Theoretical study on the gas-phase reaction mechanism between rhodium monoxide and methane for...

Theoretical Study on the Gas-Phase Reaction Mechanism

Between Rhodium Monoxide and Methane

for Methanol Production

CHAO GAO,1,2

HUA-QING YANG,1,2

JIAN XU,1,2

SONG QIN,1CHANG-WEI HU

1

1Key Laboratory of Green Chemistry and Technology, Ministry of Education,College of Chemistry, Sichuan University, Chengdu, Sichuan 610064, People’s Republic of China

2College of Chemical Engineering, Sichuan University, Chengdu, Sichuan 610065,People’s Republic of China

Received 8 February 2009; Revised 5 June 2009; Accepted 19 June 2009DOI 10.1002/jcc.21382

Published online 4 August 2009 in Wiley InterScience (www.interscience.wiley.com).

Abstract: The gas-phase reaction mechanism between methane and rhodium monoxide for the formation of metha-

nol, syngas, formaldehyde, water, and methyl radical have been studied in detail on the doublet and quartet state

potential energy surfaces at the CCSD(T)/6-3111G(2d, 2p), SDD//B3LYP/6-3111G(2d, 2p), SDD level. Over the

300–1100 K temperature range, the branching ratio for the Rh(4F) 1 CH3OH channel is 97.5–100%, whereas the

branching ratio for the D-CH2ORh 1 H2 channel is 0.0–2.5%, and the branching ratio for the D-CH2ORh 1 H2

channel is so small to be ruled out. The minimum energy reaction pathway for the main product methanol formation

involving two spin inversions prefers to both start and terminate on the ground quartet state, where the ground dou-

blet intermediate CH3RhOH is energetically preferred, and its formation rate constant over the 300–1100 K tempera-

ture range is fitted by kCH3RhOH 5 7.03 3 106 exp(269.484/RT) dm3 mol21 s21. On the other hand, the main prod-

ucts shall be Rh 1 CH3OH in the reactions of RhO 1 CH4, CH2ORh 1 H2, Rh 1 CO 12H2, and RhCH2 1 H2O,

whereas the main products shall be CH2ORh 1 H2 in the reaction of Rh 1 CH3OH. Meanwhile, the doublet inter-

mediates H2RhOCH2 and CH3RhOH are predicted to be energetically favored in the reactions of Rh 1 CH3OH and

CH2ORh 1 H2 and in the reaction of RhCH2 1 H2O, respectively.

q 2009 Wiley Periodicals, Inc. J Comput Chem 31: 938–953, 2010

Key words: rhodium monoxide; methane; methanol; B3LYP; CCSD(T)

Introduction

Methane, as one of the principal constituent of natural gas, has

been widely used in chemical synthesis, hydrogen production,

and energy production.1 However, most of the natural gas

locates in remote areas, thereby its transportation and storage

become inconvenient. Besides, the direct oxidation reaction of

methane to methanol is thermodynamically favored.2 And then,

the development of catalysts for efficiently selective conversion

of methane into more useful and easily transportable liquid

chemical compounds such as methanol is a great challenge and

has attracted a great deal of attention both experimentally and

theoretically.2–6 A lot of transition-metal derived catalysts have

been used for the controlled oxidation of methane, including

some heterogeneous, homogeneous, or enzyme catalysts.7–12 To

gain a valuable insight into the elementary steps of such con-

densed phase systems, considerable interest has been devoted to

studying the more tractable chemistry of gas-phase species, on

account of the simplest model of the condensed phase active

sites.4,13–26

The gas-phase reactions of transition metal oxide ions and

neutral transition metal oxides with methane have been explored

experimentally and theoretically by a number of groups. To

begin with, Schwarz et al. have experimentally investigated the

reaction efficiency and methanol/methyl branching ratio of the

gas phase reactions of various transition metal oxide ions with

methane. It is found that the transition metal oxide ions, ScO1,

TiO1, VO1, and CoO1, do not react, while the other transition

metal oxide ions, MnO1, FeO1, NiO1, PtO1, and OsO1, react

with methane.27,28 Additionally, Schwarz, Armentrout, and

Yoshizawa et al. have theoretically studied the gas-phase poten-

Additional Supporting Information may be found in the online version of

this article.

Correspondence to: H.-Q. Yang; e-mail: [email protected] or

C.-W. Hu; e-mail: [email protected]

Contract/grant sponsor: National Natural Science Foundation of China;

contract/grant numbers: 20503017

q 2009 Wiley Periodicals, Inc.

tial energy surfaces for methane activation by first-row transition

metal oxide ions (MO1s), where M is Sc, Ti, V, Cr, Mn, Fe,

Co, Ni, and Cu.4,25,26,29–33 It is suggested that the methane-to-

methanol conversion can take place by the following mecha-

nism: MO1 1 CH4 ? OM1(CH4) ? TS1 ? HO-M1-CH3 ?TS2 ? M1(CH3OH) ? M1 1 CH3OH, and the inserted

hydroxy intermediate, HO-M1-CH3, plays an important

role.4,25,26,29,31–34 These authors concluded that the experimen-

tally observed reaction efficiency and methanol/methyl product

branching ratio can be rationalized in terms of the calculated

barrier heights at TS1 and TS2.4,25–29,31–34 Besides, Zhang et al.

have investigated the reaction mechanism of the gas-phase

OsOn1 (n 5 1–4) with methane, and suggested that the dehydro-

genation channel of oxidative addition would be thermodynami-

cally and kinetically preferred.19

After that, in contrast to the cation reaction systems, the reac-

tion between neutral transition metal oxides and methane has

not yet received enough attention, partially because of the exper-

imental challenges faced in detecting neutral species in the gas

phase. Previously, Broclawik et al. and Hwang and coworkers

have theoretically studied the reaction mechanism of neutral

metal oxides, MO (M 5 Be, Sc, Ni, Pd, Pt, Rh), with meth-

ane.22–24,35,36 It is proposed that MO can insert into the C��H

bond of CH4, which results in the hydroxyl intermediate (HOMCH3),

and then leads to M 1 CH3OH or MOH 1 CH3.22–24,35,36

More recently, Xu et al. have theoretically studied the methane

activation to methanol or methyl radical by transition-metal

oxides, MOx (M 5 Cr, Mo, W; x 5 1, 2, 3), and Mo3O9 oxide,

and found that the trend in reactivity can be rationalized in

terms of change in electrophilicity of MOx, the strength of the

M��O p bond, and the binding property of MOx to methyl or

hydrogen.18,21 Zhou and coworkers have deliberately investi-

gated the MO (M 5 Fe, Mn, Nb, Ta) 1 CH4 and M (M 5 Sc,

Ti, Mn, Fe) 1 CH3OH model reaction regarding the mechanism

for the catalytic methane-to-methanol conversion process by

quantum chemical calculations coupled with matrix isolation

spectroscopy.15,37–40 It is proposed that for the late transition

metals, Mn and Fe, the inserted CH3MOH molecule is a critical

intermediate in both MO 1 CH4 and M 1 CH3OH reactions;

while for the group IV and V transition metals, the inserted

CH3OMH and CH3M(O)H molecules are the crucial intermedi-

ates; and for Sc, the CH3ScOH molecule is an important inter-

mediate in the ScO 1 CH4 reaction, whereas the CH3OScH is a

critical intermediate in the Sc 1 CH3OH reaction.15,37–40 Previ-

ously, we have reported the gas-phase reaction mechanism of

CH4 with MO (M 5 Mg, Ca, Sr), and put forward that the reac-

tion may proceed via two kinds of important reaction intermedi-

ates, HOMCH3 and HMOCH3, and the hydroxy intermediate

HOMCH3 is more preferable than the methoxy intermediate

HMOCH3, while the products, MOH 1 CH3, are more favorable

than M 1 CH3OH.13,14,20 Lately, we have comprehensively

investigated the gas-phase reaction mechanism of CH4 with

NiO for the formation of CO 1 2H2, HCHO, CH3OH, H2O,

and CH3 radical.41 It is suggested that the main products would

be syngas once HNiOCH3 is created on the singlet state,

whereas the main products would be methyl radical if

CH3NiOH is formed on both singlet and triplet states.41 More-

over, it is predicted that the syngas formation would be more

effective under higher temperature and photolysis reaction

conditions.41 These theoretical studies have provided some

valuable information concerning the reaction mechanism and

energetics.

