to be used for computations of large systems. In addition, the report includes the description of a computational machinery for nonlinear optical spectroscopy through an interface to the QM/MM package Cobramm. Further, a module to run molecular dynamics simulations is added and two surface hopping algorithms are included to enable nonadiabatic calculations. Finally, we report on the subject of improvements with respects to alternative file options and parallelization.

Two routes for deriving the exact two-component Hamiltonians are compared. In the first case, as already known, we start directly from the matrix representation of the Dirac operator in a restricted kinetically balanced basis and make a single block diagonalization. In the second case, not considered before, we start instead from the Foldy–Wouthuysen operator and make proper use of resolutions of the identity. The expressions are surprisingly different. It turns out that a mistake was made in the former formulation when going from the Dirac to the Schrödinger picture. The two formulations become equivalent after the mistake is corrected.

It is generally acknowledged that the inclusion of relativistic effects is crucial for the theoretical description of heavy-element-containing molecules. Four-component Dirac-operator-based methods serve as the relativistic reference for molecules and highly accurate results can be obtained-provided that a suitable approximation for the electronic wave function is employed. However, four-component methods applied in a straightforward manner suffer from high computational cost and the presence of pathologic negative-energy solutions. To remove these drawbacks, a relativistic electron-only theory is desirable for which the relativistic Fock operator needs to be exactly decoupled. Recent developments in the field of relativistic two-component methods demonstrated that exact decoupling can be achieved following different strategies. The theoretical formalism of these exact-decoupling approaches is reviewed in this paper followed by a comparison of efficiency and results.Keywords Relativistic electronic structure theory Á Fock operator Á Douglas-Kroll-Hess method Á X2C method Á Picture change error 1 Introduction

We present an efficient algorithm for one- and two-component relativistic exact-decoupling calculations. Spin-orbit coupling is thus taken into account for the evaluation of relativistically transformed (one-electron) Hamiltonian. As the relativistic decoupling transformation has to be evaluated with primitive functions, the construction of the relativistic one-electron Hamiltonian becomes the bottleneck of the whole calculation for large molecules. For the established exact-decoupling protocols, a minimal matrix operation count is established and discussed in detail. Furthermore, we apply our recently developed local DLU scheme [D. Peng and M. Reiher, J. Chem. Phys. 136, 244108 (2012)] to accelerate this step. With our new implementation two-component relativistic density functional calculations can be performed invoking the resolution-of-identity density-fitting approximation and (Abelian as well as non-Abelian) point group symmetry to accelerate both the exact-decoupling and the two-electron part. The capability of our implementation is illustrated at the example of silver clusters with up to 309 atoms, for which the cohesive energy is calculated and extrapolated to the bulk.