The ability of transition metal complexes to catalyze multistep reactions, especially the multiple carbon-carbon bonds in a single process, has been the continuous subject of transition metal catalysis. Among these reactions, 1,4-metal migration has attracted considerable interest of experimental chemists. However, the detailed mechanism of this fantastic procedure hasn’t been reported yet. Here, we make deep density functional theory (DFT) calculations
reductive elimination (RE)
OA is the rate-limited step in rh-catalyzed process and and RE is the controlling step for Ir-mediated procedure. In general, there are two directions available, with
“Forward” for polymerization and “Backward” for multi-alkylation. Interestingly, the methyl substituents and metal center have a big impact on the two directions. When introducing the methyl substituents on the reactants and replace the rhodium center with iridium, the “Backward” direction was largely suppressed. And Ir-catalysts presented to be more effective than Rh-intermediates.
What’s more, the effect of benzene ring to the directions were also studied. Our findings would be useful for further developments of 1,4-metal migration, providing theoretical foundations for the experimentalists.
Transition-metal-catalyzed reactions through C-H bond activiation has been a powerful tool in organic synthesis.
1 Among these reactions, 1,4-metal migration in particular, are eye-catching flowers for experimentalists.
23456 The first 1,4-palladium migration was reported by Dyker 3a,b , who found the first C-H activation at a methoxy group by palladium catalyzation. Several years later,
Miura and coworkers demonstrated the first 1,4-rhodium migration 2a , resulting in 2 to 4 times alkylation on aromatic rings (Scheme 1). Since then, large quantities of C-H functionalized reaction involving 1,4-metal migration have been studied.
2,3c-6 Recently, Shintani and Nozaki 2h described the first polymerization reaction related to 1,4-rhodium migration sequence, giving a new class of polymers, poly(cyclopropeneo
-phenylene)s in high efficiency 6 (Scheme 2). The same behavior for
group 9 transition-metal Co have been reported before.
2,5 Almost the same time this year, Lam and partners 6 prepared highly functionalized polycycles by iridium-catalyzed arylative cyclization of alkyones through 1,4-iridium migration for the first time. The general steps for these special metalcatalyzed carbon-carbon formation involve ligand dissociation and substitution, insertion of a carbon-carbon unsatrurated bond into a carbon-metal bond, and key step 1,4-metal migration or parts of these steps. However, there are few solid evidence and theoretical investigation for this migration. The only mechanism was proposed to undergo OA (oxidative addition) to C-H or C-X bonds, the formed trivalent intermediates for Rh-series and of tetravalent intermediates for Pdinvolved reaction, then goes RE (reductive elimination) to complete 1,4-metal migration. 2a,6,7 The energy profiles of 1,4-Rh migration of scheme 1 was presented in Figure 1. The free energy values of INA and INC are equivalent which tell us that these states are thermally accessible for the next step to undergo multi-alkylation. Reactions contain insertion step before 1,4-metal often need a
substrate like strained alkene 2a,h,7a or alkyne 2b,7a
. For strained cyclopropenes, only a few numbers of

polymerization reactions are available by controlled means.
8910 Our interests for mechanism study 11 promoted us to proceed detailed theoretical investigation of 1,4-rhodium migration based on
3,3-diarylcylopropenes polymerization and multi-alkylation on aromatic rings in scheme 2. The influence of metal center, substituents and phenyl on cyclopropenes are studied later, providing hints for further developments of new catalytic reactions.
Scheme 1. Rhodium( Ⅲ )-Catalyzed Multi-alkylation on An Aromatic Ring Involving 1,4rhodium migration.
Figure 1. Free energy profiles for the 1,4-Rh(
Ⅲ
) migration (oxidative addition and reductive elimination steps ).
The values are given in kcal/mol.
Scheme 2. Rhodium( Ⅲ )-Catalyzed Polymerization of 3,3-Diphenylcyclopropene via 1,4-
Rhodium Forward Migration.

