13 0.54 0.33 -0.13 0.54 --.33

0.04 -0.04 0.00 -0.64 -0.58

0.00 -0.26 0.24 0.00 -0.08 0.15 0.11 -0.08 0.15 -0.11

3314 a‘

0.00 0.00

0.00 0.00 0.00 0.00 0.33 -0.61 0.00 0.33 0.61

3471 a’’

0.00 0.00 0.00 0.00 0.00 -0.10 0.00 0.00

0.00 0.00 0.00 0.00 0.00 -0.33 0.57 0.00 0.33 0.57

Musaev et al.


TABLE XII: Catculated Total a d Relative Energies of CZ, and C3,Structures of RhC&+ Complex C2, structure 4, structure -Elol.au IAl State CASSCF(8/6)/II 148.62421 MR-SDCI-CASSCF(8/6)/II 148.68260 3A1 State CASSCF(8/6)/11 148.67023 MR-SDCI-CASSCF(8/6)/II 148.72691 method

MR-SDCI-CASSCF(8/8)/II

AEdJ

~~

(1

-1o.a

0.9 1.1

-2o.a

+ CH4

Rh*('D )

-30.0-

3.0 2.9

-40.0-

E d C d - E d C 2 J (in kcal/mol).

3A'

-5o.a

Finally, we have chosen a large basis set: (6s6pSd4f/ 4 ~ 4 p 4 d 2 f and ) ~ ~ 17-electron HW-ECP for Rh'j8and (1 ls6pld/ 6s3pld)'9 (ad= 0.7569)and ( 5 ~ l p / 3 s l p () a~p~= l.069)basis sets for atoms C and H, respectively. This basis set includes polarization double-zetafRh and single-zeta dc and pH functions, as well as a diffuse single-zeta dRh function (named set IIb). As seen from Table IX, the BE calculated by using this set is the largest of all the present results, 74.8 kcal/mol at the MR-SDCICASSCF(10/8) level. As was mentioned above, all of these calculations were carried out at the fixed geometry optimized at the CASSCF( 10/8)/I level. Reoptimization of geometry at the CASSCF( 10/8)/IIb level changes only slightly the geometric parameters of CH2 and RhCH2+, as shown in Tables IV and V, respectively. The BE is increased by 1.3 and 3.5 kcal/mol at the CASSCF( 10/8)/IIb and MR-SDCI-CASSCF( 10/8)/IIblevels of calculations, respectively. Our final result for binding energy of RhCH2+,obtained at the MR-SDCI-CASSCF(lO/8)/IIb/ /CASSCF(10/8)/IIb level, is 78.3 kcal/mol, which is still by 13 f 5 kcal/mol less than the experimental value of Hettich and F r e i ~ e r .A~ similar ~ result (84 f 4 kcal/mol) has been obtained by Bauschlicher et al. using similar basis sets and the ICACPF meth0d.5~ These calculations show that even larger basis sets including multiple and higher order polarization and diffuse functions would be required to recover this difference.

IV. Potential Energy Surfaces of Reaction: RhCH2++ H2 Rh+ + CH4

-

The potential energy surfacesof reaction 2 have been calculated for the ground 'Al and excited 3Al states of RhCH2+. They become IA' and 3A' states during the reaction, where the C, symmetry is mostly maintained, as will be shown later. We expect that the reactivities of low-lying 3Al and 'A2 states of RhCH2+, which are different only by lone-pair d, and d, AOs, will be very similar. This effect has been exhibited for the corresponding reaction 1 of C O C H ~ +We . ~ ~will not consider the reactions of

Rh*( 3F )

-60.0-

I,

%

e

..----

+ CH4

-7O.Q I

RhCH2*

+ H, (Hz{RhCHz*

ITS4

HkhCH3'

:S2

AhCH4'

-

I

I

Figure 9. Potential energy profiles of reaction RhCH2+ + H2 Rh+ CHI at the MR-SDCI-CASSCF(8/8)/11 level. Geometries of critical structures used are those optimized in Figures 4-8.

+

+ CH4

('D)

+ CH4

3F )

-7 -6o.a

I

RhCHP'+ HP (HP;RhCH2'

I

ITS1

HkhCHJ'

+S2

AhCHa+ I

Figure 10. Corrected potential energy profiles of reaction RhCH2+ + H2 Rh+ + CH4.

3BIand )B2states of RhCH2+, which lie 23.6 and 19.5 kcal/mol higher than ]AI,respectively, and probably do not contribute to the rate at moderate conditions. The calculated geometrical parameters of intermediates and transition states are shown in Figures 4-8. Tables X and XI show frequenciesand normal coordinates for transition states for H-H activation. Tables XII-XIV contain the total and relative energies, as well as the principal determinants and their weights at special points on the PESs of reaction 2. In Figures 9 and 10

TABLE XIII: Relative Energies (in Kilocalories per Mole) of Critical Points on Potential Energy Surfaces of Reaction 2' structure

+

RhCH2+ Hzb (Hz)RhCHz+ TSI (H2 addition) HRhCH,+ TS2 (CH4 elimination) RhCH4+, CzL Rh+-CH4, C2L

+

RhCH2+ H2 (H2)RhCH2+ TSI (H2 addition) HRhCH3+ TS2 (CHI elimination) RhCH4+, C2'. Rh+-CH4, C2r

CASSCF( 12/10)/11

CASSCF(8/8)/II

MR-SDCI-CASSCF( 8/8)/II

'A' State

0.0 -6.9 15.2 -1 1.3 -9.4 -33.5 -24.2 3.1 (O.O)d) -2.0 (-5.1) 19.4 (16.3) -23.7 (-26.8) -22.6 (-25.7) -60.0 (-63.1) -52.6 (-55.7)

