The higher-order Douglas-Kroll transformation

The higher-order Douglas-Kroll (DK) Hamiltonians in an external potential are explicitly derived. Application of an exponential-type unitary operator with the 2n+1 rule significantly simplifies the formulations of the high-order DK Hamiltonians. The third-order DK method has been implemented practically. Numerical results for one- and many-electron systems show that good accuracy can be obtained even with the DK Hamiltonian correct to third order in the external potential. (C) 2000 American Institute of Physics. [S0021-9606(00)31142-4].