All optimizations of structures with frequency calculations were carried out with the Gaussian 03 package at 298K. Density functional theory (DFT) were chose to study the mechanism of 1,4-metal migration, general seen in investigation of transition-metal catalyzed C-H activation. The standard basis set 6-31G(d) was used for C and H. Rh and Ir atoms were described by the effective core potentials (ECPs) of Hay ad Wadt with a valence double-ζ basis set (LANL2DZ). Polarizatin functions were added for Rh(ξ f
=1.350) and Ir(ξ f
=0.938). Transition states with only one imaginary frequency were examined by vibrational analysis and then submitted to instrinsic reaction coordinate (IRC) calculations to ensure that the structures are actually connecting two minima. The natural bond orbital (NBO), as implemented in Gaussian 03, was also used to get Wiberg bond indices, which are a mesure of bond strength. Structures were visualized by CYLview program.
Generally, there are two directions, “forward” and
“backward” involving in the key step 1,4-Rh migration. The polymerization process could be realized by the use of 3,3-diarylcyclopropenes as monomers in the presence of phenylrhodium catalysts (Figure 2, Forward). The desired pathway goes through alkene insertion of 3,3diarylcyclopropene into catalytic amount of arylrodium ( Ⅰ ) initiators. Subsequent intramolecular
1,4-rhodium migration to the benzene ring rooted in diarylcyclopropene (red one) gave IN3C and
IN3C.1
. This then repeats the alkene insertion—1,4-rhodium migration sequence to give poly(cyclopropyleneo -phenylene). On the contrary, a “backward” migration to the phenyl group derived from the initiator (blue one) could also take place to give arylrhodium IN1C . This “merry-
go-round type” sequence led to multi-alkylation on aromatic rings 2a,7c
. The 1,4-rhodium migration process consists of oxidative addition and reductive elimination steps and they both formed a 3- and
5-memberd rhoidium ring in the transition state. Either of the “forward” and “backward” directions had two paths to take the OA and RE steps (labelled in pink and black). In one path (pink), the tricyclic stood upright on the pentacyclic while the black path is the opposite. From figure 2, in
“Backward”, we can see that the two paths have much less difference than that in “Forward” concerning the intermediates and energy barriers (structure of IN3B.1 and IN3B.2 are illustrated in
Figure 3). So the two paths in “Backward” are reliable. However, In “Forward”, the energy barrier of TS3A.1 and TS3A is 24.7 and 16.8 kcal/mol, respectively. Moreover, the relative energy of
IN3C.1 is -24.4 kcal/mol, smaller than that of IN3C (-19.8 lcal/nol). All these compared data implied that the “pink mountain” is higher than the “black one” and has lower horizontal line which is harder to climb up in the poly-process. So the pink path in “Forward” is wiped out in the following discussion with similar system. Considering the competitive relation of the two directions, it can be seen that the energy barrier of TS1A and TS2A are 20.6 and 20.1 kcal/mol, respectively, which are higher than that of TS3A (16.8 kcal/mol). What’s more, the free energy of IN1C ( IN2C ) is -22.8 kcal/mol, which is less than IN3C of -19.8 lcal/mol. So the “Forward” direction is superior to the
“Backward” one, verified in the experiment results 2h
.

Figure 2 . Free energy profiles of the 1,4-Rh( Ⅲ ) migration for “forward” and “backward”. The values are given in kcal/mol.
Figure 3.
Structures (Å) of IN3B.1
and IN3B.2
.
During the polymerization of 3,3-diarylcyclopropenes, the desired pathway goes through a 1,4-rhodium migration in a “forward” direction to give arylrhodium IN3C
. Instead of this pathway, a “backward” migration could also take place to give
IN1C (IN2C) , resulting in multi-substitution on the aromatic and “branching” of the polymer. In contrast, when the initiators have two methyl substituents at the meta -position on the benzene ring and the monomer have a methyl-substituent at the para -position of the aryl group, the “backward” migration would be suppressed by the substituents to promote the desired 1,4-rhodium migration preferentially (see Figure 4 and Figure 5). It can be seen in figure 4 that the energy barrier of TS4A and TS5A are 27.4 and 26.5 kcal/mol, respectively, which are higher than that of TS1A and TS2A by 6.8 and 6.4 kcal/mol each. By sharp contrast, the energy barrier of TS6A is 17.1 kcal/mol, just
0.3 kcal/mol higher than TS3A (16.8 kcal/mol). What’s more, from TS1B and TS2B to IN1C
( IN2C ), the energy declined by 23.2 and 22.1 kcal/mol, respectively. However, in figure 4, it can be discovered that the same reduce of TS4B and TS5B are 25.6 and 23.6 kcal/mol, both higher than
TS1B and TS2B . Conversely, in figure 2, from TS3B to IN3C , the energy is 18.0 kcal/mol, while the same energy in figure 4 is 13.9 kcal/mol. These results indicated that the “Forward” direction in figure 4 tended to be more “flat” than that of figure 2. And just the reverse for “Backward”, the pathway was more precipitous in figure 4. As a result, “Backward” direction was heavily repressed by the methyl substituents on the phenylrhodium. The same phenomena were found when a methyl was introduced on the initiator and monomer (see figure 5).

