Concluding remarks

Non-adiabatic effects in chemical dynamics

Almost immediately after the birth of the field of chemical dynamics—the notion that atoms move along an adiabatic (Born–Oppenheimer) potential energy surface^1,2—the basic tenet of this picture was called into question. A simple equation for the probability of a “non-adiabatic transition” between Born–Oppenheimer surfaces was presented by Landau, Zener and Stueckelberg.^3–5 The nature and implications of “avoided crossings” and “conical intersections” were described,^6–9 and early quantum mechanical and semiclassical theories for non-adiabatic dynamics were developed.^10–14

In the intervening years, the extraordinary richness of chemical behaviors that arise from non-adiabaticity has become increasingly apparent. This Faraday Discussion highlights this progress and focuses attention on the critical issues that are impeding further progress. I thank Mark Child and his organizing committee for putting together this diverse and lively meeting and, of course, for inviting me to present these concluding remarks.

The wide range of powerful experimental techniques that are now being brought to bear on non-adiabatic chemical processes is truly impressive. Ultrafast lasers make it possible to follow the course of a chemical reaction in real time via pump–probe, transient absorption and coherence measurements.^15–20 Molecular beam technology allows quantum state preparation of reactants and state-resolved detection of products, revealing detailed and quantitative information sufficient to challenge any theory.^18,20–22 Novel multi-dimensional imaging and coincidence measurements provide hitherto inaccessible information about product state correlations.^18,23,24 So vast is the array of experimental tools that are now being used to probe the dynamics of non-adiabatic processes that it is not possible to represent all of them in so short a meeting as this. For example, quantum information processing with atomic, molecular or solid-state qubits is an emerging area in which non-adiabatic dynamics and decoherence play intimate roles. Another such area is single molecule spectroscopy. Single molecule vibrational spectroscopy via the scanning tunneling microscope (STM) deserves particular mention. The capability of the STM to locate molecular-sized objects on a surface has revolutionized surface chemistry. The technique will become even more valuable when the chemical nature of the objects can be identified. This has been achieved by Ho and coworkers who, by meticulously measuring the current-voltage characteristics, have observed the onset of vibrationally inelastic tunneling from a single adsorbed molecule.²⁵ The mechanism of this process is intrinsically non-adiabatic, the excitation of vibration by inelastic electron scattering.

A remarkable variety of non-adiabatic processes have been the subject of discussion at the meeting, including photochemistry, charge transfer, resonant processes, non-radiative transitions, quantum mechanical coherences, electronic energy transfer, and continuum processes. Perhaps the single most striking aspect of the meeting is the progress reported in studying non-adiabatic behavior in large systems; large molecules, transition metals, clusters, solvent caging, biological processes and dynamics in condensed phases.^{15–17,19,20,22,23,26–30} We are no longer limited to studying H₃ and F + H₂. This having been said, we also learned that unanswered questions remain even for these simple and intensively studied systems.

The accurate, detailed and extensive experimental studies reported at this meeting pose difficult challenges for theory. For example, new results suggest strongly that electronic–vibrational resonances play an important role in the reaction of F*(²P_1/2) with HD, in contradiction to the most recent calculations for this system.²¹ Similarly, vector correlation measurents were reported for dissociation of H₃ that have not as yet been accounted for by theory.²⁴ Quantum interference effects are observed even in very large systems for which it has been widely assumed that they would be destroyed by rapid decoherence processes.¹⁶ The many experimental studies reported here on systems too large to be addressed by rigorous quantum dynamical methods is daunting.

A number of theoretical advances were proposed during the meeting. Improved methods for defining diabatic potential energy surfaces are evolving.^29,31–33 Improved ab initio procedures are being developed for computing derivative, spin–orbit and coriolis couplings.^32,34,35 Robust, automated ab initio methods for locating and characterizing surface crossing seams are emerging.³⁶ Attention is now being paid to describing systems that exhibit a dense manifold or a continuum of electronic states.^37,38 Inelastic electron-molecule scattering, collisional ionization and dissociative recombination are non-adiabatic processes involving continua of electronic levels. So too are electron transfer at semiconductor surfaces and chemical reactions at metal surfaces. In fact, it is becoming clear that the adiabatic approximation is inadequate to describe the dynamics of any chemical reaction at a metal surface, a fact that is not widely appreciated in the catalysis and materials communities. The transition between discrete and continuous level density also presents interesting issues. Considerable attention has been paid to small vs. moderate vs. large molecule behavior in non-radiative transitions, where the focus is on the increasing density of vibrational levels.¹¹ In this age of nanoscience, we now have an opportunity to design systems in which the electronic density of states is tuned from discrete to effectively continuous. For example, a simple particle-in-a-box estimate for a five nanometer diameter metal sphere gives an energy splitting of about 400 cm⁻¹, comparable to vibrational spacings. As far as I am aware, this phenomenon has not been explored either theoretically or experimentally.

