Transcript PowerPoint Presentation - I. Metastable states matter in

“Van der Waals” Wells are Important
in Chemical Reactions
University of Florida, QTP Nov. 6, 2002
Acknowledgments:
Dunyou Wang (now at NASA/Ames), Tiao
Xie (Emory), David Manolopoulos (Oxford),
$$ from US Dept. of Energy
Cl + HD
D+HCl, H+DCl reaction
• Importance of this reaction
– It plays a central role in fundamental chemical kinetics, and
has served as a critical test case for bimolecular reaction
rate theory, especially transition-state and kinetic isotope
effect. And, the theory of isotope effects was derived from it.
– This reaction is also a prototype for a host of Cl reactions
that are in atmospheric chemistry and photochemical air
pollution.
– This reaction is the rate determining step in the mechanism
of the Cl2 + H2  2HCl chain reaction.
Studies of the Cl + H2 reaction
• Experimental studies:
– Rate constants for Cl + H2 and D2 reactions over the temperature
range 296-3000 K.
– Branching ratio of Cl + HD reaction has been studied in crossed
molecular beam experiment.
• Theoretical studies:
– Many potential energy surfaces have been constructed for this
reaction, among which, the G3 surface most successful one.
– VTST have been used to calculate rate constants on these
surfaces, and compared with experimental data. Truhlar and co.
– Quantum reactive scattering on G3 and a new pes
Manolopous, Werner and co-workers
The “G3” potential energy surface
• G3 surface was constructed by Truhlar et al. in 1996.
• It’s based on the so-called GQQ surface, which has been
shown to give good agreement with experiment on Cl + H2
and D2 reactions.
• G3 surface improves on the GQQ surface in the region of
Cl-H-H bending potential.
• Linear saddle point geometry:
RHCl (Å)
= 1.4011
RHH’ (Å)
= 0.9896
RH’Cl (Å)
= 2.3907
V (kcal/mol) = 7.88
G3 Success
Cl + H2
Cl + D2
Failure of the G3 surface
Branching ratio
determined in
cross-beam
experiment as a
function of
collision energy
for HD(j=0).
K. Liu (1999)
Collision energy (kcal/mol)
Contour Plot of G3 Surface
H
C
l

R
r
H
Jacobi
Coordinates
G3 surface and Bian-Werner surface
• BW and G3 surface are broadly similar
– Barrier height: (kcal/mol)
7.88 (G3)
7.61 (BW)
– Saddle point frequencies (cm-1)
bending:
581 (G3)
stretching:
1358 (G3)
540 (BW)
1360 (BW)
• Difference
– Imaginary frequency (cm-1)
1520i (G3)
1294i (BW)
This indicates that G3 surface has a thinner barrier.
– BW has a Van der Waals well with a depth of 0.5 kcal/mol at a Tshape equilibrium geometry.
G3 surface and Bian-Werner surfaces
Theory and Experiment
Manolopoulos Science (1999)
G3 and BW surfaces
Cl
H
D
D
Cl
H
Prob to form HCl reduced
On BW relative to G3
Conclusion
Van der Waals well (very shallow) in Cl+HD
has a significant effect on branching ratio
for Cl + HD(j=0) but not on rate constant
The O(3P)+HCl Reaction
A challenging reaction, non-linear
saddle point, ‘heavy-light-heavy’ system.
H. Koizumi, G. C. Schatz, and M. S. Gordon, J. Chem. Phys. (1991).
W. H. Thomp son and W.H. Miller, J. Chem. Phys. (1996).
O. I. Tolstkhin, K. Nobusada and H. Nakamura, J. Chem Phys. (1998)
F. J. Aoiz, L. Bañares, J. F. Castillo, M. Menèdez, and J. E.
Verdasco, PCCP (1999).
F. Matzkies and U. Manthe, J. Chem. Phys. (2000).
Barrier height of KSG adjusted down by KSG to get
agreement with exp on k(T). Those calculations were
not converged so later calcs showed disagreement with
Experiment - barrier height too small. New surface ‘S4’
by Ramuchandran, barrier height is higher than KSG, but ...
RATE CONSTANT FOR O(3P)+ HCl ON S4
4
16
10
Smith
Fontijn
QM/JS - S4
QM/JS - KSG
ICVT/ OMT - S4
100
3
k (cm /molec-sec)X10
1000
10
1
1.0
1.5
2.0
2.5
3.0
3.5
1000/T (deg K)
S.Z.B.A.T.L.R.G.L JPC (2001)
4.0
The exact expression for k(T)
k(T) 
1

