“Van der Waals” Wells are Important in Chemical Reactions University of Florida, QTP Nov. 6,...
-
Upload
wendy-bridges -
Category
Documents
-
view
218 -
download
0
Transcript of “Van der Waals” Wells are Important in Chemical Reactions University of Florida, QTP Nov. 6,...
![Page 1: “Van der Waals” Wells are Important in Chemical Reactions University of Florida, QTP Nov. 6, 2002 Acknowledgments : Dunyou Wang (now at NASA/Ames), Tiao.](https://reader035.fdocuments.net/reader035/viewer/2022062423/5697c0281a28abf838cd7170/html5/thumbnails/1.jpg)
“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
![Page 2: “Van der Waals” Wells are Important in Chemical Reactions University of Florida, QTP Nov. 6, 2002 Acknowledgments : Dunyou Wang (now at NASA/Ames), Tiao.](https://reader035.fdocuments.net/reader035/viewer/2022062423/5697c0281a28abf838cd7170/html5/thumbnails/2.jpg)
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.
![Page 3: “Van der Waals” Wells are Important in Chemical Reactions University of Florida, QTP Nov. 6, 2002 Acknowledgments : Dunyou Wang (now at NASA/Ames), Tiao.](https://reader035.fdocuments.net/reader035/viewer/2022062423/5697c0281a28abf838cd7170/html5/thumbnails/3.jpg)
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
![Page 4: “Van der Waals” Wells are Important in Chemical Reactions University of Florida, QTP Nov. 6, 2002 Acknowledgments : Dunyou Wang (now at NASA/Ames), Tiao.](https://reader035.fdocuments.net/reader035/viewer/2022062423/5697c0281a28abf838cd7170/html5/thumbnails/4.jpg)
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
![Page 5: “Van der Waals” Wells are Important in Chemical Reactions University of Florida, QTP Nov. 6, 2002 Acknowledgments : Dunyou Wang (now at NASA/Ames), Tiao.](https://reader035.fdocuments.net/reader035/viewer/2022062423/5697c0281a28abf838cd7170/html5/thumbnails/5.jpg)
G3 Success
Cl + H2Cl + D2
![Page 6: “Van der Waals” Wells are Important in Chemical Reactions University of Florida, QTP Nov. 6, 2002 Acknowledgments : Dunyou Wang (now at NASA/Ames), Tiao.](https://reader035.fdocuments.net/reader035/viewer/2022062423/5697c0281a28abf838cd7170/html5/thumbnails/6.jpg)
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)
![Page 7: “Van der Waals” Wells are Important in Chemical Reactions University of Florida, QTP Nov. 6, 2002 Acknowledgments : Dunyou Wang (now at NASA/Ames), Tiao.](https://reader035.fdocuments.net/reader035/viewer/2022062423/5697c0281a28abf838cd7170/html5/thumbnails/7.jpg)
Contour Plot of G3 Surface
Cl
H
H
R
r
Jacobi Coordinates
![Page 8: “Van der Waals” Wells are Important in Chemical Reactions University of Florida, QTP Nov. 6, 2002 Acknowledgments : Dunyou Wang (now at NASA/Ames), Tiao.](https://reader035.fdocuments.net/reader035/viewer/2022062423/5697c0281a28abf838cd7170/html5/thumbnails/8.jpg)
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) 540 (BW)
stretching: 1358 (G3) 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
T-shape equilibrium geometry.
