Dear Andrei Thanks a lot for your comprehensive reply. Everything related to O(N) method in Siesta manual seems to be rational now.
Best regards, Bing 2012/10/8 <[email protected]> > > Hi, siesta users: > > I noticed that one line in Siesta manual, saying: > > "The Ordern(N) subsystem is quite fragile and only > > works for systems with clearly separated occupied > > and empty states." > > > > Is there any obvious reason that it cannot handle > > metallic systems? > > > > Best regards, > > Bing > > > > Sure, Bing, it is. > In metal, the states which are close to the Fermi energy may shift > back and forth between occupied and unoccupied domains. On each iteration, > the eigenvalues are ordered by their increased values, and the > AUFBAU PRINCIPLE applied - > the so many lowest states (counted over the Brillouin zone) > are declared OCCUPIED > (and contribute to the density in the next iteration), > and the rest thrown out. > > The Order(N) approach (at list as it is implemented in Siesta, or more > general, as far as I remember) avoids diagonalization; instead it works > directly on orbitals or density matrix elements, iterating them according > to a certain criterion. Hence the method does not know eigenvalues and > goes ahead for density, total energy, and other related properties. > (But does NOT provide the density of states, say). > Therefore the method cannot systematically order the eigenvalues > and find out where the occupied ones end. Instead, it needs to know this > in advance. In practice, in addition to the number of electrons > (which is known anyway), the chemical potential has to be provided > IN ADVANCE as a measure to identify the occupied states. > If you have a gap and safely put the chemical potential inside, > the calculation may go stable. If you have a metal, it ends up in a mess; > the iteration algorithms go astray. > > Best regards > > Andrei Postnikov >
