Tuesday, February 9, 2016

Wave-function based electronic structure methods are "scientifically legitimate"

Peter Fulde [who turns 80 in 2 months!] has a nice informative 2 page Commentary Wavefunction-based electronic structure calculations for solids.

For electronic structure calculation there are two distinct alternative methods (formulations): those based on Density Functional Theory (DFT) and wave function based approaches.

Fulde directly addresses an "objection" to the latter raised by Walter Kohn in his Nobel Prize Lecture. He suggested that for more than one thousand electrons a many-body wave function is not "scientifically legitimate" because it suffers from the the "exponential wall" problem.
(i) It cannot be calculated with sufficient accuracy.
(ii) It cannot be represented numerically sufficiently well that it can be stored and later retrieved.

Fulde states

The exponential wall problem is avoided when we characterize the many-electron wavefunction not by a vector ψ(r1σ1, ... , rNσN) in Hilbert space but instead by a vector |Ω) in operator space, with the cumulant metric given by equation (3). The operator S in |Ω) = |1 + S) is a cumulant scattering operator.

The point we wish to emphasize is that a numerical representation of the results for the different contributions to |S) poses no problem. 

Although he does not spell it out (I think) the cumulants here are in quantum chemistry related to "coupled cluster" methods and in solid state physics a very simple example is a Gutzwiller projection. These kind of connections between chemistry and physics techniques are nicely brought out in Fulde's classic book, which I highly recommend. It is where I first learnt about such connections.

I thank Mohammad Sherafati for bringing the article to my attention.

1 comment:

  1. nice blog
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