List of Participants *

Executive Summary *

I. Overview *

II. Importance of Theoretical Simulation of Electron Initiated Chemistry *

A. The Elementary Processes *

B. Plasma Processing *

C. The role of electron-stimulated chemistry in the environment *

i) Plasma Remediation *

ii) Mixed Waste Storage and Treatment *

III. New Research Opportunities *

A. Advances in electron scattering *

B. Advances in structure theory and computing *

C. Important Problems That Can Be Addressed in the Near Term *

D. Problems Requiring Major Future Investment *

i) Excitation cross sections *

ii) Branching ratios and dynamics of highly excited molecules *

iii) Ionization (especially excited states) *

iv) Cross sections for processes in condensed phases and interfaces *

v) Electron transport phenomena (vibrational excitation of polyatomics) *

IV. Outline of a New National Research Program *

A. Excitation *

B. Dissociation *

C. Dissociative attachment and recombination *

D. Ionization *

E. Electron Transport *

V. Educational Impact of a New National Program *

Executive Summary

Electron-molecule and electron-atom collisions initiate almost all the relevant chemistry associated with mixed radioactive wastes, the plasma processing of materials for microelectronics, and modern electric lighting technology. In addition, in environmental remediation and chemical synthesis using plasmas and in planetary upper atmospheres electrons drive much of the chemistry. In spite of the importance of these fundamental processes, which include the fragmentation and excitation of molecules and atoms, relatively little is known about them. Only components of the fundamental physics and chemistry are well understood, and only a few of the required cross sections and rates for the multitude of important molecules are known with confidence.

Advances in electronic structure theory [1] over the last fifteen years, combined with the emergence of Terascale computing platforms, on which many of those structure codes already run, have provided an entirely new context in which to attack the electron-polyatomic molecule scattering problem. The last ten years have also seen separate advances in electron scattering theory that have made it possible to carry out multichannel electronic excitation calculations on polyatomics [2]. In addition, access to Terascale computing platforms will become more broadly available to researchers in the next five years, completing the arsenal for addressing these problems successfully. This combination of advances arising in different research communities has set the stage for the first comprehensive attack on the problem of electron-driven chemistry. The opportunity now exists to build the next generation of electron scattering codes and theories within the current context of the rich infrastructure of bound state quantum chemistry.

The principal applications for data on electron-driven chemistry require results in the near term. In environmental remediation of mixed radioactive wastes, for example, strategies for action must be developed now, before further damage and degradation at storage sites, such as Hanford, occurs. In plasma processing of microelectronics components, new technologies must be developed in a very few years to have an impact that assures the future of the industry. The fact that a new fabrication facility costs in excess of one billion dollars, most of which is in the equipment, amplifies this urgency. In addition, there is significant interest in using plasmas for molecular synthesis in order to develop new "Green" chemical processes with reduced waste streams and novel chemistries.

For these application areas, as well as for the areas of modern lighting technology and atmospheric chemistry, the time scale for performing experiments is long. The experiments are difficult because of the large number of types and states of neutral fragments that can be produced in electron collisions with polyatomics. In addition there is a large number of molecules that feature in both plasma processing and environmental chemistry for which this data is required.

It is alarming, in view of the urgent need for a quantitative understanding of electron-driven chemistry, that over the last twenty years there has been a rapid decline in the number of research groups worldwide involved in measuring various cross sections for electron scattering by atoms and molecules. Several factors have contributed to this decline, including the lack of high quality theoretical results to compare with and to aid in the analysis of the experimental data. Although a detailed outline of an experimental program to balance the theoretical and computational program described here is beyond the scope of this report, this workshop highlighted the scarcity of benchmark data to compare with theory on even the simplest systems of interest. New experiments on more complex molecules are also necessary. A wide variety of factors can influence the cross sections and branching ratios in those cases, and the availability of theoretical data will be especially important for interpreting and guiding those experiments. The value of theory for these systems stems from its unique capability of providing a means of "dissecting" interactions and determining the relative contributions of different factors (e.g. long-range through-bond interactions, spin-orbit effects, or vibronic coupling) that can influence the magnitudes of the cross sections and branching ratios. The absence of theoretical data and feedback from theorists represents a significant handicap to experimentalists, and the lack of experimental data is a continuing impediment to theory.

Although major advances have been made in the application of quantum chemical methods to bound states (as recognized by the 1998 Nobel Prize in Chemistry), progress has been much slower for the development of theoretical approaches for studying problems in which the continua must be considered explicitly. The stage is now set for similar progress in understanding electron dynamics in polyatomic collisions.

The workshop recommendations are that a large-scale, multidisciplinary and collaborative effort be mounted to solve these problems in a timely way so that their solution will have the needed impact on the urgent questions of environmental chemistry and industrial technologies. The recommendations are summarized in the proposed outline of a new national research program in this area. A theoretical and computational program is all the more urgent in view of the decades that would be necessary to address these issues by experiment alone. Each of the vast number of required experiments is intrinsically difficult, and can require extensive theory for interpretation. Moreover, it will take years to reverse the decline in the number of research groups world-wide engaged in measuring electron collision phenomena.