O.O[O.O]~ -4.3 [-4.8] 18.2 -4.1

-2.1 -29.8 -20.7 3A' State 5.6 (0.0) 0.5 (-5.1) 21.9 (16.3) -17.9 (-23.5) -16.8 (-22.4) -60.0 (-65.6) [-57.31 -53.6 (-59.2) [-49.8]

O.O[O.O]

-5.4 [-7.21 10.9 -10.9 -9.1 -35.6 -25.4 1.2 (0.0) -5.4 (-6.6) 11.3 (10.1) -23.9 (-25.1) -24.6 (-25.8) -64.2 (-65.6) [-59.01 -57.5 (-58.7) [-42.2]

a Geometries optimized in figures 4-8 are used. The total energies are -148.60874, -148.61 121, and 148.65293 au for CASSCF(I2/lO)/II, CASSCF(8/8)/II and MR-SDCI-CASSCF(8/8)/11, respectively. The numbers in brackets are with basis set I1 augmented with a set of polarization ffunction (a = 0.35) on Rh. The total energies for RhCH2+ + H2 are -148.61802 and -148.67423 au for CASSCF(8/8)/II and MR-SDCICASSCF(8/8)/II, respectively. The numbers in parentheses are relative energies with respect to the triplet of the reactants.



TABLE XIV: Important Configurational State Functions (CSF) and Their Weights (in Percent) for Singlet and Triplet States of Critical P ~ i n in t ~the PES of Reaction 2, Calculated at CASSCF(12/10)/1 and Natural Orbitals’ ~

~~~~

structure

state

3a1

1bi

2b2

la2

4al

5a1

6ai

2b1

7a1

3b2

wt

RhCH2+ t H2

’AI

2 2 2 2 1 0 2 2 1

2 0 2 2 1 2 2 0 1

2 2 2 2 2 2 2 2 2

2 2 2 2 2 2 2 2 2

2 2 0 0 2 2 1 1 2

0 0 2 2 1 2 1 1 1

0 0 0 0 0 0 0 0 0

0 2 0 0 1 0 0 2 1

2 2 2 2 2 2 2 2 2

0 0 0 0 0 0 0 0 0

86.5 4.0 2.0 1.6 1.4 1.o 90.2 3.0 1.5

2 2 2 2 2 2

2 0 2 2 2 0

2 2 2 1 2 2

2 2 2 2 2 2

2 2 0 1 1 1

0 0 2 1 1 1

0 0 0 0 0 0

0 2 0 0 0 2

2 2 2 2 2 2

0 0 0 1 0 0

88.4 4.0 1.7 1 .o 90.3 2.3

’A I

H2RhCH2+

‘AI

I

structure

state

3a‘

4a’

5a’

6a’

7a‘

8a’

9a’

loa’

2a”

3a”

wt

TSl (H2addition)

‘A’

2 2 1 1

2 2 2 2

2 2 2 0

2 0 2 2

0 2 0 0

0 0 0 2

0 0 0 0

0 0 1 1

2 2 2 2

2 2 2 2

85.7 4.4 90.2 1.7

2 2 2 1 1 1

2 2 0 2 2 0

2 0 2 2 0 2

2 2 2 2 2 2

0 0 0 1 1 1

0 0 2 0 0 2

0 2 0 0 2 0

0 0 0 0 0 0

2 2 2 2 2 2

2 2 2 2 2 2

84.6 7.3 4.4 88.4 3.1 1.2

3A’

HRhCH’+

’A’ 3A’

structure

state

3a

4a

Sa

6a

7a

8a

9a

1Oa

1l a

12a

wt

TS2 (CH4 elimination)

‘A

2 2 2 2

2 2 2 2

2 2 2 2

2 0 1 1

2 2 2 0

2 2 2 2

0 2 1 1

0 0 0 2

0 0 0 0

0 0 0 0

90.3 3.7 92.2 1.7

’A structure

state

3a1

4a I

1a2

2b2

Ibi

5a1

6a I

2bi

3b1

7a1

wt

RhCHd+

‘AI

2 2 0 2 2 1

0 2 2 2 2 1

2 0 2 2 2 2

2 2 2 2 0 2

2 2 2 0 2 2

2 2 2 2 2 2

0 0 0 0 0 0

2 2 2 2 2 2

0 0 0 0 0 0

0 0 0 0 0 0

49.0 22.1 22.1 2.6 2.3 98.0

]AI

Only CSFs with weights of 1.0% or more are shown.

are shown the profiles for reaction 2 calculated at the MR-SDCICASSCF(8/8)/II level and estimated, respectively. Geometric Parameters of the Intermediates and Transition States. Calculations show that in the first step of reaction 2 reactants yield an ion-molecule complex (H2)RhCH2+ without a barrier. As seen in Figure 4, the H-H distance in this complex in either ‘Al or 3AI state is only 0.02 A longer than that in free H2molecule. The geometric parameters of RhCH2+also change little upon complex formation; the distances R(Rh-C) and r(CH) in ’Al and ‘Al states of (H2)RhCH2+are 0.002-0.007 A longer and the HCH angle is 0.6-0.9O smaller than in correspondingstates of RhCH2+. The H2 moleculein the ion-molecule complex (H2)RhCH2+can rotate nearly freely around the Rh-X axis, X being the center of the H-H bond, with a small barrier of less than 1.0 kcal/mol. Preliminary calculations of low-lying jB1, 3B2,3A2,and ]AI states of dihydride (H)2RhCH2+ species carried out at the CASSCF( 12/10)/1 level and under Cb symmetry show that the more favorable structure has the H-H axis perpendicular to the RhCH;! plane as shown in Figure 4. The coplanar structure lies about 15-20 kcal/mol higher. For 3B1and 3B2states dihydride structure does not exist and within symmetry converges to the RhCH4+ complex without barrier. But even the more stable perpendicular structures for ‘AIand 3A2states of the dihydride complex lie about 67.0 and 60.1 kcal/mol, respectively, higher than the corresponding states of the ion-molecule complex

(H2)RhCH2+. A simple thermodynamic calculation using D,(Rh+-H) = 41.Okcal/mol,sOD,(H-H) = 104 kcal/mol,81and De(RhCH2+-H2) = 7.2 kcal/mol (our calculations to be given later) leads to 27 kcal/mol for the energy difference between these two structures. Therefore, in this paper we will not discuss the dihydride path, corresponding to oxidative addition of H2to Rh atom of RhCH2+. The next step of reaction 2 for both IA’ and 3A‘ states is activation of the H-H bond by RhCH2+. As shown in Figure 5, transition states (TS1) for this process have a four-membered ring structure, where the H-H distance is stretched by 0.38-0.39 A from that of a free H2 molecule. The distances R(Rh-C) are about 0.11 and 0.09 A longer than that in ]Al and 3Al states, respectively, of isolated RhCH2+. The distance R(Rh-H) is only 0.10 A longer than that of RhH+(2A*).82The distance r(C-H) in the four-membered region is about 0.5 A longer than that of a normal C-H bond. The normal coordinate analysis given in Tables X and XI show that these structures have only one imaginary frequency and are confirmed to be true transition states. The normal coordinate vector having the imaginary frequency, i.e., the reaction coordinate at the transition state, shown for IA’ in Figure 5 , indicates clearly that the H2 molecule is being split by RhCH2+. The cleavage of the H-H bond yields the hydridomethylrhodium complex, HRhCH3+,shown in Figure 6. For both states, optimization withc i t symmetry constraint resulted in structures

