In the context of a very recent global restructuring of COBRAMM, an automated workflow was implemented to perform transient electronic spectroscopy simulations within the TSH framework exploiting OpenMolcas as the QM software. The OpenMolcas/COBRAMM interface facilitates nonadiabatic dynamics simulations, in gas-phase and in an explicit environment through a QM/MM hybrid scheme, with various RASSCF/RASPT2 flavors and makes use of the recently implemented analytical gradients. The spectroscopy implementation consists of the extraction of geometries along the dynamics in user-defined intervals, the calculation of the manifold of spectroscopically relevant higher-lying states for every geometry, the generation of the individual time-slices at a given time step and, eventually, their convolution in the final spectrum. The COBRAMM package is available free of charge on GitLab.<sup>520</sup>

Routines for trajectory-based transient spectroscopy simulations in other spectral windows, e.g., photoelectron spectroscopy or X-ray absorption are under current development.

**6.5. Comparison of Two Techniques for Nonadiabatic Dynamics Simulations.** The ultrafast photoinduced dynamics of uridine (Urd) is used here to demonstrate the capabilities of the iSPECTRON (see section 5.2) and COBRAMM platforms, i.e., to demonstrate the difference between nonadiabatic dynamics simulations based on the DHO approximation, in combination with a second-order CGF, and on the TSH approach. Both, the DHO/CGF and TSH spectra were simulated for a water solvated Urd within a QM/MM scheme. The nucleoside conformation was taken from a classical molecular mechanics equilibration and refined at the QM-(MP2)/MM level with COBRAMM. The same level of approximation was used for the GS normal modes and frequencies required by both methods. The DHO/CGF spectra were obtained at the XMS-CASPT2/SA-20-CASSCF(14,10) level at the GS equilibrium geometry, including all π-orbitals and the oxygen lone pairs in the active space. Inhomogeneous broadening can be straightforwardly accounted for by averaging the spectrum over multiple solvent arrangements. The non-adiabatic dynamics was described by a rate-equation with a ππ* → GS decay rate of 0.01 fs⁻¹ corresponding to the reported 100 fs ππ* experimental lifetime. The TSH spectrum was obtained from a swarm of 50 trajectories at the XMS-CASPT2/SA-9-CASSCF(14,10) level, explicitly considering the lowest nπ* states in the dynamics. (The lowest nπ* state was found to represent a secondary channel with no intense transient features in the spectral window of interest; therefore, it is not further discussed.) The calculations of the spectroscopically relevant states were performed at the XMS-CASPT2/SA-20-CASSCF-(14,10) level of theory.

Cerullo and co-workers recorded the transient absorption spectrum of Urd in water by exciting the lowest bright band (ππ*) in the midultraviolet (UV) at 4.5 eV with a sub-30 fs pump pulse and probing in the 2 to 4.2 eV spectral window (Figure 29b).<sup>521</sup> The immediate rise of an intense stimulated emission (SE) band covering the 3 to 4 eV spectral range (blue in Figure 29), as well as of a photoinduced absorption (PA) feature below 2.4 eV (PA1) can be noted. Both features decay very quickly with a 100 fs time constant, giving rise to another PA band above 4 eV (PA2). The DHO/CGF (29a) and TSH (Figure 29c) approaches reproduce qualitatively the main features of the experimental spectrum, the SE and PA1 bands which are characteristic fingerprints of the initially populated ππ* state. Both approaches reveal a further PA band at early

times around 3 eV which is covered by the SE in the experiment but has been resolved for orthogonal pump and probe polarizations suppressing the SE.<sup>521</sup> The TSH model captures the red-shift of the SE as well as the delayed rise of PA2 coming from the vibrationally "hot" GS formed upon decay through the ππ*/GS conical intersection. This feature is absent in the DHO/CGF spectrum as the model does not include a "hot" GS. The DHO/CGF allows to analyze quantum beating due to coherent vibrational dynamics which are strongly suppressed in the bulk.

The theoretical spectra can be subjected to global and Fourier transform analysis as their experimental counterpart, which closes the gap between experiment and simulation.

**6.6. SI-SA-REKS Quantum–Classical Trajectories.** The spin-restricted ensemble-referenced Kohn–Sham (REKS) method, its state-averaged extension (SA-REKS), and the state-interaction state-averaged REKS (SI-SA-REKS or, for short, SSR) employ ensemble-density functional theory (eDFT)<sup>522</sup> to introduce nondynamic electron correlation into the description of the ground and excited electronic states of molecules and to obtain the excitation energies in a way reminiscent of multistate multiconfigurational methods of wave function-based theories.<sup>523–525</sup> In fact, eDFT enables a seamless incorporation of multireference effects into the description of the molecular electronic structure, where the results of standard Kohn–Sham (KS) computations are recovered for weakly correlated (e.g., single-reference) systems. As a result, the method provides an improved description of molecules with dissociating chemical bonds and electronically excited states often featuring mixtures of biradical and charge transfer electronic characters. Because of that, the performance of SI-SA-REKS in dealing with electronically excited states has been extensively benchmarked for a model biological chromophore against different wave function-based correlated methods.<sup>526</sup>

The characterization of photo and thermal reactivities of even medium-size organic molecules becomes computationally expensive when multireference methods are employed in picosecond time scale simulations of the reactive dynamics.<sup>527</sup> Here SSR offers a substantially more economical treatment of the electronic structure making, in principle, the systematic simulations of photochemical and photobiological processes feasible.<sup>528,529</sup>

The simulation of the dynamics of photochemical and photobiological processes requires an atomistic treatment of the molecular environment. This is enabled by QM/MM technologies capable to generate a model of the reacting system and to perform nonadiabatic molecular dynamics (NAMD) simulations.<sup>530</sup> For this reason, some of the authors recently incorporated the SSR method in GAMESS-US<sup>531,532</sup> that, in turn, was interfaced with Tinker to allow the construction of QM/MM models. However, such implementation does not allow the use of the robust [Open]Molcas modules Dynamix and Surfacehop, both extensively applied to photochemical and photobiological reactions.<sup>533,534</sup> On the other hand, the SSR description of the QM subsystem of QM/MM models would be particularly welcome as it makes possible to study the dynamics of this type of system faster and more accurately. Another reason for focusing on OpenMolcas is its capability, when interfaced with Tinker,<sup>535</sup> to generate automatically (i.e., without human intervention) QM/MM models of photoresponsive systems.<sup>536–538</sup> These are congruous QM/MM models that can give access to a rapid generation of the entire libraries of models to be used in systematic studies. Such studies would facilitate the search for novel light responsive
<figure><img src="image_41.png" /></figure>

**Figure 30.** Simulations of EP → ZM → ZP half-cycle of MTDP. (A) Minimum energy path EP → ZP of the MTDP motor θ (the torsion angle defining the position of rotor with respect to stator) calculated with the SSR method (triangles). The dashed energy profiles correspond to 3-root state-average XMS-CASPT2 energies calculated with a 2 electrons in 2 π-orbitals complete active space. The dotted energy profiles show the corresponding 5-root state-average with a 10 electrons in 10 π-orbitals complete active space. (B) The top panel summarizes the conformational changes of MTDP in solvent along the QM/MM trajectories. The bottom panel shows the flexible part of the MTDP in methanol QM/MM model. (C) Simulated photoisomerization of MTDP in methanol solution based on 8 productive trajectories observed using 40 initial conditions with EP-helicity character. The propagation along the S₁ PES (the black lines) is connected with the reactive propagation along the S₀ PES (the red lines) by the corresponding hop points (the red circles). (D) Picosecond-scale simulation of MTDP photoisomerization in methanol solution as demonstrated through 8 reactive CCW trajectories. The top panel shows 4 trajectories in which EP to ZP transition occurs within 2.5 ps. The bottom panel demonstrated 2 trajectories in which EP to ZP transition occurs within 6 ps. The propagation along the S₁ PES is shown with solid black lines, while the propagation along S₀ is shown with solid red lines. The hop points are marked with red circles. The point of trajectory at which ZP conformer becomes stable is identified with vertical dashed black lines.

materials such as molecular motors as well as novel photo-
receptors for optogenetics. To enable SI-SA-REKS quantum-
classical NAMD simulations an interface between Open-
Molcas and GAMESS-US was developed (see the Supporting
Information for more details on the technical details and
capacity of this interface).

