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.

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