Supporting Information for
Theoretical Study on the Gas-phase Reaction Mechanism Between Rhodium Monoxide Cation and Methane
Meng-Yao Yang1, 2, Hua-Qing Yang1, 2*, Chao Gao1, 2, Song Qin1, and Chang-Wei Hu1*
a Key Laboratory of Green Chemistry and Technology, Ministry of Education, College of Chemistry, Sichuan University, Chengdu, Sichuan, 610064, P.R. China
b College of Chemical Engineering, Sichuan University, Chengdu, Sichuan, 610065, P.R. China
Struct. Chem.
*Correspondence to:
H.-Q. Yang; E-mail: ;
C.-W. Hu; E-mail: (or)
Fax: 028-85411105
Telephone: 028-85411105
i. Table 1: Zero-point energies (ZPE) (hartree), total energies (Ec) (hartree) corrected by ZPE, and relative energies (Er) (kJ mol-1) with respect to reactants [RhO+(3Σ) + CH4] of the species in the C-H bond activation of CH4 by RhO+ calculated at the B3LYP/6-311+G(2d, 2p), SDD and CCSD(T)/6-311+G(2d, 2p), SDD levels…………………………………………………………………………………………………….Page S3
ii. Table 2: Zero-point energies (ZPE) (hartree), total energies (Ec) (hartree) corrected by ZPE, and relative energies (Er) (kJ mol-1) with respect to reactants [RhO+(3Σ) + CH4] of the species in the further reaction of CH3RhOH+, HRhOCH3+, and CH3Rh(O)H+ calculated at the B3LYP/6-311+G(2d, 2p), SDD and CCSD(T)/6-311+G(2d, 2p), SDD levels…………………………...... Page S4
iii. Table 3: Zero-point energies (ZPE) (hartree), total energies (Ec) (hartree) corrected by ZPE, and relative energies (Er) (kJ mol-1) with respect to reactants [RhO+(3Σ) + CH4] of the species plus H2O in the formation of RhC+ + H2 from RhCH2+ calculated at the B3LYP/6-311+G(2d, 2p), SDD and CCSD(T)/6-311+G(2d, 2p), SDD levels……………………………………………………………………………………………….Page S6
iv. Table 4: Zero-point energies (ZPE) (hartree), total energies (Ec) (hartree) corrected by ZPE, and relative energies (Er) (kJ mol-1) with respect to reactants [RhO+(3Σ) + CH4] of the species plus H2 in the formation of CO + H2, and HCHO from CH2ORh+ calculated at the B3LYP/6-311+G(2d, 2p), SDD and CCSD(T)/6-311+G(2d, 2p), SDD levels………………………………………………..………………..Page S7
v. Table 5: Standard orientations of the species on the triplet PES in the RhO+ + CH4 reaction calculated at the B3LYP/6-311+G(2d,2p), SDD level…………………………...……….….…………………………….Page S8
vi. Table 6: Standard orientations of the species on the closed-shell singlet PES in the RhO+ + CH4 reaction calculated at the B3LYP/6-311+G(2d, 2p), SDD level. ………...………………………………………Page S13
vii. Table 7: Standard orientations of the species on the open-shell singlet PES in the RhO+ + CH4 reaction calculated at the UB3LYP/6-311+G(2d, 2p), SDD level………………………………………………..Page S18
