Supporting Information. DFT Study on the Homogeneous Palladium-Catalyzed. N-Alkylation of Amines with Alcohols

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1 Supporting Information DFT Study on the Homogeneous Palladium-Catalyzed N-Alkylation of Amines with Alcohols Guo-Ming Zhao,, Hui-ling Liu, *, Xu-ri Huang, Xue Yang, and Yu-peng Xie Institute of Theoretical Chemistry, Jilin University, Changchun, , China College of Science, Jilin Institute of Chemical Technology, Jilin, , China Contents S1. Eqs S1-S4 for the interactions of F with the possible counteranions S2. Eqs S5-S8 for the interactions of T with the possible counteranions S3. Eqs S9-S12 for the interactions of Int4i with the possible counteranions S4. Eqs S13-S16 for the interactions of Int8i with the possible counteranions S5. Figure S1 for the schematic drawings of TS6i-Cl and TS6i-LiCl 2 S6. Figure S2 for the optimized geometries of T-Int1o and T-TS2o S7. Figure S3 for the optimized geometries of F-Int1o and F-TS2o S8. Eqs S17-S20 for the interactions of Int12i with the possible counteranions S9. Figure S4 for the schematic drawings of TS10i-Cl and TS10i-LiCl 2 S10. Figure S5 for the optimized geometries of F-Int4o and F-TS5o S11. The energetic span model S12. Fortran program for TOF and X i calculations S1

2 S13. Eqs S21-S26 for the reactions of AgOTf with LiCl 2 and the cationic three-coordinated Pd(II) species S14. Eqs S27-S32 for the reactions of AgBF 4 with LiCl 2 and the cationic three-coordinated Pd(II) species S15. Table S1 for the BSSE corrections and the entropic corrections of the proposed key species S16. Cartesian coordinates of all optimized geometries together with thermal corrections to enthalpies ( D H ) and free energies ( D G ) at the B3LYP level and their electronic energies ( E ) at the M06 level S16.1 Initiation of the active species S16.2 Formation of benzaldehyde and the Pd hydride species S16.3 Imine formation S16.4 Formation of the amine product and regeneration of the active species S17. Cartesian coordinates of the key states together with thermal corrections to enthalpies ( D H ) and free energies ( D G ) and their electronic energies ( E ) S17.1 At the M06//B3PW91 level S17.2 At the M06//TPSSTPSS level S17.3 At the M06//PBE1PBE level S17.4 At the M06//M06 level S17.5 At the wb97xd//wb97xd level S18. Cartesian coordinates of selective species in Eqs S1-S32 together with thermal corrections to enthalpies ( D H ) and free energies ( D G ) at the B3LYP level and their electronic energies ( E ) at the M06 level S2

3 S1. Eqs S1-S4 for the interactions of F with the possible counteranions S2. Eqs S5-S8 for the interactions of T with the possible counteranions S3

4 S3. Eqs S9-S12 for the interactions of Int4i with the possible counteranions S4. Eqs S13-S16 for the interactions of Int8i with the possible counteranions S4

Figure S2 for the optimized geometries of T-Int1o and T-TS2o Figure S2: Optimized geometries of T-Int1o and T-TS2o

5 S5. Figure S1 for the schematic drawings of TS6i-Cl and TS6i-LiCl 2 Figure S1: Schematic drawings of TS6i-Cl and TS6i-LiCl 2 with selected bond distances (in Å). S6. Figure S2 for the optimized geometries of T-Int1o and T-TS2o Figure S2: Optimized geometries of T-Int1o and T-TS2o with selected bond distances (in Å). S7. Figure S3 for the optimized geometries of F-Int1o and F-TS2o Figure S3: Optimized geometries of F-Int1o and F-TS2o with selected bond distances (in Å). S5

6 S8. Eqs S17-S20 for the interactions of Int12i with the possible counteranions S9. Figure S4 for the schematic drawings of TS10i-Cl and TS10i-LiCl 2 Figure S4: Schematic drawings of TS10i-Cl and TS10i-LiCl 2 with selected bond distances (in Å). S6

S10. Figure S5 for the optimized geometries of F-Int4o and F-TS5o Figure S5: Optimized geometries of F-Int4o and F-TS5o with selected bond distances (in Å). S11.

