WHEN a molecule reacts chemically, it often involves breaking at least
one of the chemical bonds holding the atoms in the molecule together. The
bond breaking happens so quickly that experimental chemists thought that
they could never observe it in the laboratory. Now, however, the latest
lasers can produce such short pulses of light that they can illuminate the
fastest of chemical changes, so allowing chemists to watch bond breaking
as it actually happens.
The simplest reaction that we can study in the laboratory is breaking
the chemical bond of a molecule containing just two atoms. Such a process
requires energy. Some molecules break in two, or dissociate, when they absorb
light energy. For instance, when sodium iodide, which has one atom of sodium
(Na) combined with one atom of iodine (I), absorbs light of the right wavelength,
one of the electrons involved in making the chemical bond becomes ‘excited’
and the molecule falls apart.
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Na I + light→(NA . . . I)→Na + I
This reaction happens extremely quickly, in picoseconds (7 million millionths
of a second), so you might think that this is fast enough to be just about
instantaneous. But chemists are very interested in what happens between
the bond being intact and being broken. They invoke a curious sort of ‘in
between’ structure called the transition state (Na . . . I). Henry Eyring,
Michael Polanyi, and M. Evans developed the concept of a transition state
in the 1930s. Since then, chemists have used this idea to interpret how
fast chemical reactions go, and why reactions follow a particular path to
produce one kind of molecule rather than another.
So, for 50 years, transition states have been useful mental constructions,
giving chemists a considerable insight into the factors that influence the
chemical reactivity of molecules. But until recently, they thought that
the detailed nature of transition states would be beyond the grasp of experimenters.
This is no longer true. Last year, Todd Rose, Mark Tasker and Ahmed Zewail
at the California Institute of Technology investigated how sodium iodide
falls apart after absorbing light. Their studies reveal, in astonishing
detail, what the transition state is like.
In its most stable form, sodium iodide, like sodium chloride (common
table salt) is an ionic molecule. The molecule forms because a sodium atom,
which consists of a positive nucleus surrounded by 11 electrons, prefers
to lose an electron to form a more stable configuration of 10 electrons
– a positively charged sodium ion (Na+); iodine, on the other hand, will
readily accept an electron to form a negative iodide ion (I-). So, the sodium
atom passes an electron to the iodine atom. The resulting positive and negative
ions then hold on to each other by electrostatic attraction. This arrangement
is called an ionic bond. The ions adjust their positions so that the energy
of the bond – the potential energy – is at a minimum.
To understand what happens when the molecule breaks up, we need to analyse
how it absorbs energy. If we give the molecule a small amount of energy,
the bond will either stretch or compress. This means that the atoms, or
specifically the nuclei of the atoms, will move correspondingly nearer or
further away from each other. Calculating exactly how the distance between
the two nuclei changes with energy requires a particular assumption. We
assume that the heavy nuclei change their positions relatively slowly, compared
with lighter, faster moving electrons surrounding each nucleus. We can then
suppose that the electrons readjust instantaneously to their arrangement
of lowest energy corresponding to the new positions of the nuclei. This
approximation, first suggested by Max Born and J. Robert Oppenheimer in
1927, is fundamental to the way in which chemists understand how atoms move
inside molecules.
The Born-Oppenheimer approximation allows us to draw an energy ‘map’,
or potential energy surface, that tells us how the energy contained in a
molecule changes with the distance between the nuclei. As we push the sodium
and iodide ions together, the mutual repulsion between the positively charged
nuclei begins to take over from the attractive electrostatic forces. The
potential energy increases rapidly (see Figure 1). When the ions are pulled
apart, the potential energy increases until they reach a point at which
the attractive forces can no longer hold them together; they become physically
separated and the chemical bond is broken.
