Nonadiabatic Reactions

Transcription

1 IMA Workshop: Chemical Dynamics, Jan , 2009 Nonadiabatic Reactions reactant product 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) 3. Hybrid methods (QM + MM) Trajectory surface hopping Tully s fewest switches TSH method 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) Electronic motions: Time-dependent Schrödinger equation Nuclear motions: Classical mechanics on a single Born Oppenheimer surface at any time Switch electronic state: Probabilistic fewest switches algorithm Velocity has to be adjusted after electronic state switching to conserve energy

2 Nonadiabatic dynamics in an adiabatic basis G. C. Schatz, L. A. Pederson and P. J. Kuntz, Far. Disc. Chem. Soc. 108, , (1997) 2 Hopping probability Φ(R,t) = c k(t) Ψk(t) k= 1 t ĉ k(t) = c k(t)exp i E k(t)dt / 0 dcˆ 1 dt dcˆ dt 2 Energy conservation: ETot = T1 + E1 = T2 + E2 HΨ t. = (R i d 12)c ˆ 2(t)exp i (E 1(t) E 2(t))dt / 0. t = (R i d ˆ 12)c 1(t)exp i (E 2(t) E 1(t))dt / 0 d = Ψ Ψ = 12 1 R 2 Ψ H Ψ 1 R 2 E E 2 1 = E Ψ k k k Issues with Fewest Switches 1. What to do if hop is forbidden 2. Adiabatic versus diabatic basis (or in-between) 3. How to determine derivative coupling or spin-orbit coupling matrix elements 4. 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.

3 Example application: S( 3 P) + H 2 SH + H Reaction The importance of intersystem crossing in the S( 3 P, 1 D) + H 2 SH + H reaction, Biswajit Maiti, G. C. Schatz and G. Lendvay, J. Phys. Chem. A, 108, (2004). Significant nonadiabatic effects in the S( 1 D) + HD reaction, Tian-Shu Chu, Ke-Li Han and George C. Schatz, J. Phys. Chem. A 111, (2007). Trajectory studies of gas/liquid reactions George C. Schatz Northwestern University

4 Gas/liquid dynamics research Dongwook Kim Brian Radak Wenfang Hu Scott Yockel T. Minton, Montana State Related work: Nesbitt, McKendrick, Tully, Hase Modeling the collision of reactive atoms with liquid surfaces 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. Hyperthermal Chemistry Gas phase reactions: O + C 2 H 6, O + C 2 H 4 Model hyperthermal O, F interacting with polymers O, F + squalane Novel (hypergolic) fuels Combustion involving ionic liquids O+[Emim][NO 3 ]

5 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, Polymer degradation in LEO Spacecraft surfaces made of polymers erode in low Earth orbit (LEO) (~ km) due to 5 ev atomic oxygen J. W. Connell, High Perform Polym 12, 43 (2000)

6 Experiments at Montana State (Tim Minton) Crossed-molecular-beams apparatus coupled to a laser detonation source E coll ~ 80 to 100 kcal/mol PULSED VALVE O 2 SUPPLY LINE SOURCE CHAMBER NOZZLE CHOPPER WHEEL ROTATABLE DETECTOR TO ION COUNTING SYSTEM QUADRUPOLE MASS FILTER O C 2 H CO 2 LASER MIRROR DIFFERENTIAL PUMPING REGION PULSED VALVE ETHANE SUPPLY LINE APERTURE IONIZER SOURCE CHAMBER MAIN SCATTERING CHAMBER C 2 H 5 O CH 3 O OH C 2 H 5 v O v C2H6 Theoretical approaches to hyperthermal (several ev) dynamics problems 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

7 Experimental and Theoretical Investigations of the Inelastic and Reactive Scattering Dynamics of O( 3 P) Collisions with Ethane Donna Minton, Tim Minton, Wen-fang Wu and GCS JPC A to be submitted OH + C 2 H 5 product 90 kcal/mol H + C 2 H 5 O product 90 kcal/mol MSINDO B3LYP Exp