I. Overview

The opening session of the workshop focused on the role of electron-driven chemistry that impacts the environment and is important in plasma processing of materials. From the initial presentations, and as the ensuing discussion unfolded, a clear theme emerged: electron-molecule collisions initiate almost all the chemistry in both of these contexts. In the case of mixed radioactive wastes, the primary products of radioactive decay interact with the surrounding matter to produce copious numbers of secondary electrons. The inelastic scattering of these electrons dissociates and excites molecules, thereby driving chemistry ranging from the production of volatile gases to the alteration of the surface properties of solids. In the case of plasma processing of microelectronics components, none of the etchant gases etch silicon before electron collisions tear them into reactive fragments. Even the newly important technique of ionized metal physical vapor deposition depends critically on excited states of metal atoms and their ions. In addition to the two areas primarily discussed at the opening of this workshop, the areas of modern lighting technology, plasma organic synthesis, and atmospheric chemistry also depend critically on electron-driven chemistry.

In most of these elementary processes it is the dissociation of polyatomic molecules that is the key step. Only the rudiments of those dissociative collisions are understood, and it is not an exaggeration to state that it is currently beyond the state of the art to predict the branching ratios of the fragments and their excited states. The central question of what reactive molecular fragments are present can only be answered by an understanding of how they are generated. The transient nature of the products, and the detailed nature of the required information about the states of the neutral fragments, makes the relevant experimental determinations on polyatomic dissociation extremely difficult. There is a paucity of even benchmark experimental data. An additional complication is that these processes happen both in gas and condensed phases. They are not yet understood even in the gas phase, and the alteration of the gas phase processes in condensed media remains an almost completely unanswered question.

The remaining sessions of the workshop dealt with the theoretical approaches to various aspects of the problem of understanding electron-driven chemistry. Over the last twenty years the worldwide community of theorists working on electron-molecule collisions has settled on a few powerful methods that solve what was once the key question about these collisions. That question was how to treat the simplest elastic scattering of electrons from polyatomic targets whose dramatically nonspherical nature makes it impractical to expand the wave function about a single center. With methods in hand that solved that problem, the effort turned in recent years to the treatment of the intricate connection of the two kinds of electron correlation operating in these collisions. The correlation between the incident electron and those of the target is actually responsible for the transfer of energy to the target, but it cannot be separated from the correlation among the target electrons that determines the excited states.

While there have been remarkable calculations for a number of diatomic and a few polyatomic molecules that treated this problem with varying levels of success, they have in general not taken advantage of many of the developments in bound-state quantum chemistry of the past fifteen years. The difficult electronic continuum problem for polyatomics has been formulated outside the context of bound state electronic structure, and components of modern quantum chemistry technology have been grafted onto it.

A second major theme of the workshop emerged from these discussions. It can be stated simply: It makes no sense to build the next generation of electron scattering codes and theories outside the context of the rich bound state quantum chemistry infrastructure of codes and approaches which now exists. Moreover, the problems associated with electron driven chemistry cannot be solved by any other theoretical approach. These two communities must collaborate to address these questions, or they will not be answered. In both the major areas of application discussed below, there are issues of timeliness as well as of accuracy of the required results. The consensus is that only a broad collaboration between the quantum chemistry and electron scattering theoretical communities, which produces a new approach to this problem from the existing theoretical components, can successfully produce results on a relevant time scale.

Finally, it has become clear that the scale of computer resources required for these calculations rivals that of any quantum chemistry application to the bound electronic states of even very large molecules. The complications of simultaneously treating the continuum and bound electrons, even for targets with less than ten atoms, will stress the largest massively parallel computers currently available in the world. The extension of these calculations to the condensed phase is a daunting computational task. It is as great as any that has been contemplated for the future computational resources that are likely to exist as massively parallel computers extend to tens of thousands of processors.

In the panel discussions the workshop turned to the planning of a national research program in this field. The outstanding theoretical questions were identified and parsed into those on which progress could be made in the short term of the next few years and those which require a longer-term investment.

The structure of this report is as follows. In the next section, Section II, the importance of theoretical simulation of electron initiated chemistry is analyzed by examining the needs of the two major practical applications discussed at the workshop, environmental chemistry and plasma processing. In Section III a collection of research opportunities is discussed, and finally in Section IV a possible new national research program which would address these problems is outlined.

II. Importance of Theoretical Simulation of Electron Initiated Chemistry

A. The Elementary Processes

Electron collisions, with a variety of different species and in a variety of environments, play a key role in creating the energetic species that drive the chemistry in extreme environments such as the low-temperature, high-density plasmas used in the etching of semiconductor materials and in plasma enhanced chemical vapor deposition. Electron collisions also figure importantly in a number of environmental chemistries, such as those driven by secondary electron cascades in mixed radioactive waste or in the plasmas used to destroy undesirable compounds or remediate NO_x. For example, modeling chemical vapor deposition requires the knowledge of the mechanisms and rates of formation of hundreds of radical and ionic fragments.

