Nonadiabatic Reactions

Methods for nonadiabatic dynamics:1. Solve the Schrodinger equation

1. Basis expansions, wavepackets, MCTDH (360)2. Path Integral methods, classical S-matrix methods

(100)2. Trajectory-based approaches

1. Ehrenfest, classical path (100)2. Trajectory Surface Hopping (250)

IMA Workshop: Chemical Dynamics, Jan. 12-16, 2009

reactant

product

3. Hybrid methods (QM + MM)

Trajectory surface hopping

• Tully’s fewest switches TSH method

Nuclear motions: Classical mechanics on a single Born Oppenheimer surface at any time

Electronic motions: Time-dependent Schrödinger equation

Switch electronic state: Probabilistic “fewest switches”algorithm

Velocity has to be adjusted after electronic state switchingto conserve energy

J. C. Tully, JCP 93, 161 (1990); S. Hammes-Schiffer and J. C. Tully, JCP 101, 4657 (1994); M. S. Topaler et al, JCP 106, 8699 (1997)

Nonadiabatic dynamics in an adiabatic basis

k k kH E=Ψ Ψ

Hopping probability

Energy conservation: Tot 1 1 2 2E T E T E= + = +

.

.

G. C. Schatz, L. A. Pederson and P. J. Kuntz, Far. Disc. Chem. Soc. 108, 357-74, (1997)

2

k kk 1

(R, t) c (t) (t)=

= ∑Φ Ψ

t

k k k0

c (t) c (t) exp i E (t)dt /⎡ ⎤

= ⎢ ⎥⎣ ⎦∫

t1

12 2 1 20

t2

12 1 2 10

ˆdc ˆ(R d )c (t) exp i (E (t) E (t))dt /dt

ˆdc ˆ(R d )c (t) exp i (E (t) E (t))dt /dt

⎡ ⎤= − −⎢ ⎥

⎣ ⎦⎡ ⎤

= − −⎢ ⎥⎣ ⎦

∫

∫

i

i

1 R 212 1 R 2

2 1

| H |d |

E E∇

= ∇ =−

Ψ ΨΨ Ψ

Issues with Fewest Switches

1. What to do if hop is forbidden2. Adiabatic versus diabatic basis (or in-between)3. How to determine derivative coupling or spin-orbit coupling matrix elements4. How to avoid integrating the TDSE to estimate transition probs

In spite of this, Tully 1990 paper has 732 citations, including papers by about half the participants of this meeting.

Example application: S(3P) + H2 → SH + H ReactionThe importance of intersystem crossing in the S(3P,1D) + H2 →SH + H reaction, Biswajit Maiti, G. C. Schatz and G. Lendvay, J. Phys. Chem. A, 108, 8772-8781 (2004).

Significant nonadiabatic effects in the S(1D) + HD reaction, Tian-Shu Chu, Ke-Li Han and George C. Schatz, J. Phys. Chem. A 111, 8286-90 (2007).

Trajectory studies of gas/liquid reactions

George C. SchatzNorthwestern University

Dongwook Kim

T. Minton, Montana State

Gas/liquid dynamics research

Related work: Nesbitt, McKendrick, Tully, Hase

Brian RadakScott Yockel

Wenfang Hu

Modeling the collision of reactive atoms with liquid surfaces

Novel (hypergolic) fuels•Combustion involving ionic liquids

Hyperthermal Chemistry•Gas phase reactions: O + C2H6, O + C2H4•Model hyperthermal O, F interacting with polymers

O+[Emim][NO3]

O, F + squalane

Motivation:Beam/surface experiments are used to study the structures of liquid interfaces, and the ability of atoms to penetrate interfaces and subsequently undergo chemical reaction.

Most abundant species in atmosphere as function of altitude

Minton, in Chemical Dynamics in Extreme Environments, (World Scientific, Singapore, 2001), pp 420.

Roble, in The Upper Mesosphere and Lower Thermosphere:A Review of Experiment and Theory, Geophysical Monograph 87, pp 1 – 21, 1995.

