John Steven Ewa Xuefei Tao JingjingAlecu Mielke Papajak Xu Yu Zheng
Annual ReportCombustion Energy
Frontier Research CenterPrinceton, NJSept. 23, 2010
Truhlar groupUniversity of Minnesota
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.
Effect of conformational entropy and torsional anharmonicity on the butanol partition function
8
12
16
20
24
28
32
0 500 1000 1500 2000 2500 3000
QM
S/Q
HO
T (K)
MS-HOMS-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.
27 structures
1-pentyl radical
5
7
9
11
13
15
0 1000 2000 3000
QM
S/Q
HO
T (K)
MS-HO
MS-T
Ratio of the conformational-rovibrational partition function of 1-pentyl radical calculated by the multi-structural method to that calculated by the single-structure HO approximation at the global minimum.
Equations: Multi-structural torsion method
Qcon-rovibMS-T = Qrot, j exp −βU j( )
j=1
J∑ Qj
HOZ j f j,ττ=1
t∏
f j,τ =ω j,τ 2πβI j,τ
M j,τexp(−βI j,τω j,τ
2 / M j,τ2 )I0(βI j,τω j,τ
2 / M j,τ2 )
Z j =gQrot, jQj
HO + (1− g)Qjimp
Qrot, jQjHO =
Qjimp = Qrot, jQj
HOZ jintZ j
coup
Z jint =
ω j,m−1
m=1
F−t∏ ω j,τ
−1
τ=1
t∏
ω j,m−1
m=1
F∏
Z jcoup =
det S j
det I jrot I j,τ
τ=1
t∏
1/2
g = tanhq j,τ
FR
Pj,τq j,τCHO
τ=1
t∏
1/ t
For other slides in this presentation, Zj is not included yet.
number of structures number of torsions
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 structuresProduct: 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
A practical approach to compute the rate constant
tunneling based on a single reaction path (ground-state
transmission coefficient)
k = κG(T )˜ k Th
mins
Q1GT,HO(T ,s)
Qcon−rovib‡,MS−T (T )
Q1‡,HO(T )
Qcon−rovibR,MS−T exp −V (s)/ ˜ k T( )
separable multi-structure anharmonicity factor
Multi-configuration Shepard Interpolation:
PES of 1-pentyl and 2-pentyl by MM3 force field 9 Shepard-points (energy, gradient, Hessian) by M06 functional
Reaction path for variational effects and tunneling
T (K) FR F‡ FP
300 6.8 2.0 11.0
600 10.0 2.2 14.1
1000 11.9 2.2 14.0
1500 12.9 2.0 11.9
2000 11.7 1.9 9.6
Multi-structure anharmonicity factors FMS-T
for reactant, TS, and product
-2 -1 0 1 2
85
90
95
100
105
110
s (bohr)
V aG
(kca
l/mol
)
0 1 2 3 4 5
-4
0
4
8
Calulated rate constant based on MS-VTST
Yamauchi et al. 1999 Miyoshi et al. 2002
1000/T (K-1)
logk
(s-1)
The 1, 4-Hydrogen Shift Isomerization of the 1-Pentyl Radical(cont.)
For this slide, Zj is not included yet.
The Reactions: CH3OH + HO2 → CH2OH + HOOH (R1a)
→ CH3O + HOOH (R1b)
CH3OH + CH3 → CH2OH + CH4 (R2a) → CH3O + CH4 (R2b)
John Alecu’s poster
Rel
ativ
e En
ergy
(kca
l mol
-1)
9.89
18.29
0.00
23.65
18.99
CH3OH + HO2
CCSDT(2)Q/CBS(aT+aQ) + CV + Rand experiment.
Rel
ativ
e En
ergy
(kca
l mol
-1)
-8.76
13.69
0.00
13.85
0.34
CH3OH + CH3
CCSDT(2)Q/CBS(aT+aQ) + CV + Rand experiment.
Accuracy vs. cost
• all calculations based on geometries optimized with M06-2X/MG3S• single-processor CPU time relative to equivalent HF/cc-pVDZ calculation
Electronic Model ChemistryMean Unsigned Error (MUE)
(kcal mol-1)∆E V‡ Average Cost
N9
CCSDT(2)Q/CBS(aT+aQ) + CV + R 0.3 0 (by def.) 78,000N8
CCSDT/CBS(T+Q) + CV + R 0.1 0.2 0.1 16,000N7
CCSD(T)-F12b/aug-cc-pVTZ 0.2 0.3 0.2 4,900CCSD(T)/CBS(D+T) 0.2 0.5 0.4 900
CBS-QB3 0.2 1.2 0.9 48MCG3-MPW 0.3 0.6 0.5 39
N6
BMC-CCSD 1.0 0.4 0.6 19N4
M08-HX/maug-cc-pVTZ 0.5 0.8 0.7 43
M08-HX/ma-TZVP 1.0 0.8 0.8 25
scaling
Fitting rate constantsConventional model
k = A T300 K
n
exp −E /RT( )
k = A T300 K
n
exp −E T +T0( )
R T 2 +T02( )
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 mechanisms
New modelproposed in J. Zheng and D. G. Truhlar, PCCP 12, 7782 (2010).