7 S10. Figure S5 for the optimized geometries of F-Int4o and F-TS5o Figure S5: Optimized geometries of F-Int4o and F-TS5o with selected bond distances (in Å). S11. The energetic span model The energetic span model developed by Kozuch and Shaik is an useful tool to calculate the turnover frequency (TOF) of a catalytic cycle from computationally obtained energy profile. The TOF (in s -1 ) in a steady state regime is given by Eq 1: 1,2 TOF= δ ' G i, j N e å i,j= 1 ìdg = í î 0 -DGrx e -1 Ti- I j-δ Gi ', j rx if i> j if i j HereD is the free energy of the entire reaction. T i and I j are the calculated free energies of Grx the ith transition state and the jth intermediate, respectively. These energies are all dimensionless quantities expressed in k b T units, i.e., I = G( I ) k T, T = G( T ) k T, DGrx = [ G(Products) G(Reactants)]/ k T. j j b i i b - The higher the TOF, the more favourable the catalytic cycle. If the TOF of a catalytic cycle is determined only by one intermediate and one transition state, the intermediate is called the TOF-determining intermediate (TDI), and the transition state is called the TOF-determining transition state (TDTS). To know the influence of every intermediate and transition state on the TOF, the degree of TOF control (X i ) is developed. It can be expressed as follows: 2 (1) b X X Ti I j = = å å j ij å å i ij e e e ' T i -I j -δg ij ' T i - I j -δg ij ' T i -I j -δg ij e ' T i -I j -δg ij (2) S7

8 The bigger the value of the degree of TOF control, the higher the influence of the corresponding intermediate or transition state on the TOF. Thus, the intermediate with the highest X I is the TDI and the transition states with the highest X T is the TDTS if only one intermediate and one transition state determine the TOF. On the basis of Eqs (1) and (2), Carvajal and co-workers design a Fortran program (see S12), 3 with which one can easily compute the TOF, and identify the TDI and TDTS. References 1. Amatore, C.; Jutand, A. J. Organomet. Chem. 1999, 576, (b) Kozuch, S.; Shaik, S. J. Am. Chem. Soc. 2006, 128, (a) Kozuch, S.; Shaik, S. J. Phys. Chem. A 2008, 112, (b) Kozuch, S.; Shaik, S. Acc. Chem. Res. 2011, 44, (c) Uhe, A.; Kozuch, S.; Shaik, S. J. Comput. Chem. 2011, 32, Carvajal, M. À.; Kozuch, S.; Shaik, S. Organometallics 2009, 28, S12. Fortran program for TOF and X i calculations! TOF PROGRAM! Reads a.ene input file and delivers the TOF and the! degree of TOF control of each intermediate and TS.! The input file must be in the following sintax:!! TEMPERATURE! FIRST INTERMEDIATE (space) FIRST TS! SECOND INTERMEDIATE (space) SECOND TS!...! N INTERMEDIATE (space) N TS! FINAL INTERMEDIATE!! All the energies must be in kcal/mol, and temperature in Kelvin.!! program TOF implicit none REAL,PARAMETER::kbh= ,kbcal= REAL,allocatable::i(:),ts(:),xi(:),xts(:) REAL::temp,ktemp,dummy,dg,delta,m=0.,tof,de,maxtsr,tsd INTEGER::step=-1,a,b,maxts,maxi CHARACTER::namefile*250 WRITE(*,*)'Name of the input file?' READ(*,*)namefile OPEN(1,FILE=TRIM(namefile)//'.ene') OPEN(2,FILE=TRIM(namefile)//'.tof') READ(1,*)dummy S8