Electronic collisions are uniquely effective in transferring energy to and from the electronic degrees of freedom of the target atom or molecule. For example, unlike "collisions" with photons, which obey a set of selection rules determined primarily by dipole interactions, collisions with electrons can produce singlet-to-triplet transitions with the same or larger probabilities than singlet-to-singlet or triplet-to-triplet transitions. Electronic collisions do not obey selection rules with regard to singlet-to-triplet excitation because the incident electron can exchange with those of the target and thereby change its spin state. Thus electron impact can excite any dissociative state of a molecule and reduce it to fragments, and this is a key mechanism by which radicals and molecular fragments are produced in situations ranging from planetary atmospheres to molecular beam sources for experiments in molecular collisions. Another important process is electron-impact ionization, because this is the mechanism by which ions are created in any gas discharge system, and because it can produce any ionic state of the target.

B. Plasma Processing

Plasma etching, deposition and cleaning are indispensable fabrication techniques in the manufacture of microelectronics components. The plasma equipment for these processes typically use partially ionized (fractional ionization less than 1%), low pressure (a few mTorr – 100s mTorr) plasmas to provide activation energy to dissociate and ionize feedstock gases. The resulting radicals and ions interact with the semiconductor surface, either removing or adding material, to define the desired features or modify the surface. The high cost of developing both the plasma equipment and processes has motivated development of less empirical methods, and modeling/simulation in particular, to speed the time to market and to reduce costs. Following a National Research Council (NRC) report in 1991 which cited the need for science based design of plasma processes [3], a modeling and simulation infrastructure was developed which can now address a wide variety of plasma tools and surface processes.

The application of this modeling infrastructure to industrially relevant problems has, to date, been limited by the availability of fundamental data (e.g., electron impact cross sections, reactive surface sticking coefficients) and validated reaction mechanisms. This situation was described in a second NRC report, "Database Needs for Modeling and Simulation of Plasma Processing"[4]. In the report, target gases were listed which require electron impact cross sections for two etching processes and one deposition process. These are not the only gases of interest, but are representative of the chemistries used for those processes. (See Table 1.) Since the report, other chemistries and types of processes have come to prominence for which databases are also required. This situation, where old chemistries/processes fall from favor and new chemistries/processes quickly come to prominence, is typical of the rapidly changing needs of the microelectronics industry. For example, Ionized Metal Physical Vapor Deposition (IMPVD) is a method whereby deep vias can be filled or lined with metals for interconnect wiring. At the time of the NRC report (written in late 1994, early 1995) IMPVD was an inconsequential process. Now, IMPVD is an exceedingly important process, and so brings with it needs for cross sections for metals, their excited states and ions. This rapid change in priorities emphasizes the need for developing rapid, computational techniques to produce cross sections on industrially relevant time scales.

The databases, that is, the cross sections and rate constants that support this modeling infrastructure, are complete for only a small subset of the gas chemistries of interest. Fluorocarbon compounds (i.e., CxHyFz) with admixtures of rare gases and O2 are typically used for etching of crystalline silicon and silicon dioxide. Chlorine containing gases (e.g., Cl2, BCl3) are typically used for poly-silicon and metal etching. With the exception of CF4 and Cl2, the electron impact and ion transport databases for these compounds are fragmentary, as is the database for reactive sticking coefficients of their radicals with the polymerized surfaces typically encountered in actual etching reactors. Since the majority of new plasma tools operate at low pressure and high plasma densities, the feedstock gases are highly fragmented, in some cases over 90% dissociated. These conditions emphasize the need for electron impact dissociation cross sections and cross sections for fragments of the feedstock gases.

The required accuracy of the database varies with the intended use. For example, to optimize the uniformity of plasma generation in an etching reactor, it is not necessary to employ the gases which will be used in the actual etch process. It is, however, important to use well-characterized gases whose behavior can be accurately modeled and which are representative of classes of the process gases. For example, well characterized cross section sets might be required for a highly attaching easily dissociated gas mixture and a weakly attaching gas mixture which is largely undissociated. On the other hand, when "screening" large numbers of different chemistries, the required accuracy may not be as critical as being able to self consistently compare many different chemistries. Hence there are needs for both ab initio and semi-empirical methods for developing databases. The first maximize accuracy and are expensive, and the second rapidly produce databases at the cost of some degree of accuracy.

Because of the paucity of reliable experimental data for most of the relevant processes, it is important for producers of the calculated cross sections to closely collaborate with plasma equipment and process modelers who will use the data. By incorporating the data into the plasma models and reproducing experimentally observed plasma behavior (e.g., plasma density vs. gas mixture at constant power), one can obtain a "working" validation of the cross section sets.

