A Theoretical Analysis of the Catalytic Cycle of. a Ni Cross-Coupling Process: Application of the. Energetic Span Model
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1 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 of Chemistry and The Lise Meitner-Minerva Center for Computational Quantum Chemistry, Givat Ram Campus, Jerusalem 91904, ISRAEL. sason@yfaat.ch.huji.ac.il; kozuchs@yfaat.ch.huji.ac.il S1. Theoretical Method S2. Fortran program for TOF and X TOF calculation. S3. XYZ Coordinates S1
2 S1. Theoretical Method Geometry Optimization Method The system was found to be sensitive to the choice of DFT functional and basis set, so the calculation method was selected by comparison with a coupled-cluster (CC) reference calculations. As the CC method is extremely resource consuming, Ni(NH 3 ) 2 MeOH was considered as a model. All the Ni-X distances are shown in table S1 for this complex. As can be seen there are no significant differences between the functionals, with BP86 and B3LYP giving close values compared to CCSD. BHandHLYP gives consistently shorter bonds. The basis set appears to be more critical than the functional for the optimization process (compare the two basis in CCSD), but no clear correlation appears when improving it. Balancing between accuracy and swiftness, BP86/lacvp * seemed to be the best choice. Table S1: Relevant distances for the model complex Ni(NH 3 ) 2 MeOH. Distances BP86 B3LYP BHandHLYP CCSD (Å) lacvp * lacv3p *+ lacvp * lacvp *+ lacv3p * lacv3p *+ lacvp * lacv3p *+ lacvp * lacv3p *+ 1 Ni-NH Ni-NH Ni-OH Ni-Me Diff I (a) Diff II (b) (a) Sum of bond distance differences between the method in the column and CCSD/lacvp *. (b) Idem with CCSD/lacv3p *+ Single Point Energy Calculation Method For the single point energy (SPE) method we used a slightly bigger model: oxidative addition of formic anhydride into Ni(CH 2 =N-CH=CH-N=CH2) complex. Again several functionals and basis sets where considered taking the geometry from a B3LYP/lacvp * optimization. Table S2: Oxidative addition energies (kcal/mol) for the SPE evaluation. HF MP2 MP4sdq CCSD CCSD(T) lacvp * lacvp * lacvp * lacvp * lacvp * lacv3p * BP86 PBE HCTH407 B3LYP lacvp * lacvp * lacvp * lacvp * lacv3p * SB98 BHandHLYP TPSS (Gaussian) lacvp * lacvp * lacv3p *+ lacvp * The system is highly correlated, as appears from the huge energy differences between HF, perturbational methods and CC. The small gap between CCSD with and without perturbational triplet excitations implies convergence in the method. For this S2
3 reaction (which shows similarities with the real complex) most of the DFT methods show poor behavior, except for the BHandHLYP (having 50% HF exchange), which gives good results.. BHandHLYP/lacv3p *+ was considered then the most accurate method for SPE. Solvent Calculation Method The solvation energy calculations require a few parameters, one critical variable is the atomic radii used to generate the solvent cavity. Several molecules whose experimental solvation energy is known were used as model for testing these radii options. As can be seen in table S3 the default UA0 model is fairly poor, and the best models are UAKS and UAHF. In here UAKS was selected also because it was designed for DFT calculations. Table S3: Average errors in kcal/mol on different models compared to experimental values taken from (Tomasi, J; Persico, M. Chem. Rev. 1994, 94, 2027). The molecules considered were benzene, acetone, ethanol, aniline and cresol. Program Radii Model Water Heptane Gaussian UA0 (Default) UAKS UAHF Pauling Bondi UFF Jaguar S3
4 S2. Fortran program for TOF and X TOF calculation:! 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 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)) S4
5 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) 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 S5
6 S3. XYZ Coordinates: TS OA 62 C C C C C C C C C C C C C C C C C C C C C C C C C C H H H H H H H H H H H H H H H H H H H H H H H H H S6
7 H H H H H N N Ni O O O TS TM 57 Ni N N C C C C C C C C C C H H H H H H H H O C C C C H O H C O C H C H C H H H H S7
8 H H C Zn C C H H H H H H C H H H H TS RE 57 Ni N N C C C C C C C C C C H H H H H H H H O C C C C H O H C O C H C S8
9 H C H H H H H H Zn C C C H H H H H H C H H H H TS LS 79 Ni N N C C C C C H H H H C C C C C H H H H C C C H H H H S9
10 H O C C C C C C H H H H H H H H H H C O O Zn H C C H H H H C C C H H H C H C H H H H C C H H C H H Ni N S10
11 N C C C C C C C C C C H H H H H H H H C C C C C C C C H H H H H H H H H H H H Ni N N C C C C C C C C C S11
12 C H H H H H H H H O C C C C H O H C O C H C H C H H H H H H Zn 57 Ni N N C C C C C C C C C C H H H H H H H H S12
13 O C C C C H O H C O C H C H C H H H H H H C Zn C C H H H H H H C H H H H Ni N N C C C C C C C C C C H H S13
14 H H H H H H O C C C C H O H C O C H C H C H H H H H H Zn C C C H H H H H H C H H H H Ni N N C C C C C H S14
15 H H H C C C C C H H H H C C C H H H H H O C C C C C C H H H H H H H H H H C O O Zn H C C H H H H S15
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