Figure 4 . Free energy profiles of the 1,4-Rh( Ⅲ ) migration with two methyl substituents on the initiator for “forward” and “backward”. The values are given in kcal/mol.
Figure 5 . Free energy profiles of the 1,4-Rh( Ⅲ ) migration with a methyl substituent on the initiator and monomer for “forward” and “backward”. The values are given in kcal/mol.
But why the energy barrier changed so much when the methyl was bring in ？ Here we presented the structures of two transition states (OA step) in figure 2 and figure 4 of “Backwad” direction to

explain why the activation energy of TS4A ( 27.4 kcal/mol) is higher than TS1A (20.6 kcal/mol).
It can be revealed that the 3-memberd transition state Rh-ring was enlarged in TS4A because of the block of methyl near the ligand of 1,5-cyclooctadiene. The steric effect can be described by the agnostic interaction with shorter distance of H … H.
It is known that the eclipsed conformer of ethane with the shortest H···H distance of 2.36 Å is less stable than the staggered conformer with that of
2.54 Å by 12 kJ/mol primarily due to steric effects 12 . As shown in Figure 6, the shortest H···H distance between the substituent methyl and the ligand in TS4A is 2.003Å, demonstrating the strong steric hindrance. To avoid unfavorable steric repulsions, the 3-member ring was expanded also.
Table 1 showed the bond lengths and angels of the tricyclic in OA step from TS1A to TS9A . It is not difficult to find that TS4A ( TS7A ) and TS5A , ( TS8A ) have longer Rh-C distances than TS1A and TS2A , respectively. The Rh-C and C-H have the same trend with a slighter change. However, in “Forward” direction, TS6A and TS9A barely distorted compared to TS1A , in agree with the little activation energy changes (0.3 and 0.7 kal/mol, respectively).
TS1A
ΔG
#
=20.6 kcal/mol
TS4A
ΔG
#
=27.4 kcal/mol
Figure 6 Structures (Å) of TS1A and TS4A .
Table 1.
Key structural parameters from TS1A to TS9A . bond length/Å
Rh-C Rh-H C-H ∠ CRhH Rh-C Rh-H
TS1A 2.084 1.580 1.689
TS4A 2.132 1.580 1.746
TS7A 2.137 1.578 1.727
TS2A 2.068 1.571 1.705
TS5A 2.103 1.572 1.787
52.7
53.7
52.9
53.8
56.0
TS1B
TS4B
TS7B
TS2B
TS5B
2.136
2.125
2.125
2.104
2.086
1.581
1.578
1.578
1.569
1.574
C-H
1.545
1.516
1.519
1.696
1.694
TS8A
TS3A
TS6A
2.109
2.073
2.070
1.572
1.576
1.577
1.785
1.682
1.680
TS9A 2.071 1.576 1.685
55.7
52.8
52.8
52.9
TS8B 2.086 1.575 1.695
TS3B 2.103 1.589 1.556
TS6B
TS9B
2.106
2.106
1.588
1.588
1.558
1.562 angle/°
∠ CRhH
46.2
45.4
45.5
52.6
52.9
52.9
47.4
47.4
47.5
Reactions involve 1,4metal migration often go with a start material like alkyne 13 and strained or phenyl-substituted
alkenes 2a,2h,14
. But how the aromatic rings influence the dynamics of 1.4-metal migration? Here, we presented the mechanism of 1,4-rhodium migration involving ethenylcyclopropene and