Spacecraft surfaces made of polymers erode in low Earth orbit (LEO) (~200-700 km) due to 5 eV atomic oxygen

J. W. Connell, High Perform Polym 12, 43 (2000)

Polymer degradation in LEO

Experiments at Montana State (Tim Minton)

Crossed-molecular-beams apparatus coupled to a laser detonation source Ecoll ~ 80 to 100 kcal/mol

v O

vC2H6

7.5°

50°

O

C2H6

OH C2H5

C2H5O

CH3O

MIRROR

SOURCECHAMBER

MAIN SCATTERING CHAMBER

CHOPPER WHEEL ROTATABLE DETECTOR

PULSEDVALVE

ETHANE SUPPLY LINE

APERTUREIONIZER

TO ION COUNTINGSYSTEM

QUADRUPOLEMASS FILTER

PULSEDVALVE

NOZZLEO2 SUPPLYLINE

SOURCECHAMBER

DIFFERENTIAL PUMPINGREGION

CO2LASER

Gas Phase Systems (O + molecule): •Direct dynamics quasiclassical trajectories with DFT (B3LYP, BMK), MP2 or semiempirical potential surfaces (MSINDO, PM3, SRP)•Use coupled-cluster calculations for calibration.•Excited state dynamics and spin-orbit interactions are possible, but difficult.

Gas/Surface Reactions (O + polymer surface): •Direct dynamics classical trajectories (thermal ensemble) with QM/MM potential surfaces. •QM uses MSINDO, QM/MM partitioning done with link atoms.•Partitioning between QM and MM atoms is dynamic

Theoretical approaches to hyperthermal(several eV) dynamics problems

Experimental and Theoretical Investigations of the Inelastic and Reactive Scattering Dynamics

of O(3P) Collisions with Ethane

Donna Minton, Tim Minton, Wen-fang Wu and GCSJPC A to be submitted

OH + C2H5 product90 kcal/mol

MSINDO

B3LYPExp

H + C2H5O product90 kcal/mol

H + C2H5O product

Branching between different products

MSINDOB3LYPExp

O + C2H4 →

C2H3+OH

CH2O+3CH2

CH2CHO+H

CH3CO+H3CH2CO+H2

1CH2CO+H2

CHO+CH3

O(3P) + Ethylene Reaction: Product Branching and ISC Effects

(Wenfang Hu, Biswajit Maiti, Diego Troya, G. Lendvay)

(abstraction)

(methylene)

(vinoxy)

(acetyl)

(methyl)

(3ketene)

(1ketene)

Experimental Product Branching

OH+C2H3 H+CH2CHOCH3+CHO CH2+CH2O H2+CH2CO H+CH3CO

ΔH kcal/mol: 7.5 -28.8 -6.6 -17.0 -85.1 -23.5Hunzinger(1981) 0.36±0.040.52―0.58

Endo(1986) 0.40±0.100.50±0.10 0.10±0.05Bley(1988) 0.50±0.10 00.44±0.15 0.06±0.03

Schmoltner(1989) 0.29±0.110.71±0.26Casavecchia (2005) 0.43±0.09 0.27±0.060.16±0.08 0.01±0.010.13±0.03

(methyl)(abstraction) (methylene) (vinoxy) (ketene) (acetyl)

O + C2H4 Reaction

O(3P)+C2H4

C2H3+OH

CH2O+3CH2CH2CHO+HCH3CO+H

3CH2CO+H2

1CH2CO+H2

CHO+CH33CH2CH2O1CH2CH2O

1CH3CHO

3CH3CHO

Adapted from: Schmoltner, Chu, Brudzynski and Y. T. Lee, J. Chem. Phys. 91(6926)1989

(acetyl)

(abstr)

(methylene)(vinoxy)

(methyl)(3ketene)

(1ketene)

O(1D)+C2H4

Methodology• “On the fly” quasiclassical trajectory

surface hopping (QCTSH) methodStep 1. QCT trajectories are initiated and propagated on

one of the adiabatic potential surfaces (UB3LYP/6-31G**)

2SO

LZ11 22

2 HP 1 expdH dHZdZ dZ

⎡ ⎤⎢ ⎥π⎢ ⎥= − −⎢ ⎥−⎢ ⎥⎣ ⎦

Step 2. The propagation is interrupted at the crossing points of the triplet/singlet surfaces. Hopping probability is computed with the Landau-Zener (or ZN) Model.

Hso is assumed to be 70 cm-1 based on CASSCF calculations.