dEN(E)exp(E/kBT)

hQreact 0
N(E) is the Cumulative Reaction Probability
J
J,K (E)
N(E)   (2J  1)   Pi,f
J0
K J i,f
J,K (E) | S J,K (E) |2
Pi,f
i,f
(Variational) Transition State Theory
‡
NTST(E)
J
(2J1) 
J 0
TS )
 (E-En,J,K
K  J n= 0
ETS
= V +ETS +ETS
n,J,K
0 vib J,K
TST Derivation
k(T) 
1

dEN(E)exp(E/kBT)

hQreact 0
NTST(E)
J
(2J1) 
J 0
TS )
 (E-En,J,K
K  J n= 0
ETS
= V +ETS +ETS
n,J,K
0 vib J,K
TS
k
T
Q
k TST(T) B
exp[(V0 +ETS
)/k
T]
B
0
h Qreact
POTENTIALS FOR O(3P)+ HCl REACTION
The O(3P)+HCl Reaction
Configuration (bohr and degrees) of the saddle point and the Van der
Waals minima in the appropriate set of Jacobi c oordinates.
O-HCl
Saddle Point
Cl-OH
vdW Well Saddle Point
vd W Well
R
4.56
6.22
4.50
4 .21
r
2. 66
2.46
2.42
1 .90

2 3.4
0.0
26.3
74.8
The O(3P)+HCl Reaction
O
H
Cl
9.8 kcal
-1.6
O
H
-5.2
Cl
O
H
Cl
The O(3P)+HCl Reaction
6.0
5.0
KSG
S4
CRP (J=0)
4.0
3.0
2.0
1.0
0.0
0.3
0.4
0.5
0.6
0.7
0.8
E (eV)
S. Skokov, T. Tsuchida, S. Nanbu, J. M. Bowman, and S. K. Gray, J Chem. Phys(2000).
K. Nobusada, H. Nakamura, Y. Lin, B. Ramachandran, J. Chem. Phys. (2000)
CRP(J=0) =
 Pi, f ( E )
i,f
The O(3P)+HCl Reaction
Xie, Wang, Bowman, Manolopoulos (2002)
10
10
0
7
-1
9
1
10
CRP (J = 0)
10
10
10
10
10
10
-2
4
5
-3
-4
8
2
6
-5
-6
3
-7
-8
0.24
0.26
0.28
0.30
0.32
E (eV)
0.34
0.36
0.38
0.40
The O(3P)+HCl Reaction
0.020
Resonance 1
CRP
0.015
0.010
0.005
0.000
0.2358480
0.2358485
0.2358490
E (eV)
0.2358495
0.2358500
The O(3P)+HCl Reaction
Quasi-bound states
Bound states
Resonances and density of states
Eth
Resonances are therefore like bound states in
some respects, or bound states are resonances
with zero widths.
Resonances and lifetimes
The more conventional relationship is given
as follows:
n

