Bohmian pathways into chemistry: A brief overview

Perhaps because of the popularity that trajectory-based methodologies have always had in Chemistry and the important role they have played, Bohmian mechanics has been increasingly accepted within this community, particularly in those areas of the theoretical chemistry based on quantum mechanics, e.g., quantum chemistry, chemical physics, or physical chemistry. From a historical perspective, this evolution is remarkably interesting, particularly when the scarce applications of Madelungs former hydrodynamical formulation, dating back to the late 1960s and the 1970s, are compared with the many different applications available at present. As also happens with classical methodologies, Bohmian trajectories are essentially used to described and analyze the evolution of chemical systems, to design and implement new computational propagation techniques, or a combination of both. In the first case, Bohmian trajectories have the advantage that they avoid invoking typical quantum-classical correspondence to interpret the corresponding phenomenon or process, while in the second case quantum-mechanical effects appear by themselves, without the necessity to include artificially quantization conditions. Rather than providing an exhaustive revision and analysis of all these applications (excellent monographs on the issue are available in the literature for the interested reader, which can be consulted in the bibliography here supplied), this Chapter has been prepared in a way that it may serve the reader to acquire a general view (or impression) on how Bohmian mechanics has permeated the different traditional levels or pathways to approach molecular systems in Chemistry: electronic structure, molecular dynamics and statistical mechanics. This is done with the aid of some illustrative examples -- theoretical developments in some cases and numerical simulations in other cases.