The presentations and subsequent discussions underscore the remarkable extent to which studies of non-adiabatic behavior have evolved from small, prototype systems to real and often very large systems. The abysmal scaling with system size of accurate numerical methods for quantum dynamics precludes their application even to moderate sized systems, never mind to the biological and condensed phase process discussed here. There is an urgency to develop more accurate and more tractable semiclassical and mixed quantum–classical dynamics theories. Indeed, state-of-the-art surface-hopping and multiple spawning algorithms were described.^26,31 In addition, procedures to reduce the number of degrees of freedom are needed, such as the use of ground and excited free energy surfaces.³⁰ The development of methods for on-the-fly calculation of ab initio forces has greatly extended the size of molecular systems amenable to ground state molecular dynamics simulation. It is now imperative to extend on-the-fly methods to non-adiabatic dynamics. An important start in this direction is underway.³⁹

Of at least as much importance as developing accurate and tractable simulation methods for non-adiabatic dynamics is the extraction of underlying physical pictures and simple models that encompass the essential dynamical behavior. Simple models of non-adiabatic processes have been extraordinarily valuable for providing insight and guiding experiment. The Landau–Zener approximation for branching at an avoided crossing,^3–5 Fermi's Golden Rule and its extensions for non-radiative transitions in molecules,¹¹ and Marcus theory of electron transfer¹⁰ are the cornerstones of the theory of non-adiabatic dynamics. The theoretical concepts and techniques discussed in this meeting properly go far beyond these elementary ideas. The location and influence of conical intersections, quantum mechanical coherence effects, Berry's phase, vector correlations, and resonance effects have played a central role in these discussions. These issues must be addressed if we are to make progress. However, an inevitable consequence is that the simple pictures are becoming more complicated and fragmented. It is essential that we begin to synthesize these new ideas into simple and compact concepts that augment the three cornerstones and provide unifying guiding principles.

Many of the concepts and issues discussed here apply not only to electronic but also to vibrational non-adiabatic processes. Quantum effects such as quantized energy levels, zero-point motion and tunneling can strongly affect chemical dynamics even when motion evolves on a single adiabatic electronic potential energy surface. Adiabatic eigenstates can be defined for the atomic coordinates, or for some subset of them, in analogy to adiabatic electronic states. Because vibrational energy levels are generally more closely spaced than electronic levels, non-adiabatic transitions between levels are correspondingly more likely and more important. Fig. 1 is a schematic illustration of proton transfer in solution. The potential energy function governing the proton is sketched for a variety of solvent configurations. In (a), the proton in its ground state wave function is localized in the left-hand well as indicated by the solid horizontal line. The lowest excited state is indicated by the dashed horizontal line. In (b), a solvent fluctuation has occurred that brings the two wells into resonance and the proton ground state is delocalized over both wells. In (c), the proton ground state is localized in the right-hand well. Within the adiabatic approximation, if the proton is initially prepared in the ground state, it will forever remain in the ground state. Thus, the proton will always switch wells whenever the energies of the wells are inverted due to a solvent fluctuation; the proton will incorrectly tunnel to the other well with unit probability no matter how high the barrier. A non-tunneling event corresponds to a non-adiabatic transition to the excited state, as illustrated in (d) and (e). Proper inclusion of non-adiabatic dynamics is therefore essential. The ground and excited states exhibit an avoided crossing with their minimum energy difference identified as the tunnel splitting. Concepts such as avoided crossings, conical intersections, surface hopping and diabatic states carry over directly to vibrational states of molecules. Exploiting this correspondence is a further challenge for the field of non-adiabatic dynamics.

Fig. 1 A schematic illustration of a double-well potential energy curve governing proton motion between donor and acceptor in solution. Proton transfer events are driven by solvent fluctuations that bring the donor and acceptor wells into near-resonance. The tunneling rate is determined by the relative probabilities of the adiabatic and non-adiabatic pathways.

This Discussion emphasizes dynamics; it is easy to become enthralled by the spirited motions of atoms and electrons, and their chemical and biological consequences. However, before we can understand motions, we must first understand the forces that govern the motions. Electronically non-adiabatic processes require accurate knowledge, not only of ground states, but also of excited state potential energy surfaces. All current methods for computing electronic excited states are inadequate for large molecular systems either because of insufficient accuracy or prohibitive computational requirements. This is arguably the most crucial impediment to further progress in the theory of non-adiabatic chemical dynamics.

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