C. The role of electron-stimulated chemistry in the environment

Low temperature plasmas are particularly attractive for treatment of low-level waste concentrations and for dealing with compounds that resist treatment by standard chemical means. One important class of these compounds is halogenated compounds such as carbon tetrachloride (CCl4), trichloroethylene (C2HCl3) and hexaflouroethane (C2F6). The destruction and treatment of such compounds is particularly important since some of the chlorinated solvents were used for decades in a wide variety of processing applications. For example, CCl4 has been used extensively in the chemical processing of irradiated nuclear materials [6]. At the Department of Energy’s Hanford site in Washington State, several hundred thousand gallons of CCl4(l) were discharged over the 40+ years of plutonium production. Presently, the most contaminated spots contain ~ 8000 ppb of CCl4 in the groundwater which greatly exceeds the drinking water standard of 5 ppb.

Remediation of large inventories of halogenated solvents clearly relies upon the development and deployment of effective and efficient treatment methods. In packed-bed coronas, the high frequency of surface collisions involving reactive and/or energetic species suggests that surface mediated processes could also effect the overall plasma efficacy. The synergism between the electron-induced plasma chemistry and surface reactions can be exploited in the treatment of waste streams as well as in reduction of nitrogen oxides in highly oxidative combustion exhaust streams. Such an approach is being developed for the treatment of diesel and automotive exhaust emissions and thus, technologies involving electron-molecule scattering may help in the reduction of urban pollution from non-stationary sources.

In addition, one can extend the concept of chemical destruction to chemical synthesis in plasmas. For example, controlled oxidation of alkanes is one of the "Grand Challenges" of industrial chemical research because of the tendency of the oxidation process to lead to the thermodynamic sink products, CO and CO₂. The ability to specifically control the site and amount of oxidation would enable the use of cheap feedstocks (simple alkanes and alkenes) to make a wide range of intermediates for further synthetic changes. In order to develop new industrial-strength processes that are more energy efficient and produce less waste, new types of technologies need to be developed. One such technology which is being investigated is the gas phase corona reactor (GPCR). The phenomena of significantly enhanced reaction rates in a gas phase plasma raises the potential of utilizing a non-equilibrium plasma for chemical synthesis reactions. Only ozone formation has to-date proven economic. It is generally recognized that plasma reactions feature the advantage of producing high energy active species which can produce different reaction pathways than those available through traditional thermal activation. However, the reaction pathways have, so far, not been controllable and have consumed too much power. Computational research would significantly enable this field to become more competitive with traditional synthesis methodologies.

Understanding the inelastic scattering of low-energy electrons with molecules such as water is also important with respect to the safe interim and long-term storage of spent nuclear fuel (SNF). Thousands of tons of metallic uranium SNF remain in water storage across the Department of Energy complex. For example, Hanford site K-basins hold 2300 tons of SNF, much of it severely corroded. The DOE plans to remove this fuel and seal it in overpack canisters for "dry" interim storage, for up to 75 years awaiting permanent disposition [7]. Chemically bound water may remain in cracks and bound to surfaces and interfaces even following proposed drying steps. Safety concerns are related to the non-thermal production of potentially explosive mixtures of hydrogen and oxygen gas in storage canisters. Studies on water thin-films indicate that dissociative electron attachment resonances [8] and the decay of excited states [9] created directly or via ion-electron recombination can lead to the direct production of molecular hydrogen. Unfortunately, the relative importance of these channels (dissociative electron attachment and dissociative recombination), ionization and reactive scattering of radicals and hot atoms on the production of molecular hydrogen and oxygen in SNF canisters have not been fully resolved. This is largely due to the fact that the theoretical and experimental information available on electron-driven processes in the gas, condensed and interfacial phases is insufficient to develop models which adequately describe DOE waste issues.

III. New Research Opportunities

In the case of atomic targets, the numerical R-matrix approach of the Belfast group has been the basis of computer programs that have described a wide range of processes at low incident energies (below the ionization threshold). These programs are now used world-wide and have formed the basis of several international collaborations, including most notably the international Opacity Project and the Iron Project.

There has also been significant new theory and methods development in the past few years. Traditionally, electron and photon collisions with atoms and ions have been described either by perturbative or non-perturbative methods, based upon the Born-series or the close-coupling expansions, respectively. Such methods are expected to yield somewhat reliable results in the limits of "high energy" (Born) or "low-energy" (close-coupling) scattering. The development of the "convergent-close-coupling" (CCC) approach has breached this gap and lead the way for other methods, such as time-dependent and other more direct approaches for the solution of the scattering equations. These methods account for the coupling between discrete and continuum target states and thus should (in principle) yield reliable results independent of the collision energy.

B. Advances in structure theory and computing

Dramatic improvements in computers have occurred over the past 20 years with the development of vector and vector/parallel computers, RISC architectures, powerful desktop computing, and, more recently, massively parallel computing systems based on lower cost RISC processors. With the availability of new high-performance computers, new algorithms and new theoretical methods have been developed to take advantage of the increased computational power. By combining workstation processors with good performance into massively parallel computing systems with distributed memory, it is now possible to attain on the order of a Teraflop of peak performance at reasonable cost. Furthermore, such computational power is no longer restricted to the sole use of specialized practitioners; access to high performance computing is becoming available to a much broader user community. Because of the dramatic increase in computational power and improved algorithms and software, computational chemistry can now be a partner with experiment in efforts to develop new materials and chemical processes. One can actually do computations with the required accuracy on molecular systems of real interest to experimental chemists across a broad range of the chemical enterprise.

