Introduction

The use of spectroscopic techniques to study crossed molecular beam scattering has been both fruitful and difficult to accomplish. The advantage of using laser spectroscopy to detect the products in crossed molecular beam scattering experiments is that one can obtain quantum-state-selective information about the scattering process. The disadvantage is that it is difficult to design an experiment with sufficient wavelength and spatial resolution and detection sensitivity. For this reason until quite recently laser induced fluorescence (LIF) was the only laser-based technique used for the quantum-state-selective detection of scattering products [1–5]. Recently the technique of ion imaging has been used to increase the sensitivity of ionization detection such that resonance-enhanced multi-photon ionization (REMPI) can now be used to detect molecular beam scattering products. Suits et al. were the first, in the early 1990s, to apply ion-imaging techniques to bimolecular scattering [6]. Since then, ion imaging has been found to be a powerful tool for the study of bimolecular inelastic scattering. Ion imaging has been used to measure differential cross-sections (DCSs) [6,7], as well as to measure collision-induced rotational alignment [8] and orientation [9]. In this chapter we will focus on a new application of ion imaging, the retrieving of correlated energy transfer distributions from crossed molecular beam ion imaging experiments.

The previous studies of bimolecular collision systems consisted of a diatomic target molecule colliding with a rare gas atom. The monatomic collider gas has no internal energy, and a single rotational state of the diatomic molecule was detected, using REMPI.

Introduction

This chapter aims to introduce you to the practical aspects of molecular dynamics research using imaging methods. Imaging is a rapidly advancing experimental technique full of possibilities. This puts you in position to make unique and important contributions to the field of reaction dynamics, and you will be the first person to see the secrets of nature appear on your camera screen. Every scientist lives in part for this exciting result and velocity map imaging more than any other method presents the full picture in living color!

Velocity map imaging is the present day variant of the ion imaging method invented by David Chandler and Paul Houston in 1987 [1]. We discovered the advantages of a simple electrostatic lens for the ion imaging method in 1997 [2]. The improvement was so dramatic that David Chandler convinced us to give it the new name, velocity map imaging. Undoubtedly, you or some other clever scientist will discover a new trick to make imaging work even better in the future. Imaging has much to offer in present-day molecular dynamics research, as illustrated in this chapter. This introduction will lead to the following chapters in this book on experimental aspects, data analysis, angular momentum theory, photoionization, and alternative methods.

Introduction

For many years two-dimensional (2-D) and three-dimensional (3-D) fragment imaging techniques have been successfully used in the study of molecular structure [1] and for the study of the dynamics of various molecular dissociation processes, such as photodissociation [2], dissociative recombination [3], atom–molecule collision induced dissociation [4], dissociative charge exchange [5], and others (see review by Zajfman and Heber [6]). The basic experimental scheme includes induced dissociation of a single molecule, from either a molecular ion beam or gas target, and the fully correlated measurement of the asymptotic velocity vectors of the outgoing fragments. If the initial velocity of the molecule is large, then all the fragments will be projected into a cone defined by the ratio of their transverse velocities and the initial beam velocity. In such a case, the transverse velocities are deduced from the 2-D position on the surface of a position sensitive detector, while the longitudinal velocities can be derived from the time of arrival at the detector. The specific physical information provided by the images depends on the particular dissociation process. In general, one obtains information about the initial molecular quantum state prior to the dissociation and the final state of the fragments and about the dynamics of the reaction, such as angular dependence, kinetic energy release or potential curves.

Introduction

One of the most exciting advances in chemical physics in recent years has been the emergence and development of femtochemistry. This has been brought about largely because of advances in ultrafast laser technology, particularly the discovery of self-mode locking in Ti:sapphire and the development of chirped pulse or regenerative amplifiers. Another important innovation has been the development of a variety of linear and nonlinear spectroscopic techniques to probe electronic and nuclear dynamics. Nonlinear methods have been particularly useful in the study of solvation dynamics in the condensed phase. In the gas phase, where the density of molecules is much lower, ionization techniques such as pump-probe mass spectrometry have more often been employed. However, mass spectrometry can only provide the time-dependent population of a chemical species, in other words, kinetic information. In order to extract more detailed information on the reaction dynamics, measurements of the velocity vectors of the photoelectrons and fragment ions produced upon ionization are required. As we have seen in the preceding chapters, an imaging detector placed at the end of a time-of-flight mass spectrometer can easily accomplish such measurements. In this chapter we explore how ultrafast lasers can be coupled with charged particle imaging to develop experimental probes of ultrafast dynamic processes in molecules, such as electronic dephasing (radiationless transitions) and intramolecular vibration energy redistribution (IVR).