As an example of the flexibility of this new interface a recent
application of the OpenMolcas-GAMESS-US/Tinker
interface to the SSR(2,2) NAMD simulation of the E to Z
photoisomerization dynamics of a specific enantiomer of (E)-3'-
(2-methyl-2,3-dihydro-1H-benzo[b]cyclo-penta[d]thiophen-1-
ylidene)pyrrolidin-2-one, here abbreviated as MTDP,⁵³⁹ is
discussed here. The new interface played a crucial role in
demonstration of the fact that the NAMD QM/MM simulations
in solution yield results consistent with the experimentally
observed transient absorption (TA) spectroscopy data. The
MTDP could function as a single-molecule rotary motor driven

by only two photochemical steps; thus avoiding the thermal
helix inversion (THI) steps of classical light-driven molecular
motors (i.e., the ZM and EM intermediates are not stable in such
system).⁵⁴⁰⁻⁵⁴⁴ To demonstrate that a two-photon only
mechanism exists, the rotary cycle was simulated at room
temperature in the gas phase and in methanol, starting from the
EP—*entgegen* and plus helicity—equilibrium configuration (the
classic mechanism of the rotary cycle is described in the SI).

In this SSR(2,2) simulation of the EP → ZM → ZP half-cycle
the QM subsystem (the entire MTDP solute molecule) is
described at the SSR(2,2) level while the surrounding solvent is
described using a parametrized MM force field. The project
started with a gas-phase benchmark study comparing the
SSR(2,2) energy profile of MTDP along a minimum energy path
(see Figure 30A) with the corresponding XMS-CASPT2 energy
profile used as a reference. As shown in Figure 30A, the system
evolves toward S₁/S₀ CoIn (shown by the red-filled triangle),
where it decays to S₀. The torsion continues on the S₀ PES, where the ZP configuration is reached without encountering an M helical local minimum. In fact, the ZM species occurs only as an inflection (i.e., a flatter region) on the S₀ PES. The benchmark showed a close agreement between SSR(2,2) and XMS-CASPT2 energies along the EP → ZP path described above.

In the gas phase SSR(2,2) NAMD simulation of EP → ZM → ZP half-cycle in MTDP 50 trajectories were utilized to study the reactivity of the system. The resulting simulations predicted 280 fs latency time required for initiating the double bond torsion, a 400 fs decay time, and a 600 fs time scale of EP → ZM → ZP transition, while the quantum yield was predicted to be 87%. The photoisomerization dynamics of a methanol solution of the EP conformer of MTDP (λ<sub>max</sub> = 305 nm) was experimentally investigated by femtosecond transient absorption (TA) spectroscopy upon 290 nm excitation. The measured S₁ lifetime was elucidated to be 600 fs, which is 200 fs slower than the prediction of gas phase simulations. Moreover, the experimental quantum yield was demonstrated to be 25%, which is substantially lower, than the value predicted with gas phase simulations. Finally, through TA spectroscopy it was observed that the stable ZP diastereomer is produced after decay to S₀ and subsequent vibrational cooling (~30 ps) of a ZM transient species, which is substantially slower than the prediction of gas phase NAMD simulation. The above findings indicate the importance of including solvent effects.

To achieve a more accurate description of MTDP photo-
chemistry, the newly introduced OpenMolcas-GAMESS-
US/Tinker interface was used to construct the models
necessary to perform QM/MM NAMD simulations of the light-
driven transformation of MTDP in methanol along the EP →
ZM → ZP half-cycle (Figure 30B). To do so 40 quantum-
classical trajectories were used treated with the TSH algorithm.
For more details regarding these simulations see the Supporting
Information. The solvent simulations predicted the average S₁
lifetime of 482 fs, while the quantum yield was predicted to be
~20%. Here it is important to note that the simulated quantum
yields and S₁ lifetimes were obtained with relatively small
statistics and are planned to be refined in the future study with
larger sampling. However, the qualitative difference between the
predictions of gas phase and solvent NAMD simulations (with
solvent simulations being substantially closer to experimental
data) is clear even with a limited statistics. In Figure 30C, the
change in the torsional angle θ during EP to ZM transition in all
reactive trajectories is reported. Most importantly, as shown in
Figure 30D, the ZM → ZP is substantially slower in solvent
simulations than in gas phase simulations.

The time scale of ZM to ZP transition places the overall EP → ZM → ZP half-cycle in the picosecond regime as opposed to the gas phase NAMD prediction that placed the entire process within less than 1 ps. Moreover, the fact that two productive trajectories did not undergo the ZM to ZP transition even within 13.5 ps is in a better agreement with ~30 ps time scale of EP → ZM → ZP transformation seen in the experiment.

**6.7. MC-PDFT Nonadiabatic Dynamics.** Recent developments of single-state<sup>264-266</sup> and multistate<sup>267</sup> MC-PDFT analytic gradients have enabled the use of MC-PDFT to study electronically nonadiabatic processes. This is achieved by using the *OpenMolcas* interface with the nonadiabatic molecular dynamics simulation package *SHARC* versions 2.0<sup>479,480,545</sup> and 3.0.<sup>268,270,502</sup> In this section some specific details with respect to

the use of the MC-PDFT approximation for nonadiabatic
dynamics is presented.

Because the MC-PDFT or the MS-PDFT energy is obtained
from the reference wave function without improving the
reference wave function, one does not have a nonadiabatic
coupling vector that corresponds to the MC-PDFT energy.
Nevertheless, one can treat electronically nonadiabatic dynam-
ics by curvature-driven methods described in section 6.3. One
can also treat intersystem crossings that are not strongly affected
by conical intersections, by performing single-state MC-PDFT
for each spin state and approximating the nonadiabatic coupling
vectors and spin-orbit couplings from the reference SA-
CASSCF wave function. The latter method was applied<sup>269</sup>
with TSH to treat intersystem crossing dynamics between the S<sub>1</sub>
and T<sub>2</sub> electronic states of thioformaldehyde (CH<sub>2</sub>S) as this
transition occurs far away from conical intersections, and it has
been shown that spin-orbit coupling in this system does not
depend strongly on external correlation (correlation involving
excitations external to a valence active space).<sup>173</sup> Previous
SHARC photodynamics simulations of CH<sub>2</sub>S using MS-
CASPT2 served as excellent comparison data.<sup>173</sup> The MS-
CASPT2(10,6) CH<sub>2</sub>S simulations showed no intersystem
crossing transitions within 500 fs, which is in agreement with
Mai et al.'s conclusion,<sup>173</sup> based on large experimental
fluorescent yields, that intersystem crossing rates are small in
CH<sub>2</sub>S. MC-PDFT(10,6) results<sup>269</sup> also showed no population
transitions between the two electronic states within 500 fs (see
Figure 2 in ref 269), in good agreement. Furthermore, MC-
PDFT was able to simulate CH<sub>2</sub>S with an active space of 12
electrons in 10 orbitals—an active space that was considered too
large to run MS-CASPT2 simulations<sup>173</sup>—and these larger-
active-space calculations showed no population transfer
between S<sub>1</sub> and T<sub>2</sub> within 500 fs.