Computational chemistry has, for many years, provided qualitative insight into chemical phenomena and guidance to experimentalists. During the past five years there has been a revolution in our ability to compute the thermodynamic properties of molecules from first principles. This revolution has resulted from a combination of factors. The first is the development of efficient computational implementations of coupled cluster methods to solve the n-body problem. The second is the development of a family of efficient, increasingly accurate basis sets, the correlation-consistent basis sets, for solving the coupled cluster equations. These basis sets provide a good solution to the one-body problem and have been made widely available through the use of modern World Wide Web technologies. The third is the continuing advancements in computer technology, both hardware and software, noted above. With current computer technology, it is possible to predict bond energies and heats of formation for molecules with 6 or fewer first row atoms, including fluorinated compounds of interest to plasma processing, as well as radicals and ions, to an accuracy of better than 1 kcal/mol. The range of molecules that can be treated will grow dramatically over the next several years as computer technology transitions to the teraflops capabilities of tomorrow and to the petaflops capabilities of the not-so-distant future.

There have been many other advances in addition to those discussed above. They include:

1. new methods for computing, approximating, and eliminating the two-electron integrals (ij|1/r₁₂|kl) in ways that scale nearly linearly with the physical size of the molecule rather than as the number of atomic orbitals, N, to the fourth power;
2. the wide use of density functional theory (DFT) by chemists, the improvement of the computational methods of DFT and the invention of new functionals that permit electron correlation and exchange to be handled more accurately (DFT has a significant computational scaling advantage over traditional methods that treat electron correlation);
3. major improvements in the efficiencies (including parallel implementation as well as strategies that permit near-linear scaling with system size) of theories that compute electron correlation energies, including the Møller-Plesset perturbation method, the configuration-interaction (CI) method, coupled-cluster (CC) theory, and multiconfigurational self-consistent field (MCSCF) theory;
4. developments of theories designed to compute energy differences (e.g., electron affinities, ionization potentials, and excitation energies) and responses to external perturbations directly; and
5. the effort to implement parallel computing techniques and to redesign existing methods to permit higher degrees of parallelization.

Although most of the calculations that are performed using modern electronic structure codes involve bound electronic states (they often involve scattering nuclear-motion states), it should be noted that most, if not all, of the advanced methods noted above have also been applied to electronic shape and Feshbach resonance states. In most such applications, only slight extensions to existing bound-state codes (e.g., to incorporate complex electronic coordinates for performing scaled coordinate calculations or to include box-normalized functions for stabilization calculations) have been necessary.

However, by making the remaining extensions of structure codes that would allow true continuum basis functions to be used, a complete interface between electronic structure theory and electron-molecule scattering can be realized. Among the methods noted above, the so-called Green’s function (GF) or equations of motion (EOM) methods seem to be especially attractive for electron-molecule scattering problems because they focus directly on the interaction of the scattering electron with the molecular target. They thereby permit the scattering electron to be described in terms of continuum and localized orbitals while retaining conventional orbitals for the other electrons. Modern GF and EOM methods permit the target to be described in a highly correlated manner (i.e., not simply in a single configuration static-exchange picture) and thus produce an electron-molecule interaction that includes electrostatic, polarization, and correlation effects.

C. Important Problems That Can Be Addressed in the Near Term

Although we have focused elsewhere on the need to improve both the incorporated physics and the numerical implementation of all methods currently in use, it is important to recognize that the computational study of electron-molecule collisions in important technological contexts is not merely a bright prospect; it is a current reality. There are many useful calculations that can be performed with currently available variational methods on a variety of technologically significant polyatomic species. These techniques have already been shown to be capable of providing highly accurate cross sections in a few important cases involving small polyatomic targets where experimental data was available for comparison. In many other cases, especially those involving reactive species and complex polyatomic target gases, theory has proved to be the "only game in town" and thus the sole source of critically needed collision data. While improvements to existing methodologies are under way, studies using existing codes will continue to be of immediate practical benefit.

One area in which such calculations can make an especially valuable contribution is the characterization of replacement gases with lower greenhouse potential than those currently used in the semiconductor industry. Although the need to identify such replacements is increasingly pressing, most of the candidate gases are as yet poorly studied experimentally. Calculations using existing methodology can provide elastic and momentum-transfer cross sections for such gases, as well as excitation cross sections for the lowest-lying electronic states. Together with selective theoretical studies of dissociation on excited-state potential surfaces, calculations of this kind would aid in identifying the most promising gases for more detailed characterization.

