The dissociative recombination (DR) of the AB(+) molecular ion with an electron has been shown to be an important component in the detailed interpretation of planetary ionosphere data. A first principles theoretical approach is developed for calculating the DR cross sections and rates for AB(+) molecular ions. The calculations focus on O2(+) and N2(+) DR, and are the first to include the indirect DR mechanism (Ryberg vibrational levels below v = 0 level of ion) for a molecule larger than H2(+). The importance of electron capture width in calculating the cross sections and rates is also examined. Electron capture widths are given for all states of O2 that are of importance to DR (lowest 10 vibrational levels of ion). Knowledge of the details of dissociative recombination will be needed for interpretation of data from future interplanetary and comet atmospheric studies

Guberman, Steven L.

English

NASA Technical Reports Server

Final Report
September 1, 1988 - October 31 , 1991
NASA Grant NAGW 1
Steven L. Guberman
Principal Investigator
Institute for Scientific Research
(Employer Identification # 22-248-7207)
33 Bedford St., Suite I9a
Lexington, MA 02173
THEORETICAL STUDIES OF IMPORTANT PROCESSES IN
PLANETARY AND COMET ATMOSPHERES
The NASA Technical Officer for this Grant is
Dr. J. T. Bergstralh
Solar System Exploration Division, Code SL
NASA Headquarters, Washington, D. C. 205^ 6
(NASA-CR-186588) THEORETICAL STUDIFS ni= "r i£ nnm ••*-**»•*• _ — - »~ « *.^»^%t» o i U L / i t r o Lit- *;«-» t n < ^ ^ ,
W92-19928
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 or centific Research) Unc1as
CSCL 038 G3/91 0053064
https://ntrs.nasa.gov/search.jsp?R=19920010686 2020-03-17T13:24:38+00:00Z
This report is a brief summary of research supported under NASA
Grant NAGW
I. The Calculation of Dissociative Recombination Cross Sections and
Rates
The dissociative recombination (DR) of the AB"1" molecular ion with an
electron is described by:
AS* +
 e~ -> A + B ( 1 )
where the product atoms may be electronically excited and the AB+ ion
may be vibrationally excited. Dissociative recombination of molecular
ions has been shown to be an important component in the detailed
interpretation of planetary ionosphere data returned by many NASA
missions ranging from the early Mariner and Viking missions to Pioneer
Venus and Voyagers I and II. Indeed, knowledge of the details of DR
will be needed for the interpretation of data from many future
missions. Unfortunately, several aspects of reaction (1 ) make it
exceedingly difficult to study in the laboratory. These include the
difficulty of generating the AB"1" ions in specified vibrational
distributions which match those found in planetary atmospheres and the
difficulty of identifying the electronic states of the products. In
order to circumvent these difficulties we have developed a first
principles theoretical approach for calculating the DR cross sections
and rates. Our calculations have focused on 0^ DR and are the first
calculations to include the indirect DR mechanism (discussed below) for
a molecule larger than H^. Below we discuss our progress in the
calculation of DR cross sections and rates.
There are two fundamental mechanisms driving DR. In direct DR,1 the
electron is captured into a repulsive state of the neutral molecule
followed by dissociation to neutral products. In indirect DR,2 electron
capture can also occur into a vibrationally excited Rydberg state which
can either autoionize or dissociate along the repulsive state of the
direct DR mechanism. These excited Rydberg levels can have the ground
state of the ion or an excited electronic state as the electronic core.
These neutral levels are resonances since they exist in the electron-
ion continuum of the ion ground state. In practice, both the direct and
1
indirect mechanisms occur simultaneously and interfere with each other.
We have used Multichannel Quantum Defect Theory and have developed an
approach3 which describes both mechanisms simultaneously yielding
complicated resonance structures in the cross section. Prior to our
work, the interaction which drives the indirect mechanism was assumed
to be primarily vibronic. In the vibronic mechanism the electron is
captured by interacting directly with the nuclear motion so as to
excite the molecular ion from the initial vibrational level to an
excited vibrational level of a Rydberg state. This mechanism involves a
breakdown of the Born-Oppenheimer approximation in which the nuclear
and electronic motion are taken to be separate and noninteracting. It
can be shown that the vibronic coupling is primarily important for
transitions in which the vibrational quantum number of the ion and the
neutral Rydberg state differ by unity. In practice this restricts the
Rydberg levels to principal quantum numbers of about n=7,8. However, we
have found that there is also a second order electronic mechanism which
also drives capture into the Rydberg states. In the electronic
