Pre-Born–Oppenheimer molecular structure theory

Abstract

In pre-Born-Oppenheimer (pre-BO) theory a molecule is considered as a quantum system as a whole, including the electrons and the atomic nuclei on the same footing. This approach is fundamentally different from the traditional quantum chemistry treatment, which relies on the separation of the motion of the electrons and the atomic nuclei. A fully quantum mechanical treatment of molecules has a great promise for future developments and applications. Its most accurate versions may contribute to the definition of new schemes for metrology and testing fundamental physical theories; its approximate versions can provide an efficient theoretical description for molecule-positron interactions and, in general, it would circumvent the tedious computation and fitting of potential energy surfaces and non-adiabatic coupling vectors. To achieve these goals, the review points out important technical and fundamental open questions. Most interestingly, the reconciliation of pre-BO theory with the classical chemistry knowledge touches upon fundamental problems related to the measurement problem of quantum mechanics. I. QUANTUM CHEMISTRY VS. QUANTUM MECHANICS AND CHEMISTRY?We start with a historical overview of the chemical theory of molecular structure and the origins of quantum chemistry, which is followed by a review of methodological details and applications of pre-Born-Oppenheimer theory. A. Historical background: Chemical structure, physical structure from organic chemistry experiments [T]he dominating story in chemistry of the 1860s, 1870s, and 1880s was neither the periodic law, nor the search for new elements, nor the early stages of the study of atoms and molecules as physical entities. It was the maturation, and demonstration of extraordinary scientific and technological power, of the "theory of chemical structure" ... Alan J. Rocke Image and Reality: Kekulé, Kopp, and the Scientific Imagination (The University of Chicago Press, Chicago and London, 2010) During the second half of the 19th century, the pioneering organic chemists generation-represented by Williamson, Kekulé, Butlerov, Crum Brown, Frankland, Wurtz, etc.-had explored an increasing number of chemical transformation in their laboratory experiments and worked towards the establishment of a logical framework for their observations. The "first chemist' conference", held in Karlsruhe on 3 September 1860, resulted in an internationally recognized definition of the atomic masses. This agreement ensured that the same molecular formula was then used for the same substance in all laboratories around the world, and thereby opened the route to the successful development of the theory of chemical structure. The development of the chemical theory has been surrounded by heated debatesabout what is reality and what is mere speculation. We note that contemporary physics (gravitation, electromagnetism) was not able to provide any satisfactory description for molecules. To give a taste of this exciting period, we reproduce a few extracts from Alan J. Rocke's chemical history bo...

Nonadiabatic, Relativistic, and Leading-Order QED Corrections for Rovibrational Intervals of He42+ ( Ferenc1, Korobov2, Mátyus3 2020Phys. Rev. Lett.Self Cite

“…. , 19) [12] and the rovibrational intervals connecting the ground and the first excited vibrational state (1, N + )-(0, 1) (N + = 1, . .…”

“…The most precise theoretical results for molecules can be obtained by including all electrons and nuclei in the non-relativistic quantum mechanical treatment [2,[16][17][18][19][20].…”

Binding of muonated hydrogen molecules and Born–Oppenheimer approximation revisited

“…It should be noted at this point that the idea of allocating wave-functions to nuclei as well as electrons is not new, with the reader being addressed to the literature [8,9,10] for details.…”

Computation of rovibronic resonances of molecular hydrogen: EFΣg+1 inner-well rotational states

“…The Born-Oppenheimer (BO) potential energy curve of EF 1 Σ + g shows a double-well feature due to an avoided crossing with the nearby GK 1 Σ + g state ( Figure 1). In a pre-Born-Oppenheimer (pre-BO) description [8][9][10], 'all' nonadiabatic couplings and 'effects' are automatically included, so we will not use po-tential energy curves, nor coupling vectors in the computations, but the curves are useful to look at and we will continue to use the electronic state labels to have a short description and reference for the computed four-particle states. Since all non-adiabatic couplings are included, also the coupling with the X 1 Σ + g (ground) state continuum is present (we cannot separate it), and thus the EF states can only be obtained as resonances within the four-body problem [9].…”

“…10-20 cm −1 lower than the energy estimated from the experimental term value. Using the QUANTEN computer program [8][9][10] (see also the Supplementary Material [27]), we optimized, in repeated refinement cycles, a starting basis set which was compiled from the extensive bound-state optimization work of Ref. [9].…”