Up to now, concerning the C��H bond activation by related

rhodium compound in the gas phase, it is found that the neutral

rhodium atom is able to activate the C��H bond of methane

under mild conditions,42–45 while rhodium ion and related rho-

dium compounds exhibit fine performances on the C��H bond

activation of hydrocarbon.5,43,46,47 Elucidation of the role of iso-

lated rhodium oxide units in heterogeneous catalysis can be

aided by the gas-phase study, which can provide insight into the

intrinsic property and reactivity of discrete and well-character-

ized species. Nevertheless, despite a few theoretical investiga-

tions of the C��H bond activation by bare RhO in the gas

phase,36 only the collinear and on top molecular complexes

between RhO and CH4, and the inserted intermediate CH3RhOH

have been reported. It is of particular interest to study the reac-

tion pathway from RhO 1 CH4 to Rh 1 CH3OH, or CH2ORh

1 H2, or Rh 1 CO 1 2 H2, or Rh 1 HCHO 1 H2, or RhCH2

1 H2O, or RhOH 1 CH3, to provide reliable structures and

vibration frequencies of the reactants, intermediates, transition

states (TSs), and products as well as their chemically accurate

energetics, to gain a better understanding of the preference of

reaction pathway, and to predict the preferred intermediate in

both the forward and reverse reactions. As the spin crossing is

often involved in the transition-metal-containing reactions,19 the

potential energy profiles for the doublet and quartet states are

investigated.

Computational Details

Computations were carried out with the Gaussian 03 program.48

Full geometry optimizations were run to locate all of the station-

ary points and transition states (TSs) on the doublet and quartet

spin states PES for the reaction of RhO 1 CH4, using

B3LYP49–51 method with 6-3111G(2d, 2p) basis set for the car-

bon, oxygen, and hydrogen atoms,52,53 and the SDD basis set

and ECP for Rh atom,54 namely B3LYP/6-3111G(2d, 2p),

SDD. Meanwhile, the test of stability of the density function

theory (DFT) wavefunction was passed. If an instability is

found, the wavefunction is reoptimized with appropriate reduc-

tion in constraints, and the stability tests and reoptimizations are

repeated until a stable wavefunction is found. The systematic har-

monic frequency calculations were performed to characterize sta-

tionary points and to take corrections of zero-point vibration

energy (ZPE) into account. For each transition state, the intrinsic

reaction coordinate (IRC) calculations were performed in both the

forward and reverse directions to connect these corresponding

intermediates at the same level.55,56 Based on the optimized

B3LYP/6-3111G(2d, 2p), SDD geometries, the relative energies

of various species were then refined at the CCSD(T)57 level with

the same basis sets, namely CCSD(T)6-3111G(2d, 2p), SDD//

B3LYP/6-3111G(2d, 2p), SDD, including ZPE correction

obtained at the B3LYP/6-3111G(2d, 2p), SDD level. Unless

otherwise mentioned, all energies are relative to reactants

[RhO(4S) 1 CH4] at the CCSD(T)/6-3111G(2d, 2p), SDD level.

939Gas-Phase Reaction Mechanism Between Rhodium Monoxide and Methane for Methanol Production

Journal of Computational Chemistry DOI 10.1002/jcc

Results and Discussion

To assess the present computational method, the geometric opti-

mization and vibration frequency calculation of some small mol-

ecules containing RhH moiety, or RhO species, or RhC moiety,

are performed at B3LYP/6-3111G(2d, 2p), SDD level, and then

compared with the experimental results. These calculated char-

acteristic vibration frequencies scaled by a factor of 0.963 are

summarized in Table 1.58

Firstly, according to the vibration analysis, for the RhH

contained complexes [HRh, H2Rh, H2RhH, (H2)RhH3, and cyc-

Rh2H2], the calculated vibration frequencies are in good agree-

ment with the corresponding experimental observation in the Ar

and Ne mediums, with only one exception of the HRhH bending

mode of cyc-Rh2H2 [the calculated value (1111 cm21) vs. the

experimental one (803.0 cm21)].59 Secondly, for the RhO con-

tained species [ORhO, ORhOO, O2RhO2, and cyc-(RhO)2], the

calculated vibration frequencies are almost consistent with the

relevant results in the Ar and Xe mediums.60,61 Thirdly, for

RhCO, the frequency of 1967 cm21, which is ascribed to the

CO stretch, is quite close to the experimental results (2023 and

2008 cm21) in the Ne and Ar mediums.62 Lastly, for Rh(CO)2,

the frequency of 2017 cm21, which is attributed to the CO

asymmetric stretch, is in accordance with the experimental

results (2031 and 2015 cm21) in the Ne and Ar mediums.62–64 It

is inferred that the calculated vibration frequencies for all spe-

cies in the reaction between RhO and CH4 will provide some

useful information for the assignment of spectroscopic results in

the corresponding experimental study. Furthermore, the ion ener-

geticses (IEs) are calculated for some experimentally available

species (Rh, ORh, O2Rh, CRh, and C2Rh) at CCSD(T)/

6-3111G(2d, 2p), SDD//B3IYP/6-3111G(2d, 2p), SDD level,

and compared with the experimental data. These calculated gas-

phase IEs are listed in Table 2. As shown in Table 2, the gas

phase IEs of these species except CRh are in good accordance

with the experimental data.65–68

It should be noted that the same method (B3LYP) and

similar basis set [6-3111G(d, p), or 6-31111G(d, p), or 6-

3111G(3df, 3pd) basis set for C, H, and O; the SDD basis set

and the corresponding ECP for Rh] were used by Zhou and

Table 1. Calculated Characteristic Vibration Frequencies Scaled by a Factor of 0.963 at the B31YP/

6-3111G(2d, 2p), SDD Level for Some Typical Species Involving RhH Species, or RhO Moiety, or

RhC Moiety.

Species

Approximate type

of vibration mode

Calculated

frequency (cm21)

Experimental

frequency (cm21) References

HRh(3D) RhH stretch 1931 1921 (Ar) 59

1936 (Ne)

H2Rh(2A0) RhH sym stretch 2116 2100 (Ne) 59

2099 (Ar)

RhH asym stretch 2050 2052 (Ne)

2053 (Ar)

H2RhH(1A0) RhH stretch 2003 2014 (Ar) 59

(H2)RhH2(2A0) RhH stretch 2100 2009 (Ne) 59

(H2)RhH3(1A0) RhH stretch 2168 2122 (Ne) 59

2070 2078 (Ne)

T-cyc-Rh2H2 HH asym. stretch 1268 1357 (Ne) 59

1345 (Ar)

HRhH bending 1111 803.0 (Ne)

D-ORhO RhO sym. stretch 892 845 (Ar) 60

RhO sym. stretch 914 900 (Ar)

D-ORhOO OO stretch 1389 1367 (Ar) 60

Q-O2RhO2 OO stretch 1147 1048 (Ar) 60, 61

1045 (Xe)

1038 (O2)

T-cyc-(RhO)2 RhORh bending and RhO stretch 578 562 (Ar) 60

RhCO(2P

) CO stretch 1967 2023 (Ne) 62

2008 (Ar)

D-Rh(CO)2 CO asym. stretch 2017 2031 (Ne) 62–64

2015 (Ar)

Table 2. The Calculated Gas-Phase Ion Energetics (IE) at the CCSD(T)/

6-3111G(2d, 2p), SDD//B31YP/6-3111G(2d, 2p), SDD Level for Some

Typical Species.

Species

Calculated IE

(kJ mol21)

Experimental

IE (kJ mol21) References

Rh (4F) ? Rh1 (3D) 674.3 719.7 65

ORh(4P

) ? ORh1 (3II) 803.2 823.7 6 41.5 66

O2Rh(2A0) ? O2Rh

1(1A0) 916.6 964.9 67

CRh(2P

) ? CRh1(1P

) 687.4 887.7 6 96.5 65

C2Rh(4P) ? C2Rh

1(3P

) 799.1 781.5 6 38.6 68

940 Gao et al. • Vol. 31, No. 5 • Journal of Computational Chemistry


coworkers and Wang and Andrews in their theoretical studies of

Rh 1 CH4 and rhodium hydrides systems.43,59 Therefore, the

present theoretical method of CCSD(T)/6-3111G(2d, 2p), SDD//

B3IYP/6-3111G(2d, 2p), SDD should be appropriate and

reliable for the RhO 1 CH4 system.

As will be shown later, we will mainly discuss the formation

of methanol in the reaction between RhO and CH4,

RhOþ CH4 ! Rhþ CH3OH (1)

Besides, the infra mentioned possible side reactions will be

taken into account. They lead to the formation of syngas, form-

aldehyde and hydrogen molecules, RhCH2 and water, methyl

radical and RhOH,

RhOþ CH4 ! Rhþ COþ 2H2 (2)

RhOþ CH4 ! Rhþ HCHOþ H2 (3)

RhOþ CH4 ! RhCH2þH2O (4)

RhOþ CH4 ! RhOHþ CH3 (5)

Therewithal, we will discuss the above five product channels

by dividing into four reaction stages: (i) C��H bond activation,

(ii) the formation of methanol, (iii) the formation of CO and H2

from CH2ORh, and (iv) the reactions starting from the above

products.

C��H Bond Activation

The optimized geometric structures of various species, the sche-

matic energy diagrams along the reaction pathways in the dou-

blet and quartet states, and the reaction pathway are depicted in

Figures 1, 2, and Scheme 1, respectively.

In the ground quartet state 4S and the lowest doublet state 2Sof RhO, as shown in Figure 1, the computed Rh��O distance is

1.730 and 1.727 A, close to the computed values by Broclawik et al.