mechanism, each Rydberg vibrational level is electronically coupled to
the repulsive states of the same electronic symmetry. Because of this
coupling, capture into the repulsive state can also populate the
Rydberg levels. In this higher order electronic coupling, the electron
is first captured into the repulsive state followed by transfer to the
Rydberg state followed finally by transfer back to the dissociative
state. Dissociation then completes this DR mechanism. In addition, the
transition is not restricted to Av=1. Indeed, the couplings are large
for Rydberg levels with low principal quantum number (n=3) and high v
(v=13). The vibronic and electronic indirect mechanisms interfere with
each other. Furthermore, interference also occurs between neighboring
Rydberg levels. Thus in addition to interference with the direct
mechanism a considerable amount of simultaneous interference is
described, leading to a complicated resonance structure in the
calculated cross sections.
An additional interesting feature of our calculation is the role
played by Rydberg vibrational levels which lie below the v=0 level of
the ion. These levels might not ordinarily be considered to be
resonances since their centers lie below the electron-ion continuum.
However, even though these states are discrete below the v=0 level of
the ion, they have wings which extend above the v=0 level. Furthermore,
these wings, which result from interfere with the direct mechanism,
play an important role in determining the magnitude of threshold cross
sections and rates. An example (see the attached reprint) is the n=3,
v=12 ^ Rydberg level of 02 found at 0.1 eV below the v=0 level of O^.
Because this level has a negative Fano profile index, q, it interferes
with the direct mechanism so as to decrease the full DR cross section
below that due to the direct mechanism. This level also causes the
calculated full rate at low electron temperatures to be below the
direct rate. The same phenomenon occurs in the v=1 and v=2 rates along
the lEU channel where below threshold resonances reduce the full rate
below the direct rate just above threshold.
We have also studied vibrational excitation cross sections and rates
which describe the following reaction:
0+(v=0) + e~ + 0+(v=1) + e~. (2)
The same approach developed for the study of DR, described in detail in
the attached reprint, can also be used to study vibrational excitation
(VE).1* In VE, the electron is emitted prior to dissociation and the
molecule is left in an excited vibrational level. The repulsive states
responsible for DR act as intermediate resonances in VE and greatly
enhance the VE rate over the small value that would be expected in the
absence of an intermediate state. Cross sections for vibrational
excitation plotted as a function of electron energy show similar
complex resonance structure as found for DR. In the case of v=0-»1
excitation including only the 'ly dissociative route of 02, we found a
rate of 1.7 x 10~llcm3/sec at 800K. While this rate is small, it
accounts for only the lz£ intermediate state. There are a number of
other channels having more favorable intersections with the ion and
these channels are being explored in current work. Vibrational
deexcitation is also being studied.
II. The Calculation of Electron Capture Widths
An important quantity needed for the calculation of cross sections
and rates is the electron capture width. These have now been calculated
for all the states of 02 that are of importance to dissociative
recombination of the lowest 10 vibrational levels of the ion. The
approach, described in more detail in prior progress reports, uses a
basis set of 18 diffuse Gaussian functions5 centered at the molecular
midpoint. Rydberg orbitals coupled to the ground state of 02 are
determined in Improved Virtual Orbital calculations. For each total
electronic symmetry an optimized set of Rydberg orbitals is generated.
The width is calculated using valence configuration interaction wave
functions for both the dissociative state and the Rydberg states. High
non-physical routes in the dissociative wave function CI are allowed to
provide correlation to the Rydberg CI wave functions. With this
procedure we are able to calculate accurate widths up to principal
quantum numbers of about 13 where the width has converged to the
limiting value (n=co). A tabulation of the calculated widths for all the
important 02 DR routes is given below in Table 1.
The largest widths calculated for 02 are for the 1 l > 3n u states.
These states are shape resonances since they correspond mostly to an
State F(eV) State r(eV)
i3nu
23nu
33nu
1 ^u21nu
3'nu
1ang
33Hg
43ng
1 'Tig2!ng3 Hg
1 3ZU
23ZQ
1 ' 17,
1 .5498
0.0137
0.0131
2.2302
0.0301
0.0163
0.0026
0.0001
0.0066
0.0003
0.0034
0.0234
0.0014
0.9065
0.0016
0.2060
4'llg 0.0000
b1!? 0.6476
2 'Eg* 0.0013
S1^ 0.0051
a'Ag 0.5595
2JAg 0.0083
1'Zy 0.2864
13Ey 0.0042
23Eu 0.0072
21ZU' 0.0164
1 IA U 0.4377
X3Eg 0.4397
23Eg 0.0319
33Eg 0.0000
