Abstract
We present for the first time real-space, arbitrarily-accurate representations of the operators required for up to second-order Douglas-Kroll-Hess (DKH), a model for constructing quasi-relativistic electronic Hamiltonians. The approach can be extended to other operator-based quasi-relativistic models. The representations are in the form of sums of Gaussian functions with positive coefficients and thus enable efficient and numerically-accurate formulations using conventional Gaussian basis sets or other bases such as multiwavelets. The operators are demonstrated with application to hydrogen-like systems using the relativistic-kinematic and first-order DKH Hamiltonians.
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