4072

Musaev et al.

The Journal of Physical Chemistry, Vol. 97, No. 16, 1993

with C, symmetry. The distances R(Rh-H) are only 0.007 and 0.01 5 A longer than in RhH+(2A*)82forsinglet and triplet states, respectively. As for R(Rh-CH3) distances, they are about 0.008 and 0.05 A longer than that calculated for RhCH3+(2E).83The LRhCH angles are close to those calculated for RhCH3+,83except the angle LRhCH4 for triplet state, which is about 15' larger. Calculations show that the CH3 group can rotate nearly freely around the Rh-C axis for the singlet state with a barrier of less than 1.0 kcal/mol. For the triplet state this barrier is a little higher, about 5.0 kcal/mol, presumably because the angle LHRhC for the triplet state is about 47O smaller than for the singlet state. The triplet structure of this complex is in a sense similar to the transition state to bediscussed in thenext paragraph. The hydride to be transferred has already moved substantially or can be considered to be incipiently activated. The transition states corresponding to CH4 elimination were determined without symmetry constraint, but the structure for triplet converged to a structure with C, symmetry, as shown in Figure 7. For the triplet state the geometric parameters of this structure are close to those of HRhCH3+ complex. In contrast, for the single state they are different. First, the angle LHRhC for the transition state is 50°, which is 63O smaller than that in HRhCH3+. Second, the distance R(Rh-C) for the transition state is about 0.074.08 A longer than that for HRhCH3+. The normal coordinate analysis shows that these structures have only one imaginary frequency and are true transition states. The mode having imaginary frequency, as shown in Figure 7, corresponds to migration of H from the Rh to the C atom. The structures with C2, and C3, symmetry of the RhCH4+ complexenergetically lie very close to each other. The energetics shown in Table XI1 indicate for both singlet and triplet states that the most stable structure has C2, symmetry. Preliminary calculations at the CASSCF(8/6)/1 level show that another structure with C3"symmetry, corresponding to coordinating one CH bond of CH4 to Rh, lies about 15 kcal/mol higher than the other structures. The present situation of the preference of bicoordination ( T ~structure ) is similar to that found theoretically for the CHI complex of R ~ C I ( P H ~ )As Z . seen ~ ~ from Figure 8, for RhCH4+the distance r(C-Hb), where Hb is a bridge H atom, is about 0.01-0.02 A longer than r(C-Ht), where Ht is a terminal H atom. The distance R(Rh-C) in the C2, structure is about 0.17 A shorter for the singlet state than for the triplet state. In contrast, for the C3, structure it is 0.08 A longer for the singlet state than for the triplet. Relative Energy of Special Pointsof PESof Reaction 2. Table XI11 shows the relative energies, calculated at the CASSCF( 12/ lO)/II and CASSCF(8/8)/II levels, respectively, of critical structures of reaction 2, whose geometries have been optimized in Figures 4-8. One can see clearly that the two methods give similar results. Therefore, it is quite acceptable to include the dynamic correlation effects by using the MR-SDCI-CASSCF( 8 / 8)/II method, the contracted CI based on the CASSCF MOs and reference wave function and including all single and double excitations from the reference. Our calculated potential energy profiles thus obtained are shown in Table XI11 and Figure 9. As seen from Table XIII, at the CASSCF(8/9)/II level the ground state of RhCH2+ + H2 is 'Al, but 3A1lies 5.6 kcal/mol higher. Inclusion of dynamic correlation effects stabilizes 3Al more than 'Al and decreases the energy difference between them to 1.2 kcal/mol. A similar result is obtained for the ion-molecule complex (HZ)RhCH,+,whichisformedin thefirststepofreaction 2; the ground state 'AI lies 4.8 and 0.03 kcal/mol lower than the first excited state 3Alat the CASSCF(8/8)/II and MR-SDCICASSCF(8/8)/II levels, respectively. The binding energies BE(H2 + RhCH2+) (H2)RhCH2+ are 4.3 and 5.1 kcal/mol at the CASSCF(8/8)/II level and 5.4 and 6.6 kcal/mol at the MR-SDCI-CASSCF(8/8)/II level for the ]Al and 3Al states, respectively. Inclusion of a set of polarization f function (a =

-