[1.80 A (4S, 2P, 2D)].36 The calculated electronic configurations

of RhO are typical as 4S(1r22r23r21p44r25r22p41d43p26r1). and2S(1r22r23r21p44r22p45r21d43p26r1). The dissociation energy

(D0), with respect to Rh(4F) 1 O(3P), is computed to be 344.9 and

316.8 kJ mol21 for 4S and 2S, respectively. Meanwhile, compared

to the experimental D0 value (405.2 kJ mol21) for RhO (4S),36 thecomputed D0 value (344.9 kJ mol21) is underestimated by 60.3 kJ

mol21 in our calculation. In the ground state 4S, roughly two of

the three unpaired electrons (spins) are localized on Rh atom, and

the remaining one unpaired electron is located on O atom.

Moreover, for the RhO (4S), three single electrons are arranged in

uniform direction on the two 3p and one 6 r orbitals, whereas for

the RhO (2S), two of the three single electrons are distributed in

different direction on the two 3p orbitals, to meet the requirement

of the quartet and doublet states, respectively. Thus, RhO has a

higher energy in the 2S state than in the ground state 4S.This can be tested by the fact that the doublet state 2S of RhO

lies 37.1 kJ mol21 above the ground state 4S of RhO, as seen in

Figure 2.

Interaction Between RhO and CH4

Concerning the initial interaction between RhO and CH4, two

models are considered: (i) two C��H bonds in methane toward

the Rh end of RhO (CH4RhO molecular complex in the pseudo-

C2m coordination mode), and (ii) a collinear C��H bond

approaching to the O-end of RhO (CH4ORh molecular complex

in the pseudo C3m coordination mode). For CH4RhO, CH4 is

bound to RhO with comparatively large stabilization energy of

41.2 and 33.8 kJ mol21 on the quartet and doublet states,

respectively, which are apparently lower than the calculated

result by Broclawik et al. (79.5 kJ mol21).36 The geometric

structure of CH4RhO is analogical to that of CH4MO (M 5Zn,16 Ni,22,41 Pd,22 Be,24 Pt,23 Mn,38,40 and Fe38,40). Alterna-

tively, for CH4ORh, the complexation energy is calculated to be

1.7 and 2.9 kJ mol21 relative to the corresponding reactants on

the quartet and doublet states, respectively. Such low complexa-

tion energy makes CH4 be loosely bound to RhO. This molecu-

lar complex, CH4ORh, is not reported in the previous study by

Broclawik et al.,36 and its geometric structure is analogical to

that of CH4OM (M 5 Ca,13 Sr,14 Zn,16 Mg,20 and Ni41).

As discussed earlier, RhO has a quartet ground state (4S)with excitation energy of 37.1 kJ mol21 to the lowest doublet

state (2S), and the methane complexes (CH4RhO and CH4ORh)

also have a quartet ground state. Then, the quartet state

Q-CH4RhO and Q-CH4ORh, stand 44.5 and 35.9 kJ mol21

below D-CH4RhO and D-CH4ORh, respectively, (here and

below prefixes ‘‘Q,’’ ‘‘T,’’ ‘‘D,’’ and ‘‘S’’ indicate quartet, triplet,

doublet, and singlet state, respectively). Thereupon, the minimal

energy reaction pathway (MERP) may start at the formation of

Q-CH4RhO and Q-CH4ORh molecular complexes from RhO(4S)1 CH4.

From these molecular complexes (CH4RhO and CH4ORh), as

shown in Scheme 1 and Figure 2, the C��H bond cleavage may

lead to three different products (CH3RhOH, HRhOCH3, and

RhOH 1 CH3).

Formation of CH3RhOH

As depicted in Scheme 1, there are two reaction pathways: one

via (2 1 2) addition and another via oxidative addition. To

begin with, from the molecular complex, CH4RhO, the (2 1 2)

addition via 1-TS1c pertains to the possible r bond metathesis

reaction. The TS, 1-TS1c, is concerted with a four-center and

four-electron cyclic one. In 1-TS1c, methane approaches the

Rh��O bond with its methyl group attacking the metal and H

attacking the oxygen, leading to the hydroxyl intermediate,

CH3RhOH. This (2 1 2) addition reaction pathway is alike to

the systems of MO 1 CH4 (M 5 Ca,13 Sr,14 Zn,16 Mg,20 Cr,21

Mo,21 W,21 Be,24 Pd,22 Mn,38,40 Fe,38,40 and Ni41). For this addi-

tion via 1-TS1c, i.e., CH4RhO ? 1-TS1c ? CH3RhOH, as

shown in Figure 2, the doublet PES sits below the quartet one,

aside from the entrance channel (CH4RhO). It is indicated that a

double-quartet intersystem crossing should occur once near

1-TS1c. If this intersystem crossing occurs, the MERP should be

RhO(4S) 1 CH4 ? Q-CH4RhO ? D-1-TS1c ? D-CH3RhOH,

with the largest energy requirement (LER) of 100.9 kJ mol21

and the energy height of the highest point (EHHP) of 59.7 kJ



mol21 at D-1-TS1c. In other words, the energy barrier for this

step can be lowered to 100.9 kJ mol21 at D-1-TS1c from 168.7

kJ mol21 at Q-1-TS1c. After the energy barrier is conquered on

the doublet PES, the later reaction should advance along the

doublet PES and lead to the intermediate D-CH3RhOH.

Alternatively, from the molecular complex, CH4RhO, one

hydrogen atom of methane transfers to the metal centre to form

the intermediate CH3Rh(O)H, which can be regarded as rhodium

acetaldehyde, i.e., CH4RhO ? 1-TS1b ? CH3Rh(O)H. This

step of oxidative addition is a 2e process, and the TS, 1-TS1b,

is concerted with a cyclic three-center and four-electron TS.

This oxidative addition reaction pathway is parallel to the sys-

tems of MO 1 CH4 (M 5 Nb,39 Ta,39 and Ni41). Next, from

CH3Rh(O)H, the hydride ligand on rhodium migrates to the oxy-

gen forming a hydroxyl ligand in the CH3RhOH complex via a

TS, 1-TS2a, i.e., CH3Rh(O)H ? 1-TS2a ? CH3RhOH. For this

oxidative addition, i.e., CH4RhO ? 1-TS1b ? CH3Rh(O)H ?1-TS2a ? CH3RhOH, the doublet PES stands below the quartet

one, except for the entrance channel (CH4RhO). Thus, an impor-

tant doublet-quartet intersystem crossing should occur once in

the vicinity of 1-TS1b. If this intersystem crossing takes place,

the MERP should be RhO(4S) 1 CH4 ? Q-CH4RhO ? D-1-

TS1b ? D-CH3Rh(O)H ? D-1-TS2a ? D-CH3RhOH, where

the reaction step of D-CH3Rh(O)H ? D-1-TS2a ?D-CH3RhOH is the step of LER with an energy barrier of 87.3

kJ mol21 and the EHHP of 43.5 kJ mol21 at D-1-TS2a. That is

to say, after the energy barrier at 1-TS1b is surpassed on the

doublet PES, the later reaction should proceed along the doublet

PES and lead to the intermediate D-CH3RhOH.

Comparing these two reaction pathways, one can see that the

oxidative addition pathway is the gross MERP for the formation

of D-CH3RhOH, on account of its comparatively small LER and

low EHHP. This phenomena is unlike to that in the NiO 1 CH4

system, where the MERP for the CH3NiOH formation is the

(2 12) addition process.41

Formation of HRhOCH3

As depicted in Scheme 1 and Figure 2, there are also two reac-

tion pathways: one via (2 1 2) addition and another via oxida-

tive addition. On the one hand, from the molecular complex,

CH4RhO, the (2 1 2) addition via 1-TS1a belongs to the possi-

Figure 1. The optimized geometric structures of the reactants, intermediates, TSs, and products in the

C��H bond activation of CH4 by RhO calculated at the B3LYP/6-3111G(2d, 2p), SDD level.



ble r bond metathesis reaction. The TS, 1-TS1a, also pertains to

a four-center and four-electron cyclic TS. In 1-TS1a, methane

accesses the Rh��O bond with its H attacking the metal and the

methyl group attacking the oxygen, resulting in the methoxy

intermediate, HRhOCH3. This (2 1 2) addition reaction pathway

is parallel to the systems of MO 1 CH4 (M 5 Ca,13 Sr,14 Zn,16

Mg,20 Cr,21 Mo,21 W,21 and Ni41). In the (2 1 2) addition path-

way, i.e., CH4RhO ? 1-TS1a ? HRhOCH3, 1-TS1a has been

only obtained on the double PES, for we failed to locate the cor-

responding TS on the quartet PES despite our extensive attempt.

Moreover, D-HRhOCH3 lies 32.8 kJ mol21 below Q-HRhOCH3.

Thereby, the MERP should be RhO(4S) 1 CH4 ? Q-CH4RhO

? D-1-TS1a ? D-HRhOCH3 with the LER of 238.8 kJ mol21,

and the EHHP of 197.6 kJ mol21 at D-1-TS1a.