viii. Table 8: Vibration frequencies scaled by a factor of 0.963 and IR intensities of the species on the triplet PES in the RhO+ + CH4 reaction calculated at the B3LYP/6-311+G(2d, 2p), SDD level…………………...Page S21
ix. Table 9: Vibration frequencies scaled by a factor of 0.963 and IR intensities of the species on the closed-shell singlet PES in the RhO+ + CH4 reaction calculated at the B3LYP/6-311+G(2d, 2p), SDD level………Page S23
x. Table 10: Vibration frequencies scaled by a factor of 0.963 and IR intensities of the species on the open-shell singlet PES in the RhO+ + CH4 reaction calculated at the B3LYP/6-311+G(2d, 2p), SDD level………Page S25
xi. Figure 1: The schematic energy diagrams along the reaction pathways in the C-H bond activation of CH4 by RhO+ on the singlet and triplet states computed at the CCSD(T)/6-311+G(2d, 2p), SDD level. Relative energies (kJ mol-1) for the corresponding species relative to RhO+(3Σ) + CH4 are shown……….……Page S27
xii. Figure 2: The schematic energy diagrams along the reaction of CH3RhOH+ (a), HRhOCH3+ (b), and CH3Rh(O)H+ (c) on the singlet and triplet states computed at the CCSD(T)/6-311+G(2d, 2p), SDD level. Relative energies (kJ mol-1) for the corresponding species relative to RhO+(3Σ) + CH4 are shown……Page S28
xiii. Figure 3: The schematic energy diagrams along the dehydrogenation of RhCH2+ on the singlet and triplet states computed at the CCSD(T)/6-311+G(2d, 2p), SDD level. Relative energies (kJ mol-1) for the corresponding species plus H2O relative to RhO+(3Σ) + CH4 are shown………….……………………Page S29
xiv. Figure 4. The schematic energy diagrams along the decomposition of CH2ORh+ on the singlet and triplet states computed at the CCSD(T)/6-311+G(2d, 2p), SDD level. Relative energies (kJ mol-1) for the corresponding species plus H2 relative to RhO+(3Σ) + CH4 are shown……………...………………….Page S30
xv. Figure 5 Arrhenius plots of rate constants in the gas phase reaction of CH4 and RhO+ calculated at the CCSD(T)/6-311+G(2d, 2p), SDD//B3LYP/6-311+G(2d, 2p), SDD level…………………….………...Page S31
Table 1: Zero-point energies (ZPE) (hartree), total energies (Ec) (hartree) corrected by ZPE, and relative energies (Er) (kJ mol-1) with respect to reactants [RhO+(3Σ) + CH4] of the species in the C-H bond activation of CH4 by RhO+ calculated at the B3LYP/6-311+G(2d, 2p), SDD and CCSD(T)/6-311+G(2d, 2p), SDD levels
ZPE / Ec / Er / Ec / Er
RhO+(3Σ) + CH4 / 0.04685 / -225.89148 / 0.0 / -224.98502 / 0.0
T-CH4RhO+ / 0.04755 / -225.92163 / -79.2 / -225.01357 / -75.0
T-1-TS1b / 0.04474 / -225.90322 / -30.8 / -224.99430 / -24.4
T-1-TS1c / 0.04319 / -225.88615 / 14.0 / -224.97468 / 27.2
T-CH3Rh(O)H+ / 0.04589 / -225.91268 / -55.7 / -225.00225 / -45.2