0.35'3) on Rh increases it to 4.8 and 7.2 kcal/mol at the CASSCF(8/8) and MR-SDCI-CASSCF(I/I) levels, respectively, for the 'Al state. For the transition state (TSl), corresponding to activation of a H-H bond, the ground state is also the singlet, but the triplet state lies only 3.7 and 0.4 kcal/mol higher at the CASSCF(8/ 8)/II and MR-SDCI-CASSCF(8/8)/11 levels, respectively. At the CASSCF(8/8)/II level the heights of the activation barriers of a H-H bond, hactrcalculated relative to ion-molecular complex (H2)RhCH2+,are 22.5 and 21.4 kcal/mol for singlet and triplet states, respectively. But inclusion of dynamic correlation effects stabilizesthe transition state more than thecomplex (H2)RhCH2+ to decrease ha,,to 16.3 and 16.7 kcal/mol, respectively. As seen from Figure 9, the singlet and triplet PESs of reaction 2 cross with each other, once or possibly three times, near the transition state, TS1. Therefore, we suspect that inclusion of the spinorbit interaction between singlet and triplet states complicates crossing and so avoid crossing. This may result in a decrease the height of this barrier by a few kilocalories per mole. In contrast to the ion-molecule complex (Hz)RhCHz+ and TS1, the ground state of the hydridomethyl metal complex, HRhCH3+,is 'A, with ]A lying about 13.8 and 13.0 kcal/mol higher at the CASSCF and MR-SDCI levels of calculations, respectively. This complexis an intermediate at the CASSCF(8/ 8)/II level of calculation, where there are an energetic barriers of 1.1 and 2.0 kcal/mol for triplet and singlet states, respectively, at the transition state (TS2) along the rearrangement HRhCH3+ RhCH4+. However, inclusion of thedynamic correlation effects again stabilizes the transition state (TS2) more than the complex HRhCH3+, and as the result the barrier for the triplet state completely disappears and for the singlet state becomes only 1.8 kcal/mol. Therefore, we conclude that HRhCHs+ cannot exist in the ground triplet state and will without any barrier become thecomplex RhCH4+. It may exist for the singlet state but would not survive long. The ground state of RhCH4+ is 3AI, and 'AI lies about 30.2 and 28.6 kcal/mol higher at the CASSCF(8/8)/II and MRSDCI-CASSCF(8/8)/IIlevelsof calculation,respectively. These values are close to the A(3FJD) energy difference for Rh+ discussed above. The interaction energies or the energies of reaction for

-

Rh+(3F)

+ CH,

Rh+(lD)

+ CH,

and

-

RhCH,+(3A,)

(3)

RhCH,+('A,)

(4) are 6.4 and 9.1 kcal/mol, respectively, at the CASSCF(8/8)/II level. At the higher MR-SDCI-CASSCF(8/8)/II level, they become 6.9 and 10.2 kcal/mol, respectively. Inclusion of a polarization fRh function increases the heats of reaction 3 to 7.5 and 16.8 kcal/mol at the CASSCF(8/8) and MR-SDCICASSCF(8/8) levels, respectively. As seen from Figure 9, the reaction RhCH,+('A,)

+ H,

-

+

-

Rh+(3F)

+ CH,

(5) is exothermic, in agreement with experiment. The heats of this reaction, obtained at the MR-SDCI-CASSCF(8/8)/II and MRS D C I - C A S S C F ( ~ / ~ ) / I I +levels, ~ R ~ are 57.5 and 42.2 kcal/mol, as shown in Table XIII. However, even our best result is about 20 kcal/mol larger than the experimentally estimated value of about 20 kcal/moll5 derived from BE(Rh+-CH2) = 91 & 5 kcal/mol65 and AE(CH2 H2 CH4) = 110 kcal/mol.*5 Since the present MR-SDCI-CASSCF(8/8)/11 potential energy profiles have some disagreement with experiment, we will make some empirical adjustments and try to obtain Ycorrected" or best estimates of the potential energy profile. First of all, the energy of reaction 5 can be considered to be represented by



-

superposition of two processes: RhCH,+(’A,)

Rh+(3F)

and

+

CH2(3Bl) H,

-

+ CH2(3B1)

(6)

CH,

(7) The binding energy for step 6 calculated at MR-SDCI-CASSCF(6/6)/11 level, corresponding to the MR-SDCI-CASSCF(8/8)/ I1level for thePESsof reaction 5, is 54.4 kcal/mol, to becompared with the experimental value of 91 f 5 kcal/mol.65 The energy of reaction 7 at this level is calculated to be 111.9 kcal/mol, to be compared with the experimental value of 110 kcal/m01.~~ Therefore, the energy of reaction 5 calculated at the present MRSDCI-CASSCF( 8/ 8)/ I1 level, 57.5 kcal/mol, is overestimated by 38.5 kcal/mol. Therefore, we shift the energy level of the Rh+(3F) CH4 in Figure 9 by 38.5 kcal/mol to A&I = -19.0 kcal/mol. Second, the energy difference between the ground )F and the excited ID state of Rh+, calculated for Rh+-CH4 at a separation of 15.0 A as shown in Table XIII, is 32.1 kcal/mol and is an overestimation of 9.8 kcal/mol in comparison with the experiment, 23.3 kcal/m01.’