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RSC theoretical and computational chemistry series

CHAPTER 5. Interactions of Atoms and Molecules in Cold Chemistry

Michał Hapka, Piotr Szymon Żuchowski

Published Jan 1, 2017• 2 citations
Publisher

Abstract

We present the basic ideas about the broad topic of molecular interactions in the context of low-energy collisions. We start by introducing the concept of the interaction energy and the crucial approximation behind it—the Born–Oppenheimer approximation. Next, we focus on understanding of molecular interactions within the framework of the perturbation theory. We discuss the essentials of symmetry-adapted perturbation theory (SAPT) which provides partitioning of the interaction energy into physically meaningful components, such as electrostatic, dispersion, induction, and exchange interactions. We examine the role of these components and how they can be calculated. We also discuss the supermolecular approach to calculation of the interaction energy with various quantum chemistry methods. We indicate potential pitfalls of the latter approach and give recommendations on how to alleviate them. To illustrate the theory presented in this chapter, we provide a detailed discussion of interactions within several systems of relevance in cold chemistry and cold collisions: He-NH(3Σ−), N-NH, He-OH(2Π), NH-NH, O2(3Σ−g)-O2. The calculations of collision rates and scattering cross-sections impose stringent requirements on the accuracy of the potential energy surfaces. To address the issue, we present the analysis of the scattering length dependence upon the potential scaling. Finally, we indicate trends in calculations of intermolecular forces stimulated by the state-of-the-art cold chemistry experiments.