T-1-TS2a / 0.04290 / -225.88457 / 18.1 / -224.97560 / 24.7
T-1-TS2b / 0.04469 / -225.87254 / 49.7 / -224.95828 / 70.2
T-HRhOCH3+ / 0.04682 / -225.94300 / -135.3 / -225.02400 / -102.3
T-CH3RhOH+ / 0.04822 / -225.96156 / -184.0 / -225.04866 / -167.1
T-CH4ORh+ / 0.04639 / -225.89427 / -7.3 / -224.98641 / -3.6
T-1-TS1d / 0.04058 / -225.89010 / 3.6 / -224.96623 / 49.3
RhOH+(4A") + CH3 / 0.04138 / -225.87632 / 39.8 / -224.96361 / 56.2
RhO+(1Δ) + CH4 / 0.04688 / -225.84803 / 114.1 / -224.95374 / 82.1
RhO+(1Σ) + CH4, <S2=1.030> / 0.04679 / -225.87893 / 33.0 / -224.97356 / 30.2
RS-CH4RhO+ / 0.04790 / -225.88496 / 17.1 / -224.98876 / -9.8
US-CH4RhO+, <S2=1.036> / 0.04744 / -225.90957 / -47.5 / -224.99985 / -38.8
RS-1-TS1b / 0.04477 / -225.86670 / 65.0 / -224.97083 / 37.3
US-1-TS1b, <S2=0.996> / 0.04464 / -225.89133 / 0.4 / -224.98073 / 11.3
RS-1-TS1c / 0.04365 / -225.86479 / 70.1 / -224.96721 / 46.8
US-1-TS1c, <S2=0.907> / 0.04334 / -225.87729 / 37.3 / -224.96167 / 61.3
RS-CH3Rh(O)H+ / 0.04506 / -225.87576 / 41.3 / -224.97629 / 22.9
US-CH3Rh(O)H+, <S2=1.007> / 0.04574 / -225.89995 / -22.2 / -224.98978 / -12.5
RS-1-TS2a / 0.04243 / -225.84451 / 123.3 / -224.93225 / 138.5
US-1-TS2a, <S2=1.014> / 0.04275 / -225.87198 / 51.2 / -224.95846 / 69.7
RS-1-TS2b / 0.04442 / -225.83950 / 136.5 / -224.93647 / 127.5
US-1-TS2b, <S2=0.998> / 0.04447 / -225.86031 / 81.8 / -224.92078 / 168.7
RS-HRhOCH3+ / 0.04696 / -225.91652 / -65.8 / -225.01221 / -71.4
US-HRhOCH3+, <S2=0.993> / 0.04676 / -225.93655 / -118.3 / -225.01427 / -76.8
RS-CH3RhOH+ / 0.04826 / -225.94118 / -130.5 / -225.02925 / -116.1
US-CH3RhOH+, <S2=0.946> / 0.04805 / -225.95290 / -161.3 / -225.03132 / -121.6
RS-CH4ORh+ / 0.04213 / -225.86167 / 78.3 / -224.95188 / 87.0
US-CH4ORh+, <S2=1.014> / 0.04637 / -225.88175 / 25.5 / -224.97262 / 32.5
RS-1-TS1d / 0.04187 / -225.83706 / 142.9 / -224.94193 / 113.1
US-1-TS1d, <S2=1.267> / 0.04092 / -225.87784 / 35.8 / -224.93291 / 136.8
RhOH+(4A") + CH3 / 0.04138 / -225.87632 / 39.8 / -224.96361 / 56.2
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Table 2: Zero-point energies (ZPE) (hartree), total energies (Ec) (hartree) corrected by ZPE, and relative Energies (Er) (kJ mol-1) with respect to reactants [RhO+(3Σ) + CH4] of the species in the further reaction of CH3RhOH+, HRhOCH3+, and CH3Rh(O)H+ calculated at the B3LYP/6-311+G(2d, 2p), SDD and CCSD(T)/6-311+G(2d, 2p), SDD levels
Species / B3LYP/6-311+G(2d, 2p), SDD / CCSD(T)/6-311+G(2d, 2p), SDDZPE / Ec / Er / Ec / Er
T-2-TS1a / 0.04086 / -225.89091 / 1.5 / -224.97880 / 16.3
T-2-TS1b / 0.04217 / -225.91097 / -51.2 / -225.00181 / -44.1
T-2-TS1c / 0.04753 / -225.91908 / -72.5 / -225.00744 / -58.9