![Page 9: “Van der Waals” Wells are Important in Chemical Reactions University of Florida, QTP Nov. 6, 2002 Acknowledgments : Dunyou Wang (now at NASA/Ames), Tiao.](https://reader035.fdocuments.net/reader035/viewer/2022062423/5697c0281a28abf838cd7170/html5/thumbnails/9.jpg)
G3 surface and Bian-Werner surfaces
![Page 10: “Van der Waals” Wells are Important in Chemical Reactions University of Florida, QTP Nov. 6, 2002 Acknowledgments : Dunyou Wang (now at NASA/Ames), Tiao.](https://reader035.fdocuments.net/reader035/viewer/2022062423/5697c0281a28abf838cd7170/html5/thumbnails/10.jpg)
Theory and ExperimentManolopoulos Science (1999)
![Page 11: “Van der Waals” Wells are Important in Chemical Reactions University of Florida, QTP Nov. 6, 2002 Acknowledgments : Dunyou Wang (now at NASA/Ames), Tiao.](https://reader035.fdocuments.net/reader035/viewer/2022062423/5697c0281a28abf838cd7170/html5/thumbnails/11.jpg)
G3 and BW surfaces
Cl H D
H
D
Cl
Prob to form HCl reduced
On BW relative to G3
![Page 12: “Van der Waals” Wells are Important in Chemical Reactions University of Florida, QTP Nov. 6, 2002 Acknowledgments : Dunyou Wang (now at NASA/Ames), Tiao.](https://reader035.fdocuments.net/reader035/viewer/2022062423/5697c0281a28abf838cd7170/html5/thumbnails/12.jpg)
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
![Page 13: “Van der Waals” Wells are Important in Chemical Reactions University of Florida, QTP Nov. 6, 2002 Acknowledgments : Dunyou Wang (now at NASA/Ames), Tiao.](https://reader035.fdocuments.net/reader035/viewer/2022062423/5697c0281a28abf838cd7170/html5/thumbnails/13.jpg)
The O(3P)+HCl Reaction
A challenging reaction, non-linearsaddle point, ‘heavy-light-heavy’ system.
H. Koizumi, G. C. Schatz, and M. S. Gordon, J . Chem. Phys. (1991).
W. H. Thompson 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 werenot converged so later calcs showed disagreement withExperiment - barrier height too small. New surface ‘S4’by Ramuchandran, barrier height is higher than KSG, but ...
![Page 14: “Van der Waals” Wells are Important in Chemical Reactions University of Florida, QTP Nov. 6, 2002 Acknowledgments : Dunyou Wang (now at NASA/Ames), Tiao.](https://reader035.fdocuments.net/reader035/viewer/2022062423/5697c0281a28abf838cd7170/html5/thumbnails/14.jpg)
RATE CONSTANT FOR O(RATE CONSTANT FOR O(33P)+ HCl ON S4 P)+ HCl ON S4
S.Z.B.A.T.L.R.G.L JPC (2001)
1
10
100
1000
104
1.0 1.5 2.0 2.5 3.0 3.5 4.0
Smith
Fontijn QM/JS - S4QM/JS - KSG
ICVT/ μ - 4OMT S
(k cm
3
/ - ) 10molec sec X
16
1000/ ( )T deg K
![Page 15: “Van der Waals” Wells are Important in Chemical Reactions University of Florida, QTP Nov. 6, 2002 Acknowledgments : Dunyou Wang (now at NASA/Ames), Tiao.](https://reader035.fdocuments.net/reader035/viewer/2022062423/5697c0281a28abf838cd7170/html5/thumbnails/15.jpg)
The exact expression for k(T)
k(T)=1
hQreactdEN(E)exp(−E/kBT)
0
∞∫
N(E) = (2J + 1) P
,i f
,J K
,i f
∑
K = − J
J
∑
J = 0
∑ ( )E
P
,i f
,J K
( )E = | S
i, f
J, K
(E) |
2
N(E) is the Cumulative Reaction Probability
![Page 16: “Van der Waals” Wells are Important in Chemical Reactions University of Florida, QTP Nov. 6, 2002 Acknowledgments : Dunyou Wang (now at NASA/Ames), Tiao.](https://reader035.fdocuments.net/reader035/viewer/2022062423/5697c0281a28abf838cd7170/html5/thumbnails/16.jpg)
NTST(E)= (2J+1)
J =0∑ θ
n=0∑
K=−J
J∑ (E-En,J,K
TS )
En,J,KTS = V0+Evib
TS+EJ,KTS
(Variational) Transition State Theory
‡
