First-principle MD studies on the reaction pathways at T=0K and at finite temperatures
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First-principle MD studies on the reaction
pathways at T=0K and at finite temperatures
First-principle MD studies on the reaction
pathways at T=0K and at finite temperatures
Artur Michalaka,b and Tom Zieglera
aDepartment of Chemistry,
University of Calgary,
Calgary, Alberta, Canada
bDepartment of Theoretical Chemistry
Jagiellonian University
Cracow, Poland
Artur Michalaka,b and Tom Zieglera
aDepartment of Chemistry,
University of Calgary,
Calgary, Alberta, Canada
bDepartment of Theoretical Chemistry
Jagiellonian University
Cracow, Poland
April 21, 2023April 21, 2023
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MD simulations along the IRPMD simulations along the IRP
A. Michalak, T. Ziegler „First-principle Molecular Dynamics along Intrinsic Reaction Paths”, J. Phys Chem. A 105, 2001, 4333-4343.
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TS
min.
• assumed reaction coordinate
• dynamics with constraint for points on assumed RP
• free energy change obtained by integration of the force on constraint (thermodynamic integration)
Reaction free energies Reaction free energies
ΔA= Fi λΔλii
npoints
∑
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TS
min.
• the reaction coordinate is changed in a continuous manner
Slow-growth simulations Slow-growth simulations
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Slow-growth simulations Slow-growth simulations
Typical problem – hysteresis in free energy profiles
A
RC
forward sampling
backward sampling
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Choice of reaction coordinate Choice of reaction coordinate
Direction perpendicular to RP
TS
min.
Rapid changes of thePES shape in the directionperpendicular to RP
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Choice of reaction coordinate Choice of reaction coordinate
Direction perpendicular to RP
TS
min.
Smooth changes of thePES shape in the directionperpendicular to RP
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Reaction free energies Reaction free energies
Standard approach:MD sampling along assumed reaction paths
Alternative approach:MD sampling along pre-determined reaction paths
dxi =-∂E∂xi
dt; xi = mi Xi
Fukui, K. Acc. Chem. Res. 1981, 14, 363.
IRP:
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MD along IRP MD along IRP
2) finite temperature sampling with linear constraint:
X→ j• f
→ j, IRC =const.=X→ j ,IRC• f
→ j, IRC = X ij ,IRC f i
j ,IRC
i∑• in slow-growth simulations the vector f and constraint valueare changed in every timestep;• for every step the force on constraint, F j, is calculated;• free-energy change is obtained by integrating F:
ΔA= F jΔsjj
nsteps
∑
Δsj =12
X→ j+1,IRC• f
→ j , IRC⎛ ⎝ ⎜
⎞ ⎠ ⎟ − X
→ j−1,IRC• f→ j, IRC⎛
⎝ ⎜
⎞ ⎠ ⎟
⎡ ⎣ ⎢
⎤ ⎦ ⎥
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Computational details Computational details
Projector augmented wave (PAW) methodBlochl, P. Phys. Rev. B 1994, 50, 17953.
DFT calculations with Becke-Perdew XCBecke A.D. Phys. Rev. A 1988, 38, 3098.Perdew, J.P. Phys. Rev. B 1986, 33, 8822.
IRC predetermined by the steepest descent in mass-weighted coordinates from TS structures
Slow-growth MD simulations along IRP at 300K
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HCN CNHTS
IRP:
HCN CNH isomerizationHCN CNH isomerization
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HCN CNH HCN CNH
MD along IRP (300K)
MD with constraintRNH -RCH = const.
IRP (T=0K)
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MD along IRP
MD with constraintRNH -RCH = const.
Hydrogen path
HCN CNHHCN CNH
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HCN CNHHCN CNH
MD along IRP
MD with constraintRNH -RCH = const.
Hydrogen path
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HCN CNHHCN CNH
MD along IRP
MD with constraintRNH -RCH = const.