The potential energy surface is the key to understanding what happens
to a molecule when it falls apart. But the situation is also complicated
by the fact that the molecules do not keep still. They vibrate as though
the nuclei were attached to each other by a spring. There are, therefore,
small changes in energy depending on the degree of vibration. These changes
are not continuous because the nuclei and electrons obey the laws of quantum
mechanics. The energy contained in a molecule must be added or taken away
only in discrete amounts, called quanta. This produces a set of vibrational
energy levels (see Figure 1). Radiation of a particular energy, or wavelength,
usually infrared radiation, will excite the molecule from a lower to higher
vibrational energy level.
Infrared radiation does not usually have enough energy to break the
bond; this requires radiation with a shorter wavelength. Visible or ultraviolet
light will excite electrons involved in bonding from their lowest energy
state to a higher electron energy state (see Figure 2). Each electronic
energy state has a different potential energy surface, with a different
set of vibrational energy levels.
Sodium iodide has two low-energy electronic states with corresponding
potential energy surfaces. Unlike the potential energy surface just described,
that associated with the higher energy state has no minimum (the surface
is said to be repulsive). It corresponds to the situation where no electron
is transferred from the sodium to the iodine atom. As the atoms are squashed
together they repel each other and no bond is formed. Bonding in which electrons
are shared (as opposed to transferred) between atoms does occur in other
molecules and is called ‘covalent’ bonding. We call the higher energy potential
surface of sodium iodide the covalent surface to differentiate it from the
lower energy ionic surface.
We can see in Figure 2 that the ionic and covalent surfaces cross in
what is called the intersection region. In fact, this allows them to ‘mix’
in the region where they cross. The resulting mixed potential surfaces,
called here surface I and surface II (indicated by the dashed lines in Figure
2), have characteristics of both the ionic and covalent surfaces. If we
now look at what happens when we bring a sodium atom close to an iodine
atom, we see that the atoms move smoothly along surface I as the electron
passes from the sodium atom to the iodine atom to form a molecule of sodium
iodide. If the atoms come together too rapidly, they sometimes ‘jump’ from
surface I to surface II. The important point about surface II is that, unlike
the covalent surface, it has a shallow minimum. This means that a weak chemical
bond exists in the electronically excited state of sodium iodide.
What happens if, instead of bringing the atoms together, we pull them
apart? When the sodium iodide molecule absorbs light the molecule jumps
from the lower to the higher electronic state, so moving from the low-energy
vibrational levels of surface I to high vibrational levels of surface II.
As a result, the bond in the excited molecule stretches and passes through
the intersection region. Occasionally, the molecule jumps onto surface I,
so that the bond breaks to form separate atoms. This is the route by which
the molecule breaks up. Excited molecules that do not jump from surface
II to surface I in the region where the curves cross do not break up, but
continue to vibrate until they do, or until they lose their energy (perhaps
by colliding with another molecule).
Zewail and his colleagues could study how the molecules moved along
these potential energy surfaces, using lasers that emit incredibly short
pulses of light lasting only a few tens of femtoseconds. A femtosecond is
an unimaginable millionth of a billionth of a second. These lasers, called
colliding pulse mode-locked (CPM) dye lasers, can emit bursts of radiation
lasting only about 60 femtoseconds .
The experiment required two bursts of light from the laser, each with
a different wavelength: one to excite the molecules and break them up, and
another to analyse what happens during the reaction. A first burst of light,
called the ‘pump’ pulse with a wavelength of 310 nanometres, (a nanometre
is a billionth of a metre), breaks up a large number of sodium iodide molecules.
After a fixed interval, a second pulse, called the ‘probe’ pulse, with a
wavelength of 589 nanometres excites the free sodium atoms produced. The
excited sodium atoms give out the familiar yellow sodium D line. This provides
the researchers with a measure of how many sodium atoms have formed at that
instant.