Introduction

Many problems in molecular dynamics demand the simultaneous measurement of a particle's speed and angular direction; the most demanding require the measurement of this velocity in coincidence with internal energy. Studies of molecular reactions, energy transfer processes, and photodissociation events can be understood completely only if the internal energies and velocities of all products are specified.

Consider the case of a monochromatic photodissociation that produces two fragments A and B. Even if the internal energy distributions of A and B were each measured separately, it would still be necessary to obtain information on their recoil speed in order to determine the internal energy of B given a selected level of A. Measurement of the coincident level of B would further require that only one parent molecule be dissociated in any particular experiment – a true coincidence experiment. Angular information is also desirable. In photodissociations, for example, the recoil angle with respect to the polarization vector of the dissociating light provides information about the transition moment in the parent molecule and the time-scale of dissociation. Because reactions in molecular beams have many of these same requirements, new techniques for simultaneous measurement of velocity and internal energy are quite important to molecular dynamics.

Many of the current techniques for making simultaneous velocity and internal energy measurements are based on imaging of product molecules or particles with microchannel plate (MCP) detectors.

Introduction

Charged particle imaging provides us with very beautiful pictures that offer graphic insight into chemical dynamics. Although it is often the case that general dynamical information can be deduced by simple inspection of the primary data, the images obtained in the typical imaging experiment are, in fact, projections of a three-dimensional (3-D) object onto a two-dimensional (2-D) screen. In order to extract all the information potentially available to us we need to consider what data recovery techniques are available to reconstruct the 3-D velocity distribution of the charged particles created in the experiment from the image we actually record.

There are two fundamentally different approaches; inversion methods and forward convolution methods. Inversion methods make use of the fact that if the original (3-D) distribution has an axis of cylindrical symmetry its (2-D) projection parallel to this axis contains enough information to unambiguously reconstruct the full (3-D) distribution. As we have seen in the previous two chapters, such an axis of symmetry in laboratory space can be found in many photodissociation or bimolecular scattering experiments. However, if there is no cylindrical symmetry in the experiment, a forward convolution method is generally necessary. Here, the experiment is simulated in a computer model that produces (2-D) data that are then compared with the experimental data. By iteratively optimizing parameters in the computer model the best reconstruction of the experimental data is sought.

Introduction

Houston and Chandler introduced ion imaging in 1987 [1], demonstrating for the first time the potential of this method to be used in chemical dynamics studies. In most chemical dynamics experiments the desired quantity to measure is the state-resolved differential cross section (dσ/dΩ) [2]. This quantity is defined as the amount of product of a chemical reaction, be it a half collision (photodissociation) or a full collision, that is scattered into a unit solid angle per unit of time. Borrowing from the methods of nuclear physics, the pioneers of scattering experiments used the time-of-flight method (TOF) [3] coupled to a rotatable detector to map out dσ/dΩ. Initial experiments employed a universal ionizer to ionize and subsequently detect the products [3]. The universality of the method made it the most successful method for studying a large number of reactive collisions. However, its limited energy resolution was insufficient for detailed studies of unimolecular processes.

It was quickly realized that using high-resolution laser spectroscopic detection of the products would yield a great deal more information than the universal detection [3]. In order to obtain information concerning dσ/dΩ the most popular methods used were Doppler spectroscopy, TOF, or Doppler coupled with TOF [3]. Ion imaging was introduced as a method that combined Doppler and TOF. Its major drawback was its limiting energy resolution, typically 15-20%, coupled with the ‘magical and mysterious’ inverse Abel transformation.

Introduction

The dynamics of chemical reactions can be probed in detail by employing a method of experimentation that is sensitive to both reactant and product internal state energy distributions and velocities and correlations between these quantities. Two main scattering techniques have emerged to study bimolecular reactions of the form A+BC → AB+C.

