Annual Report Combustion Energy Frontier Research Center Princeton, NJ Sept. 23, Truhlar group University of Minnesota

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1 Annual Report Combustion Energy Frontier Research Center Princeton, NJ Sept. 23, 2010 Truhlar group University of Minnesota John Steven Ewa Xuefei Tao Jingjing Alecu Mielke Papajak Xu Yu Zheng

2 Practical methods for including torsional anharmonicity in thermochemical calculations on complex molecules We proposed a new approximation called the multi-structural method with torsional anharmonicity (MS-T) to calculate conformational-vibrational-rotational partition functions. It is applicable for molecules with multiple torsions coupled with overall rotation, each other, and/or with other low-frequency modes Assigning each torsion to a specific normal mode is not required. It has low computational cost, requiring no torsion barriers or scans.

3 Effect of conformational entropy and torsional anharmonicity on the butanol partition function structures Q MS /Q HO T (K) MS-HO MS-T Ratio of the conformational-rovibrational partition function of butanol calculated by the multi-structural method to that calculated by the single-structure HO approximation at the global minimum.

4 1-pentyl radical Q MS /Q HO MS-HO MS-T T (K) Ratio of the conformational-rovibrational partition function of 1-pentyl radical calculated by the multistructural method to that calculated by the singlestructure HO approximation at the global minimum.

5 Equations: Multi-structural torsion method number of structures MS-T Q con-rovib J ( ) HO = Q rot,j exp βu j Q j Z j f j,τ j=1 t τ=1 number of torsions f j,τ = ω j,τ 2πβI j,τ M j,τ 2 exp( βi j,τ ω j,τ / M 2 2 j,τ )I0 (βi j,τ ω j,τ / M 2 j,τ ) Z j = gq rot,j Q j HO + (1 g)q j imp Q rot,j Q j HO Q j imp = Qrot,j Q j HO Z j int Z j coup t g = τ=1 tanh = FR q j,τ CHO P j,τ q j,τ 1/t Z j int = F t m=1 1 ω j,m F 1 ω j,m m=1 coup det S j Z j = t rot det I j For other slides in this presentation, Z j is not included yet. t 1 ω j,τ τ=1 I j,τ τ=1 1/2

Reactant: 1-pentyl 4 torsions, 15 distinct structures Product: 2-pentyl 4 torsions, 7 distinct

6 The 1, 4-Hydrogen Shift Isomerization of the 1-Pentyl Radical Multistructural anharmonicty is dominated by torsions in the potential energy surface of the reaction. Reactant: 1-pentyl 4 torsions, 15 distinct structures Product: 2-pentyl 4 torsions, 7 distinct structures Transition state: 1 torsion, but 2 distinct structures (due to the ring inter-conversion) 1-pentyl 2-pentyl TS-1 TS-2

7 A practical approach to compute the rate constant k = κ G (T ) k T h min s,ms T GT,HO Q Q 1 (T,s) con rovib (T ),HO Q 1 (T ) R,MS T Q con rovib exp( V(s)/ k T) tunneling based on a single reaction path (ground-state transmission coefficient) separable multi-structure anharmonicity factor Reaction path for variational effects and tunneling Multi-configuration Shepard Interpolation: PES of 1-pentyl and 2-pentyl by MM3 force field 9 Shepard-points (energy, gradient, Hessian) by M06 functional

8 The 1, 4-Hydrogen Shift Isomerization of the 1-Pentyl Radical (cont.) Multi-structure anharmonicity factors F MS-T for reactant, TS, and product T (K) F R F F P V a G (kcal/mol) logk (s -1 ) s (bohr) 8 Calulated rate constant based on MS-VTST Yamauchi et al Miyoshi et al For this slide, Z j is not included yet /T (K -1 )

9 John Alecu s poster The Reactions: CH 3 OH + HO 2 CH 2 OH + HOOH (R1a) CH 3 O + HOOH (R1b) CH 3 OH + CH 3 CH 2 OH + CH 4 (R2a) CH 3 O + CH 4 (R2b)

10 CH 3 OH + HO 2 Relative Energy (kcal mol -1 ) CCSDT(2) Q /CBS(aT+aQ) + CV + R and experiment.

CH 3 OH + CH 3 Relative Energy (kcal mol -1 ) 13.69 0.00 13.

11 CH 3 OH + CH 3 Relative Energy (kcal mol -1 ) CCSDT(2) Q /CBS(aT+aQ) + CV + R and experiment.

Accuracy vs. cost Mean Unsigned Error (MUE) Electronic Model Chemistry (kcal mol -1 ) scaling E V Average Cost N 9 CCSDT(2) Q /CBS(aT+aQ) + CV + R 0.3 0 (by def.) 78,000 N 8 CCSDT/CBS(T+Q) + CV + R 0.

12 Accuracy vs. cost Mean Unsigned Error (MUE) Electronic Model Chemistry (kcal mol -1 ) scaling E V Average Cost N 9 CCSDT(2) Q /CBS(aT+aQ) + CV + R (by def.) 78,000 N 8 CCSDT/CBS(T+Q) + CV + R ,000 N 7 CCSD(T)-F12b/aug-cc-pVTZ ,900 CCSD(T)/CBS(D+T) CBS-QB MCG3-MPW N 6 BMC-CCSD N 4 M08-HX/maug-cc-pVTZ M08-HX/ma-TZVP all calculations based on geometries optimized with M06-2X/MG3S single-processor CPU time relative to equivalent HF/cc-pVDZ calculation

13 Fitting rate constants Conventional model T k = A 300 K n exp( E /RT) New model proposed in J. Zheng and D. G. Truhlar, PCCP 12, 7782 (2010). T k = A 300 K n exp E ( T +T 0) R T 2 2 +T 0 ( ) This new form may be a much better way to fit curved Arrhenius plots than the almost universally used first form. This could have significant effects on combustion mechanisms and the representation of rate data in such

Accurate Computed Rate Coefficients for the Hydrogen Atom Abstraction Reactions from Methanol and n-butanol by the Hydroperoxyl Radical.

Accurate Computed Rate Coefficients for the Hydrogen Atom Abstraction Reactions from Methanol and n-butanol by the Hydroperoxyl Radical John Alecu Second Annual CEFRC Conference August 17, 2011 Acknowledgments