The researchers varied the delay between pump and probe laser pulses
between 0 and 8 picoseconds (a picosecond is 10-12 seconds), so providing
a series of ‘snapshots’ of the progress of the bond dissociation over a
time interval of 8 picoseconds. Figure 3 shows the results. Figure 3(a)
shows how the signal from the emission of light from the free sodium atoms
grows, and hence shows the growth of the number of free sodium atoms produced
by photodissociation. The signal builds up to its maximum value in about
4 picoseconds, which reflects the average time taken for the sodium iodide
molecule to fall apart. Although this appears to be fast (in 4 picoseconds,
light travels a distance of only 1 millimetre), previous experiments carried
out by Zewail’s group have shown that the photodissociation of iodine cyanide
occurs within 205 + 30 femtoseconds (¿ìè¶ÌÊÓƵ, 22 September 1988, p
32).
The careful observer will notice a couple of interesting wiggles in
the signal shown in Figure 3(a). By changing the wavelength of the probe
laser to 580 nanometres, these wiggles turn into clear oscillations, as
shown in Figure 3(b). Free sodium atoms do not absorb radiation at 580 nanometres,
but it turns out that radiation of this wavelength is absorbed by excited
sodium iodide molecules in the process of falling apart. Indeed, we could
conclude that the signal shown in Figure 3(b) represents light being emitted
from free sodium atoms following excitation of sodium iodide in the transition
state region (Na . . . I). The sodium iodide molecule is caught in the act
of falling apart.
The pump pulse of laser light at 310 nanometres excites sodium iodide
into the high vibrational energy levels of surface II. As the chemical bond
of the excited molecule stretches and passes through the transition state
region, the molecule may also absorb some of the probe radiation at 580
nanometres. The molecule falls apart rapidly as a result of this double
excitation, giving a sudden peak of emission from a free sodium atom. The
total intensity of emitted light is a measure of the number of molecules
that absorbed the probe radiation and, therefore, of the number of molecules
that passed through the transition state region at the time when the probe
pulse passed through the sample. The emission signal acts like a window
through which we can observe the motion of the molecules on surface II.
Every time a large number of molecules move past the window they give themselves
away by absorbing the probe radiation with emission of light from free sodium
atoms. The 60 femtosecond pulses used in the experiments provide a spatial
window of about 0.06 nanometres.
The oscillating signal in Figure 3(b) reflects how the collection of
excited molecules behave. Some molecules take the plunge and dissociate
the first time they pass through the intersection region, so the first peak
in the observed signal is the largest. Those molecules that do not make
it the first time have several more opportunities as their bonds vibrate
back and forth through the intersection region. There is a signal whenever
a large number of molecules pass through the observation window. The result
is an oscillating signal where the period of oscillation represents the
vibrational period of the excited molecules. Analysing the signal indicates
that each sodium iodide molecule has about a 10 per cent chance of jumping
to surface I and dissociating, every time it passes through the intersection
region.
This is a somewhat crude explanation. For a more sophisticated interpretation,
we need to return to quantum mechanics. We describe the behaviour of molecules
in terms of wavefunctions and probabilities. We said that every time a sodium
iodide molecule vibrates past the intersection region, it has the possibility
of jumping onto surface I and dissociating. This view implies that at any
given instant in time the chemical bond possesses a unique length. The Heisenberg
uncertainty principle says that the wavefunction of the vibrational energy
level is not confined to a single value – it spreads out over a range of
internuclear distances and there exists an inherent uncertainty in the value
of the bond length. According to quantum mechanics, the square of the wavefunction
is directly related to the probability of ‘finding’ the molecule in a given
configuration. So, a wavefunction with a maximum at 0.5 nanometres implies
that the molecule has a maximum probability (but not a 100 per cent probability)
of having a bond length of 0.5 nanometres. When the sodium iodide molecule
absorbs light at 310 nanometres, the wavefunction of the lowest vibrational
level of surface I is excited up to high vibrational levels of surface II.
It then begins to ‘explore’ its new surroundings. The nature of the wavefunction
is determined by the nature of the potential energy surface on which it
moves. This means that, at short bond distances, where the mixing between
the ionic and covalent surfaces is weak, the wavefunction is characteristic
of a covalent bond.