9 do READ(1,*,END=10)dummy step=step+1 END do 10 ALLOCATE(i(0:step),ts(step),xi(step),xts(step)) xts=0. xi=0. REWIND(1) READ(1,*)temp ktemp=kbcal*temp do a=0,step-1 READ(1,*)i(a),ts(a+1) i(a)=i(a)/ktemp ts(a+1)=ts(a+1)/ktemp end do READ(1,*)i(step) i(step)=i(step)/ktemp dg=i(step)-i(0) delta=exp(-dg)-1 do a=1,step maxtsr=0. do b=1,step IF(a>b)then de=exp(ts(a)-i(b)-dg) else de=exp(ts(a)-i(b)) END if xts(a)=xts(a)+de xi(b)=xi(b)+de m=m+de end do end do tof=kbh*temp*delta/m xi=xi/m xts=xts/m WRITE(*,40)tof WRITE(2,40)tof 40 FORMAT(/,' TOF=',e9.2,' 1/s',/) WRITE(2,45)temp 45 FORMAT(' Temperature=',f7.2) WRITE(2,*)" Ei Ets Xi Xts" WRITE(2,50) i(0)*ktemp,ts(1)*ktemp,xi(step),xts(1) do a=2,step WRITE(2,50) i(a-1)*ktemp,ts(a)*ktemp,xi(a-1),xts(a) S9

10 end do WRITE(2,60)i(step)*ktemp 50 FORMAT(f6.2,f6.2,f6.2,f6.2) 60 FORMAT(F6.2) end program Input and Output examples: File: test.ene File: test.tof TOF= 0.80E-07 1/s Temperature= Ei Ets Xi Xts S10

11 S13. Eqs S21-S26 for the reactions of AgOTf with LiCl 2 and the cationic three-coordinated Pd(II) species S11

12 S14. Eqs S27-S32 for the reactions of AgBF 4 with LiCl 2 and the cationic three-coordinated Pd(II) species S12

13 S15. Table S1 for the BSSE corrections and the entropic corrections of the proposed key species Table S1. Values (in kcal mol -1 ) of the BSSE Correction, BSSE-Corrected Free Energy (G BSSE ), Entropic Correction (TS 293 ), a and Entropy-Corrected Free Energy (G 293 ) for the Proposed Key Species Key species G BSSE G BSSE H TS 293 G 293 F-LiCl NH-TS T-LiCl F-TS2i T-TS2i Int4i-LiCl TS6i Int8i-LiCl T-TS2o F-TS2o TS10i Int12i-LiCl Ph-TS14i T-TS14i F-TS14i F-TS5o a Emulating Martin and co-workers method (Martin, R. L.; Hay, P. J.; Pratt, L. R. J. Phys. Chem. A 1998, 102, ), we recalculated the frequencies at K and 293 atm to obtain the entropic contributions (TS 293 ), then gave entropy-corrected free energies (G 293 ) by subtracting entropic contributions from enthalpies to further testify the mechanism obtained at the M06//B3LYP level. Here, the pressure 293 atm is merely a crude estimate, for the density ( ρ = kg m -3 ) used in the pressure p= rrt M mol is the density of benzyl alcohol rather than of the reaction solution. S16. Cartesian coordinates of all optimized geometries together with thermal corrections to enthalpies ( D H ) and free energies ( D G ) at the B3LYP level and their electronic energies ( E ) at the M06 level S16.1 Initiation of the active species dppe E = D H = D G = C H H C S13

14 H H P P C C C C H C H C H H H C C C C H C H C H H H C C C C H C H C H H H C C C C H C H S14

15 C H H H PdCl 2 E = D H = D G = Pd Cl Cl L-PdCl 2 E = D H = D G = C H H C H H P P C C C C H C H C H H H C C C C H C H C H H H C C C S15

16 C H C H C H H H C C C C H C H C H H H Pd Cl Cl LiOH E = D H = D G = O H Li F-LiCl 2 E = D H = D G = C H H C H H P P C C C C H C H S16

