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When a hydrogen molecule, H2, is hit by
a photon with enough energy to send both its electrons flying, the two
protons left behind the hydrogen nuclei - repel each other in a
so-called Coulomb explosion. In this event, called the double
photoionization of H2, the paths taken by the fleeing
electrons have much to say about how close together the two nuclei
were at the moment the photon struck, and just how the electrons were
correlated in the molecule.
Correlation means that properties of the particles
like position and momentum cannot be calculated independently. When
three or more particles are involved, calculations are notoriously
intractable, both in classical physics and quantum mechanics. In the
16 December, 2005 issue of Science the researchers report on the
first-ever complete quantum mechanical solution of a system with four
charged particles.
The groundbreaking calculations were inspired by
earlier experiments on the photofragmentation of deuterium (heavy
hydrogen) molecules, performed at beamline 9.3.2 of Berkeley Lab's
Advanced Light Source (ALS) in 2003 by a group of scientists from
Germany, Spain, and several institutions in the United States. The
experimenters were led by Thorsten Weber, then with the ALS and now at
the University of Frankfurt.
"If you were trying to do this experiment and you
didn't have access to the Advanced Light Source and a COLTRIMS
experimental device" - a sophisticated, position-sensitive detector
for collecting electrons and ions - "you'd just fire photons at a
random sample of hydrogen molecules and measure the electrons that
came out," says Thomas Rescigno of Berkeley Lab's Chemical Sciences
Division, one of the authors of the Science paper. "What made this
experiment special was that they could measure what happened to all
four particles. From their precise positions and energy they could
reconstruct the state of the molecule when it was hit."
Weber presented early experimental data at a
seminar attended by Rescigno, William McCurdy of the Lab's Chemical
Sciences Division, who is also a professor of chemistry at the
University of California at Davis, and Wim Vanroose, a postdoctoral
fellow at Berkeley Lab who is now at the Department of Computer
Science at the Katholieke Universiteit Leuven in Belgium.
Says Rescigno, "Thorsten teased us with his results,
some of which were extremely nonintuitive. What was remarkable was
that very small differences in the internuclear distance" - the
distance between the two protons at the moment the photon was absorbed
- "made for radical differences in the ways the electrons were ejected."
"When I saw the results of the molecular
experiments, in which small changes in the internuclear distance
produced large and unexpected changes in the electron ejection
patterns, it immediately occurred to me that the differences were
because of the molecule's effects on electron correlations," McCurdy
says.
McCurdy had recently been working with Fernando
Martín, a professor of chemistry at the Universidad Autónoma de
Madrid, merging computational techniques developed by Martín with a
method McCurdy, Rescigno, and others had developed for calculating
systems of three charged particles. Martín and McCurdy extended these
methods to the helium atom, a system that, technically speaking, has
four charged particles. But because the helium atom's two protons are
bound together in the nucleus, the calculated distribution of
electrons ejected by the absorption of an energetic photon tend to be
quite symmetrical around the nucleus, with most pairs flying off in
opposite directions.
The picture can look quite different for a hydrogen
or deuterium molecule, in which a plot of the likelihood that
electrons will be ejected at certain angles groups into lobes that
grow increasingly asymmetric as the bond length between the two
hydrogen atoms grows longer. McCurdy read this as the effect of the
bond length on the correlation of the shared electrons. Indeed, this
is what Weber and his colleagues speculated when they published the
results of their deuterium photofragmentation studies in Nature in
2004.
Rescigno pointed out a fly in the ointment, however
- namely that instead of being caused by electron correlations, large
differences in ejection patterns caused by small differences in
internuclear distance "could just be kinematics."
In other words, the scattered electrons might be
sharing some of the potential energy stored by the Coulomb repulsion
between the two like-charged protons. The closer together these two
nuclei are at the moment the photon breaks up the molecule, the more
energy goes into the Coulomb explosion, some of which could be
transmitted to the outgoing electrons and affect their flight paths.
How to decide between kinematic effects or electron
correlations? The experimental results could not address the question,
since all the data were collected at the same photon energy; whether
the electrons were acquiring additional kinetic energy was unknown.
But, says Vanroose, "because we were doing
computations, we could do experiments the experimenters couldn't do.
We had much more flexibility to fix the conditions."
Using supercomputers at the Department of Energy's
National Energy Research Scientific Computing Center (NERSC) at
Berkeley Lab, at UC Berkeley, and in Belgium, Vanroose was able to
rerun the hydrogen molecule experiments "in silico," this time with
different photon energies, distributed so that the outgoing electrons
always shared exactly the same kinetic energy no matter what the
distance between the protons at the moment of photon absorption.
The results turned out to be remarkably similar in
all cases. Even when kinetic energy made no contribution, the
electrons flew off in patterns determined by the length of the bond
between the nuclei. Therefore the differences were due almost entirely
to the way the electrons were correlated in their orbital paths around
the molecule's two nuclei.
Martín of UA Madrid sees the new calculations,
which are a complete numerical solution for the Schrödinger equation
of the photoionization of H2, as "just the beginning.
Probing the complicated physics of electron correlations will lead the
way to more comprehensive methods combining theory and experiment to
address some of the most pressing problems in chemistry."
Vanroose credits their success to day-in, day-out
collaboration between top-notch theorists and experimenters at
Berkeley Lab, "who are talking to each other all the time. The ability
of experimentalists to call on the latest computational techniques is
good for both; it's why we're two years ahead of other theorists in
this field."
To Rescigno, the latest results show that "what
began as blue-sky physics theory is now connecting with the nuts and
bolts of practical experiment."
Says McCurdy, "These large-scale theoretical
calculations, stimulated by the need to interpret novel experiments at
the ALS, are already stimulating new experiments and establishing a
new line of inquiry at Berkeley Lab."
"Complete photo-induced breakup of the H2 molecule
as a probe of molecular electron correlation," by Wim Vanroose,
Fernando Martín, Thomas N. Rescigno, and C. William McCurdy, appears
in the 16 December, 2005 issue of Science.
"Complete photo-fragmentation of the deuterium
molecule," by T. Weber, A. O. Czasch, O. Jagutzki, A. K. Müller, V.
Mergel, A. Kheifets, E. Rotenberg, G. Meigs, M. H. Prior, S. Daveau,
A. Landers, C. L. Cocke, T. Osipov, R. Díez Muiño, H. Schmidt-Böcking,
and R. Dörner, appeared in the 23 September, 2004 issue of Nature. |