Shortly after it is created, the excited wavefunction feels the effects
of the repulsive wall of surface II and consequently moves out to longer
distances (the bond lengthens). After about 200 femtoseconds, the wavefunction
meets the intersection region and, because surface II has much more ionic
character in this region, the wavefunction begins to develop an ionic component
(see Figure 4). After 500 femtoseconds, the wavefunction has moved beyond
the intersection region and has large ionic and small covalent components.
The covalent component can escape through the intersection region leading
to the production of free sodium and iodine atoms. After 700 femtoseconds,
the covalent component, representing the separated sodium and iodine atoms,
has moved out to 2.2 nanometres and the ionic component has turned around
at the outer wall of surface II and is moving back towards the intersection
region. As it passes back through the intersection region it takes on a
predominantly covalent character once more. After 1300 femtoseconds (1.3
picoseconds) the wavefunction hits the repulsive wall of surface II. Reflection
off the repulsive wall sets the cycle of motion going again.
Probe light at 580 nanometres can excite only the covalent component
of the wavefunction, which explains why the observed signal starts to fall
after about 200 femtoseconds, just as the wavefunction is becoming more
ionic. The transition state of sodium iodide is effectively oscillating
between being almost completely covalent to being almost completely ionic
and, consequently, the period of this oscillation, 1.3 picoseconds, is the
period of the oscillations in the observed emission signal.
It may seem odd that the initial wavefunction develops into two, one
representing separated sodium and iodine atoms and one representing intact
sodum iodide molecules. But remember that the square of the wavefunction
represents a probability of finding the molecule in a specified configuration.
When one of the two possibilities (molecule broken or molecule intact) is
realised as a result of experimental measurement, the other possibility
vanishes (the wavefunction is said to ‘collapse’). When the wavefunction
has split and before we make the measurement, the molecule is both broken
and intact: both possibilities exist in the wavefunction.
Experiments, such as those of Zewail and his colleagues, have opened
up a whole new world of chemical reaction ‘dynamics’. Isaac Asimov has compared
these experiments to taking a balloon only four billionths of an inch across
– the size of an average molecule – and sticking a pin into it. The experimental
techniques that Zewail’s group developed are astonishing in their ability
to reveal the finest details of a chemical reaction. They allow chemists
to observe chemistry as it happens, following the progress of a reaction
from the reacting atoms or molecules, through the transition state to the
products. Zewail’s ultimate goal is to use the information available from
his experiments to determine the shapes of the potential energy surfaces
on which chemical reactions occur. He will then be able to compare them
with those calculated using different theories. This will give us not only
a better understanding of chemical reactivity, but also of the theoretical
foundations of physical chemistry.
* * *
The technology of femtosecond lasers
AN ARGON ion laser produces a blue-green, pencil-thin continuous beam
of concentrated light. People often use it in light shows. The output of
the argon ion laser is beautiful, powerful and practical, but not ideally
suited to the needs of an experimental chemist. It produces light only at
certain wavelengths (principally at 488.0 and 514.5 nanometres), so cannot
be tuned to produce a range of wavelengths.
The dye laser, on the other hand, is fully tunable. It relies on an
organic dye dissolved in a viscous solvent, which is continuously circulated
and formed, in a small region of the flow, into a thin jet stream. The focused
beam of an argon laser ‘pumps’ the dye laser, exciting a large number of
dye molecules present in the stream. Spontaneous light emission from a few
excited dye molecules triggers further, stimulated emission from others.
Highly reflecting mirrors form an optical cavity around the jet stream of
dye molecules, causing the emitted light to be turned back into the dye
stream, triggering more stimulated emission and, therefore, amplification
of the light.
One of the mirrors is partially transmitting and the light that escapes
from the cavity provides the laser beam. You can design organic dyes to
operate over a wide range of continuously variable wavelengths. Specially
designed optical elements inside the cavity allow full tunability over the
range of wavelengths of a given dye. As an example, the dye rhodamine 6G
emits laser light in the range 560-640 nanometres (green-yellow through
to red).