One is the crossed molecular beam technique [1], in which molecular beams of the reactants A and BC, with well-defined beam velocities, are intersected at some angle. The AB and/or C product velocity and angular distributions are then measured with a form of universal ionization (such as electron impact ionization) and time-of-flight mass spectrometry (TOF–MS). The universal ionization step is used because the product densities are usually too small to allow a form of state selection, such as that of laser ionization, which provides small detection volumes.

Another method is a single beam technique [2,3], in which reactants or their precursors are premixed and co-expanded through a pulsed nozzle thus forming a single molecular beam. A photolysis laser is used to generate hot-atom reactants that subsequently react with other molecules in the beam. After a suitable time delay (typically 50–500 ns) that allows a sufficient density of products to build up, a second (probe) laser is used to state-selectively probe the reaction products, which are then detected with a velocity-sensitive technique (either TOF–MS, or Doppler spectrometry).

The field of molecular reaction dynamics has made enormous progress since the pioneering experiments of Yuan Lee, Dudley Herschbach and John Polanyi. The intervening years have seen numerous developments in both experimental techniques and theoretical methods. For the authors of this book one of the most exciting of these advances was the introduction of charged particle imaging by Dave Chandler and Paul Houston described in their 1987 paper ‘Two-dimensional imaging of state selected photodissociation products detected by multiphoton ionization’ published in the Journal of Chemical Physics.

I was extremely fortunate to be able to join Paul Houston in Ithaca in 1988/89 where we constructed the second imaging machine (Dave Chandler's original machine in Sandia having been temporarily put out of action in an unfortunate accident that Paul describes in the first chapter). It was an extraordinarily exciting experience to be involved in those earlier experiments and I am extremely grateful to Paul for the opportunity. The early data showed the power of the technique to provide graphic insight into chemical mechanism but it was difficult to obtain quantitative information because of instrumental problems to do with the arrangement of the ion optics. These were overcome by André Eppink and Dave Parker working in Nijmegen.

Introduction

As we have seen in the previous chapters inversion algorithms are required in conjunction with two-dimensional (2-D) detection methods in order to reconstruct the velocity (speed and angle) distributions of the products of photodissociation processes. Since these generally need to make certain assumptions about the symmetry of the measured distributions it would be desirable to measure the velocity distribution directly by making a simultaneous measurement of the position and arrival time of each of the photoproducts. In the previous chapter we saw how two charge-coupled device (CCD) cameras can be used in conjunction to make such a measurement. The present chapter develops this idea further by describing a newly developed three-dimensional (3-D) photofragment imaging technique. In this context the term ‘3-D imaging’ refers to the simultaneous measurement of all three coordinates of a single particle, which are defined by the spatial position in the 2-D surface of the position-sensitive detector (PSD) and by the time of arrival at the detector (the third dimension) of the ionized product of a photodissociation process. The transverse velocity components (vx, vy) of the initial velocity of the product are determined from the measured 2-D impact position on the PSD surface, while the measured time of arrival gives the longitudinal component (vz) of the velocity. Hereafter the laboratory axes X, Y, and Z are directed along the laser beam, the molecular beam, and the accelerating electric field, respectively (Fig. 6.1).

A book whose title refers to the spectroscopy of diatomic molecules is, inevitably, going to be compared with the classic book written by G. Herzberg under the title Spectroscopy of Diatomic Molecules. This book was published in 1950, and it dealt almost entirely with electronic spectroscopy in the gas phase, studied by the classic spectrographic techniques employing photographic plates. The spectroscopic resolution at that time was limited to around 0.1 cm−1 by the Doppler effect; this meant that the vibrational and rotational structure of electronic absorption or emission band systems could be easily resolved in most systems. The diatomic molecules studied by 1950 included conventional closed shell systems, and a large number of open shell electronic states of molecules in both their ground and excited states. Herzberg presented a beautiful and detailed summary of the principles underlying the analysis of such spectra. The theory of the rotational levels of both closed and open shell diatomic molecules was already well developed by 1950, and the correlation of experimental and theoretical results was one of the major achievements of Herzberg's book. It is a matter of deep regret to us both that we cannot present our book to ‘GH’ for, hopefully, his approval. On the other hand, we were both privileged to spend time working in the laboratory in Ottawa directed by GH, and to have known him as a colleague, mentor and friend.