On the other hand, as depicted in Scheme 1, following the

formation CH3Rh(O)H via oxidative addition reaction pathway,

the methyl ligand on rhodium migrates to the oxygen forming a

methoxy ligand in the HRhOCH3 complex via a TS, 1-TS2b,

CH3Rh(O)H ? 1-TS2b ? HRhOCH3. This oxidative addition

reaction pathway is semblable to that in the system of NiO 1CH4.

41 As shown in Figure 2, for this oxidative addition path-

way, i.e., CH4RhO ? 1-TS1b ? CH3Rh(O)H ? 1-TS2b ?HRhOCH3, all species but CH4RhO on the doublet state locate

below those on the quartet one, respectively. One can expect

that the doublet-quartet intersection may occur once near

1-TS2b. If this doublet-quartet intersection takes place, the

MERP should be RhO(4S) 1 CH4 ? Q-CH4RhO ? D-1-TS1b

? D-CH3Rh(O)H ? D-1-TS2b ? D-HRhOCH3, where the

reaction step of D-CH3Rh(O)H ? D-1-TS2b ? D-HRhOCH3 is

the step of LER with an energy barrier of 162.2 kJ mol21, and

the EHHP of 118.4 kJ mol21 at D-1-TS2b. With regard to these

two reaction pathways, one can conclude that the second

reaction pathway should be the entire MERP for the formation

of D-HRhOCH3, in virtue of its comparatively small LER and

Figure 2. The schematic energy diagrams along the reaction pathways in the C��H bond activation of

CH4 by RhO in the doublet and quartet states computed at the CCSD(T)/6-3111G(2d, 2p), SDD//

B3LYP/6-3111G(2d, 2p), SDD level. Relative energies (kJ mol21) for the corresponding species

relative to RhO(4S) 1 CH4 are shown. [Color figure can be viewed in the online issue, which is

available at www.interscience.wiley.com.]



low EHHP. This result is analogical to that in the NiO 1 CH4

system, where the MERP for the HNiOCH3 formation is the

oxidative addition process.41

Formation of RhOH 1 CH3

As depicted in Scheme 1, following the formation of CH4ORh,

a hydrogen atom of CH4 moiety is directly abstracted by the

oxygen atom of RhO moiety via a TS, 1-TS1d, leading to the

radical products (RhOH 1 CH3). This H abstraction via 1-TS1d

is a 1e process. This process of hydrogen abstraction is similar

to those in the systems MO 1 CH4 (M 5 Mg,20 Ca,13 Sr,14

Ni,41 Be,24 Pd22). As shown in Figure 2, the quartet PES lies

below the doublet one. It is indicated that the MERP should

kinetically proceed along the quartet PES, i.e., RhO(4S) 1 CH4

? Q-CH4ORh ? Q-1-TS1d ? RhOH(3A) 1 CH3, with an

Scheme 1. The reaction pathway in the C��H bond activation of CH4 by RhO.

Scheme 2. The reaction pathway for the formation of Rh 1 CH3OH from CH3RhOH and HRhOCH3.



energy barrier of 133.4 kJ mol21. However, the reaction of

RhO(4S) 1 CH4 ? RhOH(3A) 1 CH3 is calculated to be endo-

thermic by 95.5 kJ mol21. Such large quantity of endothermicity

makes this reaction thermodynamically unfavorable. This phe-

nomena is completely different from those in the MO 1 CH4

(M 5 Ca,13 Sr,14 Mg,20 Ni,41 Pd,22 Pt,23 and Be24) systems,

where the main products are the MOH and methyl.

In view of the MERPs for the formation of both

D-CH3RhOH and D-HRhOCH3, the corresponding two reactions

are largely exothermic by 119.5 and 59.7 kJ mol21, respectively.

Then, both D-CH3RhOH and D-HRhOCH3 are thermodynami-

cally favorable. Nevertheless, D-CH3RhOH lies 59.8 kJ mol21

below D-HRhOCH3, and the corresponding EHHP at D-1-TS2a

for the formation of D-CH3RhOH is 74.9 kJ mol21 lower than

that at D-1-TS2b for the formation of D-HRhOCH3. In that

case, D-CH3RhOH is thermodynamically and kinetically more

preferable than D-HRhOCH3. In other words, it is predicted that

D-CH3RhOH should be more facilely detected than

D-HRhOCH3 in RhO 1 CH4 system. This result is parallel to

those in the MO 1 CH4 (M 5 Mn and Fe) systems,38,40 where

the intermediate CH3MOH has been observed experimentally in

the gas phase.

Formation of Rh 1 CH3OH

The reaction pathway is depicted in Scheme 2. The optimized

geometric structures of various species are collected in Figure 3.

The schematic energy diagrams on the doublet and quartet states

are shown in Figure 4.

Rh 1 CH3OH Products

As depicted in Scheme 2, there are three reaction pathways to

generate Rh 1 CH3OH: two from CH3RhOH and the other from

HRhOCH3. Firstly, from CH3RhOH, a reductive elimination

may take place, where a methyl shifts to the oxygen on the

��OH fragment, leading to a molecular complex b-RhCH3OH

via the three-member TS, 2-TS1c, i.e., CH3RhOH ? 2-TS1c ?b-RhCH3OH. In the course of the doublet and quartet PESs, as

shown in Figure 4, the doublet PES sits below the quartet one,

aside from the exit channel (b-RhCH3OH). One can expect that

the doublet-quartet intersection may take place once near

b-RhCH3OH. After the energy barrier at 2-TS1c is cleared on

the doublet PES, the intersystem crossing can lead to the

Q-b-RhCH3OH. Finally, the molecular complex, Q-b-RhCH3OH,

can break up into the ultimate products, Rh(4F) 1 CH3OH, and

then conserving the quartet state. Thereupon, if the spin inver-

sion occurs once, the MERP for this reaction pathway should be

D-CH3RhOH ? D-2-TS1c ? Q-b-RhCH3OH ? Rh(4F) 1CH3OH, with an energy barrier of 239.8 kJ mol21 and the

EHHP of 120.3 kJ mol21 at D-2-TS1c.

Then, from HRhOCH3, a reductive elimination may also

occur, where the hydrogen atom on Rh atom moves to the oxy-

gen atom, forming a molecular complex b-RhCH3OH via a

three-member TS, 2-TS1e, i.e., HRhOCH3 ? 2-TS1e ?b-RhCH3OH. Regarding both the doublet and quartet PESs, as

shown in Figure 4, the doublet PES stands below the quartet

one, except for the exit channel (b-RhCH3OH). It is indicated

that the doublet-quartet intersection may occur once near

b-RhCH3OH. After the energy barrier at 2-TS1e is conquered on

the doublet PES, the spin inversion can lead to the formation of

Q-b-RhCH3OH. In that case, the MERP for this reaction path-

way should be D-HRhOCH3 ? D-2-TS1e ? Q-b-RhCH3OH ?Rh(4F) 1 CH3OH, with an energy barrier of 110.9 kJ mol21

and the EHHP of 51.2 kJ mol21 at D-2-TS1e.

Finally, from CH3RhOH, one hydrogen atom of CH3 group

can transfer to the Rh atom via a three-member TS, 2-TS1b, to

form the CH2Rh(H)OH isomer. The CH2Rh(H)OH molecule is a

methylidene hydrido hydroxide complex. From CH2Rh(H)OH,

hydroxyl can migrate to the C atom via a three-member TS,

2-TS2a, to produce the HOCH2RhH isomer. From HOCH2RhH,

the hydrogen atom on Rh atom can shift to the C atom via the

three-member TS, 2-TS3b, to generate a molecular complex

a-RhCH3OH. Lastly, the molecular complex, a-RhCH3OH, can

decompose into the eventual products, Rh 1 CH3OH. In view

of both the doublet and quartet PESs, as shown in Figure 4, the

doublet PES lies below the quartet one, aside from a-RhCH3OH

and Rh 1 CH3OH. One can see that the doublet-quartet inter-

section may take place once. Thus, the MERP for this reaction

pathway should be D-CH3RhOH ? D-2-TS1b ?D-CH2Rh(H)OH ? D-2-TS2a ? D-HOCH2RhH ? D-2-TS3b

? Q-a-RhCH3OH ? Rh(4F) 1 CH3OH, with the LER of 113.6

kJ mol21 and the EHHP of 22.9 kJ mol21 at D-2-TS2a, if the

spin inversion occurs once. Furthermore, comparing these

three reaction pathways, one can expect that the reaction path-

way via D-2-TS1b is the gross MERP for the formation of

Rh(4F) 1 CH3OH, owing to its comparatively small LER and

low EHHP.