7. BASIS SETS, AB INITIO MODEL POTENTIALS, AND ORBITAL ROTATION

Finally, three additional features are reported here. First,
efficient and relatively small basis sets are important for fast
multiconfigurational calculations. Hence, a new basis set for the
relativistic X2C Hamiltonian, ANO-R, has been developed for
the atoms from H to Rn. It has subsequently been tested in
various applications. Second, embedded cluster models (a
quantum part, a layer of model potentials and point charges) can
be used in combination with multiconfigurational theory for
electronic structure calculations of ionic solids. A simple and
straightforward protocol for construction of embedding is a key
function. For that purpose, a new code for the generation of ab
initio model potentials (SCEPIC) has been developed. Lastly, a
tool for rotating molecular orbital coefficients along with the
molecular structure is provided. More details of these develop-
ments are listed below.

**7.1. ANO-R Basis Set.** Basis sets of ANO type<sup>546</sup> are a special class of functions, which allow a very flexible change of the size and accuracy by selecting different contractions. This flexibility is essential for computational methods with very high scaling with respect to the basis set size. In consequence, basis sets of ANO type are the most popular among MOLCAS/OpenMolcas users in multiconfigurational calculations. The construction of the ANO basis sets also includes the option of variable density fitting based on selected electronic states of atoms and ions, which makes these basis sets “ready” for describing these electronic features.
For the last two decades, the ANO-RCC basis set⁵⁴⁷,⁵⁴⁸ has been widely used by the community. ANO-RCC is a relativistic basis set based on the second-order Douglas-Kroll-Hess (DKH2) Hamiltonian. The ANO-RCC basis set was developed based on a reuse of exponents of previously optimized primitive functions, and many individual decisions for each element with respect to the selection of electronic states were applied.

In contrast, the development of the new ANO-R basis set was based on the following principles: systematic construction to achieve a balanced description of all elements included as well as compactness of the basis set to ensure efficient usage in calculations. First, through systematic computation of a wide range of different sets of primitive basis functions, the minimum number of functions with a given energy difference to the complete basis set limit was selected. Then, upon selection of a common set of electron reference states and by systematic application of a natural orbital occupation number threshold, minimal sizes of density-matrix averaged⁵⁴⁹ ANO-contracted basis sets were built. The so-constructed ANO-R basis sets are only one possible form. Among the primitive basis functions, a set of functions and energy error was selected that yields a number of primitive functions for atoms H-Rn slightly smaller than the number of primitive functions in the ANO-RCC basis set for the same elements. However, based on our work, both smaller and larger primitive basis sets can be easily constructed. Likewise, the contracted form of the ANO-R basis sets can be adjusted for individual needs, both by choosing different occupation number thresholds and by using different electronic states in the density-averaging.⁵⁵⁰,⁵⁵¹

On average, the ANO-R basis set is 10% smaller than ANO-RCC while maintaining a similar quality. However, it is important to note that the most common molecules that have to be treated with relativistic calculations, usually contain only one or two heavy elements, and all the rest is constructed from the light elements (but they also have to be described by relativistic basis set⁵⁵²). In this case, the use of ANO-R basis set provides a good performance improvement as shown in a recent benchmark study.⁵⁵³

Anions were not included into density fitting for ANO-R basis set. Thus, the description of anionic states is a hard test for the ANO-R basis set. The electron affinity (EA) of oxygen is well-known experimentally with a very high precision (1.461 112 972(87) eV⁵⁵⁴). Theoretical studies, with close to exact methods, predict an EA of oxygen in the range of 1.26 to 1.29 eV.⁵⁵⁵ Employing CASSCF calculations with an active space including 1s2s2p3s3p orbitals, followed by CASPT2, one can obtain the energies for neutral oxygen and anion. In this approach, the use of the small ANO-R-1 (3s2p1d) basis has proven to be insufficient, predicting even the sign of EA wrongly. ANO-R-2 (4s4p2d1f) estimates EA(O) as 0.82 eV, ANO-R with contraction 10s8p4d2f as 1.23 eV. The ANO-RCC basis set for the oxygen atom also contains higher angular momentum functions (g and h). Adding uncontracted g and h functions to the ANO-R basis set only slightly improves the results, reaching 1.30 eV for EA(O).

For such demanding cases, like the electron affinity of oxygen, the standard (and low-end) contraction schemes should be avoided, and a larger basis set must be used. At the same time, in many practical applications which involve oxygen atoms in a molecule, the effect of the basis set size is not that large,⁵⁵³ and reasonable results can be obtained with the ANO-R-2 basis set.

**7.2. Ab Initio Model Potentials.** Ab initio model potentials (AIMP) are a convenient way to create a layer between an ionic

cluster and an electrostatic environment. Such a system can be treated by any computational techniques from DFT to multiconfigurational methods. The reader is referred to Barandiarán et al.'s⁵⁵⁶,⁵⁵⁷ extensive introduction to the application of AIMPs in electronic structure calculations of ionic solids. The critical limitation of this approach is the need to reconstruct the potentials for any new crystal structure.

A new code, SCEPIC, automatizes the routine of computing the AIMPs. SCEPIC is a stand-alone code, available from its home page⁵⁵⁸ under the Academic Free License (AFL). SCEPIC does not require any installation and it works out of the box with OpenMolcas. The input for SCEPIC contains information about crystal structure, proposed formal charges, and a set of computational details, which will be used to calculate an ion in the layer of AIMPs. The minimization procedure is used to optimize the basis set for AIMPs (both basis set-free and for potentials with a hydrogen-like basis set). The output of SCEPIC contains a ready-to-use library, which can be appended to the AIMP library in OpenMolcas.

SCEPIC also can be used to construct the input for the GATEWAY module, which contains the quantum part, AIMP layer, and a set of point charges. The latter layer is constructed algorithmically,⁵⁵⁹ so the total system is electroneutral and dipole and higher multiple moments are compensated.

The quality of the embedding, if AIMPs are used, can be verified by comparison of electron density and the properties computed from it, between calculations made with the same setup (functional, basis set) with periodic boundary conditions, e.g., with the CP2K code, and with OpenMolcas.⁶⁰

The AIMP embedding has proven useful in the theoretical description of luminescent materials that are activated by local dopants. Particularly, in the case of lanthanide ion activators, the nature of recorded luminescence spectra can be very complex. If the spectra can be attributed to a single crystal site one has to deal with sets of electronic states originating from lanthanide element open shell configurations $4f^N, 4f^{N-1}5d, 4f^{N-1}6s$ under the influence of a crystal matrix. AIMP embedding opens a possibility of application of multireference methods which are properly suited for solving this kind of problems. L. Seijo and Z. Barandiarán published a number of theoretical studies on local impurity states.

