The consideration of spin-orbit coupling is crucial for photochemistry , enabling, even for light atoms, the coupling of energetically close lying excited states of different spin multiplicity and thus resulting in a splitting of spectral lines and inducing spin-forbidden transitions. The latter play an emerging role in materials science, e.g. for light-induced excited-state spin trapping or upconversion processes. Sophisticated quantum-mechanical descriptions of spin-orbit coupling (SOC), the interaction between orbital angular momenta and spin angular momenta of electrons, based on the Dirac-Coulomb-Hamiltonian comprise four-or two-component approaches combined with various electronic-structure methods. Computational costs of excisting relativistic schemes are however at least one order of magnitude larger than comparable non-relativistic or scalar-relativistic computations, motivating the use of perturbative SOC ansätze . Relying on (quasi)degenerate perturbation theory , spin-free states are thereby provided within a non-relativistic framework and coupled via approximate spin-orbit Hamiltonians as the perturbation. A perturbative treatment of SOC was found to be reliable as long as SOC interactions are of small magnitude, which was found to be the case for molecules not containing 6p-or 7p-block elements. As highlighted by Cheng et al, it were perturbative SOC ansätze that pioneered the original description of intersystem crossing and current implementations for the dynamic description of ISC relying on surface hopping nonadiabatic molecular dynamics are nearly exclusively formulated as perturbative correction . Both spin-diabatic and adiabatic representations to include SOC in trajectory-based surface hopping procedures have been pioneered by Persico and Granucci. Within a perturbative description, common approximate spin-orbit Hamiltonians comprise Breit-Pauli spin-orbit operators and Douglas-Kroll transformed spin-orbit operators . Furthermore, the perturbational expansion of the Dirac equation to lowest order, the zero-order regular approximation (ZORA), is state-of-the-art and the approximate ZORA Hamiltonian was shown to provide an accurate description of spin-orbit coupling effects on properties of heavy element diatomic molecules. Van Wüllen furthermore proposed to use a model potential to construct the ZORA kinetic energy operator, circumventing the intrinsic problems of the ZORA Hamiltonian of gauge noninvariance and nonstationarity of the energy. Van Wüllen's model potential brings the advantage that the ZORA operator is then no longer dependent on the Kohn-Sham orbitals and, thus, that thereon based ionization potentials are improved, with remaining errors being comparable to original ZORA computations corrected with the electrostatic shift approximation and related to deficiencies of the exchange-correlation potential. Moreover, applying a model potential enables analytical expressions for nuclear gradients. To apply the mentioned approximate Hamiltonians not only to all-electron computations, but also to heavier-element chemistry relying on pseudopotentials, Kleinmann , Bachelet and Schlüter and Hybertsen and Louie pioneered the construction of pseudopotentials that account for spin-orbit coupling. Kleinman showed that the SOC-pseudopotentials are correctly including not only core-electron orthogonality effects, but also relativistic effects up to order α 2 with α being the fine-structure constant . Following the suggested norm-conserving construction scheme of Bachelet and Schlüter, Hartwigsen et al. furthermore constructed dual-space Gaussian pseudopotentials , featuring the general advantage of the Goedecker-Tetter-Hutter-potentials to being separable into a local and non-local part, with the integration of the latter scaling quadratically with system size. SOC-GTHpseudopotentials were parameterized with respect to two-component Dirac computations, thus including scalar-relativistic and SOC effects. They were shown to accurately reproduce bond lengths of an extended list of small molecules containing various heavy elements. In general, SOC-including PPs were also validated for a broader spectrum of molecular properties, e.g. yielding accurate predictions of spin-orbit splittings of band structures . The combination of the mentioned approximate Hamiltonians with time-dependent density functional theory (TDDFT) poses the challenge that SOC matrix elements are defined with respect to many-electron wave functions. Tavernelli et al. therefore proposed the usage of so-called auxiliary many-electron wave functions (AMEW) based on the Casida ansatz , with the auxiliary functions being constructed relying on the TDDFT response functions and thereon defined creation and annihilation operators. Corresponding implementations for the Sternheimer ansatz of LR-TDDFT within the CPMD program package were based on the Breit-Pauli Hamiltonian and conventional pseudopotentials without empirical reparameterization of the effective nuclear charges. Lowestenergy SOC matrix elements for formaldehyde were validated with respect to multi-configuration quasi-degenerate perturbation theory computations and the implementation was extended to NAMD on spin-diabatic surfaces, not requiring nuclear forces due to the perturbative ansatz, but providing SOC-corrected transition probabilities using the Landau-Zener formula. Bussy and Hutter presented an analogous implementation for core excitations enabling the efficient modeling of X-ray absorption spectra implying periodic boundary conditions , decoupling the investigated core states by considering only a small number of localized donor core orbitals. Through reduced resolution-of-the-identity basis sets located solely at the excited atom and acceleration by the auxiliary density matrix method, the authors demonstrated that the so-obtained SOC-corrected L-edge spectra are in agreement with experimental data at sub-cubic scaling of computational cost. Malis and Luber presented perturbative spin-orbit couplings for the delta self-consistent field ansatz analogously relying on the AMEW ansatz. The implementation within a mixed Gaussian and plane wave framework implying pseudopotentials was validated for formaldehyd with respect to LR-TDDFT reference values obtained with the ORCA program package . Within this context, we present an efficient implementation of a perturbative spin-orbit coupling ansatz relying on AMEW as suggested by Tavernelli et al. for the Tamm-Dancoff approximation (TDA) of linear-response time-dependent density functional perturbation theory, implemented within the mixed Gaussian and plane wave framework of the CP2K program package . The presented implementation is based on the mentioned related implementation for core excitations of Bussy and Hutter , extending the formulation to valence excitations (section 2.1) and SOC-corrected pseudopotentials of Hartwigsen et al. (section 2.2). Pseudopotential-based spin-orbit couplings are validated with respect to all-electron computations performed with the ORCA program package (section 3.3) and benchmarked for a test set of 13 organic molecules against multi-reference configuration interaction (CI) reference data (section 3.2). Computational timings and comparison with experimental spectra are outlined for the bismuth-containing CAU7 metal-organic framework (MOF) (section 3.4).