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9.1.3 Single band, steepest descent scheme


The Davidson iteration scheme optimizes all bands simultaneously. Optimizing a single band at a time would save the storage necessary for the NBANDS gradients. In a simple steepest descent scheme the preconditioned residual vector tex2html_wrap_inline4867 is orthonormalized to the current set of wavefunctions i.e.


Then the linear combination of this 'search direction' tex2html_wrap_inline4869 and the current wavefunction tex2html_wrap_inline4825 is calculated which minimizes the expectation value of the Hamiltonian. This requires to solve the tex2html_wrap_inline4873 eigenvalue problem


with the basis set


Mon Mar 29 10:38:29 MEST 1999