If there is no complete oxidation or reduction of dopant one can restrict calculations to a single active site. In this framework, spectra of CaF₂:Pr³⁺ were studied⁵⁶¹ showing that $4f² A₁g(1s0)$ overlaps with the 4f5d($e_g$) manifold, indicating that in this $O_h$ site symmetry no quantum cutting occur. Moreover, the experimental 4f5d($e_g$) → $4f²$ emission spectrum was successfully reproduced assuming simultaneous emission from two levels ($¹T_{2u}$ and $¹E_u$) of the 4f5d manifold. Another feature of experimental spectra that can be studied within a single active ion cluster are impurity trapped exciton (ITE) manifolds. They appear in the calculations as electronic states where an electron occupies an orbital having significant electron density outside the first coordination shell. This electron is attracted to an impurity trapped by a hole on the 4f created in the excitation.⁵⁵⁶,⁵⁶¹ Ligand-to-metal charge transfer (LMCT) processes can be studied using medium-size clusters. Barandiarán et al.⁵⁶² studied LMCT in CaTiO₃:Pr³⁺ and CaZrO₃:Pr³⁺ and showed that LMCT states can be used to control balance between greenish-blue and red emission in those materials.

Cluster embedding with AIMPs is not restricted to 3D periodicity; it can also be used to model surfaces of ionic crystals and chemical reactions on surfaces. An example of such system is
the diffusion of an oxygen adatom on the MgO(001) surface. This reaction has previously been proposed to be an example of a spin-crossing, where the lowest energy route would correspond to changing between singlet and triplet spin-states.⁵⁶³ Obviously, a multiconfigurational treatment is essential for the investigation of spin-crossing.

**7.3. Rotation of Molecular Orbitals in Space.** It is not uncommon to require or wish to transform the results of a particular calculation to a different reference frame. It may be needed, for example, to compare calculations done with different molecular orientations, or to compute interactions in different aggregates. Some properties like the energy are invariant to rotations and translations, and other properties like electric multipoles are trivial to transform. In the case of the molecular wave function—or the molecular orbitals (MO) in which it is based—it should also be invariant to translations and rotations; however, the MO coefficients with respect to the basis functions are not invariant to rotations. The angular components of basis functions for $l > 0$—as Cartesian or spherical harmonic functions—are always expressed in the absolute “laboratory” reference frame, such that while the MO coefficients would not change if the basis functions were rotated with the molecule, they do change when the basis functions are only translated to follow the nuclei, but not rotated. The same applies to most integrals between the basis functions: even if a property is invariant to rotations, the individual integrals from which the property can be computed could need modification. It is therefore nontrivial—but not necessarily too complicated—to transform the integrals and MO coefficients to a different molecular orientation. Explicit expressions have been given at least by Sherman and Grinter⁵⁶⁴ and Ivanic and Ruedenberg.⁵⁶⁵,⁵⁶⁶

A simple tool is provided in OpenMolcas (Tools/mort/mort.py) that simplifies these transformations, as well as changing the order of the atoms in a molecule and desymmetrizing the orbitals and integrals from a calculation done with symmetry constraints. With this, the results saved in an HDF5 file from time-consuming calculations can easily be transformed to a different frame, with minimal loss of precision, and reused for further calculation or analysis, avoiding the need for reconverging previous calculations sometimes faced by users.

## 8. SUMMARY

The developments of the OpenMolcas program suite over the last three years have been reported throughout six thematic sections. A compact summary of each topic follows.

In the “Electronic Structure Theory” section, a number of new methods and interfaces are described, which enable novel features based on the framework of multiconfigurational SCF. In particular, improvements to the Stocastic-CI and the DMRG approaches are reported. The interfaces to Dice, RelaxSE, COLUMBUS, and GronOR are described. Moreover, three new options to the CASPT2 functionality are presented—the RMS and XDW versions of multistate CASPT2, a regularization as an alternative to level-shifting, and the frozen natural orbital option as implemented for the RASPT2 model. Finally, extensions of the MC-PDFT model are put forward. In connection with this, the LibXC infrastructure has been introduced both at the DFT and the MC-PDFT levels of approximation.

Under the theme “Electronic Spectroscopy” several extensions are reported, which facilitate the derivation of anisotropic exchange for binuclear systems beyond the Lines model, the study of model Hamiltonians for one or two spin centers with

arbitrary angular momenta, the study of the hyperfine coupling at the exact two-component relativistic level, of spin-forbidden transitions, of autoionization processes using the one-center-approximation, and of Frenkel’s excitonic coupling terms. These extensions also allow the use of the semiclassical light-matter interaction operator, the simulation of photoionization processes using Dyson orbitals and of ultrafast electron dynamics.

In the “Gradients and Molecular Structure Optimization” section, the analytical nuclear gradients at the CASPT2 and MC-PDFT levels of approximation are introduced. In association with this, a molecular structure optimization algorithm based on machine-learning techniques is reported.

The following section, “Vibrational and Vibrationally Corrected Electronic Spectroscopy”, reports additional new tools in association with spectroscopy, however, here in a context beyond a fixed molecular structure. For example, the nuclear ensemble approach for vibrational corrections is available through MULTISPEC, and the displaced harmonic oscillator approximation to the nuclear wave packet approach is supported with the interface to iSpectron. Here the incorporation of tools for the study of molecular magnetism within the approximation of analytic linear vibronic coupling and a two-step approach to reduce the computational expense for vibronic coupling in the case of multiroot investigations are also described. The section is completed with a report of a new module – LEVEL – for enhanced and improved simulations of ro-vibrational spectroscopy for dinuclear systems.

The “Ab Initio Molecular Dynamics” section includes reports on tools to generate initial conditions for semiclassical molecular dynamics simulations. Additionally, improvements of non-adiabatic dynamics using the SURFACEHOP module and of the SHARC package versions 2.0 and 3.0, as interfaced to OpenMolcas, are reported. This section is concluded with the presentation of the COBRAMM interface for simulations of transient UV/vis spectroscopy, a comparison of different simulations techniques for nonadiabatic dynamics—trajectory surface hopping vs the displaced harmonic oscillator model, the newly developed OpenMolcas-GAMESS-US/Tinker interface, with an example of a nonadiabatic molecular dynamics simulation of a molecular motor, and at last some notes on the use of the MC-PDFT model in connection with simulations of nonadiabatic processes.

Finally, the “Basis Sets, Ab Initio Model Potentials and Orbital Rotation” section describes briefly new basis sets, tools to develop AIMPs and to transform molecular orbitals, consistent with the corresponding manipulations of a rigid molecular structure.

To conclude, the open-source model of software development has been very beneficial to the OpenMolcas project. The past few years have seen a surge in new developments and an expansion of the community of OpenMolcas developers. In this respect OpenMolcas and associated external programs/ interfaces have developed into an open-source simulation infrastructure in the form of a web, where the core functionalities and file formats of OpenMolcas represents the spider in the center. Agile researchers in the electronic structure theory and molecular dynamics fields are invited to contribute to further developments of the web, either with novel implementations or improvements of existing software. If the recent rate of development is of any measure of the path forward, one should expect the project to continue to develop and the community to grow. You are all welcome to participate and enjoy.
■ ASSOCIATED CONTENT

● Supporting Information

The Supporting Information is available free of charge at
https://pubs.acs.org/doi/10.1021/acs.jctc.3c00182.