T-H2ORhCH2+ / 0.04764 / -225.98018 / -232.9 / -225.07253 / -229.8
T-CH2Rh(H)OH+ / 0.04379 / -225.91344 / -57.7 / -224.99923 / -37.3
T-2-TS2a / 0.04250 / -225.88281 / 22.8 / -224.97165 / 35.1
T-HOCH2RhH+ / 0.04848 / -225.96081 / -182.0 / -225.04905 / -168.1
T-2-TS3b / 0.04766 / -225.95745 / -173.2 / -225.04604 / -160.2
T-H2RhOCH2+ / 0.04264 / -225.98317 / -240.7 / -225.08129 / -252.8
T-RhCH2+ + H2O / 0.04391 / -225.93088 / -103.4 / -225.02234 / -98.0
T-CH2ORh+ + H2 / 0.03900 / -225.96242 / -186.3 / -225.05143 / -174.4
T-2-TS1e / 0.04550 / -225.91596 / -64.3 / -225.00077 / -41.3
T-b-RhCH3OH+ / 0.05289 / -225.99112 / -261.6 / -225.08242 / -255.7
Rh+(3F) + CH3OH / 0.05118 / -225.93494 / -114.1 / -225.03073 / -120.0
T-2-TS1f / 0.03963 / -225.85217 / 103.2 / -224.94311 / 110.0
T-(H2)ORhCH2+ / 0.04074 / -225.87089 / 54.1 / -224.96282 / 58.3
T-ORhCH2+ + H2 / 0.03610 / -225.85617 / 92.7 / -224.94698 / 99.9
T-2-TS2b + H2 / 0.03550 / -225.82826 / 166.0 / -224.90996 / 197.1
T-2-TS1g / 0.04093 / -225.87027 / 55.7 / -224.95060 / 90.4
T-2-TS1h / 0.04347 / -225.90261 / -29.2 / -224.98867 / -9.6
RS-2-TS1a / 0.04363 / -225.91579 / -63.8 / -225.01039 / -66.6
RS-2-TS1b / 0.04357 / -225.92433 / -86.3 / -225.01689 / -83.7
RS-2-TS1c / 0.04746 / -225.89542 / -10.3 / -224.98663 / -4.2
US-2-TS1c, <S2=0.871> / 0.04755 / -225.90978 / -48.1 / -224.99853 / -35.5
RS-H2ORhCH2+ / 0.04751 / -225.98043 / -233.5 / -225.07462 / -235.3
US-H2ORhCH2+, <S2=0.473> / 0.04751 / -225.98279 / -239.7 / -225.07157 / -227.2
RS-CH2Rh(H)OH+ / 0.04554 / -225.93916 / -125.2 / -225.03248 / -124.6
RS-2-TS2a / 0.04511 / -225.91944 / -73.4 / -225.01280 / -72.9
RS-HOCH2RhH+ / 0.05007 / -225.97023 / -206.8 / -225.06172 / -201.4
US-HOCH2RhH+, <S2=0.659> / 0.04810 / -225.95151 / -157.6 / -225.02962 / -117.1
RS-2-TS3a / 0.04352 / -225.91865 / -71.3 / -225.01001 / -65.6
RS-2-TS3b / 0.04870 / -225.94287 / -134.9 / -225.03149 / -122.0
US-2-TS3b, <S2=0.732> / 0.04783 / -225.95218 / -159.4 / -225.03865 / -140.8
RS-H2RhOCH2+ / 0.04549 / -225.96377 / -189.8 / -225.05325 / -179.1
US-H2RhOCH2+, <S2=0.883> / 0.04447 / -225.98205 / -237.8 / -225.07159 / -227.3
RS-RhCH2+ + H2O / 0.04390 / -225.93373 / -110.9 / -225.02693 / -110.0
US-RhCH2++H2O, <S2=0.395> / 0.04383 / -225.93533 / -115.1 / -225.02328 / -100.4
RS-CH2ORh+ + H2 / 0.03940 / -225.92725 / -93.9 / -225.01704 / -84.1
US-CH2ORh+ + H2, <S2=0.931> / 0.03910 / -225.94909 / -151.3 / -225.04328 / -153.0
RS-2-TS1e / 0.04424 / -225.89912 / -20.0 / -224.98994 / -12.9
US-2-TS1e, <S2=0.274> / 0.04404 / -225.89968 / -21.5 / -224.98741 / -6.3
RS-b-RhCH3OH+ / 0.05357 / -225.95767 / -173.8 / -225.05187 / -175.5