~ Therefore, we shift up the energy of Rh+(’D) CH4 in Figure 9 by 29.7 (=38.5 - 8.8) kcal/mol to M,,I= +4.4 kcal/mol. In addition, the present level of calculation gives the binding energy of the RhCH4+ complex for 3A1to be 6.9 kcal/mol, to be compared witha more reliable 16.8kcal/mol withanf polarization function. Therefore, we use this latter value for the corrected binding energy. In ‘AI,for which we did not carry out calculation with thef polarization function,weassume that the binding energy is 10 kcal/mol larger than the calculated value of 10.2 kcal/mol at the present level. We assume further that the relativeenergetics for the RhCH2+ H2 to TS1 in Figure 9 need not be adjusted. From TS1 we smoothlyadjust the relative energies to reach the above-mentioned corrected values for RhCH4+ and Rh+ CHI. The resultant best estimated potential energy profiles are shown in Figure 10. Analysis of Wave Functions of Critical Structures on PESs of Reaction 2. The wave functions of reactants (RhCHZ+ and H2) and products (Rh+ and CH4) of reaction 2 have already been discussed in section 111. Therefore, here we analyze only those for intermediates and transition states of this reaction. In our discussion we will use the wave functionsobtained with CASSCF(12/10)/1, naturalorbitalsshowninTableXIV. AscanofTable XIV indicates that for this reaction of RhCH2+the wave functions of all the intermediates and transition states as well [except for RhCH4+(IAl)] are qualitatively single determinant-like, with the principal determinant contributing over 85%. As will be discussed later, this is in clear contrast with the reaction of CoCH2+,which has been studied in a separate paper.59 As seen from Table XIV, the principal determinants of wave functions of ’AIand 3AIstates of the (H2)RhCH2+complex are exactly the same as those of the reactants. The nature of MOs is very similar between RhCH2+ Hz and (Hz)RhCH2+. We only note that the 7al and 3bz MOs are bonding and antibonding orbitals of the H2 molecule. Therefore, one can refer to the discussions we have given in a preceding section for RhCH2+. The principal determinants of wave functions of ‘A‘ and )A‘ states of TS1 are

bonding and the 9a’, 8a’, and 7a‘ MOs are antibonding orbitals of C-HI-HZ, Rh-H1-H2-C, and Rh-C bonds, respectively. The principal determinants of wave functions of IA’ and 3A‘ states of HRhCH3+are the same as those for TSl with 84.6 and 88.4% weights, respectively. The 3a’, 7a’, 2a”. and 3a” MOs of these determinants are lone-pair d orbitals. On the other hand, 4a‘-8a‘, 5af-9a’, and 6a’-10a’ pairs are bonding and antibonding MO pairs of Rh-H, Rh-C, and newly formed C-H bonds, respectively. The wave functions of ‘A and 3A states of TS2, the transition state for CH4 elimination, have weights of 90.3 and 92.2%, respectively, for the determinants (3a)2(4a)2(5a) 2( sa)’( 7a),( 8a)2

+

+

+

+

+

(3a’)2(4a’)2(5a’)2(6a’)2(2a’’)2(3a’’)2 and

’

(3a’) (4a’)2(5a’) ,( sa’),( 7a’) (2a”) ,( 3a”) respectively. The weights of these determinants are 85.7 and 90.276, respectively. The 2a”, 3a”, 3a’, and loa’ orbitals correspond to lone-pair d orbitals. The 4a’, 5a‘, and 6a’ MOs are

Here 3a, 4a, and 9a MOs are a lone-pair d orbitals. The 6a MO has a large d character but corresponds to a Rh-CH3-H bonding orbital. 5a and loa, 7a and 1la, and 8a and 12a MOs are bonding and antibonding pairsof Rh-H, Rh-C, and activated C-H bonds, respectively. The wave functions of singlet and triplet electronic states of RhCH4+ are very close to those of products, Rh+ CH4 (cf. Table 14). The 3al, 4al, la2, 2b2, lbl, and 7al MOs belong to Rh+ and the 5al, 6al, 2b1, and 3bl MOs to two correlated CH bonds and antibonds of CH4. The fact that the ‘AIwave function consists of three principal determinants originates from the same requirement for the lD state of Rh+.

+

V. Conclusions for RbCHZ+ + Hz System We can summarize our conclusions for the RhCH2+ + H2 reaction system as follows. 1. The ground state of RhCH2+ is ‘Al,but nearly degenerate )Al and 3A2states lie 4-5 kcal/mol higher and 3BI and 3B2states 20-25 kcal/mol higher. 2. The best calculated binding energy BE [RhCH2+(’Al) Rh+(3F) CH2(3Bl)] is 78.3 kcal/mol, which is about 12.7 f 5 kcal/mol less than the present experiment result, 91 f 5 kcal/ mol, obtained by Hettich and Freiser.65 For accurate calculation of BE both dynamic correlation effects and polarization ( f ~ h ,dc, and J J H ) and diffuse ( d ~functions ) play an important role. In view of the more reasonable agreement between theory and experiment for BE of CoCH2+,however, this disagreement seems to be a little excessive. 3. The behaviors of the PES of the reaction RhCH*+ + HZ Rh+ CH4 for the ground ‘A1and the excited 3A, (probably also 3A2) states of RhCH2+ are very similar. 4. Reaction 2 is calculated to be exothermic by 35-40 kcal/ mol, about a 20 kcal/mol overestimation. The first step gives an ion-molecule complex (H2)RhCHz+, for which the BE(H2RhCH2+)is calculated to be 7.2 kcal/mol. The activation barrier of the H-H bond is calculated to be 16.3 kcal/mol. Inclusion of spin-orbit interaction may make this smaller by a few kilocalories per mole. 5. Probably, hydridomethylrhodiumcomplex,HRhCH3+,d m not exist in the ground triplet state and will rearrange to an ionmolecule complex RhCH4+ without barrier. The BE for RhCH4+(IAI) Rh+(SF) CH4 is calculated to be 16.8 kcal/ mol. 6. The CASSCF(12/10) and CASSCF(8/8) methods give similar results for reaction 2. The d lone-pair electrons are not required to be included in the active space for calculation of relative energies. The dynamic correlation by means of MRSDCI on the CASSCF(8/8) wave function substantially modifies the behavior of the PESs.

