Dissociative Electron Attachment to H2O (& H2S) in Full Dimensionality
Dan Haxton, Zhiyong Zhang, Tom Rescigno, C. William McCurdy (Lawrence Berkeley National Lab and UC-Berkeley)
Hans-Dieter Meyer (The University of Heidelberg, Germany)
Free electrons attach to gas-phase water
molecules, creating transient H2O- species which
dissociate to H2 + O- or H- + OH.
For OH- + H- production via the 2B1 resonance, we
have performed fixed-nuclei scattering calculations
with electronically correlated targets, and treated
the full rovibrational nuclear dynamics of the
dissociation using the Multi-Configuration TimeDependent Hartree (MCTDH) method, to obtain
(PRA 69, 062713 & 062714) nearly quantitative
agreement with experiment with regard to total
cross section and degree of vibrational excitation.
At left are the total and OH (n) vibrationallyresolved cross sections as a function of incident
electron energy. Our results (curves), when shifted
right +0.34 eV but not in magnitude as in this
figure, agree well with the data of Belic, Landau
and Hall (JPB 14 p175) (connected squares).
H- + OH
e-
+ H2O
H2 +
O-
DEA to H2O via Feshbach resonances
2B (~ 6.5 eV)
1a122a121b223a121b114a12
1
2A (~ 9 eV)
1a122a121b223a111b124a12
1
2B (~ 12 eV)
1a122a121b213a121b124a12
2
However we calculate a larger cross section for
DEA to D2O than observed and in fact reverse the
isotope effect. A higher OD peak, as calculated, is
consistent with a survival probability near 1.
0
1
-
D from D2O
2
-
H from H2O
3
4
5
6
7
Peak heights from Compton and Christophorou, PR 113
(1967) marked with arrows; curves, our calculation.
O- + H2
These calculations used three-dimensional representations of the real
and imaginary components of the complex-valued Born-Oppenheimer
resonance potential energy surfaces (PES). At left are shown 2D cuts
of the real parts for the 2B1 (top) and diabatized 2A1 and 2B2 (bottom)
resonance PES’s as calculated in C2v geometry (r1 = r2). R is distance
between O and H2 center of mass. These are global fits which pass
exactly through each calculated point. The 2A1 and 2B2 resonances
undergo a conical intersection and it
Contours 0.25 eV
O +H
bond lengths in bohr
is therefore necessary to perform the
nuclear dynamics calculation in a
diabatic basis. (Coupling not
shown.) At right are two cuts of the
width of the 2B1 resonance
(imaginary component of energy 
2), calculated with the complex
Kohn variational method.
O- + H2 (1sg1su)
-
2
Conical intersection
of 2A1 & 2B2 resonances (CI results)
(Hartree)
r1 + r2 = 3.62 a0
Contours 0.5meV
bond lengths in bohr
q = 104.5o
The conical intersection has dimension N-2 = 1, a line.
This 2D cut is  to this line, we see a point.
Conical intersection location (degeneracy of 2A1 and 2B2 diabatic states), dotted line.
Branch point intersections: E   for resonances
Conical intersection model for Jahn-Teller
intersecting resonance: Re(Eres).
In addition to its conical intersection with the 2A1 state, the 2B2 Feshbach resonance appears to have an isolated branchpoint degeneracy with a 2B2 shape resonance. The 2B2 shape and Feshbach resonances are thus two components of a doublevalued resonant potential energy surface. Following these adiabatic resonance states around the degeneracy seam leads to their
interchange. This behavior is reflected in the stereogram below (look through the page to superimpose the right and left pictures
in your visual field for 3D effect). The locations of these resonances (Hartree) calculated via the complex Kohn method are
plotted. The closed loop in nuclear configuration space transforms the Feshbach resonance (top end) into the shape resonance
(bottom end). A model complex symmetric eigenvalue spectrum with this same behavior is shown at lower left.
This topology has no direct analogue in bound-state theory, although the literature on “Hidden Crossings” (see Doll,
George, and Miller, JCP 58, p1343 (1973); Macek and Ovchinnikov, PRA 50, p468 (1994)) explains how bound-state avoided
crossings betray similar branch points in the plane of complex nuclear coordinates. In the resonant case, the branch point
behavior in the eigenvalue spectrum is seen as a function of real (i.e., physical) nuclear coordinates.
The 2A1/2B2 conical intersection is actually two such seams, which border a ribbon-shaped set of points at which the real
parts of the resonance energies are equal. See model, left & Estrada, Cederbaum, and Domcke, JCP 84, 152 (1985).
Model of single branch point degeneracy
for 2B2 shape/Feshbach intersection.
Complex Kohn resonance pole trajectories near conical intersection
as bond angle is varied from q = 71o to 74o
r1  r2
r1 = r2
ANGULAR DISTRIBUTION OF PRODUCTS:
H2O
1
STATE OF H2O & H2S
The angular distribution of H- fragments with respect to scattering angle q (NOT the bond angle) from the 2B1 resonance of H2O is
independent of the OH vibrational quantum number n. Up to n=7 is produced with similar angular distributions. This is not the case for
DEA via the analagous Feshbach resonance and fragment of H2S. For production of SH, n=1 and 2 are produced, but at high incident
electron energies n=1 dominates in the backward direction1. We have reproduced this effect as can be seen below. For an electron
scattering resonance on a molecular target, many partial waves may mix into the entrance amplitude, and for H2S, this mixing varies with
geometry within the Franck-Condon region, giving rise to
1See Azria et al., JPB 12 p679 (1979)
Partial (differential in angle) width at qHSH=92o, r1 + r2 = 5 bohr
this effect.
OH
eData from Belic, Landau, and Hall, J Phys B 14, 175 (1981),
squares, and Trajmar and Hall, J Phys B 7, L458 (1974), circles.
2B
q
H-
Scattering angle
q, (see diagram,
left), or 2nd Euler
angle which
orients vector R
going from SH
center of mass to
Hr1 is nondissociative, r2 is dissociative bond
q = 165o
H2S
q = 90o
H2S