![Page 17: “Van der Waals” Wells are Important in Chemical Reactions University of Florida, QTP Nov. 6, 2002 Acknowledgments : Dunyou Wang (now at NASA/Ames), Tiao.](https://reader035.fdocuments.net/reader035/viewer/2022062423/5697c0281a28abf838cd7170/html5/thumbnails/17.jpg)
TST Derivation
k(T)=1
hQreactdEN(E)exp(−E/kBT)
0
∞∫
kTST(T)=kBT
hQTS
Qreactexp[−(V0+E0
TS)/kBT]
NTST(E)= (2J+1)
J =0∑ θ
n=0∑
K=−J
J∑ (E-En,J,K
TS )
En,J,KTS = V0+Evib
TS+EJ,KTS
![Page 18: “Van der Waals” Wells are Important in Chemical Reactions University of Florida, QTP Nov. 6, 2002 Acknowledgments : Dunyou Wang (now at NASA/Ames), Tiao.](https://reader035.fdocuments.net/reader035/viewer/2022062423/5697c0281a28abf838cd7170/html5/thumbnails/18.jpg)
POTENTIALS FOR O(POTENTIALS FOR O(33P)+ HCl REACTIONP)+ HCl REACTION
![Page 19: “Van der Waals” Wells are Important in Chemical Reactions University of Florida, QTP Nov. 6, 2002 Acknowledgments : Dunyou Wang (now at NASA/Ames), Tiao.](https://reader035.fdocuments.net/reader035/viewer/2022062423/5697c0281a28abf838cd7170/html5/thumbnails/19.jpg)
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 coordinates.
O-HCl Cl-OH
Saddle Point vdW Well Saddle Point vdW Well
R 4.56 6.22 4.50 4.21
r 2.66 2.46 2.42 1.90
γ 23.4 0. 0 26.3 74.8
![Page 20: “Van der Waals” Wells are Important in Chemical Reactions University of Florida, QTP Nov. 6, 2002 Acknowledgments : Dunyou Wang (now at NASA/Ames), Tiao.](https://reader035.fdocuments.net/reader035/viewer/2022062423/5697c0281a28abf838cd7170/html5/thumbnails/20.jpg)
The O(3P)+HCl Reaction
O H Cl
O HCl
O H
Cl
-1.6
9.8 kcal
-5.2
![Page 21: “Van der Waals” Wells are Important in Chemical Reactions University of Florida, QTP Nov. 6, 2002 Acknowledgments : Dunyou Wang (now at NASA/Ames), Tiao.](https://reader035.fdocuments.net/reader035/viewer/2022062423/5697c0281a28abf838cd7170/html5/thumbnails/21.jpg)
The O(3P)+HCl Reaction
0.0
1.0
2.0
3.0
4.0
5.0
6.0
0.3 0.4 0.5 0.6 0.7 0.8
KSG
S4
CRP (J=0)
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,fi,f∑ (E )
![Page 22: “Van der Waals” Wells are Important in Chemical Reactions University of Florida, QTP Nov. 6, 2002 Acknowledgments : Dunyou Wang (now at NASA/Ames), Tiao.](https://reader035.fdocuments.net/reader035/viewer/2022062423/5697c0281a28abf838cd7170/html5/thumbnails/22.jpg)
The O(3P)+HCl ReactionXie, Wang, Bowman, Manolopoulos (2002)
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
0.24 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40
CRP (J = 0)
E (eV)
1
3
4
2
5
6
7
8
9
![Page 23: “Van der Waals” Wells are Important in Chemical Reactions University of Florida, QTP Nov. 6, 2002 Acknowledgments : Dunyou Wang (now at NASA/Ames), Tiao.](https://reader035.fdocuments.net/reader035/viewer/2022062423/5697c0281a28abf838cd7170/html5/thumbnails/23.jpg)
The O(3P)+HCl Reaction
0.000
0.005
0.010
0.015
0.020
0.2358480 0.2358485 0.2358490 0.2358495 0.2358500
Resonance 1
CRP
E (eV)
![Page 24: “Van der Waals” Wells are Important in Chemical Reactions University of Florida, QTP Nov. 6, 2002 Acknowledgments : Dunyou Wang (now at NASA/Ames), Tiao.](https://reader035.fdocuments.net/reader035/viewer/2022062423/5697c0281a28abf838cd7170/html5/thumbnails/24.jpg)
The O(3P)+HCl Reaction
Bound states
Quasi-bound states
![Page 25: “Van der Waals” Wells are Important in Chemical Reactions University of Florida, QTP Nov. 6, 2002 Acknowledgments : Dunyou Wang (now at NASA/Ames), Tiao.](https://reader035.fdocuments.net/reader035/viewer/2022062423/5697c0281a28abf838cd7170/html5/thumbnails/25.jpg)
Resonances and density of states
Resonances are therefore like bound states in some respects, or bound states are resonances with zero widths.