Of course, there are practical limitations on what can be expected from current methods without substantial future investment. For very large target molecules, the calculations are currently limited to the use of simple target wave functions. Electronic excitation can be studied using only a small number of coupled states and the extent to which polarization effects, which are very important at energies below a few electron volts, can be accurately treated depends very strongly on the complexity of the target. An investment now will allow investigators to leverage existing methods and computational platforms to make an immediate impact on both plasma processing and environmental chemistry. Benchmarking against experimental measurements will be essential to bring the credibility that will be needed for a sustained future effort.

The importance of Ionized Metal Physical Vapor Deposition (IMPVD) is creating a need for cross sections for electron collisions with metal atoms, particularly for electron impact on excited states and ions. Most of the atomic data made available from the Opacity and Iron Projects can already be used for modeling purposes at sufficiently low energies, and the accuracy for transitions involving many targets with low and intermediate (<30) nuclear charge Z may be increased if necessary. For intermediate energies, the above mentioned CCC and the recently developed "R-matrix with pseudo-states" (RMPS) methods have shown to give very reliable results for a few benchmark cases, and so have time-dependent close-coupling (TDCC) approaches. Both excitation and ionization can be treated in these methods. Due to the computational demands, however, their application is currently restricted to simple quasi-one and quasi-two electron atomic targets that can be described in a non-relativistic model.

Finally, distorted-wave methods are available for complex atomic and molecular targets. These should yield reliable results for sufficiently high incident energies and the dominant, optically allowed transitions. Also, estimates of electron-impact ionization cross sections for many atoms and molecules from the ground state can be made using the "Binary-Encounter-Bethe" (BEB) method.

D. Problems Requiring Major Future Investment

Despite the availability of methods and codes for studying a wide range of electron scattering problems, it has become clear that very large problems of crucial importance in many applications cannot be tackled by the present generation computer programs. The treatment of hundreds and probably thousands of coupled channels clearly requires both major rethinking of the underlying theory and a complete and fundamental rewriting of the corresponding codes. The existing ensemble of computer codes assembled by the international community working in this area undoubtedly runs to many hundreds of thousands of lines, and the scale of the effort required is to replace it all. The new effort will have to be made in the context of modern quantum chemistry codes which will themselves have to be modified, possibly extensively, to provide the appropriate infrastructure for the simultaneous treatment of continuum and bound electron dynamics.

For collisions above the ionization threshold, there are still fundamental theoretical questions to be answered and accurate calculations of ionization cross sections are still only possible for simple atomic systems. Calculations of excitation cross sections that involve Rydberg states pose significant technical problems for both atomic and molecular targets. And finally, the treatment of post-collision dynamics in polyatomic excitation, the elucidation of dissociation pathways and the determination of branching ratios is a grand challenge scale problem that will require an interdisciplinary effort involving quantum chemists, electron collision theorists and heavy-particle dynamicists before significant progress can be made.

In light of the current revolution in scientific research arising from the rapid advances in computer power and computational methods and algorithms, particularly the development of massively parallel processors (MPPs), major advances towards the solution of these problems can be expected within the next few years. However, the novel architecture of the MPPs requires the rewriting of many program packages for optimal use on such machines. Moreover, effective use of the teraflop-scale computers that are likely to be available in the near future will require careful program design or redesign, even for methods that already deliver tens of gigaflops on today's architectures. Potential bottlenecks that will emerge in areas such as the user interface and I/O must be anticipated and addressed if detailed studies of large polyatomics, possibly encompassing many channels and/or nuclear geometries, are to become feasible. The porting of the Schwinger multi-channel codes to highly parallel MPP platforms represents a significant step. In the case of electron-atom scattering, substantial efforts are already underway in the UK along this direction, with special emphasis on the further development of the R-matrix codes. The current status of this work is summarized in a recent special issue of Computer Physics Communications [10].

Excited-state dynamics is a field of its own and the difficulty in computing excited state surfaces, much less computing the relevant spin-orbit and non-adiabatic coupling matrix elements, has limited the number of workers in this field. It is possible to put a correlated wave function on a dissociative surface and follow the gradient to the dissociation products. It is also possible to obtain the coupling matrix elements along this trajectory. If only this piece of the excited state surface is adequate, then considerable progress can be expected in this area as well. Several codes are currently available to compute these quantities, but they need to be updated and are definitely not user friendly.

The scale of calculations involving both the steps of electron impact excitation of dissociative states of polyatomics and the subsequent heavy-particle dynamics is hard to exaggerate. Either of these steps alone is at the current limits of ambition of the theoretical communities engaged in solving them separately. The challenges associated with predicting dissociation dynamics following electron-impact excitation are not, of course, new or unfamiliar; in particular, they have been encountered over the years in studies of photochemistry. What is perhaps new is the need to undertake such studies for rather large molecules, in which both the density of excited states and the dimensionality of the potential energy surface are increased. Moreover, excitations that are not relevant in photochemistry will figure prominently in electron-initiated chemistry, which does not respect optical selection rules. The number of dissociative states, their surface crossings and nonadiabatic nuclear motion which feature in this problem will require calculations of a scale that will tax the largest massively parallel computers envisioned for ten years from now.