Workflow and input examples for spin adaptation with GUGA-FCIQMC. Input examples for spin-purification, Stochastic-GASSCF and deterministic spin-averaged MCSCF with the NECI interface. Computational details, active spaces, discussion and input example for HCI-SCF with the Dice interface. Details and input examples for uncontracted MRCI with the RelaxSE interface. Input example for the FNO-RASPT2 method. Complete table of anisotropic magnetic exchange parameters and input examples for the Dy<sup>III</sup>Mn<sup>II</sup> binuclear system. Input example for relativistic hyperfine coupling calculation. Input files for single- and two-photon spectra with the exact semiclassical operator. Input and output example for a LEVEL calculation. Complete computational details (including optimized geometries, extra basis functions, active space orbitals, computed energetics, and example input files), data acquisition, and its discussion for the evaluation of Frenkel's excitonic coupling terms and the corresponding absorption spectra. Input examples and discussion for the calculation of ssDCH and Auger spectra. Input example for the RhoDyn module. Input examples for the original and two-step procedures for the analytic evaluation of vibronic coupling. Example input and output files for the SHARC-OpenMolcas interface. Descriptions of the capabilities of the Open-Molcas-GAMESS-US/Tinker interface and information about the software supporting the interface followed with a number of input examples, details of MTDP simulations in solvent. Calculated electron affinity of the oxygen atom with different ANO-R contractions. Examples of the use of SCEPIC for input generation of a bulk system and a surface (PDF, ZIP)

■ AUTHOR INFORMATION

Corresponding Authors

Giovanni Li Manni - Electronic Structure Theory Department,
Max Planck Institute for Solid State Research, 70569
Stuttgart, Germany; ● orcid.org/0000-0002-3666-3880;
Email: g.limanni@fkf.mpg.de

Ignacio Fdez. Galván - Department of Chemistry - BMC, Uppsala University, SE-75123 Uppsala, Sweden;
● orcid.org/0000-0002-0684-7689;
Email: Ignacio.Fernandez@kemi.uu.se

Roland Lindh - Department of Chemistry - BMC, Uppsala University, SE-75123 Uppsala, Sweden; Uppsala Center for Computational Chemistry (UC₃), Uppsala University, SE-75123 Uppsala, Sweden; ● orcid.org/0000-0001-7567-8295;
Email: roland.lindh@kemi.uu.se

Authors

Ali Alavi - Electronic Structure Theory Department, Max Planck Institute for Solid State Research, 70569 Stuttgart, Germany; Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge CB2 1EW, United Kingdom

Flavia Aleotti - Department of Industrial Chemistry "Toso Montanari", University of Bologna, 40136 Bologna, Italy;
● orcid.org/0000-0002-7176-5305

Francesco Aquilante - Theory and Simulation of Materials (THEOS) and National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland; ● orcid.org/0000-0003-4422-3938

Jochen Autschbach - Department of Chemistry, University at Buffalo, State University of New York, Buffalo, New York 14260-3000, United States; ● orcid.org/0000-0001-9392-877X

Davide Avagliano - Department of Industrial Chemistry "Toso Montanari", University of Bologna, 40136 Bologna, Italy;
● orcid.org/0000-0001-5539-9731

Alberto Baiardi - ETH Zurich, Laboratory for Physical Chemistry, 8093 Zurich, Switzerland; ● orcid.org/0000-0001-9112-8664

Jie J. Bao - Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States; ● orcid.org/0000-0003-0197-3405

Stefano Battaglia - Department of Chemistry - BMC, Uppsala University, SE-75123 Uppsala, Sweden; Present Address: Department of Chemistry, University of Zurich, Winterthurerstrasse 190, Zurich 8057, Switzerland;
● orcid.org/0000-0002-5082-2681

Letitia Birnoschi - The Department of Chemistry, The University of Manchester, M13 9PL Manchester, U.K.

Alejandro Blanco-González - Chemistry Department, Bowling Green State University, Bowling Green, Ohio 43403, United States; ● orcid.org/0000-0001-7379-2588

Sergey I. Bokarev - Chemistry Department, School of Natural Sciences, Technical University of Munich, 85748 Garching, Germany; Institut für Physik, Universität Rostock, 18059 Rostock, Germany; ● orcid.org/0000-0003-0779-5013

Ria Broer - Theoretical Chemistry, Zernike Institute for Advanced Materials, University of Groningen, 9747AG Groningen, The Netherlands; ● orcid.org/0000-0002-5437-9509

Roberto Cacciari - Dipartimento di Biotecnologie, Chimica e Farmacia, Università di Siena, 53100 Siena, Italy;
● orcid.org/0000-0001-8290-4297

Paul B. Calio - Department of Chemistry, Pritzker School of Molecular Engineering, James Franck Institute, Chicago Center for Theoretical Chemistry, The University of Chicago, Chicago, Illinois 60637, United States; ● orcid.org/0000-0001-8385-2628

Rebecca K. Carlson - Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States; ● orcid.org/0000-0002-1710-5816

Rafael Carvalho Couto - Division of Theoretical Chemistry and Biology, School of Engineering Sciences in Chemistry, Biotechnology and Health, KTH Royal Institute of Technology, SE-106 91 Stockholm, Sweden; ● orcid.org/0000-0003-4020-0923

Luis Cerdán - Instituto de Ciencia Molecular, Universitat de València, 46980 Paterna, Spain; Instituto de Óptica (IO-CSIC), Consejo Superior de Investigaciones Científicas, 28006 Madrid, Spain; ● orcid.org/0000-0002-7174-2453

Liviu F. Chibotaru - Department of Chemistry, KU Leuven, 3001 Leuven, Belgium; ● orcid.org/0000-0003-1556-0812

Nicholas F. Chilton - The Department of Chemistry, The University of Manchester, M13 9PL Manchester, U.K.;
● orcid.org/0000-0002-8604-0171
**Jonathan Richard Church** — Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel; ● orcid.org/0000-0001-5986-1305

**Irene Conti** — Department of Industrial Chemistry “Toso Montanari”, University of Bologna, 40136 Bologna, Italy; ● orcid.org/0000-0001-7982-4480

**Sonia Coriani** — Department of Chemistry, Technical University of Denmark, 2800 Kongens Lyngby, Denmark; ● orcid.org/0000-0002-4487-897X

**Juliana Cuéllar-Zuquin** — Instituto de Ciencia Molecular, Universitat de València, 46980 Paterna, Spain; ● orcid.org/0000-0002-0127-579X

**Razan E. Daoud** — Dipartimento di Biotecnologie, Chimica e Farmacia, Università di Siena, 53100 Siena, Italy; ● orcid.org/0000-0001-7034-0770

**Nike Dattani** — HPQC Labs, Waterloo N2T 2K9 Ontario, Canada; HPQC College, Waterloo N2T 2K9 Ontario, Canada; ● orcid.org/0000-0001-5667-3632

**Piero Decleva** — Istituto Officina dei Materiali IOM-CNR and Dipartimento di Scienze Chimiche e Farmaceutiche, Università degli Studi di Trieste, I-34121 Trieste, Italy; ● orcid.org/0000-0002-7322-887X

**Coen de Graaf** — Department of Physical and Inorganic Chemistry, Universitat Rovira i Virgili, Tarragona 43007, Spain; ICREA, 08010 Barcelona, Spain; ● orcid.org/0000-0001-8114-6658

**Mickaël G. Delcey** — Division of Theoretical Chemistry and Biology, School of Engineering Sciences in Chemistry, Biotechnology and Health, KTH Royal Institute of Technology, SE-106 91 Stockholm, Sweden; ● orcid.org/0000-0001-9883-3569

**Luca De Vico** — Dipartimento di Biotecnologie, Chimica e Farmacia, Università di Siena, 53100 Siena, Italy; ● orcid.org/0000-0002-2821-5711