ethenylrhodium to find the difference between phenyl-substituted one. Obviously, there’s only one direction because of the same results of “Backward” and “Forward”. It can be concluded from
Figure 7 that the black path is more favorable than the pink one because the energy barrier from
IN10A to TS10A is 18.2 kcal/mol while from IN11A to TS11A
, it’s 23.7 kcal/mol. Figure 8 illustrated the structures of TS2A , TS19A and TS11A . Because of the more flexible enthenyl, the
H atom of 3-membered rhodium ring tend to be closer and crowded, the repel effect would be stronger than TS2A . While put the tricyclic down straight the pentacyclic ( TS10A ), the more spacious, the less energy barrier than TS11A . The prediction is similar to the discussion for TS3A and TS3A.1 of the Forward” direction.
Figure 7 . Free energy profiles of the 1,4-Rh(
Ⅲ
) migration without benzene ring on monomers and initiators . The values are given in kcal/mol.
TS2A
ΔG
#
=20.1 kcal/mol
TS10A
ΔG
#
=18.2 kcal/mol
TS11A
ΔG
#
=23.5 kcal/mol
Figure 8 Structures (Å) of TS2A , TS10A and TS11A .
Lam and coworkers reported 1,4-iridium migration for the first
time this year 6 , and proved experimentally that the more effective catalytic activity than rhodium
complex for arylative cyclization of alkynones to get polycycles. It’s a fancy discovery and promoted us to find the difference between Rh- and Ir-catalyst based on reaction mechanism. The same system above used for rhodium was included. Figure 9 and 10 manifested the process for 1,4iridium migration and the substituents effect. Table 2 listed the barrier of OA steps and RE steps of
Rh-mediated and Ir-mediated pathway. It can be seen from figure 9 and the table that the energy barriers of OA steps was less than RE steps, meaning the rate determining step turned from OA to
RE, contrasted to rhodium-catalyzed process. Considering the “Forward” and “Backward” direction of figure 9, we can conclude from OA and RE steps in table 2 that there’s no obvious competitive

advantage for “Forward” one. However, when two methyl substituents were introduced, the energy barriers of TS15A (13.1 kcal/mol) and TS16A (17.6 kcal/mol) were highly raised compared to
TS12A (9.5 kcal/mol) and TS13A (9.5 kcal/mol), respectively. In contrary, the barriers of TS17A and TS17B changed slightly compared to entry 14 in Table 2. Meanwhile ， the energy variation in
“Forward” direction of Ir-mediated with methyl substituents were smaller than that Rh-mediated one (see Table 2, entry 6 and 17 ).
Figure 9 . Free energy profiles of the 1,4-Ir(
Ⅲ
) migration for “forward” and “backward”. The values are given in kcal/mol.
Figure 10 . Free energy profiles of the 1,4-Ih( Ⅲ ) migration with two methyl substituents on the initiator for “forward” and “backward”. The values are given in kcal/mol.

Table 2 . Compared barriers (in kcal/mol) of OA and RE steps of Rh- and Ir-centred pathway. a OA is the free energy needed from INnA to TSnA and RE is the free energy needed from INnB to TSnB , when n counts from 1-6 and
12-13 .
2
3
4
Compound
1
5
6
OA a (Rh)
20.6
20.1
16.8
27.4
26.5
17.1
RE a (Rh)
8.1
6.9
9.8
8.9
9.5
9.3
12
13
14
15
16
17
OA a (Ir)
9.5
9.5
7.5
13.1
17.6
7.3
RE a (Ir)
13.0
13.1
16.0
13.7
15.8
14.8
The mechanism of 1,4-metal migration, especially 1,4-rhodium and -iridium mediated, by the use of 3,3-diarylcyclopropenes as monomers in the presence of rhodium catalyst, has been thoroughly investigate by a DFT study. The effect of methyl substituents, aromatic ring on the reactants and the metal center were examined systematically. Mainly there are two directions (“Forward” and
“Backward”) and three paths available to get the 1,4-migration product. The three paths include one in “Forward” with 3-membered rh-ring down straight the 5-membered rh-ring, and two in
“Backward” with tricyclic up and dowm straight the pentacyclic. The novel 1,4-metal migration always undergo alkene or alkyne insertion ahead to give rhodium ( Ⅰ ) intermediate. The second step is OA and is the rate-limited step in rh-catalyzed process ( 1A~9A ). However, for Ir-mediated path ( 12A~14A ), the key point of dynamics is the third RE step. Otherwise, when methyl substituents were introduce on phenyliridium, the “Backward” direction of both rhodium- and iridium-catalyzed were restrained, especially raised the energy barriers of OA steps, by reasons of shorter H … H of methyl and the ligand. While for “Forward” direction, the influence is very small
(see 3 and 6 , 14 and 17 in Table 2). In addition, Ir-catalysts tend to more effective than Rhintermediates because of the lower energy barriers generally. And the aromatic ring on monomers and initiators can fix the benzene ring just over the head of 3-membered rh-ring in “Backward” direction, leaving enough space and resulting in the similar energy barrier to the other path. In summary, our results reveal the reaction kinetics of 1,4-metal migration with different factors and provide theoretical basis for guiding the experiments.
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