17 C H H H C C C C H C H C H H H C C C C H C H C H H H C C C C H C H C H H H Pd Cl Cl O Li H S17

18 LiCl E = D H = D G = Li Cl F-Cl E = D H = D G = C H H C H H P P C C C C H C H C H H H C C C C H C H C H H H C C C C H C H C H S18

19 H H C C C C H C H C H H H Pd Cl O H LiCl 2 E = D H = D G = Li Cl Cl F E = D H = D G = C H H C H H P P C C C C H C H C H H H C S19

20 C C C H C H C H H H C C C C H C H C H H H C C C C H C H C H H H Pd O H Cl E = D H = D G = Cl Li(OH)Cl E = D H = D G = O H Li Cl S20

21 PhNH 2 E = D H = D G = C C C C C C H H H H H N H H NH-Int1 E = D H = D G = C H H C H H P P C C C C H C H C H H H C C C C H C H S21

22 C H H H C C C C H C H C H H H C C C C H C H C H H H Pd O H N C H C C C H C H C H H H H S22

23 NH-TS2 E = D H = D G = C H H C H H P P C C C C H C H C H H H C C C C H C H C H H H C C C C H C H C H H H C C S23

24 C C H C H C H H H Pd O H N C H C C C H C H C H H H H NH-Int3 E = D H = D G = C H H C H H P P C C C C H C H C S24

25 H H H C C C C H C H C H H H C C C C H C H C H H H C C C C H C H C H H H Pd O H N C H C C S25

26 C H C H C H H H H H 2 O E = D H = D G = O H H T E = D H = D G = C H H C H H P P C C C C H C H C H H H C C C C H C H C H S26

27 H H C C C C H C H C H H H C C C C H C H C H H H Pd N C C C C H C H C H H H H T-LiCl 2 E = D H = D G = C H H C S27

28 H H P P C C C C H C H C H H H C C C C H C H C H H H C C C C H C H C H H H C C C C H C H S28

29 C H H H Pd N C C C C H C H C H H H H Cl Li Cl T-Cl E = D H = D G = C H H C H H P P C C C C H C H C H H H C C S29

30 C C H C H C H H H C C C C H C H C H H H C C C C H C H C H H H Pd N C C C C H C H C H H H S30

31 H Cl Int4i-Cl E = D H = D G = C H H C H H P P C C C C H C H C H H H C C C C H C H C H H H C C C C H C H C H H S31

32 H C C C C H C H C H H H Pd O C H H C C C C H C H C H H H Cl Int8i-Cl E = D H = D G = C H H C H H P P C C C C H S32

33 C H C H H H C C C C H C H C H H H C C C C H C H C H H H C C C C H C H C H H H Pd H Cl Int12i-Cl E = D H = D G = S33

34 C H H C H H P P C C C C H C H C H H H C C C C H C H C H H H C C C C H C H C H H H C C C S34

35 C H C H C H H H Pd C H H C C C C H C H C H H H N C C C C H C H C H H H Cl PhCH 2 OH E = D H = D G = C H H O H C S35

36 C C C H C H C H H H T-Int1i E = D H = D G = C H H C H H P P C C C C H C H C H H H C C C C H C H C H H H C C S36

37 C C H C H C H H H C C C C H C H C H H H Pd N C C C C H C H C H H H H O C H H C C C C H C S37

38 H C H H H H T-TS2i E = D H = D G = C H H C H H P P C C C C H C H C H H H C C C C H C H C H H H C C C C H C S38

39 H C H H H C C C C H C H C H H H Pd N C C C C H C H C H H H H O C H H C C C C H C H C H H S39

A Theoretical Analysis of the Catalytic Cycle of. a Ni Cross-Coupling Process: Application of the. Energetic Span Model

Supporting Information for: A Theoretical Analysis of the Catalytic Cycle of a Ni Cross-Coupling Process: Application of the Energetic Span Model Sebastian Kozuch*, Sophia E. Lee, Sason Shaik* [*] Institute