Chemical Dynamics in the Gas Phase

Chemical Dynamics in the Gas Phase

B. Theoretical Studies of Potential Energy
Surfaces

Lawrence B. Harding

Research Objective

The goals of this program are to calculate potential energy
surfaces and to use these surfaces to extract various
thermochemical and kinetic data needed in combustion
simulations. Modeling combustion phenomena is a daunting
task due to the large range of relevant temperatures and
pressures. Theoretical techniques are uniquely suited to
treating at least some aspects of this problem. In this program
an emphasis is placed on the use of state-of-the-art, ab initio,
electronic structure theory.

Approach

Our approach is to use electronic structure methods, such as
density functional (DFT), multi-reference configuration
interaction (MR-CI) and coupled cluster (CC) calculations,
to characterize multi-dimensional potential energy surfaces.
Depending on the nature of the problem, the calculations may
focus on local regions of a potential surface (for example, the
vicinity of a minimum or transition state), or may cover the
surface globally. Extensive use is also made of reduced
dimensional surfaces. For example, we have often found that
in dissociation-recombination reactions a global treatment is
required for the transitional modes whereas the conserved modes
can often be treated simply as harmonic oscillators or, in some
cases, neglected entirely.

A second part of this program involves the use of direct
dynamics for high dimensional problems to by-pass the need
for surface fitting. To date, our direct dynamics work has
consisted of both trajectory calculations, employing inexpensive
(DFT) electronic structure theory, and statistical direct dynamics,
for which we have now demonstrated the feasibility of using
state-of-the-art, MR-CI, electronic structure theory.

Highlights of Recent Work
(November 1998 - November 2001)

O + Alkyl Radical Reactions. Most combustion models assume
the reaction of CH₃ with O atoms occurs as CH₃+O ® CH₃O
® H+H₂CO. In 1992, Seakins and Leone reported the
observation of CO as a direct product in this reaction. This result
has now been confirmed by three, more recent experiments.
However, extensive calculations using a variety of methods,
including CCSD(T)/aug-cc-pvtz, have failed to find any accessible
reaction paths leading to the observed CO product. In a
collaboration with Stephen Klippenstein (SNL) we have now
completed a direct dynamics, classical trajectory, B3LYP/6-31G*
simulation of this reaction. The simulation predicts a CO yield
of ~15%, in excellent agreement with the most recent experiments.
Analysis of the trajectories shows that the CO is produced in a
step-wise process, CH₃+O ® CH₃O ® H₂+HCO ®
H+H₂+CO where the second step (elimination of H₂ from
CH₃O) occurs over a barrier but not through a saddle point.
Due to the large amount of excess energy available to the
chemically activated methoxy radicals, some trajectories cross
into the H₂+HCO valley even though the only readily accessible
saddle points for decomposition of methoxy lead to H+H₂CO.
One trajectory showing a typical path for this second step is
shown as a .pdf file. Our calculations also predict that the
branching ratio for formation of CO in the CD₃+O reaction
is significantly smaller than in CH₃+O. The calculated isotope
effect on the branching ratio is in quantitative agreement with
a recent measurement by Leone and coworkers.

We are now in the process of extending these calculations to
the reaction of O atoms with ethyl radicals. The three dominant
product channels are, simple abstraction forming OH and C₂H₄,
and addition followed by a simple bond cleavage, forming either
H atom plus acetaldehyde or methyl radical plus formaldehyde.
However, in addition to these channels we have also found
trajectories forming CH₄+HCO, H₂+CH₃CO, H₂O+vinyl radical
and H+ethylene oxide. The first three of these we believe would
not be predicted by any simple statistical theory, i.e. there are no
saddle points or reaction paths directly connecting the ethoxy
radical minimum with any of these three product channels.

The OH + CO Potential Surface. The following reaction
sequence,

OH + CO ® [HOCO]* ® H + CO₂

¯M

HOCO

is the principal source of CO₂ in all hydrocarbon flames and
the primary sink for OH in the atmosphere. The kinetics of this
reaction are controlled by two transition states, TS1, for the
initial addition forming HOCO, and TS2, for the subsequent
decomposition of HOCO to the H+ CO₂ products. To date
neither theory nor experiment has yielded a definitive
determination of either barrier.

