Reading Roundup - April 2023
Myths and Legends in High-Performance Computing
The director of my institute and some of my colleagues have written a very interesting paper surveying the future of HPC. They break down a number of topics such as accelerators, quantum computing, cloud computing, etc. A couple of their opinions on things like memory bandwidth are particularly worth paying attention to.
Linear-scaling implementation of molecular electronic self-consistent field theory
Recently I'm getting interested in the minimization approach for O(N) DFT. This paper is based on the exponential paramterization of the density matrix $D(X) = exp[-P(X)S]Dexp[SP(X)]$, where the exponential is used to keep the density matrix idempotent. One of the nice features of this paper is that they consider simultaneously minimization for a fixed Hamiltonian and for the self-consistent Hamiltonian.
Generating accurate density matrices on the tangent space of a Grassmann manifold
On a related note, starting from a given good density matrix, how do you predict a better one for a new potential or set of atomic coordinates, given the constraints (idempotency, trace)? This is a topic that been addressed recently using the (at least obscure to me) framework of Grassmann mainfolds. This recent work by Tan and Lao show that you can even use this extrapolation technique for constructing potential energy surfaces.
Mistakes in Fortran 90 Programs That Might Surprise You
This one is as advertised, I definitely made several of these mistakes when first getting used to Fortran.