**Werner Dobrautz** — Chalmers University of Technology, Department of Chemistry and Chemical Engineering, 41296 Gothenburg, Sweden; ● orcid.org/0000-0001-6479-1874

**Sijia S. Dong** — Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States; Department of Chemistry and Chemical Biology, Department of Physics, and Department of Chemical Engineering, Northeastern University, Boston, Massachusetts 02115, United States; ● orcid.org/0000-0001-8182-6522

**Rulin Feng** — Department of Chemistry, University at Buffalo, State University of New York, Buffalo, New York 14260-3000, United States; Department of Chemistry, Fudan University, Shanghai 200433, China; ● orcid.org/0000-0002-9812-3804

**Nicolas Ferré** — Institut de Chimie Radicalaire (UMR-7273), Aix-Marseille Univ, CNRS, ICR, 13013 Marseille, France; ● orcid.org/0000-0002-5583-8834

**Michael Filatov(Gulak)** — Department of Chemistry, Kyungpook National University, Daegu 702-701, South Korea; ● orcid.org/0000-0002-1541-739X

**Laura Gagliardi** — Department of Chemistry, Pritzker School of Molecular Engineering, James Franck Institute, Chicago Center for Theoretical Chemistry, The University of Chicago, Chicago, Illinois 60637, United States; Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States; ● orcid.org/0000-0001-5227-1396

**Marco Garavelli** — Department of Industrial Chemistry “Toso Montanari”, University of Bologna, 40136 Bologna, Italy; ● orcid.org/0000-0002-0796-289X

**Leticia González** — Institute of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, A-1090 Vienna, Austria; ● orcid.org/0000-0001-5112-794X

**Yafu Guan** — State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, People's Republic of China

**Meiyuan Guo** — SSRL, SLAC National Accelerator Laboratory, Menlo Park, California 94025, United States; ● orcid.org/0000-0003-2474-6264

**Matthew R. Hennefarth** — Department of Chemistry, Pritzker School of Molecular Engineering, James Franck Institute, Chicago Center for Theoretical Chemistry, The University of Chicago, Chicago, Illinois 60637, United States; ● orcid.org/0000-0002-6601-2253

**Matthew R. Hermes** — Department of Chemistry, Pritzker School of Molecular Engineering, James Franck Institute, Chicago Center for Theoretical Chemistry, The University of Chicago, Chicago, Illinois 60637, United States; Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States; ● orcid.org/0000-0001-7807-2950

**Chad E. Hoyer** — Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States; Department of Chemistry, University of Washington, Seattle, Washington 98195, United States

**Miquel Huix-Rotllant** — Institut de Chimie Radicalaire (UMR-7273), Aix-Marseille Univ, CNRS, ICR, 13013 Marseille, France; ● orcid.org/0000-0002-2131-7328

**Vishal Kumar Jaiswal** — Department of Industrial Chemistry “Toso Montanari”, University of Bologna, 40136 Bologna, Italy; ● orcid.org/0000-0002-5090-7984

**Andy Kaiser** — Institut für Physik, Universität Rostock, 18059 Rostock, Germany

**Danil S. Kaliakin** — Chemistry Department, Bowling Green State University, Bowling Green, Ohio 43403, United States; ● orcid.org/0000-0002-9354-8248

**Marjan Khamesian** — Department of Chemistry — BMC, Uppsala University, SE-75123 Uppsala, Sweden

**Daniel S. King** — Department of Chemistry, Pritzker School of Molecular Engineering, James Franck Institute, Chicago Center for Theoretical Chemistry, The University of Chicago, Chicago, Illinois 60637, United States; ● orcid.org/0000-0003-0208-5274

**Vladislav Kochetov** — Institut für Physik, Universität Rostock, 18059 Rostock, Germany

**Marek Krośnicki** — Institute of Theoretical Physics and Astrophysics, Faculty of Mathematics, Physics and Informatics, University of Gdańsk, 80-952 Gdańsk, Poland

**Arpit Arun Kumaar** — HPQC Labs, Waterloo N2T 2K9 Ontario, Canada

**Ernst D. Larsson** — Division of Theoretical Chemistry, Chemical Centre, Lund University, SE-22100 Lund, Sweden; ● orcid.org/0000-0001-7655-2993

**Susi Lehtola** — Molecular Sciences Software Institute, Blacksburg, Virginia 24061, United States; Department of
Chemistry, University of Helsinki, FI-00014 University of Helsinki, Finland; ● orcid.org/0000-0001-6296-8103

Marie-Bernadette Lepetit - Condensed Matter Theory Group, Institut Néel, 38042 Grenoble, France; Theory Group, Institut Laue Langevin, 38042 Grenoble, France; ● orcid.org/0000-0001-8730-4282

Hans Lischka - Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409-1061, United States; ● orcid.org/0000-0002-5656-3975

Pablo López Ríos — Electronic Structure Theory Department, Max Planck Institute for Solid State Research, 70569 Stuttgart, Germany

Marcus Lundberg – Department of Chemistry – Ångström Laboratory, Uppsala University, SE-75120 Uppsala, Sweden; ● orcid.org/0000-0002-1312-1202

Dongxia Ma — Electronic Structure Theory Department, Max Planck Institute for Solid State Research, 70569 Stuttgart, Germany; Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States

Sebastian Mai — Institute of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, A-1090 Vienna, Austria; ● orcid.org/0000-0001-5327-8880

Philipp Marquetand — Institute of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, A-1090 Vienna, Austria; ● orcid.org/0000-0002-8711-1533

Isabella C. D. Merritt — Nantes Université, CNRS, CEISAM, F-44000 Nantes, France; ● orcid.org/0000-0002-7965-7798

Francesco Montorsi — Department of Industrial Chemistry “Toso Montanari”, University of Bologna, 40136 Bologna, Italy

Maximilian Mörchen — ETH Zurich, Laboratory for Physical Chemistry, 8093 Zurich, Switzerland

Artur Nenov — Department of Industrial Chemistry “Toso Montanari”, University of Bologna, 40136 Bologna, Italy; ● orcid.org/0000-0003-3071-5341

Vu Ha Anh Nguyen — Department of Chemistry, National University of Singapore, 117543, Singapore; Present Address: School of Physics, Trinity College Dublin, The University of Dublin, College Green, Dublin 2, Ireland; ● orcid.org/0000-0002-4177-0656

Yoshio Nishimoto — Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan; ● orcid.org/0000-0001-5581-4712

Meagan S. Oakley — Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States; ● orcid.org/0000-0001-5072-7572

Massimo Olivucci — Dipartimento di Biotecnologie, Chimica e Farmacia, Università di Siena, 53100 Siena, Italy; Chemistry Department, Bowling Green State University, Bowling Green, Ohio 43403, United States; ● orcid.org/0000-0002-8247-209X

Markus Oppel — Institute of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, A-1090 Vienna, Austria; ● orcid.org/0000-0001-6363-2310

Daniele Padula — Dipartimento di Biotecnologie, Chimica e Farmacia, Università di Siena, 53100 Siena, Italy; ● orcid.org/0000-0002-7171-7928

Riddhish Pandharkar — Department of Chemistry, Pritzker School of Molecular Engineering, James Franck Institute, Chicago Center for Theoretical Chemistry, The University of

Chicago, Chicago, Illinois 60637, United States; Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States; ● orcid.org/0000-0003-4086-4308

Quan Manh Phung — Department of Chemistry, Graduate School of Science, Nagoya University, Nagoya, Aichi 464-8602, Japan; Institute of Transformative Bio-Molecules (WPI-ITbM), Nagoya University, Nagoya, Aichi 464-8601, Japan; ● orcid.org/0000-0001-8205-5328