To put it simply, for the formation of Rh(4F) 1 CH3OH, the

MERP is as follows: RhO(4S) 1 CH4 ? Q-CH4RhO ?D-1-TS1b ? D-CH3Rh(O)H ? D-1-TS2a ? D-CH3RhOH ?D-2-TS1b ? D-CH2Rh(H)OH ? D-2-TS2a ? D-HOCH2RhH

? D-2-TS3b ? Q-a-RhCH3OH ? Rh(4F) 1 CH3OH, where

the reaction step of D-CH2Rh(H)OH ? D-2-TS2a ?D-HOCH2RhH involving hydroxyl migration to the C atom is

the step of LER with 113.6 kJ mol21, and the EHHP is 43.5 kJ

mol21 at D-1-TS2a, regarded as the hydride ligand on rhodium

in CH3Rh(O)H displacement to the oxygen forming a hydroxyl

ligand in CH3RhOH, CH3Rh(O)H ? 1-TS2a ? CH3RhOH. As

a result, the whole reaction of RhO(4S) 1 CH4 ? Rh(4F) 1CH3OH is calculated to be endothermic only by 8.8 kJ mol21.

The doublet intermediate CH3RhOH locates in deep well. One

can see that this intermediate D-CH3RhOH is energetically

preferred in the reaction of RhO 1 CH4.

Then again, in the course of the entire reaction pathways

in Scheme 2 and Figure 4, there are three possible byproduct

reaction channels (forming CH2ORh 1 H2, RhCH2 1 H2O,

and RhOH 1 CH3) in the formation of Rh(4F) 1 CH3OH.

CH2ORh 1 H2 Byproducts

As shown in Scheme 2, there are three reaction pathways for

the generation of CH2ORh 1 H2: two from both HRhOCH3 and

HOCH2RhH including one TS and one intermediate, and



the other from CH3Rh(O)H involving two TSs and two

intermediates.

To begin with, from HRhOCH3, one hydrogen on the methyl

group shifts to the hydrogen on the ��RhH group via a four-

member TS, 2-TS1g, forming a hydrogen molecule, i.e.,

HRhOCH3 ? 2-TS1g ? H2RhOCH2. The molecular complex,

H2RhOCH2, can break up into the side products, CH2ORh 1H2. As depicted in Figure 4, the doublet PES lies below the

quartet PES. That is, the MERP for this reaction pathway should

advance on the doublet PES. Hence, the thorough MERP for

this reaction pathway should be as follows: RhO(4S) 1 CH4 ?Q-CH4RhO ? D-1-TS1b ? D-CH3Rh(O)H ? D-1-TS2b ?D-HRhOCH3 ? D-2-TS1g ? D-H2RhOCH2 ? D-CH2ORh 1H2, where the reaction step of D-CH3Rh(O)H ? D-1-TS2b ?D-HRhOCH3 is the step of LER of 162.2 kJ mol21 and the

EHHP is 118.4 kJ mol21 at D-1-TS2b.

Figure 3. The optimized geometric structures of the reactants, intermediates, TSs, and products in the for-

mation of Rh1 CH3OH from CH3RhOH and HRhOCH3 calculated at the B3LYP/6-3111G(2d, 2p), SDD

level. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.]



Next, from CH3Rh(O)H, one hydrogen on the methyl group

displaces to the hydrogen on the ��RhH group via a four-mem-

ber TS, 2-TS1f, forming a hydrogen molecule, i.e., CH3Rh(O)H

? 2-TS1f ? (H2)ORhCH2. Then, the molecular complex,

(H2)ORhCH2, can dissociate into ORhCH2 1 H2. After that,

from ORhCH2, the oxygen on rhodium can shift to the carbon

via a three-member TS, 2-TS2b, forming CH2ORh. As shown in

Figure 4, the doublet PES lies below the quartet PES. One can

see that the MERP for this reaction pathway should proceed

along the doublet PES. As a result, the integrative MERP for

this reaction pathway is the following: RhO(4S) 1 CH4 ?Q-CH4RhO ? D-1-TS1b ? D-CH3Rh(O)H ? D-2-TS1f ? D-

(H2)ORhCH2 ? D-ORhCH2 1 H2 ? D-2-TS2b ? D-CH2ORh

1 H2, where the reaction step of D-CH3Rh(O)H ? D-2-TS1f

? D-(H2)ORhCH2 is the step of LER of 130.4 kJ mol21 and

the EHHP is 86.6 kJ mol21 at D-2-TS1f.

Finally, from HOCH2RhH, the hydrogen on the hydroxyl

transfers to the hydrogen on the ��RhH group, forming a hydro-

gen molecule via a four-member TS, 2-TS3a, i.e., HOCH2RhH

? 2-TS3a ? H2RhOCH2. As shown in Figure 4, the doublet

PES stands below the triplet one. It is indicated that the MERP

for this reaction pathway should keep on the doublet PES. Con-

sequently, the complete MERP for this reaction pathway is as

follows: RhO(4S) 1 CH4 ? Q-CH4RhO ? D-1-TS1b ?

D-CH3Rh(O)H ? D-1-TS2a ? D-CH3RhOH ? D-2-TS1b ?D-CH2Rh(H)OH ? D-2-TS2a ? D-HOCH2RhH ? D-2-TS3a

? D-H2RhOCH2 ? D-CH2ORh 1 H2, where the reaction step

of D-HOCH2RhH ? D-2-TS3a ? D-H2RhOCH2 including the

hydrogen on the hydroxyl transformation to the hydrogen on

the ��RhH group, is the step of LER with 129.4 kJ mol21, and

the EHHP is 43.5 kJ mol21 at D-1-TS2a, regarded as the

hydride ligand on rhodium in CH3Rh(O)H displacement to the

oxygen forming a hydroxyl ligand in CH3RhOH, CH3Rh(O)H

? 1-TS2a ? CH3RhOH. Moreover, comparing these three reac-

tion pathways, one can conclude that the reaction pathway from

HOCH2RhH is the gross MERP for the formation of D-CH2ORh

1 H2, thanks to its comparatively small LER and low EHHP.

Consequently, the whole reaction of RhO(4S) 1 CH4 ? D-

RhOCH2 1 H2 is calculated to be exothermic by 10.9 kJ mol21.

RhCH2 1 H2O Byproducts

As depicted in Scheme 2, there is unique reaction pathway to

engender the byproducts, RhCH2 1 H2O. Following the genera-

tion of CH3RhOH, one hydrogen atom on the methyl group

moves to the oxygen atom on the ��OH fragment via a TS, 2-

TS1a, forming a water molecule, i.e., CH3RhOH ? 2-TS1a ?H2ORhCH2. The product complex, H2ORhCH2, can be considered

Figure 4. The schematic energy diagrams along the formation of Rh 1 CH3OH from CH3RhOH and

HRhOCH3 in the doublet and quartet states computed at the CCSD(T)/6-3111G(2d, 2p),

SDD//B3LYP/6-3111G(2d, 2p), SDD level. Relative energies (kJ mol21) for the corresponding species

relative to RhO(4S) 1 CH4 are shown. [Color figure can be viewed in the online issue, which is

available at www.interscience.wiley.com.]



as a metal-carbene complex binding to a water molecule. Then, it

can release the water molecule, leaving on RhCH2, and thereby

completing the reaction sequence. As shown in Figure 4, the dou-

blet PES stands below the quartet PES, it is indicated that the

MERP should energetically proceed along the doublet PES.

In short, the gross MERP for the formation of RhCH2 1H2O is as follows: RhO(4S) 1 CH4 ? Q-CH4RhO ?D-1-TS1b ? D-CH3Rh(O)H ? D-1-TS2a ? D-CH3RhOH ?D-2-TS1a ? D-H2ORhCH2 ? D-RhCH2 1 H2O, where the

reaction step of D-CH3RhOH ? D-2-TS1a ? D-H2ORhCH2 is

the step of LER with 198.8 kJ mol21, and the EHHP locates

79.3 kJ mol21 at D-2-TS1a. As a result, the reaction of RhO(4S)1 CH4 ? D-RhCH2 1 H2O is calculated to be exothermic by

53.0 kJ mol21.

RhOH 1 CH3 Byproducts

As depicted in Schemes 1 and 2, there are three reaction path-

ways to engender the byproducts, RhOH 1 CH3. Firstly, from

CH3RhOH, the simple bond Rh��C cleavage leaves RhOH 1CH3 as end products. Q-CH3RhOH lies 25.7 kJ mol21 below

D-CH3RhOH. If the reaction starts from the ground

D-CH3RhOH, the LER of RhOH(3A) 1 CH3 shall be 215.0 kJ

mol21. Secondly, from b-RhCH3OH, the C��O bond cleavage

leads to RhOH 1 CH3 via the TS, 2-TS2d, i.e., b-RhCH3OH ?2-TS2c ? RhOH 1 CH3. As shown in Figure 4, the quartet

PES sits below the doublet PES. Then, the MERP for this reac-

tion pathway should maintain on the quartet PES, with LER of

146.7 kJ mol21 and EHHP of 132.8 kJ mol21 at Q-2-TS2c.