Hydrogen path
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cyclobutene TS gauche-butadiene
Conrotatory ring opening of cyclobuteneConrotatory ring opening of cyclobutene
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cyclobutene TS gauche-butadiene
IRP:
Conrotatory ring opening of cyclobuteneConrotatory ring opening of cyclobutene
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Cl- + CH3Cl TS Cl-CH3 + Cl-
Prototype SN2 reaction : Cl- + CH3Cl CH3Cl + Cl- Prototype SN2 reaction : Cl- + CH3Cl CH3Cl + Cl-
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Cl- + CH3Cl TS Cl-CH3 + Cl-
IRP ( T = 0 K ):
Prototype SN2 reaction : Cl- + CH3Cl CH3Cl + Cl- Prototype SN2 reaction : Cl- + CH3Cl CH3Cl + Cl-
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0 1 2 3 s[amu-1 bohr]0
30
60
90
120
150
180
Angle
Cl1-C-Cl2
IRC
Cl1-C-H
0 1 2 3 s [amu-1 bohr]
2
3
4
5
R [A]
IRC
C-Cl2
Cl1-C
Cl1 - Cl2
0 1 2 3 s[amu-1 bohr]
-5
-4
-3
-2
-1
0
E [kcal/mol]
IRC
G
ETS
vdW complex
Prototype SN2 reaction : Cl- + CH3Cl CH3Cl + Cl- Prototype SN2 reaction : Cl- + CH3Cl CH3Cl + Cl-
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Cl -CH2-CH=CH2 TS CH2=CH-CH2-Cl
IRP (TS R):
CH2=CH-CH2Cl isomerizationCH2=CH-CH2Cl isomerization
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Cl-CH2-CH=CH2Cl-CH2-CH=CH2
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Cl-CH2-CH=CH2Cl-CH2-CH=CH2
TS
conf. 2 (gauche)
conf. 1 (cis)
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Cl-CH2-CH=CH2Cl-CH2-CH=CH2
TS
conf. 2 (gauche)
conf. 1 (cis)
IRP (T = 0 K)
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Cl-CH2-CH=CH2Cl-CH2-CH=CH2
TS
conf. 2 (gauche)
conf. 1 (cis)
IRP (T = 0 K )
T = 300 K
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0 2 4 6 8 s [amu-1 bohr]
-40
-30
-20
-10
0
E [kcal/mol]
E
G
IRC
0 2 4 6 8 s [amu-1 bohr]1
2
3
4
R [A]
IRCCl-C3Cl-C1
C1-C2C2-C3
0 2 4 6 8 s [amu-1 bohr]
0
30
60
90
120
Angle
Cl-C1-C2-C3
Cl-C1-C2
IRC
C1-C2-C3
TS
cis-
CH2=CH-CH2Cl isomerizationCH2=CH-CH2Cl isomerization
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Final product
Ethylene + butadiene cycloadditionEthylene + butadiene cycloaddition
finite separation
separated reactants
TS
Cs product
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torsion
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Ethylene/methyl acrylate copolymerization
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Ethylene/methyl acrylate copolymerization
Pd- and Ni-diimine catalystsactive inactive
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Ethylene polymerization mechanismEthylene polymerization mechanism
-agostic
-complex
+ ethylene
-agostic
-agosticinsertion
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Methyl acrylate/ethylene copolymerizationMethyl acrylate/ethylene copolymerizationMethyl acrylate/ethylene copolymerizationMethyl acrylate/ethylene copolymerization
Two possible acrylate binding modes:
O-complex-complex
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Ni- (inactive):O-complex preferred
Pd- (active) -complex preferred
- / O- complexes- / O- complexes
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Ni: Ni:
Pd: OPd: O
Ni: ONi: O
Pd: Pd:
timestep
R [A]
RPd-C (300K)
RPd-O (300K)
timestep
R [A]
timestep
R [A]
timestep
R [A]
RNi-C (300K)
RNi-O (300K)
RNi-C (300K)RNi-C (700K)RNi-O (300K)RNi-O (700K)
RPd-C (300K)RPd-C (700K)RPd-O (300K)RPd-O (700K)
35
Fig 5. The two M-C() and the M-O distances from the unconstrained MD simulations for the MA O- and - complexes with the Ni- and Pd-diimine catalysts.
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Pd- Pd-
Ni- Ni-
-complex / O-complex isomerization reactions
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O-complex -complex isomerization – Pd-catalyst
MD simulation with constraint R(Pd-C)-R(Pd-O)=const.
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O-complex -complex isomerization – Ni-catalyst
MD simulation with constraint R(Pd-C)-R(Pd-O)=const.
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O-complex -complex isomerization – Ni-catalyst
MD simulation with constraint R(Pd-C)-R(Pd-O)=const.
Reaction product:O,C-bound complexMINIMUM on PES
Reaction product:O,C-bound complexMINIMUM on PES
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Chelate formation after acrylate insertion
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Chelate opening: ethylene insertionChelate opening: ethylene insertion
MD simulations with constraint R(Colefin-Calkyl) =const.
E [
kca
l/m
ol]
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Two-step chelate openingTwo-step chelate opening
very high insertion barrierslower for Ni-catalyst
Ni – high barrier (higher than insertion)Pd – low barrier (lower than insertion)
low insertion barriers,comparable to insertion
barriers in ethylene homocopolymerization
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Acknowledgements. This work was supported by the National Sciences and Engineering Research Council of Canada (NSERC), Nova Chemical Research and Technology Corporation as well as donors of the Petroleum Research Fund, administered by the American Chemical Society (ACS-PRF No. 36543-AC3). A.M. acknowledges NATO Fellowship. Important parts of the calculations was performed using the UofC MACI cluster.
Acknowledgements. This work was supported by the National Sciences and Engineering Research Council of Canada (NSERC), Nova Chemical Research and Technology Corporation as well as donors of the Petroleum Research Fund, administered by the American Chemical Society (ACS-PRF No. 36543-AC3). A.M. acknowledges NATO Fellowship. Important parts of the calculations was performed using the UofC MACI cluster.
ConclusionsConclusions
This in not a MD movie (yet...)