Felix Plasser — Department of Chemistry, Loughborough University, Loughborough LE11 3TU, U.K.; ● orcid.org/0000-0003-0751-148X

Gerardo Raggi — Department of Chemistry — BMC, Uppsala University, SE-75123 Uppsala, Sweden; Quantum Materials and Software LTD, London EC1V 2NX, United Kingdom

Elisa Rebolini — Scientific Computing Group, Institut Laue Langevin, 38042 Grenoble, France

Markus Reiher — ETH Zurich, Laboratory for Physical Chemistry, 8093 Zurich, Switzerland; ● orcid.org/0000-0002-9508-1565

Ivan Rivalta — Department of Industrial Chemistry “Toso Montanari”, University of Bologna, 40136 Bologna, Italy; Present Address: ENSL, CNRS, Laboratoire de Chimie UMR 5182, 46 allée d’Italie, 69364 Lyon, France; ● orcid.org/0000-0002-1208-602X

Daniel Roca-Sanjuán — Instituto de Ciencia Molecular, Universitat de València, 46980 Paterna, Spain; ● orcid.org/0000-0001-6495-2770

Thies Romig — Institut für Physik, Universität Rostock, 18059 Rostock, Germany; ● orcid.org/0000-0002-9424-2398

Arta Anushirwan Safari — Electronic Structure Theory Department, Max Planck Institute for Solid State Research, 70569 Stuttgart, Germany; ● orcid.org/0000-0003-4511-8902

Aitor Sánchez-Mansilla — Department of Physical and Inorganic Chemistry, Universitat Rovira i Virgili, Tarragona 43007, Spain; ● orcid.org/0000-0002-2601-190X

Andrew M. Sand — Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States; Department of Chemistry and Biochemistry, Butler University, Indianapolis, Indiana 46208, United States; ● orcid.org/0000-0002-7166-2066

Igor Schapiro — Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel; ● orcid.org/0000-0001-8536-6869

Thais R. Scott — Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States; Department of Chemistry, Pritzker School of Molecular Engineering, James Franck Institute, Chicago Center for Theoretical Chemistry, The University of Chicago, Chicago, Illinois 60637, United States; Department of Chemistry, University of California, Irvine, California 92697, United States; ● orcid.org/0000-0002-5746-5517

Javier Segarra-Martí — Instituto de Ciencia Molecular, Universitat de València, 46980 Paterna, Spain; ● orcid.org/0000-0002-2076-3406

Francesco Segatta — Department of Industrial Chemistry “Toso Montanari”, University of Bologna, 40136 Bologna, Italy; ● orcid.org/0000-0003-4150-6676
**Dumitru-Claudiu Sergentu** - Department of Chemistry,
University at Buffalo, State University of New York, Buffalo,
New York 14260-3000, United States; Laboratory RA-03,
RECENT AIR, A. I. Cuza University of Iași, Iași 700506,
Romania; ● orcid.org/0000-0001-6570-5245

**Prachi Sharma** - Department of Chemistry, Chemical Theory
Center, and Minnesota Supercomputing Institute, University of
Minnesota, Minneapolis, Minnesota 55455-0431, United
States

**Ron Shepard** - Chemical Sciences and Engineering Division,
Argonne National Laboratory, Lemont, Illinois 60439, USA;
● orcid.org/0000-0002-0272-0824

**Yinan Shu** - Department of Chemistry, Chemical Theory
Center, and Minnesota Supercomputing Institute, University of
Minnesota, Minneapolis, Minnesota 55455-0431, United
States; ● orcid.org/0000-0002-8371-0221

**Jakob K. Staab** - The Department of Chemistry, The University
of Manchester, M13 9PL Manchester, U.K.

**Tjerk P. Straatsma** - National Center for Computational
Sciences, Oak Ridge National Laboratory, Oak Ridge,
Tennessee 37831-6373, United States; Department of
Chemistry and Biochemistry, University of Alabama,
Tuscaloosa, Alabama 35487-0336, United States

**Lasse Kragh Sørensen** - University Library, University of
Southern Denmark, DK-5230 Odense M, Denmark;
● orcid.org/0000-0002-1931-1867

**Bruno Nunes Cabral Tenorio** - Department of Chemistry,
Technical University of Denmark, 2800 Kongens Lyngby,
Denmark; ● orcid.org/0000-0002-9702-998X

**Donald G. Truhlar** - Department of Chemistry, Chemical
Theory Center, and Minnesota Supercomputing Institute,
University of Minnesota, Minneapolis, Minnesota 55455-
0431, United States; ● orcid.org/0000-0002-7742-7294

**Liviu Ungur** - Department of Chemistry, National University of
Singapore, 117543, Singapore; ● orcid.org/0000-0001-
5015-4225

**Morgane Vacher** - Nantes Université, CNRS, CEISAM, F-
44000 Nantes, France; ● orcid.org/0000-0001-9418-6579

**Valera Veryazov** - Division of Theoretical Chemistry, Chemical
Centre, Lund University, SE-22100 Lund, Sweden;
● orcid.org/0000-0002-0172-7047

**Torben Arne Voß** - Institut für Physik, Universität Rostock,
18059 Rostock, Germany; ● orcid.org/0000-0001-6408-
5822

**Oskar Weser** - Electronic Structure Theory Department, Max
Planck Institute for Solid State Research, 70569 Stuttgart,
Germany; ● orcid.org/0000-0001-5503-1195

**Dihua Wu** - Department of Chemistry, Chemical Theory
Center, and Minnesota Supercomputing Institute, University of
Minnesota, Minneapolis, Minnesota 55455-0431, United
States; ● orcid.org/0000-0001-8508-8723

**Xuchun Yang** - Chemistry Department, Bowling Green State
University, Bowling Green, Ohio 43403, United States;
● orcid.org/0000-0002-1500-1773

**David Yarkony** - Department of Chemistry, Johns Hopkins
University, Baltimore, Maryland 21218, United States;
● orcid.org/0000-0002-5446-1350

**Chen Zhou** - Department of Chemistry, Chemical Theory
Center, and Minnesota Supercomputing Institute, University of
Minnesota, Minneapolis, Minnesota 55455-0431, United
States

**J. Patrick Zobel** - Institute of Theoretical Chemistry, Faculty of
Chemistry, University of Vienna, A-1090 Vienna, Austria;
● orcid.org/0000-0002-9601-7573

Complete contact information is available at:
https://pubs.acs.org/10.1021/acs.jctc.3c00182

Author Contributions

‡G.L.M., I.F.G., R.L.: These authors contributed equally to this
manuscript.