Thirdly, as mentioned previously, from CH4ORh, one hydrogen

atom of CH4 moiety can be straightly captured by the oxygen

atom of RhO moiety resulting in the radical products (RhOH 1CH3). The MERP for this reaction pathway should kinetically

proceed along the quartet PES, i.e., RhO(4S) 1 CH4 ? Q-

CH4ORh ? Q-1-TS1d ? RhOH(3A) 1 CH3, with an energy

barrier of 172.9 kJ mol21.

To sum up, for the formation of RhOH(3A) 1 CH3, the gross

MERP is as follows: RhO(4S) 1 CH4 ? Q-a-CH4RhO ?D-1-TS1b ? D-CH3Rh(O)H ? D-1-TS2b ? D-HRhOCH3 ?D-2-TS1e ? Q-b-RhCH3OH ? Q-2-TS2c ? RhOH(3A) 1CH3, with EHHP of 132.8 kJ mol21 at Q-2-TS2c. Furthermore,

the reaction of RhO(4S) 1 CH4 ? RhOH(3A) 1 CH3 is calcu-

lated to be strongly endothermic by 95.5 kJ mol21. Such large

quantity of endothermicity and very high EHHP make the for-

mation of RhOH(3A) 1 CH3 both thermodynamically and

kinetically unfavorable. That is to say, the side products,

RhOH(3A) 1 CH3, can be ruled out in the reaction between

CH4 and RhO. This result is thoroughly different from those in

the analogous MO 1 CH4 (M 5 Ca,13 Sr,14 Mg,20 Ni,41 Pd,22

Pt,23 and Be24) systems, where main products are predicted to

be MOH and methyl.

Now, let us contrast the formation of Rh 1 CH3OH,

CH2ORh 1 H2, and RhCH2 1 H2O on each MERP, as depicted

in Scheme 2 and Figure 4, because they are competitive with

each other. First of all, as discussed earlier, the reaction of

RhO(4S) 1 CH4 ? Rh(4F) 1 CH3OH, or D-CH2ORh 1 H2, or

D-RhCH2 1 H2O, is calculated to be exothermic by only 28.8,

or 10.9, or 53.0 kJ mol21, respectively. It is indicated that these

products are almost thermodynamically favorable. On the other

hand, as mentioned previously, the LERs are 113.6, 129.4, and

198.8 kJ mol21, and the EHHPs are 43.5, 43.5, and 79.3 kJ

mol21, for the formation of Rh 1 CH3OH, CH2ORh 1 H2, and

CH2ORh 1 H2 on each MERP, respectively. In that case, with a

view of kinetics, the magnitude order of product formation is

predicted to be Rh(4F) 1 CH3OH [ D-CH2ORh 1 H2 [D-RhCH2 1 H2O. In other words, Rh(4F) 1 CH3OH are the

main products, whereas D-CH2ORh 1 H2 are the secondary

byproducts, and D-RhCH2 1 H2O are the minor byproducts.

As discussed earlier, the intermediate D-CH3RhOH sits deep

well on the PES in the reaction between RhO and CH4. Further-

more, for the D-RhCH2 1 H2O, D-CH2ORh 1 H2, and Rh(4F)

1 CH3OH formation, all MERPs proceed via the key intermedi-

ate D-CH3RhOH. Then, it is necessary to estimate quantitatively

the reactivity for the D-CH3RhOH formation and selectivities

for the three kinds of products [D-RhCH2 1 H2O, H2 1D-CH2ORh, and Rh(4F) 1 CH3OH] in the reaction between

RhO and CH4. The rate constants have been evaluated, based

upon conventional transition state theory (TST),69 including tun-

neling correction according to Winger’s formulation.70

For the D-CH3RhOH formation, assuming efficient doublet-

quartet intersystem crossing, the MERP should be RhO(4S) 1CH4 ? Q-CH4RhO ? D-1-TS1b ? D-CH3Rh(O)H ? D-1-

TS2a ? D-CH3RhOH with the EHHP at D-1-TS2a. Based on

the rate-determining step for the D-CH3RhOH formation,

RhO(4S) 1 CH4 were taken as reactants, while D-1-TS2a served

as transition state. The rate constants of the D-CH3RhOH forma-

tion (k1) calculated over the 300–1100 K temperature range can

be fitted by the following expression (in dm3 mol21 s21):

k1 ¼ 7:03 3 106 expð�69:484=RTÞ

The rate constant k1 is calculated to be only 6.605 3 1025

dm3 mol21 s21 at 300 K and increases to 3.532 3 103 dm3

mol21 s21 at 1100 K.

From the intermediate D-CH3RhOH, there are two main

reaction pathways: one is D-CH3RhOH ? D-2-TS1b ?D-CH2Rh(H)OH ? D-2-TS2a ? D-HOCH2RhH with the

EHHP at D-2-TS2a, and another is D-CH3RhOH ? D-2-TS1a

? D-H2ORhCH2 ? D-RhCH2 1 H2O with the EHHP at D-2-

TS1a. That is to say, from the key intermediate D-CH3RhOH,

the D-RhCH2 1 H2O and D-HOCH2RhH formation are compet-

itive each other. Moreover, the former reaction pathway is the

part of MERPs for the Rh(4F) 1 CH3OH and D-CH2ORh 1 H2

formation, and the later reaction pathway is the part of MERP

for the D-RhCH2 1 H2O formation. Thereby, the rate constants

for D-RhCH2 1 H2O (k2) and D-HOCH2RhH (k3) formation

were taken into account, where D-CH3RhOH was taken as reac-

tant, while D-2-TS1a and D-2-TS2a served as transition states.

For the D-RhCH2 1 H2O and D-HOCH2RhH formation, the rate

constants calculated over 300–1100 K temperature range can be

fitted by the following expressions (in s21):

k2 ¼ 5:32 3 1012 expð�203:706=RTÞ

k3 ¼ 5:41 3 1012 expð�146:838=RTÞ



The branching ratio for the D-HOCH2RhH formation is

calculated to be almost 100% at 300 K and decreases only to

99.8% at 1100 K. In other words, from the key intermediate

D-CH3RhOH, the D-HOCH2RhH channel is predominated,

whereas the D-RhCH2 1 H2O channel should be ruled out.

From the intermediate D-HOCH2RhH, there are also two

reaction pathways: one is D-HOCH2RhH ? D-2-TS3b ? D-a-

RhCH3OH ? Rh(4F) 1 CH3OH with the EHHP at D-2-TS3b,

and another is D-HOCH2RhH ? D-2-TS3a ? D-H2RhOCH2 ?D-CH2ORh 1 H2 with the EHHP at D-2-TS3a. Furthermore, the

former reaction pathway is the part of the MERP for the Rh(4F)

1 CH3OH formation, and the later reaction pathways is the part

of the MERP for D-CH2ORh 1 H2 formation. In that case, from

the intermediate D-HOCH2RhH, the Rh(4F) 1 CH3OH and D-

CH2ORh 1 H2 formation are competitive each other. Therefore,

the rate constants for D-CH2ORh 1 H2 (k4) and Rh(4F) 1CH3OH (k5) formation were considered, where D-HOCH2RhH

was taken as reactant, while D-2-TS3a and D-2-TS3b served as

transition states. For the D-CH2ORh 1 H2 (k4) and Rh(4F) 1CH3OH (k5) formation, the rate constants calculated over 300–

1100 K temperature range can be fitted by the following expres-

sions (in s21):

k4 ¼ 6:30 3 1012 expð�132:553=RTÞ

k5 ¼ 1:33 3 1013 expð�106:014=RTÞ

As one can see, the rate of the Rh(4F) 1 CH3OH (k5) forma-

tion is 1–4 orders of magnitude higher than the rate of the D-

CH2ORh 1 H2 (k4) formation. The branching ratio for the

Rh(4F) 1 CH3OH channel is almost 100% at 300 K and

decreases to 97.5% at 1100 K, whereas the branching ratio for

the D-CH2ORh 1 H2 channel is almost 0.0% at 300 K and

increase to 2.5% at 1100 K. That is to say, the Rh(4F) 1CH3OH channel is dominated over 300–1100 K temperature

range. However, with an increase in temperature, the branching

ratio for the D-CH2ORh 1 H2 channel rises. Then, the

D-CH2ORh 1 H2 channel should not be neglected. Therewithal,

we will infra discuss the further decomposition reaction of

CH2ORh.

Formation of CO 1 H2 from CH2ORh

The reaction pathway is depicted in Scheme 3. The optimized

geometric structures of various species are collected in Figure 5.

The schematic energy diagrams on both the doublet and quartet

states are shown in Figure 6. As depicted in Figure 6, there are

two reaction pathways for the generation of Rh 1 CO 1 H2

from CH2ORh. One is typical of the preferential release of CO,

and another is characteristic of the underlying release of H2.