Knowledge of vibrational excitation cross sections is crucial for modeling plasmas. Being able to account for the distribution of vibrationally excited molecules is especially important given that dissociative attachment (DA) cross sections can be orders of magnitude greater upon electron impact on vibrationally hot than on vibrationally cold molecules. In many cases the vibrational excitation will be dominated by the decay of temporary anions. Modeling these processes theoretically is particularly challenging due to the coupling of the temporary anion state to the autoionization continuum and the necessity of treating nuclear dynamics over a wide range of geometries. A further complication is presented by the fact that many of the molecular species present in plasmas are radicals, opening up the possibility that spin-orbit or Coriolis effects may be important.

IV. Outline of a New National Research Program

There are number of key areas that must be addressed by a national research program if it is to solve the problems raised in the foregoing sections. The attack on these problems is discussed below, and the specific theoretical difficulties are explained. It is useful to summarize these areas of challenge and inquiry as shown in Table 2. The scale of the calculations that will be necessary in each of these areas is indicated in a relative way

Table II. Areas and Problems for a new national research program

 
 

Area/Problem	Fundamental Questions	Scale of Calculations
Electronic excitation	Do close-coupling expansions converge?	Very large, equal to largest quantum chemistry
Dissociation	What are the branching ratios and dynamics on excited polyatomic surfaces?	Largest, larger than current reactive scattering
Dissociative Attachment and Dissociative Recombination	What is the importance of multidimensional effects in nuclear dynamics?	Largest, but even more complicated than simple dissociation
Ionization	There is no known formulation that is practical for molecules	Very large, even atomic calculations tax current computers
Electron transport	The N and N+1 electron correlation problems are not optimally described by conventional CI methods	Large
Condensed phases/ Interfaces	How can gas phase methods be extended to condensed media?	Largest, at least of the scale of the largest materials calculations now contemplated

 

A. Excitation

Electron impact electronic excitation plays a crucial role in molecular plasmas for a number of reasons: it is the main route to electron impact dissociation, electronically excited states are chemically very active, and the process leads to electron cooling. In many cases part of the energy transmitted into excited states will be lost to the plasma by emission of photons.

Reliable electron impact excitation calculations are base upon the simultaneous accurate representation of many electronic states of the target, and of the complicated interactions between these states and the impacting electron. So far only relatively crude target state representations have been used in collision calculations. This problem can be resolved by harnessing the latest advances in quantum chemistry. More difficult is the finding that the standard close-coupling expansions, used to represent polarization interactions, do not converge well. This problem is exacerbated by both the presence of low-lying diffuse (Rydberg) states in most molecules and the many such states at intermediate energies. New methods to address this problem will need to be developed. Possible approaches include the use of very large (pseudostate) expansions, now being widely used in electron-atom collision calculations, or the development of suitable optical potential methods to model these effects.

B. Dissociation

Electron impact dissociation resulting in the formation of neutral fragments remains a process where the available data is sparse. The development of new computational and experimental techniques is therefore needed. An exciting possibility is a new type of experiment utilizing ion storage rings that may provide a major advance in the study of molecular dissociation. Initial experiments may not include those molecular systems directly involved in plasma processing but should provide valuable information on the dynamics of electron impact dissociation.

The characterization of how a molecule fragments following electron impact excitation is perhaps the single most important process to understand in modeling low temperature plasma processing and electron-driven environmental chemistries. Many of the low-lying electronic states of polyatomic molecules are dissociative (indeed for technologically important systems like CH4 or CF4, all electronically excited states are believed to be dissociative). It will be important to extend current methods to be able to handle large numbers of excited states and to incorporate the most recent advances in quantum chemistry in describing these states. Coupling the study of the post-electron-collision dissociation dynamics to the electron-molecule scattering problem will require excited-state energy surfaces, coupling elements and chemical dynamics in a truly interdisciplinary effort.

C. Dissociative attachment and recombination

Dissociative electron attachment is perhaps the best characterized electron interaction with many of the molecular systems pertinent to plasma processing and is the subject of considerable theoretical effort. However, most of the theory has used a simplified one-dimensional model for the nuclear dynamics, which is only correct for diatomics. The importance of multidimensional effects in DA to polyatomic targets remains largely unexplored. Moreover, the role of internal excitation within the target remains to be quantified.

Dissociative recombination (DR) remains a difficult process to study either theoretically or experimentally. The construction of storage ring facilities have led to major advances in our understanding of the dissociative recombination process but some key cross sections remain controversial. Ab initio theory has proven to be very useful in the interpretation of experimental DR data but may produce absolute cross sections that are in error by one or more orders of magnitude.

The chloroalkanes are an example of a class of molecules for which some of the experimental results on these processes are not well understood. Most noteworthy, the large differences in the vertical electron attachment energies (VAE) and dissociative attachment (DA) cross sections between C2H5Cl and CH3Cl have yet to be accounted for on the basis of first principles calculations. Knowledge of the branching ratios is particularly important when different reaction pathways yield products of widely differing reactivity, as, for example, in the dissociation of oxygen containing compounds to yield O(3P), O(1D), and O(1S).

