X2C Hamiltonian Models in ReSpect: Bridging Accuracy and Efficiency.

Since its inception, the ReSpect program has been evolving to provide powerful tools for simulating spectroscopic processes and exploring emerging research areas, all while incorporating relativistic effects, particularly spin-orbit interactions, in a fully variational manner. Recent developments have focused on exact two-component (X2C) Hamiltonian models that go beyond the standard one-electron X2C approach by incorporating two-electron picture-change corrections. This paper presents the theoretical foundations of two distinct atomic mean-field X2C models, amfX2C and extended eamfX2C, which offer computationally efficient and accurate alternatives to fully relativistic four-component methods. These models enable simulations of complex phenomena such as time-resolved pump-probe spectroscopies and cavity-modified molecular properties, which would otherwise be computationally prohibitive. ReSpect continues to evolve, providing state-of-the-art quantum chemical methods and postprocessing tools, all available free of charge through our Web site (www.respectprogram.org) to support researchers exploring relativistic effects across various scientific disciplines.