Ten years ago we reported calculations that predicted the
existence of two, van der Waals complexes between OH
and CO. Both complexes are predicted to be linear, the
more stable one having an OH-CO orientation, with an OH
overtone frequency shift, D2nOH, of -26 cm^-1, and the less
stable one being OH-OC with D2nOH= +28 cm^-1. Lester
and coworkers (University of Pennsylvania) have recently
observed, via infrared action spectroscopy, a species with
D2nOH=-30 cm^-1. Both the frequency shift and the observed
moments of inertia strongly support the assignment of this
species as the more stable OH-CO complex. A total of five
combination bands associated with this complex have also
been observed.

We have an ongoing collaboration in this area with the
Lester group. The goals of this collaboration are to use the
experimental vibrational levels to calibrate the accuracy of the
electronic structure calculations in the entrance channel region
and to use the theory to guide the experiments as to what kinds
of vibrational excitation will probe TS1. To these ends, a four
dimensional, CCSD(T)/aug-cc-pvdz, potential surface in which
the diatomic OH and CO distances are kept fixed, has been
completed. A two dimensional slice of this potential is shown
as a .pdf file. We are now in the process of extending this surface
to include variations in the OH distance. This will allow for
a more realistic modeling of the experiments.

Initiation Reactions. Little is known about the reactions
responsible for the initiation of combustion even in the simplest
systems (H₂-O₂). This is partly because these reactions are so
slow, that measurement of the rates is quite challenging. We
have undertaken a joint theoretical-experimental study of two
initiation reactions. The following are brief summaries of the
key findings from this work:

(i) H₂/O₂: Three possible initiation reactions were considered:

H₂+O₂ ® HOO+H (1)

H₂+O₂ ® 2HO (2)

H₂+O₂ ® O+H₂O (3)

Extensive transition state searches using both CCSD(T) and
MR-CI methods were made for all three. A transition state
was found for (1) while no transition states could be found
for reactions (2) and (3). High level electronic structure
calculations, CCSD(T)/cc-pvqz, on reaction (1), coupled
with conventional transition state theory calculations yield
rate constants in good agreement both with new high
temperature measurements by Michael and with older low
temperature measurements on the reverse reaction by
Kaufman, Keyser and others.

(ii) H₂CO/O₂: In the second joint theoretical/experimental
project, the reaction of formaldehyde with molecular oxygen
was examined using CCSD(T)/cc-pvdz calculations. The
calculations find a transition state for the reaction H₂CO+O₂
® HOO+HCO and predict the existence of a loose long-range
complex on the product side, bound by 5.3 kcal/mole relative
to HOO+HCO. The barrier separating the complex and the
reactants is predicted to lie slightly below the energy of the
products. Conventional transition state theory using the ab
initio transition state parameters were found to yield a rate
constant in good agreement both with new high temperature
measurements by Michael and earlier low temperature
measurements by Baldwin. (See research summary of A.
Wagner for more details).

Radical Radical Reactions: H + Allyl and H + Propargyl.
We have continued a series of calculations on H atom plus
radical reactions. The reactions studied previously include
H+HCO, H+HO₂, H+H₂CCH and H+H₃CCH₂. We have
now extended this study to include reactions involving
resonance stabilized radicals:

H+CH₂CHCH₂ ® H₃CCHCH₂ (5)

H+H₂CCCH ® H₃CCCH (6a)

H+H₂CCCH ® H₂ CCCH₂ (6b)

As in previous calculations, three-dimensional potential surfaces
were characterized at the CAS+1+2/cc-pvdz level (the geometry
of the hydrocarbon radical fragment is kept fixed). These
calculations predict no barriers for any of these reactions. In a
collaboration with Klippenstein (SNL) the potential surfaces
characterized in this study were used to calculate rates for
these three reactions. The calculated, 298°K, rate constants
for reactions (5), (6a) and (6b) are 2.0x10^-10, 1.3x10^-10
and 0.6x10^-10 cm³/molecule-sec, respectively. The results
for reaction (5) are in good agreement with literature values
reported by Tsang and Pilling, while the rate for reaction
(6a)+(6b) is 5-10 times faster than previously reported rates.
It is interesting to note that the calculations predict that these
resonance stabilized radicals undergo recombination reactions
at somewhat faster rates than non-resonance stabilized radicals
such as H₂CCH and H₃CCH₂.

