Response to “Comment on ‘Quasirelativistic theory equivalent to fully relativistic theory’ ” [J. Chem. Phys. 123, 241102 (2005)]

A recent Communication by the present authors and an older paper by Dyall both deal with the transformation of the matrix representation of the Dirac operator in a kinetically balanced basis to a quasirelativistic Hamiltonian matrix. The main body of our Communication concerns the iterative construction of this transformation, and the numerical comparison of various iterative schemes, which has not been a topic of Dyall’s paper. Our formalism is strictly energy independent (state universal), while Dyall has studied both energy-dependent matrices (valid for a single state) and energy-independent ones. The possibility of an iterative construction of an energy-independent quasirelativistic Hamiltonian matrix has shortly been addressed by Dyall, but has not been considered seriously as basis for a working algorithm. The iteration scheme explicitly worked out by us and that implicit in Dyall’s paper are significantly different, although they have a common starting point.