D. Ionization

The "intermediate energy regime", ranging from approximately one to five times the ionization threshold, poses tremendous problems for ab initio theory, since the infinity of energetically accessible final states precludes us, in principle, from writing down a wave function that describes all possible scattering events. Moreover, perturbative methods based on the Born or distorted-wave approximation are only reliable at much higher energies. Nevertheless, the intermediate energy regime is an important region for practical applications, since many cross sections peak in this energy range.

In view of its obvious importance to any chemistry where electron collision processes occur, research on electron-impact ionization of molecules should be an important core component of any serious program in electron-driven chemistry. It will be important to see if the early successes of methods such as convergent-close-coupling, R-matrix with pseudo-states, time-dependent close-coupling or the direct grid methods can be extended beyond simple atomic systems and whether any of these techniques will be applicable to molecular targets. There is clearly a need for new computational methods in the field of molecular ionization. There is a rich, early literature on various methods based on the use of complex basis functions, Padé approximants, analytic continuation and extrapolations from complex energies. In view of the fact that today’s computer resources are vastly more powerful than anything envisioned at the time these methods were first proposed, they are worth a fresh look since, ultimately, the solution to the molecular ionization problem will depend on new methodologies.

E. Electron Transport

Electron-molecule collision cross sections (elastic, momentum transfer and vibrational excitation) in the low energy regime from threshold up to a few electron volts are of critical importance in modeling low temperature plasmas. These cross sections play a critical role in determining electron transport properties, mobilities and electron energy distribution functions. Although calculations in this energy range generally restricted to electronically elastic processes, it is essential to include target polarization and distortion effects if meaningful results are to be obtained. Features such as Ramsauer-Townsend minima, shape resonances and virtual states, which can dominate the electron-impact cross sections for molecular targets, are extremely sensitive to the incorporation of target distortion and, consequently, to the careful balance of correlation differences in the N- and (N+1) electron systems. Although methods are available, they are computationally demanding. Moreover, the methods that have been developed are based on traditional configuration-interaction approaches. This problem has many similarities to the problem of accurately determining electron affinities in bound-state quantum chemistry. Some of the most promising approaches in this area are based on coupled-cluster methods and many-body perturbation theory, but little of this new technology has been incorporated into the collision methods. The low-energy regime is an ideal one in which to explore incorporating recent advances in quantum chemistry into the "continuum electronic structure" problem.

The potential of using Time-Dependent-Density Functional Theory (TD-DFT) and direct-calculation methods such as Green’s function and Equations of Motion, each of which can describe the target at levels of accuracy including SCF, MPn, CI, and CC, presents other exciting possibilities. Using TD-DFT could provide an inexpensive way to describe target states, and hence it is possible that an inexpensive method for screening cross sections could be based on such a formalism. The direct methods could offer great computational savings in very accurate calculations. It remains an open theoretical question to determine how target state polarization would be treated in electron collisions using these methods.

V. Educational Impact of a New National Program

There is a growing need for scientists and engineers who are skilled at working together in teams to solve complex problems that are inherently multidisciplinary. The proposed initiative is ideally suited for training students in this mode of research. First, the new generation of computer codes required will necessarily combine algorithms from different areas of computational chemistry/physics and will have to be designed to perform well on parallel processing computers. Secondly, the systems to be studied are important in a wide range of applications, including modeling of plasma processing in fabrication of electronic devices and modeling of atmospheric chemistry.

On the computational side, it will be necessary to develop computer programs that more closely integrate state-of-the-art algorithms from the electron scattering and electronic structure communities. Moreover, for tackling complex systems (e.g., polyatomics with a large number of energetically accessible states) it will be necessary to develop software that effectively exploits parallel processing platforms. Building that software will require students and postdoctoral fellows with individual expertise in scattering theory, electronic structure methods, and software methods for parallel computers to work together in teams that may include chemists, physicists, applied mathematicians, and computer scientists. The synergy of such efforts allows for the development of the highest performing software with the best algorithms and the longest in-use lifetime. Thus, the participants working on these projects would gain valuable experience in working in teams. This experience, combined with the skills and knowledge about computer architectures that they will acquire, would help prepare them for a range of jobs in the computer modeling/simulations area.

The theory students involved in the initiative should also have the opportunity to interface directly with researchers involved in modeling of plasma reactors and atmospheric chemistry as well as with experimental scientists and engineers working in these areas. As a result, they would develop an understanding and appreciation of the relevancy of calculations/measurements of fundamental quantities (e.g., cross sections and branching ratios) to technological applications and environmental applications. This will provide the students with more real-world experience and make them more employable in a broad range of modern high technology industries as well as in the traditional academic routes.

References

1. For a current picture of state-of-the-art electronic structure theory, see "Modern Electronic Structure Theory", ed. D. Yarkony (World Scientific, 1995).

2. For a comprehensive review of current theoretical methods being used in electron-molecule collision theory, see "Computational Electron-Molecule Scattering", eds. W. ,Huo and F. Gianturco (Plenum, 1996).

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