13AU 0.0393
23A,, 0.0077
Table 1. Calculated electron capture widths for 02.
electron being captured by the ion into a 3<Ju orbital without any
rearrangement of the other electrons. Using orbitals optimized for the
1Ilu states we find that the n=7 widths for 1,2,33nu repulsive states
are 1.55, 0.01^, and 0.013eV respectively while the widths for 1,2,3lnu
are 2.23, 0.030, and O.OlSeV respectively. The upper two states have
small capture widths because their configurations differ by a triple
excitation from the ion plus a free electron. All widths in Table 1.
are for a single internuclear distance, R=2.28l9ao, the equilibrium
separation of the ground state. Table 1. allows us to reduce the
possible routes that can lead to DR in Oj to a very small number of
probable routes. The Table shows that the 13nu, 11IIU, 1llul 1 3Eu« 1 ll^»
and 1'Au states are the primary routes for DR of Oz. Note that while
the X, a, and b states have significant calculated widths they are
unlikely DR routes since their potential curves do not cross the ion
curve. The Table shows that for symmetries having a large width, i.e.
>0.1eV, the large width occurs in only a single root of that symmetry
and always in the lowest root. We are currently studying other
molecules, including OH and N2 in order to see if their electron
capture widths show a similar variation.
III. DR of N+
We have recently completed calculations of the DR of N2.6 In order
to obtain accurate results, these calculations employed configuration
interaction (CI) wave functions having over one million terms. As in
the study of 02, we found that the cross section has a complex
structure due to many interacting resonances. We also found that the
indirect DR mechanism decreased the full DR rate below the rate due the
direct mechanism. As in 02, this effect is due to an important
resonance lying below the v=0 level of the ion. The calculated rate for
electron temperatures (Te) between 100K and 1000K was found to be
1.6 X 10~7X (Te/300)~-37cm3/sec in excellent agreement in both
magnitude and temperature dependence with prior microwave results.7 The
calculations also show that the primary DR channel is the C|3nu state
which generates "S and ZD nitrogen atoms having 1.72eV kinetic energy.
This energy is sufficient for escape from the Martian atmosphere and DR
is a very important component of models of the N density and of the
N 1VN 1 5 isotope ratio. The latter quantity is affected because N 1 5,
which needs 1.86eV to escape, will not be able to escape from DR of
v=0. The net effect is isotope enhancement from DR of v=0.8 A reprint
giving more details is attached to this report.
IV. References
1. D. R. Bates, Phys. Rev. ^78, 492 (1950).
2. J. N. Bardsley, J. Phys. B J_, 365 (1968).
3. S. L. Guberman and A. Giusti-Suzor, J. Chem. Phys. 95, 2602 (1991).
4. S. L. Guberman, in preparation.
5. K. Kaufmann, W. Baumeister, and M. Jungen, J. Phys. B 22, 2223(1989).
6. S. L. Guberman, Geophys. Res. Lett. 18, 1051 (1991).
7. F. J. Mehr and M. A. Biondi, Phys. Rev. 181, 264 (1969); E. C. Zipf,
Geophys. Res. Lett. 7., 645 (1980).
8. J. Fox, Dissociative Recombination in Aeronomy, in Dissociative
Recombination: Theory. Experiment and Applications, edited by J. B. A.
Mitchell and S. L. Guberman, (World Scientific, Singapore, 1989),
p.264.
V. Publications Acknowledging NASA Support
1 . S. L. Guberman, Ab Initio Studies of Dissociative Recombination, in
Dissociative Recombination: Theory, Experiment and Applications, ed.
by J. B. A. Mitchell and S. L. Guberman (World Scientific, Singapore,
1989), p.H5.
2. J.-H. Yee, S. L. Guberman, and A. Dalgarno, Collisional Quenching of
0(1D) by 0(3P), Planet. Space Sci. 38, 64? (1990).
3. S. L. Guberman, Dissociative Recombination of the Ground State of
N+, Geophys. Res. Lett. J_8, 1051 (1991). (See Appendix).
iJ. S. L. Guberman and A. Giusti-Suzor, The Generation of 0(1S) from the
Dissociative Recombination of Q\, J. Chem. Phys. 95, 2602 (1991).(See
Appendix).
5. S. L. Guberman and A. Dalgarno, Dipole Moments and Transition
Probabilities of the i3ng-b3Zu, c3nu-a3Eg, and i3ng-c3nu Systems of
Molecular Hydrogen, Phys. Rev. A., submitted for publication.
6. S. L. Guberman, The Calculation of Molecular Threshold Capture
Widths, J. Chem. Phys., to be submitted.
7. S. L. Guberman, The Dissociative Recombination of 0^ Leading to
0(1D). J. Chem. Phys., to be submitted.
Book
The author is co-editor with J. B. A. Mitchell of a volume entitled:
Dissociative Recombination: Theory, Experiment, and Applications,
published by World Scientific, Singapore, in 1989.
VI. Appendix
1. S. L. Guberman and A. Giusti-Suzor, The Generation of 0('S) from the
Dissociative Recombination of 0^, J. Chem. Phys. 95, 2602 (1991).
2. S. L. Guberman, Dissociative Recombination of the Ground State of
N+, Geophys. Res. Lett. 18, 1051 (1991).


Theoretical studies of important processes in planetary and comet atmospheres

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