8 H + C 2 H 5 O product Branching between different products MSINDO B3LYP Exp

9 O( 3 P) + Ethylene Reaction: Product Branching and ISC Effects (Wenfang Hu, Biswajit Maiti, Diego Troya, G. Lendvay) O + C 2 H 4 CH 2 CHO+H CH 3 CO+H 3 CH 2 CO+H 2 1 CH 2 CO+H 2 CHO+CH 3 CH 2 O+ 3 CH 2 C 2 H 3 +OH (vinoxy) (acetyl) ( 3 ketene) ( 1 ketene) (methyl) (methylene) (abstraction) Experimental Product Branching OH+C 2 H 3 CH 3 +CHO CH 2 +CH 2 O H+CH 2 CHO H 2 +CH 2 CO H+CH 3 CO (abstraction) (methyl) (methylene) (vinoxy) (ketene) (acetyl) ΔH kcal/mol: Hunzinger(1981) ±0.04 Endo(1986) 0.50± ± ±0.10 Bley(1988) 0.44± ± ± Schmoltner(1989) 0.71± ±0.11 Casavecchia (2005) 0.43± ± ± ± ±0.01

10 O + C 2 H 4 Reaction O( 1 D)+C 2 H 4 C 2 H 3 +OH (abstr) O( 3 P)+C 2 H 4 CH 2 O+ 3 CH 2 (methylene) CH 2 CHO+H (vinoxy) 3 CH 3 CO+H (acetyl) CH 2 CH 2 O 3 CHO+CH 3 (methyl) CH 3 CHO 3 1 CH 2 CO+H CH 2 ( 2 CH 2 O 3 ketene) 1 CH 2 CO+H 2 ( 1 ketene) 1 CH 3 CHO Adapted from: Schmoltner, Chu, Brudzynski and Y. T. Lee, J. Chem. Phys. 91(6926)1989 Methodology On the fly quasiclassical trajectory surface hopping (QCTSH) method Step 1. QCT trajectories are initiated and propagated on one of the adiabatic potential surfaces (UB3LYP/6-31G**) 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. 2 2πHSO PLZ = 1 exp dh dh Z dz dz H so is assumed to be 70 cm -1 based on CASSCF calculations.

11 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% (methyl) (methylene) (vinoxy) (ketene) (acetyl) CH 3 +CHO CH 2 +CH 2 O H+CH 2 CHO H 2 +CH 2 CO H+CH 3 CO Extrap(%) Expt 0.43± ± ± ± ±.005 Simulations are hyperthermal energies (few ev) lead to shorter intermediate complex lifetimes, less ISC. Also, dominant products are allowed on triplet state. O + SAM modelling using QM/MM Hyperthermal collisions: Diego Troya and George C. Schatz, J. Chem. Phys., 120, 7696 (2004) Thermal energies: G. Li, S. B. M. Bosio and W. L. Hase, J. Mol. Struct 556, 43 (2000) V Total = V MM (all) + V QM (QM) V MM (QM) V QM = MSINDO V MM =TINKER (MM2) QM Part ~ MM Part

12 O( 3 P)+hydrocarbon self-assembled monolayers Inelastic and reaction probabilities at E coll =5 ev θ, φ 30º, 0º 30º, 180º 45º, 0º 45º, 180º 60º, 0º 60º, 180º Inelastic H abstraction H elimination C-C breakage H 2 O φ= φ=0 Surface normal Tilt angle Chain vector O + Squalane (C 30 H 62 ) Dongwook Kim and GCS, J. Phys. Chem. A 111, 5019 (2007). Highly branched hydrocarbon 8 Pri., 16 Sec., 6 Tert. carbons Extremely low vapor pressure Boiling point : C at 1 Torr Density : g/cm -3

13 Crossed molecular beams studies of hyperthermal oxygen 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 : g/cc at 298 K MM3 : g/cc at 298 K 1.2 ns at 400K and 0.6 ns at 298K In NPT ensemble 0.6 ns at 400K and 2 ns at 298K In NVT ensemble

14 Translational energy of atom O[ 3 P] : 5 ev 3 incident angles (θ) : 30, 45, 60 Collision Model azimuthal angles (φ) 13 Å : 0, 90, 180, 270 Calculation time : 3 ~ 5 ps 15 Å Moving atoms (~2000) 5 Å Fixed atoms (~3000) 5 Å 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 V Total = V MM (all) + V QM (QM) V MM (QM) V QM = MSINDO V MM =TINKER (OPLS)

15 QM/MM Calculations (QM calculations done with MSINDO) t = 20 a.u. t = 350 a.u. t = 500 a.u. t = 2000 a.u. t = 1500 a.u. t = 750 a.u. OH formation H elimination CH 3 O formation

16 Product Branching Trapped Gas phase 0 O OH H2O H C-C cleavage etc O OH H2O H C-C cleavage etc O OH H2O H C-C cleavage etc Reaction Statistics (IV) : Products of C-C cleavage 0.25 Alkyl Alkoxy 0.2 Probability Number of Carbon

17 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.