i(
E

i
)t /
rn
iE nt /
2
n ( t )   ne
  ne
n
 iEr n t /  2 t /
  ne
e
Pn ( t )  Pn ( 0 )en t /
This is unimolecular decay of an (isolated) resonance,
with a decay rate equal to  /
The (quasi) bound state approach
Resonances are quasibound eigenstates
with complex energy eigenvalues, Er,n-i n /2
HC = H - ilU(R)
30
0.12
HN -> H+N
25
2
0.10
2
0.08
F 00 (R)
15
V
min
(R)
20
10
0.06
0.04
x 200
0.02
0.00
5
-0.02
0
2.0
3.0
4.0
5.0
6.0
2.0
3.0
4.0
5.0
R (bohr)
R (bohr)
6.0
7.0
8.0
Quasibound State calculations
A primitive basis of twenty Legendre functions,
Eight vibrational functions of HCl for O+HCl
(range: 1.6 a0 to 3.3a0) and 8 OH vibrational functions
for Cl + OH (range 1.2a0 to 3.6a0) and
100 sine functions in R for each arrangement
Ranges of R are [3.4a0 ,10.2a0] for the O+HCl channel and
[3.2a0 , 8.0a0] for the C+lOH channel.
Length of the absorbing potential: 2.0a0
A contraction scheme was used to reduce the direct product
basis from to 16,000 to 4770.
400 of the real wavefunctions used to construct complex H-matrix.
The range of l was 0.001 to 0.5 h, in
steps of 0.01 h.
Quasibound State calculations
O-HCl well
(vR, , r)
Energy (eV)
Cl-OH well
(vR, , r)
Energy (eV)
(1,6,0)
0.2361
(5,0,0)
0.1939
(0,7,0)
0.2496
(2,1,0)
0.2040
(0,8,0)
0.2702
(6,0,0)
0.2124
(1,8,0)
0.2750
(3,1,0)
0.2246
(0,9,0)
0.2935
(0,2,0)
0.2355
(0,10,0)
0.3194
(4,1,0)
0.2414
(1,10,0)
0.3243
(1,2,0)
0.2580
(0,11,0)
0.3787
(2,2,0)
0.2751
(0,3,0)
0.3110
Comparison of resonance energies and quasibound
State energies of VdW wells (eV)
Resonance Peak position
Quasibound state energy
O-HCl w ell
1
0.2359
0.2361
2
0.2417
3
0.2497
4
0.2584
5
0.2755
0.2750
6
0.2923
0.2935
7
0.3113
8
0.3252
0.3243
9
0.3761
0.3787
Cl-OH w ell
0.2355
0.2414
0.2496
0.2580
0.2751
0.3110
Comparison of resonance energies and quasibound
state energies of VdW wells (eV)
Overlap = quasibound density in the saddle point region
Resonance
Probability
Width
VdW Well
Overlap
1
0.169E-01
0.001
O-HCl Cl-HO
1.2e-12 9 .3e-5
2
0.677E-04
1.02
Cl-HO
1.6e-6
3
0.405E-06
11.3
O-HCl
7.5e-12
4
0.331E-02
0.306
Cl-HO
6.0e-6
5
0.613E-03
5.65
O-HCl Cl-HO
1.7e-11 1 .2e-5
6
0.261E-04
66.5
O-HCl
7.0e-9
7
0.701E-01
0.677
Cl-HO
2.80e-4
8
0.220E-02
50.0
O-HCl
1.24e-8
9
0.377E-01
69.3
O-HCl
1.48e-6
Assignment of resonances
10
10
0
Cl
-1
O
Cl
10
CRP (J = 0)
10
10
10
10
10
10
-2
Cl
Cl
-3
-4
O
Cl
O
-5
-6
O
-7
-8
0.24
0.26
0.28
0.30
0.32
E (eV)
0.34
0.36
0.38
0.40
Quasibound state wavefunctions
O-HCl state at 0.2496 eV
150
3.0
r (bohr)
gamma (deg)
120
90
2.5
60
2.0
30
4
6
8
R (bohr)
10
4
6
8
R (bohr)
10
Quasibound state wavefunctions
Cl-HO state at 0.2414 eV
3.5
150
3.0
r (bohr)
gamma (deg)
120
90
2.5
2.0
60
30
1.5
4
5
6
R (bohr)
7
4
5
6
R (bohr)
7
CONCLUSIONS
Resonances in the tunneling region due to
Van der Waals minima.
Important effect on k(T) - increasing, why?
a) Resonances “prepare complexes”
b) Non-adiabaticity?
TS
= V +ETS +ETS
Recall En,J,K
0 vib J,K
Question bend zpe. Do wells destroy bending
Adiabaticity?
Other examples
OH+HNO3
Negative T-dependence
indicates fairly complex
and positive T-dependence
indicates a barrier, as
usual.