-

+

-

+

-

+


VI. Comparison between the CoCHz+ + HZand the RICH*+ + H2 Systems In a separatepaper,s9we have studied thestructureandstability of CoCH2+, as well as its reactivity with H2 by using the level of calculations very similar to that of the present study. Here we briefly compare the results obtained for CoCHz+ with those for RhCHZ+. 1. The ground state of CoCHz+ is nearly degenerate 3A1and 'A2 states, and 'Al is about 26-27 kcal/mol higher. In contrast, for RhCHz+, IAl is the ground state and 3Al and 3A2lie about 4-5 kcal/mol higher. 2. The calculated binding energies of M+=CHz are 80.3 and 78.3 kcal/mol vs experimentalgas-phasephotodissociationresults of 84 f 5 (77.5 f 2.3) (ion-beam61results in parentheses) and 91 f 5 kcal/mol, for M = C O and ~ ~Rh,65respectively. 3. The wave functions of intermediates and transition states for the RhCH2+ + Hz reaction system are more single determinant-like than for the CoCH2+ + HZsystem. 4. The reaction mechanism

+

MCH2+ H,

-

M+ + CH4

(3) is qualitatively similar between CoCH2+ and RhCH2+ on both their ground and first excited states. In the first step, reactants yield an ion-molecule complex (Hz)MCH*+,with a stabilization energies of 6.4 and 7.2 kcal/mol for M = Co and Rh, respectively. Then the H-H bond activation process takes place through a four-centered transition state with activation barriers of 33.5 and 16.3 kcal/mol, respectively, for M = Co and Rh. The resultant complex, HMCH3+,does not exist for either metal. It rearranges without barrier into an ion-molecule complex MCH4+,which is stable relative to the dissociation limit M+(3F,d8) CH4(IA,) by 21.4 and 16.8 kcal/mol for M = Co and Rh, respectively. 5. Reaction 3 is exothermic by 27.0 and 3 5 4 0 kcal/mol for RhCHz+and CoCHz+, respectively. The barrier height for the rate determinants H-H bond activation step for RhCH2+ is, as shown in the preceding paragraph, about half that for CoCHz+. Therefore, the reaction of RhCH2+with H2 should be easier than that of CoCH2+. This conclusion is also in good agreement with ion-beam FTMS experiments, which show that RhCH2+ is more reactive with H2 than CoCHz+.

+

Musaev et al. (14) (a) Jacobson, D. B.; Freiser, B. S. J . Am. Chem. Soc. 1985,107, 2605. (b) Jacobson, D. B.; Freiser, B. S.J . Am. Chem. SOC.1985,107,67. (c) Jacobson, D. B.; Freiser, B. S.J . Am. Chem. Soc. 1985,107,4373. (15) Jacobson, D.B.; Freiser, B. S.J . Am. Chem. SOC.1985,107,5870. (16) For example, see: (a) Fisher, E. R.; Armentrout, P. B. J . Am. Chem. Soe. 1992,114,2039. (b) Schultz, R. H.; Elkind, J. L.; Armentrout, P. B. J . Am. Chem. SOC.1988,110,411.(c) Van Koppen, P. A. M.; Kemper, P. R.; Bowers, M. T. J. Am. Chem. Soc. 1992, 114, 1083. (17) Hoffmann, R.; Jemmis, E.; Goddard, R. J. J . Am. Chem. Soc. 1980, 102,1667. (18) Hoffmann, R.; Eisenstein, 0.; Rossi, R. J . Am. Chem. SOC.1981, 103, 82. (19) Rappe, A. K.; Goddard, W. A., 111. In Potential Energy Surfaces and Dynamic Calculations; Truhlar, D. G., Ed.; Plenum: New York, 1981; p 661. (20) Hall, M. B.; Taylor, T. E. J. Am. Chem. SOC.1984,106, 1576. (21) Hall, M. B. In Quantum Chemistry: The Challenge of Transition Metals and Coordination Chemistry; Veillard, A., Ed.; Reidel: Dordrecht, The Netherlands, 1986;p 319. (22) Vincent, M. A.; Yoshioka, Y.; Schaefer, H. F., 111. J . Phys. Chem. 1982,86,3905. (23) Brooks, B.; Schaefer. H. F., 111. Mol. Phys. 1977,34, 193. (24) Brooks, B.; Schaefer, H. F., 111. In$. J . Quantum Chem. 1978,14, 603. (25) Ushio, J.; Nakatsuji, H.; Yonezawa, Y. J . Am. Chem. SOC.1983, 105,426. (26) Ushio, J.; Nakatsuji, H.; Yonezawa, Y. J . Am. Chem. SOC.1984, 106, 5892. (27) Goddard, W. A., 111; Rappe, A. K. J . Am. Chem. Soe. 1977,99, 3966. (28) Goddard, W. A., 111; Rappe, A. K. J . Am. Chem. Soc. 1980, 102, 5114. (29) Goddard, W. A., 111; Rappe, A. K. J . Am. Chem. Soc. 1982,104, 297. (30) Goddard, W. A., 111; Rappe, A. K. J . Am. Chem. Soc. 1982, 104, 448. (31) Carter, E. A.; Gcddard, W. A., 111. J . Am. Chem. Soe. 1986,108, 2180. (32) Carter, E. A.; Goddard, W. A., 111. J . Phys. Chem. 1984,88.1485. (33) Carter, E. A.; Goddard, W. A., 111. J. Phys. Chem. 1984,88,1485. (34) Carter, E. A.; Goddard, W. A., 111. Organometallics 1988,7,675. (35) Upton, T. H.; Rappe, A. K. J . Am. Chem. Soc. 1985, 107, 1206. (36) Upton, T.H.; Rappe, A. K. Organometallics 1984,3, 1440. (37) Spangler, D.; Wendoloski, J. J.; Dupuis, M.; Chen, M.M. L.;Schaefer, H. F., 111. J. Am. Chem. Soc. 1981,103, 3985. (38) Marynick, D.S.; Kirkpatrick, C. M. J . Am. Chem. Soc. 1985,107, 1993. (39) Alvarad*Swaisgood, A. E.; Allison, J.; Harrison, J. F. J . Phys. Chem. 1985.89.2517. (40) Alvarado-Swaisgood, A. E.; Harrison, J. F. J . Mol. Strucr. (THEOCHEM) 1988,169, 155. (41) Alvarado-Swaisgood, A. E.; Harrison, J. F. J . Phys. Chem. 1988,92, ~

--.--.