Before a continuous dye laser settles down to its stable, steady-rate
emission, it produces a spontaneous emission whose intensity fluctuates
wildly. ¿ìè¶ÌÊÓƵs can exploit these fluctuations to turn a continuous laser
into a pulsed laser, using a technique known as passive mode-locking. A
solution containing a different organic dye is introduced into a second
jet stream inside the optical cavity. First, you choose the concentration
of the second dye to absorb the emission produced inside the cavity until
the intensity of the emission reaches a threshold intensity, at which point
the dye becomes saturated (it ‘bleaches’) and light is transmitted through
it. For this reason, the second dye is called the saturable absorber.
The fluctuations of spontaneous emission from the laser dye can be very
rapid and can reach very high intensities, sufficient to bleach the dye,
which then recovers. The result is a short pulse of emitted light, which
passes through the saturable dye and travels on around the cavity. The ‘gate’
provided by the saturable absorber is opened whenever the pulse passes through
it and closed at all other times. Of course, when the pulse passes through
the laser dye, it triggers more stimulated emission, causing the pulse to
grow in intensity. So, the output from such a laser is a train of ultrashort
light pulses, each lasting a few tens of picoseconds. The time between each
pulse is the time taken to complete one round trip through the cavity, usually
about 10 nanoseconds. Because the eye cannot detect changes in the intensity
of a light beam if they occur on the timescale of a nanosecond, the output
beam, although pulsed, still looks continuous.
But pulses of this kind of length are still too long for the experiments
described here. In a further development of the passively mode-locked dye
laser, Charles Shank and his colleagues at AT & T Bell Laboratories
organised the optical cavity into a ring. The fluctuating spontaneous emission
travels in both directions around the cavity of a ring laser and the concentration
of the saturable dye is adjusted so that it will bleach only when two pulses,
travelling in opposite directions, meet inside the jet stream. The joint
intensity of the pulses is now needed to open the ‘gate’. This arrangement
preferentially transmits the intense, central parts of the pulses, while
the less intense ‘tails’ are absorbed. The selective absorption in the saturable
absorber narrows the pulses, and they continue their journey around the
cavity, triggering more stimulated emission from the laser dye. The technique
is aptly called colliding pulse mode-locking, or CPM for short. The arrangement
is remarkably simple, but it can produce light pulses as short as 90 femtoseconds.
The story does not stop there. With a special arrangement consisting
of four prisms inside the cavity, we can obtain pulse widths of the order
of 30 femtoseconds. Further so-called pulse-compression techniques, using
short lengths of optical fibre, can be applied to reduce the laser pulse
widths down to the order of a few femtoseconds.
In the experiments carried out in Zewail’s laboratory, the femtosecond
laser produces pulses lasting about 40 femtoseconds with a wavelength of
620 nanometres. These pulses are then amplified and split between two ‘trains’
of pulses. Each pulse train passes through a small glass cell containing
flowing water, which converts the 620-nanometre light into light with a
broad range of wavelengths across the whole of the visible region of the
spectrum.
Optical devices are then used to select the appropriate wavelengths
for the pump and probe laser pulses. The pump pulses are formed by selecting
620-nanometre light, which is passed through a small piece of crystalline
material. This converts the wavelength of the 620-nanometre pulses to 310
nanometres, or doubles the frequency. These pulses are further amplified.
The probe pulses are formed by slecting pulses of 580 or 589 nanometres,
and are delayed with respect to the pump pulses by forcing them to take
a longer path to the chamber containing the sample of sodium iodide. The
length of this path is determined by mirrors whose positions can be adjusted
with a precision of less than a millionth of a metre. Increasing the path
length by about 30 millionths of a metre increases the delay between pump
and probe pulses by about 100 femtoseconds, which is the time that light
takes to travel this distance. The sample chamber consists of a heated oven
fitted with windows to allow the laser pulses to pass through, and a detector
to measure the amount of light emitted from free sodium atoms. The sodium
iodide is present as a vapour at a temperature of about 600 Degree C.
Jim Baggott is a freelance science writer based in Reading.