As shown in Scheme 3 and Figure 6, for the release of CO

before H2, there are five reaction steps resulting in Rh 1 CO 1H2 from CH2ORh. In the first step, one hydrogen atom in

��CH2 group shifts to rhodium via a four member TS, 4-TS1,

forming HRhCHO. Next, from HRhCHO, the hydrogen in ��CH

group migrates to rhodium via a three-member TS, 4-TS2,

forming HRh(H)CO. HRh(H)CO can be regarded as the complex

between HRhH and CO molecules. And then, in the following

step, from HRh(H)CO, the release of CO molecule may take

place, leaving HRhH behind. In the fourth step, from HRhH, a

reductive elimination occurs leading to H2Rh, which can be con-

sidered as the complex between Rh atom and H2 molecule.

Lastly, from H2Rh, the release of H2 may take place, resting on

Rh, and then accomplishing the reaction sequence. As shown in

Figure 6, for this reaction pathway, all species but the exit chan-

nel (Rh 1 CO 1 H2) on the doublet PES locates below those

on the quartet one. One can expect that the doublet-quartet inter-

system crossing may take place once near the exit channel (Rh

1 CO 1 H2). That is to say, aside from Rh 1 CO 1 H2, the

MERP for this reaction pathway should proceed along the dou-

blet PES, aside from Rh 1 CO 1 H2, with the LER of 98.7 kJ

mol21 and EHHP of 63.5 kJ mol21 at Rh(4F) 1 CO 1 H2.

Alternatively, for the release of H2 before CO, the former

two steps [CH2ORh ? 4-TS1 ? HRhCHO ? 4-TS2 ?

Scheme 3. The reaction pathway for the formation of CO and H2 from CH2ORh. [Color figure can be

viewed in the online issue, which is available at www.interscience.wiley.com.]



HRh(H)CO] out of this reaction pathway are identical to those

among the preceding one. In the third step, from HRh(H)CO,

the two hydrogen atoms recombine via a TS, 4-TS3b, to form a

hydrogen molecule, which interacts with RhCO to generate the

molecular complex H2RhCO. In the fourth step, from H2RhCO,

the hydrogen molecule may be released, leaving RhCO behind.

Lastly, from RhCO, the release of CO finishes the reaction path-

way. As shown in Figure 6, the doublet PES locates below the

quartet one, with an exception of the exit channel (Rh 1 CO 1H2). Thereby, a significant doublet-quartet spin inversion may

Figure 5. The optimized geometric structures of the reactants, intermediates, TSs, and products in the

formation of CO and H2 from CH2ORh calculated at the B3LYP/6-3111G(2d,2p) level. [Color figure

can be viewed in the online issue, which is available at www.interscience.wiley.com.]

Figure 6. The schematic energy diagrams along the formation of CO and H2 from CH2ORh in the dou-

blet and quartet states computed at the CCSD(T)/6-3111G(2d, 2p), SDD//B3LYP/6-3111G(2d, 2p),

SDD level. Relative energies (kJ mol21) for the corresponding species relative to RhO(4S) 1 CH4 are

shown. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.

com.]



occur near the exit channel. Ultimately, the reaction terminates

on the quartet state [Rh(4F) 1 CO 1 H2]. This reaction pathway

involves the LER of 160.5 kJ mol21 and EHHP of 63.5

kJ mol21 at [Rh(4F) 1 CO 1 H2].

Compared with these two reaction pathways to form Rh 1CO 1 H2 from CH2ORh, it is obvious that the reaction pathway

via the preceding release of CO is kinetically more preferable

than the other via the foregoing release of H2, owing to its lower

energy barrier of the corresponding step of LER (98.7 vs. 160.5

kJ mol21). This phenomenon is similar to that in the CH2ONi

? Ni 1 CO 1 H2 reaction system.41 The whole reaction of D-

CH2ORh ? Rh(4F) 1 CO 1 H2 is computed to be largely

endothermic by 74.4 kJ mol21. Such large quantity of endother-

micity makes this forward reaction thermodynamically unfavora-

ble. However, these reaction stages of both D-CH2ORh ?D-HRh(H)CO and D-CH2ORh ? D-H2RhCO are strongly exo-

thermic by 184.6 and 141.5 kJ mol21, with the LER of only

21.6 kJ mol21 and EHHP of 10.7 kJ mol21 at D-3-TS1. Further-

more, both D-HRh(H)CO and D-H2RhCO locate in deep well,

as shown in Figure 6. On can see that both D-HRh(H)CO and

D-H2RhCO are thermodynamically and kinetically preferable in

the decomposition process of CH2ORh.

Then again, CH2ORh can be regarded as the complex

between Rh and HCHO, where the O and C in HCHO synchro-

nously coordinate to Rh. As a result, from CH2ORh, HCHO

molecule can be released, resting on Rh atom. As shown in Fig-

ure 6, the doublet state CH2ORh stands below the quartet state

CH2ORh, but the relative order is reverse for the products (Rh

1 HCHO). Then, an important doublet-quartet spin inversion

may take place near the exit channel. If the spin inversion takes

place at the exit channel, the decomposition of D-CH2ORh into

Rh(4F) 1 HCHO would be 97.2 kJ mol21 endothermic. Finally,

the reaction halts on the quartet state [Rh(4F) 1 HCHO]. In

addition, once Rh 1 HCHO are formed, they are prone to

decompose into Rh 1 CO 1 H2, because the reaction of Rh(4F)

1 HCHO ? Rh(4F) 1 CO 1 H2 is calculated to be exothermic

by 22.8 kJ mol21, with the LER of only 98.7 kJ mol21.

As shown in Scheme 3 and Figure 6, from CH2ORh, the

formation of Rh(4F) 1 HCHO and Rh(4F) 1 CO 1 H2 are

competitive with each other. Their generation possibilities are

thermodynamically almost equal, in virtue of their close

endothermicities (97.2 vs. 74.4 kJ mol21), while their formation

feasibilities are kinetically almost equivalent, on account of their

similar LERs (97.2 vs. 98.7 kJ mol21).

Related Reactions

While the catalytic processes consist of a complicated sequence

of interrelated reactions, the investigation of the reactions start-

ing from different products of the above discussed reactions,

such as Rh 1 CO 1 H2, CH2ORh 1 H2, Rh 1 CH3OH, and

RhCH2 1 H2O, can potentially provide quantitative information

regarding the thermodynamics and mechanisms for the catalytic

methane-to-methanol conversion processes. Here, we will inves-

tigate the aforementioned four reaction mechanisms, and predict

the most possible intermediates which can be experimentally

observed.

Rh 1 CO 1 H2

As shown in Scheme 3 and Figure 6, from Rh 1 CO 1 H2,

there is just the unique product (Rh 1 HCHO) channel. The

MERP for the formation of Rh 1 HCHO should be Rh(4F) 1CO 1 H2 ? D-RhCO 1 H2 ? D-H2RhCO ? D-3-TS3b ?D-HRh(H)CO ? D-3-TS2 ? D-HRhCHO ? D-3-TS1 ?D-CH2ORh ? Rh(4F) 1 HCHO, with the LER of 97.2 kJ

mol21. In the meantime, both D-H2RhCO and D-HRh(H)CO

stand in deep well (2184.6 and 2141.5 kJ mol21), as shown in

Figure 6. It is indicated that the two intermediates [D-H2RhCO

and D-HRh(H)CO] are energetically dominated in the reaction

of Rh 1 CO 1 H2.

CH2ORh 1 H2

From CH2ORh 1 H2, as depicted in Schemes 1 and 2, and Fig-

ures 2 and 4, there are two main product channels: one is Rh 1CH3OH, and another is RhO 1 CH4. For the formation of Rh 1CH3OH, the MERP should be D-CH2ORh 1 H2 ? D-

H2RhOCH2 ? D-2-TS1g ? D-HRhOCH3 ? D-2-TS1e ? Q-b-

RhCH3OH ? Rh(4F) 1 CH3OH, with an endothermicity of

19.7 kJ mol21, the LER of 110.9 kJ mol21, and the EHHP of

51.2 kJ mol21 at D-2-TS1e. Alternatively, for the formation of

RhO 1 CH4, the MERP should be D-CH2ORh 1 H2 ? D-

H2RhOCH2 ? D-2-TS3a ? D-HOCH2RhH ? D-2-TS2a ? D-

CH2Rh(H)OH ? D-2-TS1b ? D-CH3RhOH ? D-1-TS2a ?D-CH3Rh(O)H ? D-1-TS1b ? Q-CH4RhO ? RhO(4S) 1CH4, with an exothermicity of only 10.9 kJ mol21, the LER of

163.0 kJ mol21, and the EHHP of 43.5 kJ mol21 at D-1-TS2a.

Thereby, Rh(4F) 1 CH3OH is kinetically more preferable than

RhO(4S) 1 CH4, owing to its smaller LER [110.9 for Rh(4F) 1CH3OH vs. 163.0 kJ mol21 for RhO(4S) 1 CH4], whereas both

Rh(4F) 1 CH3OH and RhO(4S) 1 CH4 are thermodynamically

almost equal, because of their similar quantity of endothermicity

(19.7 vs. 10.9 kJ mol21). In view of the PESs in Figures 2 and

4, D-H2RhOCH2 sits in deep well (2109.8 kJ mol21). One can

expect that this intermediate is energetically favored in the

reaction between CH2ORh and H2.