Publications, Submissions, and Talks (1998 – 2001)

Publications and Submissions

Thermal Rate Constant and Branching Ratio for CN + HD
® HCN/DCN + D/H from T = 293 to 375 K, G. He,
I. Tokue, L. B. Harding, and R. G. Macdonald, J. Phys.
Chem. A 102 (39), 7653-7661 (1998)

A Theoretical Analysis of the Reaction of H with C₂H₅,
L. B. Harding and S. J. Klippenstein, 27th Symposium
(International) on Combustion, 151-157 (1998)

New Studies of the Unimolecular Reaction NO₂ « O +
NO. Part 2. Relation Between High Pressure Rate
Constants and Potential Parameters, L. B. Harding,
H. Stark, J. Troe, and V. G. Ushakov, Phys. Chem.
Chem. Phys. 1, 63-72 (1999)

Exploring the Reaction Dynamics of Nitrogen Atoms: A
Combined Crossed Beam and Theoretical Study of N(²D)
+ D₂ ® ND + D, M. Alagia, N. Balucani, L. Cartechini,
P. Casavecchia, G. G. Volpi, L. A. Pederson, G. C. Schatz,
G. Lendvay, L. B. Harding, T. Hollebeek, T.-S. Ho, and
H. Rabitz, J. Chem. Phys. 110 (18), 8857-8860 (1999)

Potential Energy Surface and Quasiclassical Trajectory
Studies of the N(²D) + H₂ Reaction, L. A. Pederson,
G. C. Schatz, T.-S. Ho, T. Hollebeek, H. Rabitz,
L. B. Harding, and G. Lendvay, J. Chem. Phys. 110 (18),
9091-9100 (1999)

A Theoretical Study of the Kinetics of C₂H₃ + H,
S. J. Klippenstein and L. B. Harding, Invited Article,
Phys. Chem. Chem. Phys. 1, 989-997 (1999)

A Direct Transition State Theory Based Study of Methyl
Radical Recombination Kinetics, S. J. Klippenstein and
L. B. Harding, J. Phys. Chem. A 103 (47), 9388-9398
(1999)

An Empirical Potential Energy Surface of the Ne-OH/D
Complexes, H.-S. Lee, A. B. McCoy, L. B. Harding,
C. C. Carter, and T. A. Miller, J. Chem. Phys. 111 (22),
10053-10060 (1999)

Reaction of H with Highly Vibrationally Excited Water:
Activated or Not?, G. C. Schatz, G. Wu, G. Lendvay,
D.-C. Fang, and L. B. Harding, Faraday Discuss. 113,
151-165 (1999)

Classical Trajectory Calculations of the High Pressure
Limiting Rate Constants and of Specific Rate Constants
for the Reaction H + O₂ ® HO₂: Dynamic Isotope Effects
Between Tritium + O₂ and Muonium + O₂, L. B. Harding,
J. Troe, and V. G. Ushakov. Phys. Chem. Chem. Phys. 2,
631-642 (2000)

A Summary of "A Direct Transition State Theory Based
Study of Methyl Radical Recombination Kinetics",
S. J. Klippenstein and L. B. Harding, J. Phys. Chem. A
104 (11), 2351-2354 (2000)

Potential Energy Surface of the Ã State of NH₂ and the
Role of Excited States in the N(²D) + H₂ Reaction,
L. A. Pederson, G. C. Schatz, T. Hollebeek, T.-S. Ho,
H. Rabitz, and L. B. Harding, J. Phys. Chem. A 104, (11),
2301-2307 (2000)

Initiation in H₂/O₂: Rate Constants for H₂+O₂ ® H+HO₂
at High Temperature, J. V. Michael, J. W. Sutherland,
L. B. Harding, and A. F. Wagner, 28th Symposium
(International) on Combustion 28,1471-1478 (2000)

Theoretical Kinetic Estimates for the Recombination of
Hydrogen Atoms with Propargyl and Allyl Radicals,
L. B. Harding and S. J. Klippenstein, 28th Symposium
(International) on Combustion 28,1503-1509 (2000)

Barrier to Methyl Radical Internal Rotation of
1-Methylvinoxy Radical in the X(²A") and B(²A") States:
Experiment and Theory, S. Williams, L. B. Harding,
J. F. Stanton, and J. C. Weisshaar, J. Phys. Chem. A
104,10131-10138 (2000)

A New Potential Surface and Quasiclassical Trajectory
Study of H+H₂O ® OH+H₂, G.-S. Wu, G. C. Schatz,
G. Lendvay, D.-C. Fang, L. B. Harding, J. Chem. Phys.
113, 3150-3161 (2000)