~~~

*.(ell

L/>/.

(42) Mintz, E. A.; Gregory, A. R. J . Am. Chem. Soc. 1985,107,2179. (43) Kostic, N. M.; Fenske, R. F. J. Am. Chem. SOC.1982,104,3879. (44) Block, T. F.; Fenske, R. F.; Casey, C. P. J . Am. Chem. SOC.1976, Acknowledgment. D.G.M. thanks the Japan Society for the 98,441. Promotion of Science for postdoctoral fellowship support. The (45) Sodupe, M.; Lluche, J. M.; Olive, A.; Bertran, J. Organometallics present research is supported in part by grants-in-aid from the 1989,8, 1837. Ministry of Education,Science and Culture. Part of the numerical (46) Francl, M. M.; Pietro, W. J.; Hout, R. F.; Hehre, W . J. Organometallics 1983,2, 28 1. calculations were carried out at the Computer Center, Institute (47) Francl, M. M.; Hehre, W. J. Organometallics 1983,2,457. for Molecular Science. (48) Francl, M. M.; Pietro, W. J.; Hout, R. F.; Hehre, W . J. Organometallics 1983,2, 815. (49) Planelles, J.; Merchan, M.; Nebot-Gil, I.; Tomas, F. J . Phys. Chem. References and Notes 1989,93,6596. (50) Planelles, J.; Merchan, M.; Tomas, F. Chem. Phys. Lert. 1988,149, (1) Armentrout, P. B. In StructurelReactiuity and Thermochemistry of 222. Ions; Ausloos, P., Lias, S. G., Eds.; Reidel: Dordrecht, The Netherlands, (51) Takahara, Y.;Yamaguchi, K.; Fueno, T. Chem. Phys. Left. 1989, 1987;pp 97-184. 158, 95. (2) Armentrout, P. B. In Gas Phase Inorganic Chemistry; Russell, D. (52) Mochieuki, Y.; Tanaka, K.; Ohno, K.; Tatewaki, H.; Yamamoto, S. H., Ed.; Plenum: New York, 1989;pp 1-42. Chem. Phys. Lett. 1988,152,457. (3) Armentrout, P. B. In Selective Hydrocarbon Activation: Principles (53) Rappe, A. K. Organometallics 1987,6, 354. und Progress; Davies, J. A,, Watson, P. L., Liebman, J. F., Greenberg, A,, (54)Cundari, T. R.; Gordon, M. S. J . Am. Chem. SOC.1991,113,5231. Eds.; VCH: New York, 1990;pp 467-533. (55) Cundari, T.R.; Gordon, M. S. J . Am. Chem. Soc. 1992,114,539. (4) Armentrout, P. B.; Sunderlin, L. S. In Transition Metal Hydrides; (56) Russo, N.; Salahub, D. R.; St-Amant, A.; Toscano, M. Presented at Dedieu, A., Ed.; VCH: New York, 1992;pp 1-64. the 7th International Congress on Quantum Chemistry, Menton, France, July (5) MacMillan, D. K.; Gross, M. L. In Gas Phase Inorganic Chemistry; 2-5, 1991;p 228. Russell, D. H., Ed.; Plenum: New York, 1989;pp 369-401. (57) Bauschlicher, C. W., Jr.; Langhoff, S. R.; Partridge, H. J. Phys. (6) Buckner, S. W.; Freiser, B. S. In Gas Phase Inorganic Chemistry; Chem. 1991, 95,6191. Russell, D. H., Ed.; Plenum: New York, 1989;pp 279-322. (58) Bauschlicher, C. W., Jr.; Partridge, H.; Sheehy, J. A.; Langhoff, S. (7) Roth, L. M.; Freiser, B. S. Mass Spectrom. Rev. 1991,10, 303. R.; Rosi, M. J. Phys. Chem. 1992, 96,6969. (8) Eller, K.; Schwarz, H. Chem. Reu. 1991,91, 1121. (59) Musaev, D. G.; Koga, N.; Morokuma, K.; Cundari, T. R.; Gordon, (9) Sweany, R. L. In Transition Metal Hydrides; Dedieu, A,, Ed.; VCH: M. S., to be published. New York, 1992;pp 65-101. (60) See, for example: (a) Dotz, K. H.; Fischer, H.; Hoffman, P.; Kreissl, (10) Irikura, K. K.; Beauchamp, J. L. J. Phys. Chem. 1991,95,8344. F. R.; Schubert, U.; Weiss, K. In Transition Metal Carbene Complexes; (1 1) Irikura, K. K.; Beauchamp, J. L. J. Am. Chem. Soc. 1989,I 1I , 75. Verlag Chemie: Deerfield Beach, FL, 1984. (b) Gallop, M. A.; Roper, W. (12) Buckner, S . W.; MacMahon, T. J.; Byrd, G. D.; Freiser, B. S. Inorg. R. Adv. Organomet. Chem. 1986,25, 121. (c) Collman, J. P.; Hegedus, L. Chem. 1989,28,3511. S.;Norton, J. R.; Finke, R. G. Principlesand Applicationsof Organotransition (13) Irikura,K.K.;Beauchamp,J.L.J.Am.Chem.Soc.1991,113,2769. Metalchemistry; UniversityScienceBook: Mill Valley,CA, 1987. (d) Roper,

