Accurate Potential Energy Surfaces and Beyond: Chemical Reactivity, Binding, Long-Range Interactions, and Spectroscopy

Abstract

Beginning with the seminal paper of Born and Oppenheimer (BO) [1] in 1927, the concept of the potential energy surface (PES) plays a critical role in the description, simulation, and modeling of molecular systems. It provides the basis [2] for understanding the processes associated with the nuclear motions in molecules. By going beyond the characteristic stationary points and barriers, full dimensional, accurate potential energy surfaces have a very broad range of applications in many areas of physical chemistry; for example, they provide insight into structure, reactivity, and spectroscopy of molecules.While the majority of stable structures on PES are associated with the covalent or ionic bonding [3], the regions of PES dominated by van derWaals interactions are essential for low-temperature phenomena and molecular stacking which are critical for understanding biomolecular structures involving DNA and RNA molecules [4]. Furthermore, the advances in “cold chemistry” [5] make it possible to test the theoretical predictions (see, e.g., [6]) involving very small barriers of <15 K. At such low temperatures the quantum effects, for example, tunneling, play a significant role in chemical reactivity. For instance, the large de Broglie wavelength of ultracold molecules entirely changes the nature of reaction dynamics [7], and energy barriers on the PES play a different role because, in this regime, quantum tunneling becomes the dominant reaction pathway [8]. In addition, our understanding of potential energy surfaces has benefitted greatly from the ability of experimentalists to study chemical reactions and “observe” transition states in real time using the transition-state spectroscopy [9]. Due to the recent advances in ab initio method development [10] primarily focusing on the solution of the nonrelativistic Schr¨odinger equation, the theoretical data representing PESs is of higher quality and the cost and timing for such calculations is considerably improved. Furthermore, the relativistic corrections [11] can be significant and should be included if high accuracy of PESs is needed. For instance, the inclusion of the spin-orbit coupling effect (relativistic phenomenon) may turn a crossing of two potential energy curves into an avoided crossing [12]. Finally, given the raw ab initio data, efficient fitting techniques [13] are capable of generating excellent analytical representations of potential energy surfaces. One example is the functional representation of a PES using the double many-body expansion method [14]. Another important class of PESs corresponds to the ones that are constructed to be explicitly invariant with respect to all permutations of equivalent atoms [15, 16]. It is well recognized that one of the most stringent criteria of the quality of the PES is its ability to reproduce the experimental rotational-vibrational spectrum with the “near-spectroscopic” accuracy [12] of about 10cm− 1 or better [17]. Occasionally, the empirical refinements for ab initioPESs are used in order to achieve a very close agreement (<0.1 cm−1) with experiment for rovibrational transitions [18]. In many cases the BO approximation is valid to a high degree, and a single PES is sufficient to describe the motion of nuclei. However, when several electronic states get close in energy, the coupling between different potential energy surfaces becomes significant. The crossings of several PESs (e.g., conical intersections) or avoided crossings require a more refined treatment of nuclear dynamics which extends nuclear motion to more than one BO surface [19]. The conical intersections or “seams” [20, 21] play an important role in photochemistry, for example, contributing to the photostability of DNA and participating in the isomerization process of cofactor retinal that initiates visual reception.