Eth
![Page 26: “Van der Waals” Wells are Important in Chemical Reactions University of Florida, QTP Nov. 6, 2002 Acknowledgments : Dunyou Wang (now at NASA/Ames), Tiao.](https://reader035.fdocuments.net/reader035/viewer/2022062423/5697c0281a28abf838cd7170/html5/thumbnails/26.jpg)
Resonances and lifetimes
Ψn(t)=ψ ne−iEnt / h =ψ ne
−i(Ern−iΓn2
)t/ h
=ψ ne−iErnt/ h
e−
Γn2
t / h
Pn(t)=Pn(0)e−Γnt/ h
The more conventional relationship is givenas follows:
This is unimolecular decay of an (isolated) resonance,with a decay rate equal to Γ / h
![Page 27: “Van der Waals” Wells are Important in Chemical Reactions University of Florida, QTP Nov. 6, 2002 Acknowledgments : Dunyou Wang (now at NASA/Ames), Tiao.](https://reader035.fdocuments.net/reader035/viewer/2022062423/5697c0281a28abf838cd7170/html5/thumbnails/27.jpg)
The (quasi) bound state approach
Resonances are quasibound eigenstates
with complex energy eigenvalues, Er,n-i n /2
HC = H - iU(R)
-0.02
0.00
0.02
0.04
0.06
0.08
0.10
0.12
2.0 3.0 4.0 5.0 6.0 7.0 8.0
F00
(R)
R (bohr)
x 200
0
5
10
15
20
25
30
2.0 3.0 4.0 5.0 6.0
HN2 -> H+N
2
Vmin
(R)
R (bohr)
![Page 28: “Van der Waals” Wells are Important in Chemical Reactions University of Florida, QTP Nov. 6, 2002 Acknowledgments : Dunyou Wang (now at NASA/Ames), Tiao.](https://reader035.fdocuments.net/reader035/viewer/2022062423/5697c0281a28abf838cd7170/html5/thumbnails/28.jpg)
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 was 0.001 to 0.5 h, in
steps of 0.01 h.
