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.

我们首次展示了二阶Douglas-Kroll-Hess（DKH）所需的算子的真实空间，任意精度的表示形式，该模型是构造准相对论电子哈密顿量的模型。该方法可以扩展到其他基于运营商的准相对论模型。表示形式是具有正系数的高斯函数之和，因此可以使用常规的高斯基集或其他基数（例如多小波）来进行有效且精确的数值表示。使用相对论运动学和一阶DKH哈密顿量证明了算子在类氢系统中的应用。