Statistical Rate Theory for the HO+O ® HO₂ ® H+O₂
Reactions System: SACM/CT Calculations Between 0 and
5000 K, L. B. Harding, A. I. Maergoiz, J. Troe, and
V. G. Ushakov, J. Chem. Phys. 113, 11019-11034 (2000)

Exploring the OH+CO Reaction Coordinate Via Infrared
Spectroscopy of OH-CO Reactant Complexes, M. I. Lester,
B. V. Pond, D. T. Anderson, L. B. Harding, A. F. Wagner,
J. Chem. Phys. 113, 9889-9892 (2000)

Barrier to Methyl Radical Internal Rotation of Cis and
Trans 2-Methylvinoxy Radical in the X(²A") and B(²A")
States: Experiment and Theory, S. Williams, L. B. Harding,
J. F. Stanton, and J. C. Weisshaar, J. Phys. Chem. A 104,
9906-9913 (2000)

Evidence for a Lower Enthalpy of Formation of Hydroxyl
Radical and a Lower Gas Phase Bond Dissociation Energy
of Water, B. Ruscic, D. Feller, D. A. Dixon, K. A. Peterson,
L. B. Harding, R. A. Asher, and A. F. Wagner, J. Phys.
Chem. A 105, 1-4 (2001)

Construction of Reproducing Kernal Hilbert Space
Potential Energy Surfaces for the ¹A" and ¹A' states of the
Reaction N(²D)+H₂, T. Hollebeek, T.-S. Ho, H. Rabitz and
L. B. Harding, J. Chem. Phys. 114, 3945-3948 (2001)

Comment on "On the High Pressure Rate Constants for the
H/Mu +O₂ Addition Reactions", L. B. Harding, J. Troe, and
V. G. Ushakov, Phys. Chem. Chem. Phys. 3, 2630-2631 (2001)

Theoretical and Experimental Investigations of the Dynamics of
the Production of CO from the CH₃+O and CD₃+O Reactions,
T. P. Marcy, R. R. Diaz, D. Heard, S. R. Leone, L. B. Harding
and S. J. Klippenstein, J. Phys. Chem. A 105,8361-8369 (2001)

A Direct Transition State Theory Analysis of the HNN + OH
Reaction and its Implications for the Branching in NH₂ + NO,
D.-C. Fang, L. B. Harding, S. J. Klippenstein, and J. A. Miller,
Abstract, Faraday Discussion 119, University of Leeds,
United Kingdom (in press)

Mapping the OH + CO ® HOCO Reaction Pathway Through
Infrared Spectroscopy of the OH-CO Reactant Complex,
M. I. Lester, B. V. Pond, M. D. Marshall, D. T. Anderson,
L. B. Harding, and A. F. Wagner, Faraday Disc. (in press)

On the Enthalpy of Formation of Hydroxy Radical and Gas-Phase
Bond Dissociation Energy of Water and Hydroxyl, B. Ruscic,
A. F. Wagner, L.B. Harding, R.L. Asher, D. Feller, D. A. Dixon,
K. A. Peterson, Y. Song, X. Qian, C.-Y. Ng, J. Liu and W. Chen,
J. Phys. Chem. (in preparation)

Rate Constants, 1100<T<2000 K, for the Reaction, H + NO₂ ® OH + NO, Using Two Shock Tube Techniques: Comparison
of Theory to Experiment, M.-C. Su, S. S. Kumaran, K. P. Lim,
A. F. Wagner, L. B. Harding, and J. V. Michael, J. Phys. Chem.
A (in preparation)

Talks and Presentations

Radical-Radical Reactions: H+C₂H₅ and CH₃+CH₃,
L. B. Harding and S. J. Klippenstein, Invited Talk, 215th
American Chemical Society National Meeting, Dallas, Texas
(1998)

Potential Energy Surface and Quasiclassical Trajectory Studies
of the N(²D) + H₂/D₂ Reaction, L. A. Pederson, G. C. Schatz,
T. Hollebeek, T.-S. Ho, H. Rabitz, L. B. Harding, and G. Lendvay,
Poster, 31st Midwest Theoretical Chemistry Conference,West
Lafayette, Indiana (1998)

A Theoretical Analysis of the Reaction of H with C₂H₅,
L. B. Harding and S. J. Klippenstein, 27th Symposium
International on Combustion, Boulder, Colorado (1998)

