A global ab initio-based potential energy
surface for of H5+, vibrational zero-point,
and reaction dynamics of H3+ + HD
JMB, Bas Braams, Zhen Xie,
Emory University,
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National Science Foundation, Office of Naval Research
Issues in Astrophysics
• Deuterium fraction
• Spectroscopy
• Thermochemistry
• Reaction rates
D. Gerlich, E. Herbst, and E. Roueff, Planet Space Sci. 50, 1275
(2002)
D. Gerlich, S. Schlemmer, , Planet. Space Science 50, 1287(2002)
Challenges for Theoretical Chemistry
• Potential energy surfaces
• Spectroscopy
• Thermochemistry/ZPE
• Dynamics
Previous Theoretical Work
Ab initio electronic structure
R. Prosmiti, P. Villarreal, G. Delgado-barrio, (2001,2003) - DIM-fit PES
H. Müller and W. Kutzelnigg, PCCP (2000) - CC-R12, stationary pts, De
Y. Yamaguchi, J. F. Gaw, R. B. Remington, H. F. Schaefer III, (1987) -
Dynamics
I.Stich, D.Marx, M.Parinello, T.Terakura (1997) - PI/DFT
W.P.Kraemer, V.Spirko, and O.Bludsk (1994) - Red Dim vibrations
G. Moyano and M. Collins, (2003) - “GROW” QCT k(T)
H5+ Potential Landscape
Stationary Points
H5+ Potential Landscape Stationary Points
H5+ Potential Energy Surface (2005)
• Ca 105 ab initio energies [CCSD(T)/aug-cc-pVTZ]
• Fit with a polynomial basis the is invariant wrt
any permutation of the 5 H atoms.
• Many-body representation that gives the
fragments H3+ and H2
• Use a switching function to describe
long-range electrostatic interaction.
Z. Xie, B. J. Braams, and J. M. Bowman J. Chem. Phys. 122, 224307 (2005).
Permutational Invariance: H2CO Example
 Cn1...n6 S{y1n1 y 2n2 y 3n3 y 4n 4 y 5n5 y 6n6 }
r6 ) 
V (r1
n1 ,n 2 ...n 6
y  1 ea(rr0 ) ; y 
r  re
; etc
r
3
H’

2
4
H
4
6
1
1
5
n
n
n
n
n
n
n
n
6
2
H’
H
n
3
5
n
Cn1 ...n 6 y1 1 y 6 6 (y 2 2 y 3 3 y 4 4 y 5 5  y 2 5 y 3 4 y 4 3 y 5 2 )
RMS Fitting Error
H3+ Fragment
H5+ Potential Energy Surface (2005)
a Muller
& Kutzelnigg, b Prosmiti et al. eMoyano & Collins
Spectroscopy and Thermochemistry
HD + H3+  [H4D+]  H2+ + H2D+
Thermochemistry - get the ZPEs
accurately. HO?
Spectroscopy - detect reactant and
products and maybe stabilized H4D+
M. Okumura, L. I. Yeh, and Y. T. Lee (1988) - H5+
Thermochemistry
H5+  H3+ + H2 , D0 = 6.9±0.3 kcal/mole
Recall D0 = De + DZPE
ZPE H3++H2
ZPE H5+
De
Thermochemistry
H5+  H3+ + H2 , D0 = 6.8±0.3 kcal/mol
• The most accurate De = 8.58 kcal/mol
• The present PES De = 8.30 kcal/mol
• Using HO ZPEs PES gets D0 = 5.57 kcal/mol
(Not in good agreement with experiment)
Quantum Diffusion Monte Carlo ZPEs
Solution to the TDSE
(t) 

 n (0)  nei(E n E0 )t ; H n  En  n
n0
E0 is the exact ZPE
Let t = it

(t ) 

 n (0)  ne(E n E0 )t
n0

  0 (0)  0
t 
(t ) H (t )