Rh 1 CH3OH

There are two main reaction pathways to form RhO 1 CH4 and

one primary reaction pathway to form D-CH2ORh 1 H2 in the

reaction of Rh 1 CH3OH, as shown in Schemes 1 and 2, and

Figures 2 and 4.

The first reaction pathway for the formation of RhO 1 CH4

should be Rh(4F) 1 CH3OH ? Q-b-RhCH3OH ? D-2-TS1e ?D-HRhOCH3 ? D-1-TS2b ? D-CH3Rh(O)H ? D-1-TS1b ?Q-CH4RhO ? RhO(4S) 1 CH4, with the LER of 178.1 kJ

mol21 and EHHP of 118.4 kJ mol21 at D-1-TS2b. The second

reaction pathway for the formation of RhO 1 CH4 should be

Rh(4F) 1 CH3OH ? Q-b-RhCH3OH ? D-2-TS1c ?D-CH3RhOH ? D-1-TS2a ? D-CH3Rh(O)H ? D-1-TS1b ?Q-CH4RhO ? RhO(4S) 1 CH4, with the LER of 163.0 kJ

mol21 and EHHP of 120.3 kJ mol21 at D-2-TS1c. It is obvious

that these two reaction steps (Q-b-RhCH3OH ? D-2-TS1e ?D-HRhOCH3 among the first reaction pathway and Q-b-



RhCH3OH ? D-2-TS1c ? D-CH3RhOH among the second

reaction pathway) are competitive with each other, where D-2-

TS1e lies 69.1 kJ mol21 below D-2-TS1c, and the formation of

D-HRhOCH3 and D-CH3RhOH are exothermic by 68.5 and

128.3 kJ mol21, respectively. One can conclude that D-

HRhOCH3 is kinetically more predominated than D-CH3RhOH,

while both D-HRhOCH3 and D-CH3RhOH are thermodynami-

cally favorable. This phenomena is semblable to those in the M

1 CH3OH (M 5 Sc,37,40 Ti,40 Mn,38,40 and Fe38,40) systems,

where HMOCH3 are detected experimentally in the gas phase.

Therefore, the first reaction pathway should be kinetically more

favorable than the second one, although these two reaction path-

ways include the close values of LER and EHHP.

The MERP for the formation of CH2ORh 1 H2 should be

Rh(4F) 1 CH3OH ? Q-b-RhCH3OH ? D-2-TS1e ? D-

HRhOCH3 ? D-2-TS1g ? D-H2RhOCH2 ? D-CH2ORh 1 H2,

with the LER of 65.1 kJ mol21 and EHHP of 51.2 kJ mol21 at

D-2-TS1e. Comparing these MERPs for the formation of

CH2ORh 1 H2 and RhO(4S) 1 CH4, it is obvious that the steps

of Q-b-RhCH3OH ? D-2-TS1e ? D-HRhOCH3 among the

CH2ORh 1 H2 formation and D-HRhOCH3 ? D-1-TS2b ? D-

CH3Rh(O)H among the RhO(4S) 1 CH4 formation are competi-

tive with each other. Because D-2-TS1e lies 67.2 kJ mol21

below D-1-TS2b and the intermediate D-H2RhOCH2 stands 89.7

kJ mol21 below the intermediate D-CH3Rh(O)H, the intermedi-

ate D-H2RhOCH2 is both thermodynamically and kinetically

more favorable than the intermediate D-CH3Rh(O)H, and then

the main products should be D-CH2ORh 1 H2 other than

RhO(4S) 1 CH4.

RhCH2 1 H2O

As shown in Schemes 1 and 2, and Figures 2 and 4, there are

two dominant product channels (Rh 1 CH3OH and RhO 1CH4) in the reaction of RhCH2 1 H2O. For the formation of Rh

1 CH3OH, the MERP should be D-RhCH2 1 H2O ? D-

H2ORhCH2 ? D-2-TS1a ? D-CH3RhOH ? D-2-TS1b ? D-

CH2Rh(H)OH ? D-2-TS2a ? D-HOCH2RhH ? D-2-TS3b ?Q-a-RhCH3OH ? Rh(4F) 1 CH3OH, with the LER of 113.6 kJ

mol21 and EHHP of 79.3 kJ mol21 at D-2-TS1a. Then again,

for the formation of RhO 1 CH4, the MERP should be D-

RhCH2 1 H2O ? D-H2ORhCH2 ? D-2-TS1a ? D-CH3RhOH

? D-1-TS2a ? D-CH3Rh(O)H ? D-1-TS1b ? Q-CH4RhO ?RhO(4S) 1 CH4, with the LER of 163.0 kJ mol21 and EHHP of

79.3 kJ mol21 at D-2-TS1a. Furthermore, these two reaction

steps [D-CH3RhOH ? D-2-TS1b ? D-CH2Rh(H)OH among

the Rh 1 CH3OH production and D-CH3RhOH ? D-1-TS2a ?D-CH3Rh(O)H among the RhO 1 CH4 production] are competi-

tive with each other, where D-2-TS1b stands 119.5 kJ mol21

below D-1-TS2a, and D-CH2Rh(H)OH locates 46.9 kJ mol21

below D-CH3Rh(O)H. It is indicated that D-CH2Rh(H)OH is

both thermodynamically and kinetically more advantaged than

D-CH3Rh(O)H. In that case, the main product is expected to be

methanol other than methane. In addition, with regard to the

MERP for the formation of Rh 1 CH3OH, the intermediate

CH3RhOH posits in deep well on the PES. Thereupon, this inter-

mediate is energetically advantageous in the reaction of RhCH2

1 H2O.

In summary, the main products shall be Rh(4F) 1 CH3OH in

the reactions of RhO(4S) 1 CH4, CH2ORh 1 H2, Rh(4F) 1 CO

1 2H2, and RhCH2 1 H2O, whereas the main products shall be

CH2ORh 1 H2 in the reaction of Rh 1 CH3OH. The doublet in-

termediate H2RhOCH2 is predicted to be energetically favored

both in the reactions of Rh 1 CH3OH and CH2ORh 1 H2. Fur-

thermore, the doublet intermediate CH3RhOH is predicted to be

energetically predominated in the reaction of RhCH2 1 H2O.

Moreover, the doublet intermediates [H2RhCO and HRh(H)CO]

are predicted to be energetically dominated in the reaction of

Rh(4F) 1 CO 1 H2.

Conclusion

The gas-phase reaction mechanism between methane and rho-

dium monoxide for the formation of Rh 1 CH3OH, Rh 1 CO

12H2, Rh 1 HCHO 1 H2, RhCH2 1 H2O, and RhOH 1 CH3,

has been investigated in detail on the doublet and quartet state

potential energy surfaces. For some simple species involving Rh

atom [HRh, Rh(H2), HRh(H2), (H2)RhH2, (H2)RhH3, RhCO,

cyc-(RhO)2, cyc-Rh2H2, O2RhO2, ORhO, ORhOO, and

Rh(CO)2], the calculated vibration frequencies are in good

agreement with the experimental observation. The following key

points may be made from the results presented here.

In the reaction of RhO 1 CH4, the main products shall be

Rh(4F) 1 CH3OH, while the byproducts shall be D-CH2ORh 1H2 and D-RhCH2 1 H2O. Over the 300–1100 K temperature

range, the branching ratio for the Rh(4F) 1 CH3OH channel is

97.5–100%, whereas the branching ratio for the D-CH2ORh 1H2 channel is 0.0–2.5%, and the branching ratio for the D-

CH2ORh 1 H2 channel is so small to be ruled out. The mini-

mum energy reaction pathway (MERP) for the main product

methanol formation, involving two spin inversions, prefers to

both start and terminate on the ground quartet state, where the

ground doublet intermediate CH3RhOH is crucial and energeti-

cally preferred, and its formation rate constant over the 300–

1100 K temperature range is fitted by kD-CH3RhOH 5 7.03 3

106 exp(269.484/RT) dm3 mol21 s21.

On the other hand, the main products shall be Rh(4F) 1CH3OH in the reactions of RhO(4S) 1 CH4, CH2ORh 1 H2,

Rh(4F) 1 CO 12H2, and RhCH2 1 H2O, whereas the main

products shall be CH2ORh 1 H2 in the reaction of Rh 1CH3OH. Meanwhile, the doublet intermediate H2RhOCH2 is pre-

dicted to be energetically favored both in the reactions of Rh 1CH3OH and CH2ORh 1 H2. Furthermore, the doublet intermedi-

ate CH3RhOH is predicted to be energetically predominated in

the reaction of RhCH2 1 H2O. In addition, the doublet inter-

mediates [H2RhCO and HRh(H)CO] are predicted to be energet-

ically dominated in the reaction of Rh(4F) 1 CO 1 H2.

Acknowledgments

The authors are grateful to the two referees for their pertinent

comments and good suggestions concerning our original manu-

script.



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