Analytic energy gradients for the spin-free exact two-component theory using an exact block diagonalization for the one-electron Dirac Hamiltonian Available to Purchase

We report the implementation of analytic energy gradients for the evaluation of first-order electrical properties and nuclear forces within the framework of the spin-free (SF) exact two-component (X2c) theory. In the scheme presented here, referred to in the following as SFX2c-1e, the decoupling of electronic and positronic solutions is performed for the one-electron Dirac Hamiltonian in its matrix representation using a single unitary transformation. The resulting two-component one-electron matrix Hamiltonian is combined with untransformed two-electron interactions for subsequent self-consistent-field and electron-correlated calculations. The “picture-change” effect in the calculation of properties is taken into account by considering the full derivative of the two-component Hamiltonian matrix with respect to the external perturbation. The applicability of the analytic-gradient scheme presented here is demonstrated in benchmark calculations. SFX2c-1e results for the dipole moments and electric-field gradients of the hydrogen halides are compared with those obtained from nonrelativistic, SF high-order Douglas-Kroll-Hess, and SF Dirac-Coulomb calculations. It is shown that the use of untransformed two-electron interactions introduces rather small errors for these properties. As a first application of the analytic geometrical gradient, we report the equilibrium geometry of methylcopper (CuCH₃) determined at various levels of theory.