US-b-RhCH3OH+, <S2=0.942> / 0.05334 / -225.98195 / -237.5 / -225.07849 / -245.4
Rh+(1D) + CH3OH / 0.05118 / -225.85912 / 85.0 / -224.98737 / -6.2
Rh+(1F) + CH3OH, <S2=0.999> / 0.05118 / -225.91484 / -61.3 / -225.02731 / -111.0
RS-2-TS1f / 0.03926 / -225.83644 / 144.5 / -224.94271 / 111.1
US-2-TS1f, <S2=0.597> / 0.03878 / -225.83888 / 138.1 / -224.93671 / 126.8
RS-(H2)ORhCH2+ / 0.04118 / -225.85050 / 107.6 / -224.95055 / 90.5
US- (H2)ORhCH2+, <S2=1.011> / 0.04066 / -225.85837 / 86.9 / -224.95183 / 87.2
RS-ORhCH2+ + H2 / 0.03568 / -225.82546 / 173.3 / -224.92588 / 155.3
US-ORhCH2+ + H2, <S2=0.999> / 0.03607 / -225.84416 / 124.2 / -224.93695 / 126.2
RS-2-TS2b + H2 / 0.03575 / -225.79945 / 241.6 / -224.90547 / 208.9
RS-2-TS1g / 0.04230 / -225.86962 / 57.4 / -224.95688 / 73.9
RS-(H)2RhOCH2+ / 0.04523 / -225.97557 / -220.8 / -225.06229 / -202.9
RS-2-TS2g / 0.04246 / -225.94231 / -133.4 / -225.03319 / -126.5
Table 3: Zero-point energies (ZPE) (hartree), total energies (Ec) (hartree) corrected by ZPE, and relative energies (Er) (kJ mol-1) with respect to reactants [RhO+(3Σ) + CH4] of the species plus H2O in the formation of RhC+ + H2 from RhCH2+ calculated at the B3LYP/6-311+G(2d, 2p), SDD and CCSD(T)/6-311+G(2d, 2p), SDD levels
ZPE / Ec / Er / Ec / Er
T-RhCH2+ / 0.04391 / -225.93088 / -103.4 / -225.02234 / -98.0
T-4-TS1 / 0.03699 / -225.87164 / 52.1 / -224.96746 / 46.1
T-HRhCH+ / 0.03873 / -225.87897 / 32.8 / -224.97494 / 26.5
T-4-TS2 / 0.03383 / -225.80457 / 228.2 / -224.90391 / 213.0
T-(H)2RhC+ / 0.03511 / -225.80647 / 223.2 / -224.90461 / 211.1
T-4-TS3 / 0.03460 / -225.79171 / 262.0 / -224.88755 / 255.9
T-H2RhC+ / 0.03658 / -225.83615 / 145.3 / -224.93753 / 124.7
RhC+(3Σ) + H2 / 0.03357 / -225.82412 / 176.9 / -224.92534 / 156.7
Rh+(3F)+CH2(3B1) / 0.03855 / -225.80725 / 221.2 / -224.90876 / 200.2
RS-RhCH2+ / 0.04390 / -225.93373 / -110.9 / -225.02693 / -110.0
US-RhCH2+, <S2=0.395> / 0.04383 / -225.93533 / -115.1 / -225.02328 / -100.4
RS-4-TS1 / 0.03860 / -225.89603 / -11.9 / -224.99655 / -30.3
RS-HRhCH+ / 0.04042 / -225.90106 / -25.1 / -225.00208 / -44.8
RS-4-TS2 / 0.03620 / -225.78382 / 282.7 / -224.89369 / 239.8
US-4-TS2, <S2= 0.555 / 0.03620 / -225.78382 / 282.7 / -224.89033 / 248.6
RS-(H)2RhC+ / 0.03762 / -225.87488 / 43.6 / -224.97804 / 18.3
RS-4-TS3 / 0.03673 / -225.87574 / 41.3 / -224.97902 / 15.8
RS-H2RhC+ / 0.03813 / -225.89865 / -18.8 / -225.00120 / -42.5
RhC+(3Σ) + H2 / 0.03408 / -225.88084 / 27.9 / -224.98438 / 1.7
Rh+(1D)+CH2(1A1) / 0.03801 / -225.71370 / 466.8 / -224.84843 / 358.6
Rh+(1F)+CH2(1A1), <S2=0.999> / 0.03801 / -225.76942 / 320.5 / -224.88836 / 253.8
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