DOI
10.1039/9781782626800-00203

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We present the basic ideas about the broad topic of molecular interactions in the context of low-energy collisions. We start by introducing the concept of the interaction energy and the crucial approximation behind it—the Born–Oppenheimer approximation. Next, we focus on understanding of molecular interactions within the framework of the perturbation theory. We discuss the essentials of symmetry-adapted perturbation theory (SAPT) which provides partitioning of the interaction energy into physically meaningful components, such as electrostatic, dispersion, induction, and exchange interactions. We examine the role of these components and how they can be calculated. We also discuss the supermolecular approach to calculation of the interaction energy with various quantum chemistry methods. We indicate potential pitfalls of the latter approach and give recommendations on how to alleviate them. To illustrate the theory presented in this chapter, we provide a detailed discussion of interactions within several systems of relevance in cold chemistry and cold collisions: He-NH(3Σ−), N-NH, He-OH(2Π), NH-NH, O2(3Σ−g)-O2. The calculations of collision rates and scattering cross-sections impose stringent requirements on the accuracy of the potential energy surfaces. To address the issue, we present the analysis of the scattering length dependence upon the potential scaling. Finally, we indicate trends in calculations of intermolecular forces stimulated by the state-of-the-art cold chemistry experiments.
In the preceding four chapters, we have mainly described the fundamentals of formal scattering theory at low energy. In this chapter, we apply this theory to cold atomic collisions. We first discuss the applications to atomic scattering in the absence and then in the presence of an external field. In the millikelvin or submillikelvin temperature regime, atomic hyperfine (HF) interactions—that is, interactions between the nuclear and electronic spins of an atom—become important in atomic collisions, even in the absence of any external field, because the energy scale associated with the HF interaction is typically on the order of 100 mK. Therefore, to understand low-energy atomic collisions, it is instructive to begin with a general introduction to atomic HF interactions. It is also essential to have a basic understanding of the origin and the method of constructing diatomic molecular potentials to understand low-energy atomic scattering from first principles. A detailed discussion of these topics, which would require some knowledge of atomic and molecular structure, is beyond the scope of this book.
High Resolution Image Download MS PowerPoint Slide Long-range intermolecular interaction plays an essential role in (ultra)cold collisions. For monomers with degenerate electronic states, an accurate description of the long-range interaction can be challenging due to the potential breakdown of the Born–Oppenheimer approximation. In this work, we developed a general method to construct long-range interaction potential energy surfaces (IPESs) between arbitrary molecules using the degenerate perturbation theory of Schrödinger. To further simplify the application of this method, a group-theoretical method is introduced to identify nonzero components of electrostatic properties of monomers, especially for the nonlinear molecules. To demonstrate this approach, we report the long-range IPESs of the O( 3 P)–OH( 2 Π) and OH( 2 Π)–OH( 2 Π) systems. The excellent agreement with ab initio calculations in large separations, even near electronic degeneracies, confirms the accuracy of our approach. The method is expected to lay the groundwork for the accurate investigation of (ultra)cold collisional dynamics involving open-shell species.
Studying chemical reactions at very low temperatures is of importance for the understanding of fundamental physical and chemical processes. At very low energies, collisions are dominated by only a few partial waves. Thus, studies in this regime allow the characterization of quantum effects which depend on the collisional angular momentum, e.g., reactive scattering resonances and tunneling through centrifugal barriers. Additionally, the dynamics of ultralow-energy collisions is dominated by long-range interactions, i.e., “universal” chemical forces. Thus, experiments in this domain probe the details of intermolecular interactions which is of general relevance for the understanding of chemical processes. Moreover, the increasingly more precise experiments provide valuable data for benchmarking theoretical models and quantum chemical calculations. Studies of cold ion–neutral reactions in the laboratory rely on techniques for the generation of cold ions and cold neutrals. Over the last decades, the technology in this domain has made impressive progress. Many of these techniques allow not only the translational cooling of the molecules, but also a precise preparation of their internal quantum state. Thus, by an accurate preparation of both the energy and state of the reaction partners as well as by the application of external electric, magnetic or optical fields, prospects open up to study and control chemical processes at an unprecedented level of accuracy. In this chapter, we review salient theoretical concepts and recent experimental developments for studies of ion–molecule reactions at low temperatures. We first discuss the theoretical background for the description of low-energy ion–molecule reactions. Next we present key experimental methods for laboratory studies of cold ion–molecule reactions. The chapter concludes with a review of illustrative results and an outlook on future directions.
Studying chemical reactions at very low temperatures is of importance for the understanding of fundamental physical and chemical processes. At very low energies, collisions are dominated by only a few partial waves. Thus, studies in this regime allow the characterisation of quantum effects which depend on the collisional angular momentum, e.g., reactive scattering resonances and tunneling through centrifugal barriers. Additionally, the dynamics of ultralow-energy collisions is dominated by long-range interactions, i.e., "universal" chemical forces. Thus, experiments in this domain probe the details of intermolecular interactions which is of general relevance for the understanding of chemical processes. Moreover, the increasingly more precise experiments provide valuable data for benchmarking theoretical models and quantum-chemical calculations. Studies of cold ion-neutral reactions in the laboratory rely on techniques for the generation of cold ions and cold neutrals. Many of these techniques do not only allow the translational cooling of the molecules, but also a precise reparation of their internal quantum state. Thus, by an accurate preparation of both the energy and state of the reaction partners as well as by the application of external electric, magnetic or optical fields, prospects open up to study and control chemical processes at an unprecedented level of accuracy. In this chapter, we will review salient theoretical concepts and recent experimental developments for studies of ion-molecule reactions at low temperatures. We first discuss the theoretical background for the description of low-energy ion-molecule reactions. Next we present key experimental methods for laboratory studies of cold ion-molecule reactions. The chapter concludes with a review of illustrative results and an outlook on future directions.
Over the last two decades cold atoms have emerged as a most useful platform for exploring quantum science and quantum technology. Cooling, trapping and manipulating atomic systems require understanding of low energy collisions physics. The purpose of this book is to bridge the gap between graduate teaching in scattering theory, particularly atomic scattering, and the emergent fields of cold atoms and cold molecules. Although this book presents basics of collisions physics as applicable to different branches of physics and chemistry, it is written with a particular emphasis on the physics of low energy quantum collisions and its applications to cold atoms. Key features • Pedagogic description of the topics will make this book suitable for graduate students taking courses on quantum scattering theory and cold atomic physics. • Each chapter will have exercises and worked examples. • Emphasises applications of theory to current research topics in several inter-related areas. • Incorporates numerical techniques. • Self-contained, with appendices summarising related topics needed by students.
Collision cross sections are calculated for the three systems O2-He{\text{O}}_{2}\text{-He}O2​-He, Na2-Na{\text{Na}}_{2}\text{-Na}Na2​-Na and K2-K{\text{K}}_{2}\text{-K}K2​-K at cold and ultracold temperatures. We discuss their relevance for cold molecule formation by buffer-gas cooling and by other cooling methods where collisions between molecules and atoms are important, e.g photoassociation. The molecule is treated as a rigid rotator in the electronic and vibrational ground state. We have calculated ab initio the potential energy surfaces for the three systems with special emphasis on the long range potential which is very important at low energies. With relevance to buffer gas cooling, we have also studied the thermalization process between O2{\text{O}}_{2}O2​ molecules and He atoms as determined by the calculated cross sections.