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

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.

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

∑

TS

min.

• the reaction coordinate is changed in a continuous manner

Slow-growth simulations Slow-growth simulations

Slow-growth simulations Slow-growth simulations

Typical problem – hysteresis in free energy profiles

A

RC

forward sampling

backward sampling

Choice of reaction coordinate Choice of reaction coordinate

Direction perpendicular to RP

TS

min.

Rapid changes of thePES shape in the directionperpendicular to RP

Choice of reaction coordinate Choice of reaction coordinate

Direction perpendicular to RP

TS

min.

Smooth changes of thePES shape in the directionperpendicular to RP

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:

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⎛

⎝ ⎜

⎞ ⎠ ⎟

⎡ ⎣ ⎢

⎤ ⎦ ⎥

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

HCN CNHTS

IRP:

HCN CNH isomerizationHCN CNH isomerization

HCN CNH HCN CNH

MD along IRP (300K)

MD with constraintRNH -RCH = const.

IRP (T=0K)

MD along IRP

MD with constraintRNH -RCH = const.

Hydrogen path

HCN CNHHCN CNH

HCN CNHHCN CNH

MD along IRP

MD with constraintRNH -RCH = const.

Hydrogen path

HCN CNHHCN CNH

MD along IRP

MD with constraintRNH -RCH = const.

Hydrogen path

cyclobutene TS gauche-butadiene

Conrotatory ring opening of cyclobuteneConrotatory ring opening of cyclobutene

cyclobutene TS gauche-butadiene

IRP:

Conrotatory ring opening of cyclobuteneConrotatory ring opening of cyclobutene

Cl- + CH3Cl TS Cl-CH3 + Cl-

Prototype SN2 reaction : Cl- + CH3Cl CH3Cl + Cl- Prototype SN2 reaction : Cl- + CH3Cl CH3Cl + Cl-

Cl- + CH3Cl TS Cl-CH3 + Cl-

IRP ( T = 0 K ):

Prototype SN2 reaction : Cl- + CH3Cl CH3Cl + Cl- Prototype SN2 reaction : Cl- + CH3Cl CH3Cl + Cl-

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-

Cl -CH2-CH=CH2 TS CH2=CH-CH2-Cl

IRP (TS R):

CH2=CH-CH2Cl isomerizationCH2=CH-CH2Cl isomerization

Cl-CH2-CH=CH2Cl-CH2-CH=CH2

Cl-CH2-CH=CH2Cl-CH2-CH=CH2

TS

conf. 2 (gauche)

conf. 1 (cis)

Cl-CH2-CH=CH2Cl-CH2-CH=CH2

TS

conf. 2 (gauche)

conf. 1 (cis)

IRP (T = 0 K)

Cl-CH2-CH=CH2Cl-CH2-CH=CH2

TS

conf. 2 (gauche)

conf. 1 (cis)

IRP (T = 0 K )

T = 300 K

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

Final product

Ethylene + butadiene cycloadditionEthylene + butadiene cycloaddition

finite separation

separated reactants

TS

Cs product

torsion

Ethylene/methyl acrylate copolymerization

Ethylene/methyl acrylate copolymerization

Pd- and Ni-diimine catalystsactive inactive

Ethylene polymerization mechanismEthylene polymerization mechanism

-agostic

-complex

+ ethylene

-agostic

-agosticinsertion

Methyl acrylate/ethylene copolymerizationMethyl acrylate/ethylene copolymerizationMethyl acrylate/ethylene copolymerizationMethyl acrylate/ethylene copolymerization

Two possible acrylate binding modes:

O-complex-complex

Ni- (inactive):O-complex preferred

Pd- (active) -complex preferred

- / O- complexes- / O- complexes

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.

Pd- Pd-

Ni- Ni-

-complex / O-complex isomerization reactions

O-complex -complex isomerization – Pd-catalyst

MD simulation with constraint R(Pd-C)-R(Pd-O)=const.

O-complex -complex isomerization – Ni-catalyst

MD simulation with constraint R(Pd-C)-R(Pd-O)=const.

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

Chelate formation after acrylate insertion

Chelate opening: ethylene insertionChelate opening: ethylene insertion

MD simulations with constraint R(Colefin-Calkyl) =const.

E [

kca

l/m

ol]

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

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...)