 E0
t 
(t ) (t )
H5+  H3+ + H2
H3+ + H2
H5+
ZPE H5+ = 20.6 kcal/mol(= 2.48De)
(Application of DMC requires a global PES)
H5+  H3+ + H2
From the DMC ZPEs we get D0 = 6.33±.03 kcal/mol
Exp* = 6.8±0.3 (HO = 5.57)
*Exp1 = 6.6 ±0.3, Exp2 = 7.0 ±0.1
Present De is low by 0.28 compared
to most accurate ab intio value
So, our estimate would be 6.6 kcal/mol
More DMC-based Energetics
H4D+  H3+ + HD D0 = 6.63 kcal/mol
 H2D+ + H2
D0 = 6.37 kcal/mol
H3+ + HD  H2D+ + H2 , DE = -90 cm-1 (-0.26 kcal/mol)
Dynamics and Reaction Rates
HD + H3+  H2+ + H2D+
k(T)  vQi 

b2
2
Qi  2  d( )P(b,E col )  bmax
2

0

Qi 


 (2J  1) | SiJ (E col ) | 2
2Ecol J0
HD + H3+  H4D+  H2+ + H2D+
Structure of the Global Minimum
Three distinct localized locations for D
HD + H3+  H4D+  H2+ + H2D+
Structure of the Global Minimum
Three distinct localized locations for D
HD + H3+  H2+ + H2D+
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Ecoll= 95 K
HD + H3+  H4D+  H2 + H2D+
( H’D + H3+)
Statistical expectations
Always form a “collision complex” - Langevin xsection
Classically 60% to H2 + H2D+, P(b) = 0.6
and 40% to H’D+ H3+ with
P(b) = 0.3 for H’≠H
P(b) = 0.1 H’=H
HD + H3+  H4D+  H2 + H2D+
( H’D + H3+)
Virtually no exchange, P(b) 0.05
Reaction Cross Sections Vs. Collision Energy
Ecoll= 95 K
A sample direct trajectory
H3+(J=1)+HD, Ecoll = 100 cm-1
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Ecoll= 95 K
Start with ZPE/2
Thermal Rate Constant Calculation and Exp
Summary So Far
• Global PES done - PI, dissociates, VLR ad hoc
• DMC calcs of ZPEs and Do
• QCT calculations of xsection and rate constant
(Not statistical, mostly proton hopping)
To Do
• Quantum calculations of vibrational energies
and IR spectrum. (This is feasible with Multimode.)
• Quantum calculation of the rate constant. (This is
very hard to do in full dimensionality.)
CH5+  CH3+ + H2
CH5+
Like H5+ there are 5! equivalent
Minima, saddle points.
Fit to 36173 CCSD(T)/aug-cc-pVTZ
Does CH5+ have a structure?
• Oka’s unassigned spectrum
• Marx and Parinello
• Schaefer, Scheiner, Schlyer
Klopper and Kutzelnigg
Science 6 January 2006:Vol. 311. no. 5757, pp. 60 - 63
6e-5
Multimode
Harmonic
LIR spectrum
a
intensity (a.u.)
5e-5
LIR - Asvany,
Schlemmer
d
4e-5
3e-5
b
2e-5
c
1e-5
0
0
1000
2000
3000
wave numbers (cm-1)
4000
A. Brown, B. J. Braams, K. Christoffel, Z. Jin,
and J. M. Bowman, J. Chem. Phys., 2003, 119, 8790. - fit and MD spectrum
A. Brown, A. B. McCoy, B. J. Braams, Z. Jin,
and J. M. Bowman, J. Chem. Phys., 2004, 121, 4105. - fit and DMC
A.B. McCoy, B .J. Braams, A. Brown
et al., J. Phys. Chem. A, 2004, 108, 4991. - DMC isotopmers
DMC Calculation of the ZPEs
CH3++H2
CH5+
CH4D+  CH3+ + HD, CH2D+ + H2
Close to statistical and independent of initial geometry