Electronic and Geometric Structure of RhCH2+ W. R. Advances in Metal Carbene Chemistry; Schubert, U., Ed.; Kluwer Academic: Hingham, MA, 1989; p 27. (0 Mayer, J. M.; Nugent, W. A. Metal-Ligand Multiple Bond; Wiley: New York, 1989. (61) Armentrout, P. B.;Sunderlin, L. E.; Fisher, E. R. Inorg. Chem. 1989, 28, 4436. (62) Hettich, R. L.; Freiser, B. S . J . Am. Chem. SOC.1986, 108, 2537. (63) Tonkyn, R.; Ronan, M.; Weisshaar, J. C. J . Phys. Chem. 1988,92, 92. (64) Kempter, P. R.; Bowers, M. T. J . Am. SOC.Mass Specrrom. 1990, I , 197. (65) Hettich, R. L.; Freiser, B. S. J . Am. Chem. SOC.1987, 109, 3543. (66) Hay, P. J.; Wadt, W. R. J . Chem. Phys. 1985, 82, 270. (67) Dunning, T. H., Jr. J . Chem. Phys. 1970.53, 2823. (68) Hay, P. J.; Wadt, W. R. J. Chem. Phys. 1985,82, 299. (69) Dunning, T. H., Jr.; Hay, P. J. In Methods ofElectronic Structure Theory; Schaefer, H. F., 111, Ed.; Plenum: New York, 1977; Vol. 1. (70) GAMESS (General Atomic and Molecular Electronic Structure

System): Schmidt, M. W.; Baldridge, K. K.; Boatz, J. A.; Jensen, J. H.; Koseki, S . ; Gordon, M. S . ; Nguyen, K. A.; Windus, T. L.; Elbert, S.T. QCPE Bull. 1990, No. 10, 52. (71) MOLPRO: Werner, H.-J.;Knowles,P. J. UniversiryofSussex, 1991. See also: (a) Werner, H.-J.; Knowles, P. J. J . Chem. Phys. 1985, 82, 5053. (b) Knowles, P. J.; Werner, H.-J. Chem. Phys. Lett. 1985, 115, 259. (72) Moore, C. F. Aromic Energy Levels, NSRD-NBS; US. Government Printing Office: Washington, DC, 1971; Vol. 3.

The Journal of Physical Chemistry, Vol. 97, No. 16, 1993 4075 (73) Balasubramanian, K.; Liao, D. W. J . Phys. Chem. 1988, 92,6259. (74) Bunker, P. R.; Jensen, P.; Kraemer, W. P.; Beardsworth, R. J . Chem. Phys. 1986,85, 3724. (75) Bauschlicher, C. W., Jr.; Langhoff, S. R.; Taylor, P. R. J . Chem. Phys. 1987,87, 387. (76) Stevens, W. J.; Krauss, M.; Basch, H.; Jasien, P. G. Can. J . Chem. 1992, 70, 612. (77) (a) Hariharan, P. C.; Pople, J. A. Theor. Chim. Acta 1973,28,213.

(b) Francl, M. M.; Pietro, W. J.; Henre, W. J.; Binkley, J. S.; Gordon, M. S.; DeFrees, D. J.; Pople, J. A. J. Chem. Phys. 1982, 77, 3654. (78) Langhoff, S . R.; Pettersson, L. G. M.; Bauschlicher, C. W., Jr.; Partridge, H. J. Chem. Phys. 1987, 86, 268. (79) Dunning, T. H., Jr. J . Chem. Phys. 1971, 55, 716. (80) Mandich, M. L.; Halle, L. F.; Beauchamp, J. L. J . Am. Chem. SOC. 1984, 106,4403. (81) Weast, R. C.; Astle, M. J.; Beyer, W. H. Handbook of Chemistry and Physics, 68th ed.; CRC Press: Boca Raton, FL, 1987-1988; p F-171. (82) Schilling, J. B.;Gcddard, W. A., 111; Beauchamp, J. L.J. Am. Chem. SOC.1987, 109. 5565. (83) Bauschlicher, C. W., Jr.; Langhoff, S . R.; Partridge, H.; Barnes, L. A. J. Chem. Phys. 1989, 91, 2399. (84) Koga, N.; Morokuma, K. J . Phys. Chem. 1990, 94, 5454. (85) Jones, M.; Moss, R. A. Carbenes; Wiley: New York, 1972, 1975;

Vol. I, 11.

Ab initio molecular orbital study of the electronic and geometric

Recommend Documents