Results (E=0.56 eV)141 reactive, integrated for 3.4 ps (almost all initial triplet adducts have decayed)Singlet branching: 70% Experimental value: 55%

H+CH2CHOCH3+CHO CH2+CH2O H2+CH2CO H+CH3CO

Extrap(%) 0.560.43±.09

0.040.16±.08

0.160.27±.06

0.220.13±.03

0.020.01±.005Expt

(methyl) (methylene) (vinoxy) (ketene) (acetyl)

Simulations are hyperthermal energies (few eV) lead to shorter intermediate complex lifetimes, less ISC. Also, dominant products are allowed on triplet state.

QM Part

~

O + SAM modelling using QM/MMHyperthermal collisions: Diego Troya and George C. Schatz, J. Chem. Phys., 120, 7696 (2004)

MM Part

Thermal energies: G. Li, S. B. M. Bosio and W. L. Hase, J. Mol. Struct 556, 43 (2000)

VTotal = VMM(all) + VQM(QM) – VMM(QM)

VQM = MSINDO

VMM=TINKER (MM2)

θ, φ 30º, 0º 30º, 180º 45º, 0º 45º, 180º 60º, 0º 60º, 180ºInelastic 0.51 0.35 0.42 0.52 0.40 0.72 H abstraction 0.38 0.40 0.38 0.29 0.25 0.20 H elimination 0.08 0.18 0.13 0.10 0.32 0.05C-C breakage 0.02 0.05 0.01 0.07 0.02 0.03H2O 0.01 0.02 0.06 0.02 0.01

O(3P)+hydrocarbon self-assembled monolayersInelastic and reaction probabilities at Ecoll=5 eV

Tiltangle

60°

45°30°30°45°

60°φ=0°φ=180°

Surf

ace

norm

al

Chai

n ve

ctor

O + Squalane (C30H62)

• Highly branched hydrocarbon– 8 Pri., 16 Sec., 6 Tert. carbons

• Extremely low vapor pressure– Boiling point : 210 - 215 °C at 1 Torr

• Density : 0.809 g/cm-3

Dongwook Kim and GCS, J. Phys. Chem. A 111, 5019 (2007).

Crossed molecular beams studies of hyperthermaloxygen collisions (T. Minton)

MD simulation of bulk liquid• To obtain surface structure of liquid squalane• 48 squalane molecules• Tinker with OPLS-AA force field

– OPLS-AA : 0.796 g/cc at 298 K– MM3 : 0.696 g/cc at 298 K

1.2 ns at 400K and 0.6 ns at 298KIn NPT ensemble

0.6 ns at 400K and 2 ns at 298KIn NVT ensemble

Collision Model• Translational energy of atom O[3P]

: 5 eV

• 3 incident angles (θ): 30 °, 45 °, 60 °

• 4 azimuthal angles (φ)

: 0 °, 90 °, 180 °, 270 °

• Calculation time : 3 ~ 5 ps

5 Å

5 Å

13 Å

15 Å

30°45°

60°

Fixed atoms (~3000)

Moving atoms (~2000)

QM/MM Direct Dynamics with Dynamic Allocation of Atoms

• Dynamic allocation of QM region– Spherical QM region around seed atoms. Seeds are typically

radicals, and these can be added or subtracted as system evolves.

– Forces are discontinuously switched when atoms move into/out of QM regions. Switching only occurs where atoms are close to equilibrium.

– Size of QM sphere can be increased to insure convergence

VTotal = VMM(all) + VQM(QM) – VMM(QM)

VQM = MSINDO

VMM=TINKER (OPLS)

t = 20 a.u. t = 350 a.u. t = 500 a.u.

t = 2000 a.u. t = 1500 a.u.t = 750 a.u.

QM/MM Calculations (QM calculations done with MSINDO)

OH formation H elimination CH3O formation

Product Branching

0

0.1

0.2

0.3

0.4

O

OH

H2O H

C-C

cle

avag

e

etc O

OH

H2O H

C-C

cle

avag

e

etc O

OH

H2O H

C-C

cle

avag

e

etc

30° 45° 60°

Trapped

Gas phase

Reaction Statistics (IV) :Products of C-C cleavage

0

0.05

0.1

0.15

0.2

0.25

Prob

abili

ty

1 5 9 13 17 21 25 29

Number of Carbon

Alkyl Alkoxy

Summary• Direct dynamics provides useful simulation

tool for hyperthermal reactions, providing evidence for previously unsuspected reaction paths. Nonadiabatic processes sometimes important.

• QM/MM simulations can be extended to gas/liquid collisions. Hyperthermal dynamics can be done with cheap electronic structure methods.