First principles vs. toy models

One of the hot topics at the workshop I attended was the proper role of "first principles" calculations in trying to understand electronic conduction at the atomic and molecular scale.  In this business, there tend to be two approaches.  The first, which I call for lack of a better term the "toy model" paradigm, constructs models that are highly idealized and minimalistic, and you hope that they contain the essential physics needed to describe real systems.  An example of such a model would be the single-level Anderson-Holstein model of transport through a molecule.  Instead of worrying about all of the detailed electronic levels of a molecule and the many-electron physics there, you would concentrate on a single electronic level that can either be empty, singly occupied, or doubly occupied.  Instead of worrying about the detailed band structure of the electrodes, you would treat them as ideal electronic reservoirs, and there would be some couplings that allows electrons to hop between the level and the reservoirs.  Instead of considering all of the possible molecular vibrations, you would assume a single characteristic vibrational mode that "lives" on the molecule, and there would be some additional energy cost for having that vibration excited while there is an electron occupying the level.  While this sounds complicated, it is still a comparatively idealized situation that can be described by a handful of characteristic energies, and it contains rich physics.

On the other hand, one can consider trying to model a specific molecule in detail, worrying about the precise electronic and vibrational levels appropriate for exactly that molecule bonded in a particular configuration to a specific kind of metal electrode surface.  While this sounds in some ways like it's what you "really" ought to do, this "first principles" approach is fraught with challenges.  For example, just solving for the electronic levels of the molecule and their relative alignment with the electronic levels in the electrodes is extremely difficult in general.  While there are impressive techniques that can work well in certain situations (e.g., density functional theory), very often the circumstances where those methods work best (quasi-equilibrium, far away from resonances, in situations where electron correlation effects are minimal) are often not too interesting. 

It's interesting to watch the gradual convergence of these approaches.  As computing power grows and increasingly sophisticated treatments are developed, it looks like first-principles calculations are getting better.  One direction that seems popular now, as our condensed matter seminar speaker yesterday pointed out, is using such calculations as guidelines for correctly estimating the parameters that should be fed into the essential physics toy models.  Interesting times are on the horizon.