![Page 29: “Van der Waals” Wells are Important in Chemical Reactions University of Florida, QTP Nov. 6, 2002 Acknowledgments : Dunyou Wang (now at NASA/Ames), Tiao.](https://reader035.fdocuments.net/reader035/viewer/2022062423/5697c0281a28abf838cd7170/html5/thumbnails/29.jpg)
Quasibound State calculations
O-HCl well Cl-OH well(vR, ν, νr) Ener (gy eV) (vR, ν, νr) Ener (gy eV)
(1,6, 0) 0.2 361 (5,0, 0) 0.1 939
(0,7, 0) 0.2 496 (2,1, 0) 0.2 040
(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
![Page 30: “Van der Waals” Wells are Important in Chemical Reactions University of Florida, QTP Nov. 6, 2002 Acknowledgments : Dunyou Wang (now at NASA/Ames), Tiao.](https://reader035.fdocuments.net/reader035/viewer/2022062423/5697c0281a28abf838cd7170/html5/thumbnails/30.jpg)
Resonance Peak position Quasibound state energy
O-HCl well Cl-OH well
1 0.2359 0.2361 0.2355
2 0.2417 0.2414
3 0.2497 0.2496
4 0.2584 0.2580
5 0.2755 0.2750 0.2751
6 0.2923 0.2935
7 0.3113 0.3110
8 0.3252 0.3243
9 0.3761 0.3787
Comparison of resonance energies and quasiboundState energies of VdW wells (eV)
![Page 31: “Van der Waals” Wells are Important in Chemical Reactions University of Florida, QTP Nov. 6, 2002 Acknowledgments : Dunyou Wang (now at NASA/Ames), Tiao.](https://reader035.fdocuments.net/reader035/viewer/2022062423/5697c0281a28abf838cd7170/html5/thumbnails/31.jpg)
Comparison of resonance energies and quasiboundstate energies of VdW wells (eV)
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
Overlap = quasibound density in the saddle point region
![Page 32: “Van der Waals” Wells are Important in Chemical Reactions University of Florida, QTP Nov. 6, 2002 Acknowledgments : Dunyou Wang (now at NASA/Ames), Tiao.](https://reader035.fdocuments.net/reader035/viewer/2022062423/5697c0281a28abf838cd7170/html5/thumbnails/32.jpg)
Assignment of resonances
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
0.24 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40
CRP (J = 0)
E (eV)
O
Cl
Cl
Cl
O
Cl
O
OCl
![Page 33: “Van der Waals” Wells are Important in Chemical Reactions University of Florida, QTP Nov. 6, 2002 Acknowledgments : Dunyou Wang (now at NASA/Ames), Tiao.](https://reader035.fdocuments.net/reader035/viewer/2022062423/5697c0281a28abf838cd7170/html5/thumbnails/33.jpg)
Quasibound state wavefunctions
4 6 8 10
150
120
90
60
30
R (bohr)
gamma (deg)
4 6 8 10
3.0
2.5
2.0
R (bohr)
r (bohr)
O-HCl state at 0.2496 eV
![Page 34: “Van der Waals” Wells are Important in Chemical Reactions University of Florida, QTP Nov. 6, 2002 Acknowledgments : Dunyou Wang (now at NASA/Ames), Tiao.](https://reader035.fdocuments.net/reader035/viewer/2022062423/5697c0281a28abf838cd7170/html5/thumbnails/34.jpg)
Quasibound state wavefunctions
Cl-HO state at 0.2414 eV
4 5 6 7
150
120
90
60
30
R (bohr)
gamma (deg)
4 5 6 7
3.5
3.0
2.5
2.0
1.5
R (bohr)
r (bohr)
![Page 35: “Van der Waals” Wells are Important in Chemical Reactions University of Florida, QTP Nov. 6, 2002 Acknowledgments : Dunyou Wang (now at NASA/Ames), Tiao.](https://reader035.fdocuments.net/reader035/viewer/2022062423/5697c0281a28abf838cd7170/html5/thumbnails/35.jpg)
CONCLUSIONSCONCLUSIONS
Resonances in the tunneling region due toVan der Waals minima.
Important effect on k(T) - increasing, why?a) Resonances “prepare complexes”b) Non-adiabaticity?
Recall
Question bend zpe. Do wells destroy bending Adiabaticity?
En,J,KTS = V0+Evib
TS+EJ,KTS
![Page 36: “Van der Waals” Wells are Important in Chemical Reactions University of Florida, QTP Nov. 6, 2002 Acknowledgments : Dunyou Wang (now at NASA/Ames), Tiao.](https://reader035.fdocuments.net/reader035/viewer/2022062423/5697c0281a28abf838cd7170/html5/thumbnails/36.jpg)
Other examplesOther examples
![Page 37: “Van der Waals” Wells are Important in Chemical Reactions University of Florida, QTP Nov. 6, 2002 Acknowledgments : Dunyou Wang (now at NASA/Ames), Tiao.](https://reader035.fdocuments.net/reader035/viewer/2022062423/5697c0281a28abf838cd7170/html5/thumbnails/37.jpg)
OH+HNO3
Negative T-dependence
indicates fairly complex
and positive T-dependence
indicates a barrier, as usual.