Notes

The authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

F.Aq., J.C.Z., and J.S.M. acknowledge the support of a fellowship
from "La Caixa" Foundation (ID 100010434), from the
European Union's Horizon 2020 research and innovation
programme under the Marie Skłodowska-Curie grant agreement
No 847648, fellowship code "LCF/BQ/PI20/11760022", and
from the Spanish Ministerio de Ciencia e Innovación
(MICINN) within the Unit of Excellence María de Maeztu
programme (CEX2019-000919-M) and Proyectos de Gener-
ación de conocimiento (PID2021-128490NA-I00). J.A. ac-
knowledges support from the US Department of Energy, Office
of Science, Basic Energy Sciences grants DE-SC0020169
(hyperfine coupling, NTOs) and DE-SC0001136 (X-ray
spectroscopy of f-element compounds). S.B. acknowledges the
Swiss National Science Foundation (SNSF) for the funding
received through the Postdoc Mobility fellowship (Grant No.
199192). R.C., R.E.D., L.D.V., and D.P. acknowledge support
provided by MIUR (Ministero dell'Istruzione, dell'Università e
della Ricerca) grant "Dipartimento di Eccellenza 2018-2022".
R.C.C. and M.L. acknowledge support from the Carl Trygger
Foundation (Grant No. CTS-17:297). L.C. and D.R.S.
acknowledge support from the Spanish Agencia Estatal de
Investigación of the Ministerio de Ciencia e Innovación
(MICINN) and the European Regional Development Fund
(FEDER) through project No. PID2021-127199NB-I00.
N.F.C., J.K.S. and L.B. thank the ERC (ERC-2019-STG-
851504), the Royal Society (URF191320) and The Ministry
of Defence for funding, and the Computational Shared Facility
at the University of Manchester for computational resources and
assistance. J.R.C. acknowledges the Zuckerman STEM leader-
ship program for their support. S.C., B.N.C.T., P.D., T.A.V., and
S.I.B. acknowledge support from the European Union's Horizon
2020 Research and Innovation Programme under the Marie
Skłodowska-Curie Individual Fellowship (B.N.C.T. and S.C.
Grant Agreement No. 101027796), from the Independent
Research Fund Denmark-Natural Sciences, DFF-RP2 Grant No.
7014-00258B (S.C.), from the Deutsche Forschungsgemein-
schaft (Grant No. BO 4915/1-1) (S.I.B.) and from the
European Cooperation in Science and Technology, COST
Action CA18222, Attochem. R.E.D. and L.D.V. acknowledge
the Italian Ministry of University and Research (MUR) for a
"Bando PON 37 ciclo - REACT-EU FSE DM 1061" grant. N.D.
thanks Digital Research Alliance of Canada for CPU time via
project BMH-491-09. C.d.G., A.S.M., R.B. and T.P.S. acknowl-
edge PRACE for awarding access to JUWELS at GCS@FZJ,
Germany, and financial support provided by the Spanish
Ministerio de Ciencia, Innovación y Universidades (Projects
RTI2018-095460-BIO00, PID2020-113187GB-I00 and the Ex-
cellence María de Maeztu grant MDM-2017-0767) and by the
Generalitat de Catalunya (Projects 2017SGR13 and 2017-
SGR629). M.G.D. and M.L. acknowledge support from the Foundation Olle Engkvist Byggmästare (Grant No. 183-0403). W.D. acknowledges funding from the European Union's Horizon Europe research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 101062864. A.K. acknowledges support from the Deutsche Forschungs-gemeinschaft (DFG, German Research Foundation) - SFB 1477 "Light-Matter Interactions at Interfaces", project number 441234705. M.Kr. acknowledges support from NCBIR Grant No. PL-TW/VIII/1/2021. E.D.L. acknowledges kind support from Luis Seijo. S.L. thanks the National Science Foundation for financial support under grant no. CHE-2136142, as well as the Academy of Finland for financial support under project numbers 350282 and 353749. R.L. acknowledges financial support from the Knut and Alice Wallenberg Foundation (Grant No. KAW-2013.0020) and the Swedish Research Council (VR, Grant No. 2020-03182). H.L. acknowledges the support by the National Science Foundation [grant number 2107923], Division of Chemistry. P.L.R. and A.A. acknowledge support from the European Centre of Excellence in Exascale Computing TREX, funded by the Horizon 2020 program of the European Union under grant no. 952165. I.C.D.M. acknowledges thesis funding from Nantes University. Y.N. acknowledges JSPS KAKENHI (Grant Nos. 19H02682 and 20K15230). M.Ol. and D.S.Ka. acknowledge the support by NSF grant CHE-SDM A (No. 2102619). M.Ol., D.S.Ka., M.H.R., N.F., M.F.G., and X.Y. acknowledge the EU funding within the MUR PNRR "National Center for Gene Therapy and Drugs based on RNA Technology" (Project no. CN00000041 CN3 RNA). D.P. acknowledges the Italian Ministry of University and Research (MUR) for a "Rita Levi Montalcini" grant (PGR18PJMBW), and Università di Siena for funding (F-CUR research support contribution). F.P., F.M., F.S., A.N. and M.Ga. acknowledge the Department of Energy-USA Federal Award No: DE-SC0022225. G.R., R.L. and I.F.G. acknowledge support from the Swedish Research Council (VR, Grant No. 2016-03398) and the Olle Engkvist foundation (grant 18-2006). M.R. and A.B. acknowledge the fundings through the "Quantum for Life Center" funded by the Novo Nordisk Foundation (grant NNF20OC059939). M.R. and M.M. acknowledge support through ETH Research Grant ETH-43 20-2. D.C.S. acknowledges infrastructure support from the Operational Program Competitiveness 2014-2020, Axis 1, under POC/448/1/1 Research infrastructure projects for public R&D institutions/Sections F 2018, through the Research Center with Integrated Techniques for Atmospheric Aerosol Investigation in Romania (RECENT AIR) project, under grant agreement MySMIS no. 127324. R.S. acknowledges the support by the US Department of Energy, Office of Science, Basic Energy Sciences, Chemical Sciences, Geosciences, and Biosciences Division, Gas Phase Chemical Physics program through Argonne National Laboratory under Contract DE-AC02-06CH11357. L.U. acknowledges the financial support of the research projects R-143-000-A65-133, A-8000709-00-00, and A-8000017-00-00 of the National University of Singapore. V.V. thanks eSSENCE@LU grant 7:3. D.W. acknowledges the Air Force Office of Scientific Research by grant no. FA9550-11-0078. D.Y. acknowledges the support by NSF grant CHE-1954723. J.P.Z. and L Go. acknowledge the support from the Deutsche Forschungs-gemeinschaft (SPP 2102, project GO 1059/8-2). The authors at the University of Vienna thank the Vienna Scientific Cluster for computer resources. The work carried out at the University of Minnesota and the University of Chicago was supported in part

by the Air Force Office of Scientific Research by grant FA9550-20-1-0360, the National Science Foundation under grant CHE-2054723, the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under award DE-SC0015997, and the Catalyst Design for Decarbonization Center, an Energy Frontier Research Center, which is funded by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES) under award DE-SC0023383. The authors thank the Research Computing Center (RCC) at the University of Chicago and the Minnesota Supercomputing Institute (MSI) at the University of Minnesota for access to computational resources. The NOCI work used resources through the INCITE program of the Oak Ridge Leadership Computing Facility (OLCF) at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC05-00OR22725. The authors of the anisotropic exchange ab initio calculations thank the ASPIRE-1 cluster (www.nscc.sg) under the projects 11001278 and 51000267 and the HPC-NUS for computer resources. Part of the calculations were performed on computer resources provided by the Swedish National Infrastructure for Computing (SNIC), partially funded by the Swedish Research Council (grant 2018-05973), at the National Supercomputer Centre in Sweden (NSC, Linköping University), UPPMAX (Uppsala University) and LUNARC (Lund University), and on the CNRS-IDRIS computer center IDRIS and the regional computer center CRIANN, under projects No. 91842 and No. 2007013, and using HPC resources from GENCI-IDRIS (Grant 2021-101353) and CCIPL/Glicid (Le centre de calcul intensif des Pays de la Loire).

## DEDICATION

†Dedicated to the fond memory of the late Prof. Josef Paldus and his invaluable contributions to GUGA.

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