Radical Combination Reactions, L. B. Harding, Invited Talk,
Physical Chemistry Seminar, Ohio State University, Columbus,
Ohio (1999)

Potential Surfaces for Unimolecular Reactions, L. B. Harding,
Invited Talk, 217^th American Chemical Society National Meeting,
Anaheim, California (1999)

Radical Recombination Reactions, L. B. Harding, Invited Talk,
American Conference on Theoretical Chemistry, Boulder,
Colorado (1999)

The H+H₂O Potential Surface Revisited, D.-C. Fang,
L. B. Harding, G. C. Schatz, G. Wu, and G. Lendvay, Poster,
American Conference on Theoretical Chemistry, Boulder,
Colorado (1999)

Radical Recombination Reactions. L. B. Harding, Invited Talk,
Chemistry Colloquia, Case Western Reserve University,
Cleveland, Ohio (1999)

Transition States and Direct Statistics for Barrierless Reactions,
S. J. Klippenstein, B. J. Serve, D.-C. Fang, and L. B. Harding,
Invited Talk, 219th American Chemical Society National
Meeting, San Francisco, California (2000)

Initiation H₂/O₂: Rate Constants for H₂ + O₂ ® H + HO₂
at High Temperature, J. V. Michael, J. W. Sutherland,
L. B. Harding, and A. F. Wagner, 28th Symposium
(International) on Combustion, Edinburgh, Scotland (2000)

Rate Constants for H₂CO + O₂ ® HCO + HO2 at High
Temperature, J. V. Michael, M.-C. Su, J. W. Sutherland,
D.-C. Fang, L. B. Harding, and A. F. Wagner, Poster,
28th Symposium (International) on Combustion, Edinburgh,
Scotland (2000)

Mapping the OH + CO ® HOCO Reaction Pathway
Through Infrared Spectroscopy of the OH-CO Reactant
Complex, M. I. Lester, B. V. Pond, M. D. Marshall,
D. T. Anderson, L. B. Harding, and A. F. Wagner, Poster,
Gordon Research Conference, Ventura, California (2001)

Mapping the OH + CO ® HOCO Reaction Pathway
Through Infrared Spectroscopy of the OH-CO Reactant
Complex. M. I. Lester, B. V. Pond, M. D. Marshall,
D. T. Anderson, L. B. Harding, and A. F. Wagner.
Faraday Discussion 118, University of Durham, United
Kingdom (2001)

A Direct Transition State Theory Analysis of the HNN + OH
Reaction and its Implications for the Branching in NH₂ + NO,
D.-C. Fang, L. B. Harding, S. J. Klippenstein, and J. A. Miller,
Faraday Discussion 119, University of Leeds, United Kingdom
(2001)

Radical-Radical Recombination Reactions: O + CH₃,
L. B. Harding, Invited Talk, 5^th International Conference on
Chemical Kinetics NIST, Gaithersburg, Maryland (2001)

LAWRENCE B. HARDING

Office Address:
Chemistry Division
Argonne National Laboratory
9700 South Cass Avenue
Argonne, IL 60439
630-252-3591 Fax: 630-252-9292
E-mail: harding@anl.gov

Education:
California Institute of Technology, Ph.D. in Chemistry, 1979
Wesleyan University, B.A. in Chemistry and Mathematics, 1973

Research Experience:
3/98–Present - Senior Scientist, Chemistry Division, Argonne
National Laboratory
6/84-3/98 - Scientist, Chemistry Division, Argonne National Laboratory
9/92-9/93 - Visiting Fellow, Joint Institute for Laboratory Astrophysics,
Boulder, Colorado
10/79-6/84 - Assistant Scientist, Chemistry Division, Argonne National Laboratory
10/78-10/79 - National Science Foundation National Needs Fellow, Carnegie-Mellon University

Areas of Research and Expertise:
Applications of Ab Initio electronic structure theory to reactive
and non-reactive potential energy surfaces.

Professional Organizations:
Phi Beta Kappa
American Chemical Society
Combustion Institute
American Association for the Advancement of Science

Argonne National Laboratory Committees:
Chemistry Division Assistant Scientist Promotion Committee,
1992-1994
Chemistry Divsion Library Committee, 1994-1996
Chemistry Division Assistant Scientist Promotion Committee
(Chair), 1997-2000
Physical Research, Programmatic and Operations Committee-Hires
and Promotions, 2001-

Awards:
Graham Prize in the Natural Sciences, 1973
Herbert Newby McKoy Award, 1978

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