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We present the theory and implementation of a fully variational wave function-density functional theory (DFT) hybrid model, which is applicable to many cases of strong correlation. We denote this model as the multiconfigurational self-consistent on-top pair-density functional theory (MC-srPDFT) model. We have previously shown how the multiconfigurational short-range DFT (MC-srDFT) hybrid model can describe many multiconfigurational cases of any spin symmetry and also state-specific calculations on excited states [Hedegård et al., J. Chem. Phys. 148(21), 214103 (2018)]. However, the srDFT part of the MC-srDFT has some deficiencies that it shares with Kohn-Sham DFT; in particular, (1) self-interaction errors (albeit reduced because of the range separation), (2) that different MS states incorrectly become non-degenerate, and (3) that singlet and non-singlet states dissociating to the same open-shell fragments incorrectly lead to different electronic energies at dissociation. The model that we present in this paper corrects these deficiencies by introducing the on-top pair density as an auxiliary variable replacing the spin density. Unlike other models in the literature, our model is fully variational and employs a long-range version of the on-top pair density. The implementation is a second-order optimization algorithm ensuring robust convergence to both ground and excited states. We show how MC-srPDFT solves the mentioned challenges by sample calculations on the ground state singlet curve of H2, N2, and Cr2 and the lowest triplet curves for N2 and Cr2. Furthermore, the rotational barrier for ethene is investigated for the S0 and T1 states. The calculations show correct degeneracy between the singlet and triplet curves at dissociation and the results are invariant to the choice of the MS value for the triplet curves., (© 2025 Author(s). Published under an exclusive license by AIP Publishing.)

In this paper, we present the theory and implementation of nuclear magnetic resonance shielding constants with gauge-including atomic orbitals for the hybrid multiconfigurational short-range density functional theory model. As a special case, this implementation also includes Hartree-Fock srDFT (HF-srDFT). Choosing a complete-active space (CAS) wave function as the multiconfigurational parameterization of the wave function, we investigate how well CAS-srDFT reproduces experimental trends of nuclear shielding constants compared to DFT and complete active space self-consistent field (CASSCF). Calculations on the nucleobases adenine and thymine show that CAS-srDFT performs on average the best of the tested methods, much better than CASSCF but only marginally better than HF-srDFT. The performance, compared to regular DFT, is similar when functionals containing exact exchange are used. We generally find that the inclusion of exact exchange is important for an accurate description of the shielding constants. In cases where no exact exchange is included, we observe that the HF- and CAS-srDFT often outperform regular DFT. For calculations on transition metal nuclei in organometallic compounds with significant static correlation, the CAS-srDFT method again outperforms CASSCF compared to experimental shielding constants, and the change from HF-srDFT is substantial. In conclusion, the static correlation posed by the metal complexes seems to be captured by CAS-srDFT, which is promising since this type of correlation is not well described by regular DFT.

The Dalton Project provides a uniform platform access to the underlying full-fledged quantum chemistry codes Dalton and LSDalton as well as the PyFraME package for automatized fragmentation and parameterization of complex molecular environments. The platform is written in Python and defines a means for library communication and interaction. Intermediate data such as integrals are exposed to the platform and made accessible to the user in the form of NumPy arrays, and the resulting data are extracted, analyzed, and visualized. Complex computational protocols that may, for instance, arise due to a need for environment fragmentation and configuration-space sampling of biochemical systems are readily assisted by the platform. The platform is designed to host additional software libraries and will serve as a hub for future modular software development efforts in the distributed Dalton community.

DIRAC is a freely distributed general-purpose program system for one-, two-, and four-component relativistic molecular calculations at the level of Hartree-Fock, Kohn-Sham (including range-separated theory), multiconfigurational self-consistent-field, multireference configuration interaction, electron propagator, and various flavors of coupled cluster theory. At the self-consistent-field level, a highly original scheme, based on quaternion algebra, is implemented for the treatment of both spatial and time reversal symmetry. DIRAC features a very general module for the calculation of molecular properties that to a large extent may be defined by the user and further analyzed through a powerful visualization module. It allows for the inclusion of environmental effects through three different classes of increasingly sophisticated embedding approaches: the implicit solvation polarizable continuum model, the explicit polarizable embedding model, and the frozen density embedding model.

Linear response theory for the multiconfigurational short-range density functional theory (MC-srDFT) model is extended to triplet response with a singlet reference wave function. The triplet linear response equations for MC-srDFT are derived for a general hybrid srGGA functional and implemented in the Dalton program. Triplet excitation energies are benchmarked against the CC3 model of coupled cluster theory and the complete-active-space second-order perturbation theory using three different short-range functionals (srLDA, srPBE, and srPBE0), both with full linear response and employing the generalized Tamm-Dancoff approximation (gTDA). We find that using gTDA is required for obtaining reliable triplet excitations; for the CAS-srPBE model, the mean absolute deviation decreases from 0.40 eV to 0.26 eV, and for the CAS-srLDA model, it decreases from 0.29 eV to 0.21 eV. As expected, the CAS-srDFT model is found to be superior to the HF-srDFT model when analyzing the calculated triplet excitations for molecules in the benchmark set where increased static correlation is expected.

Many chemical systems cannot be described by quantum chemistry methods based on a single-reference wave function. Accurate predictions of energetic and spectroscopic properties require a delicate balance between describing the most important configurations (static correlation) and obtaining dynamical correlation efficiently. The former is most naturally done through a multiconfigurational (MC) wave function, whereas the latter can be done by, e.g., perturbation theory. We have employed a different strategy, namely, a hybrid between multiconfigurational wave functions and density-functional theory (DFT) based on range separation. The method is denoted by MC short-range DFT (MC-srDFT) and is more efficient than perturbative approaches as it capitalizes on the efficient treatment of the (short-range) dynamical correlation by DFT approximations. In turn, the method also improves DFT with standard approximations through the ability of multiconfigurational wave functions to recover large parts of the static correlation. Until now, our implementation was restricted to closed-shell systems, and to lift this restriction, we present here the generalization of MC-srDFT to open-shell cases. The additional terms required to treat open-shell systems are derived and implemented in the DALTON program. This new method for open-shell systems is illustrated on dioxygen and [Fe(H 2 O) 6 ] 3+ .

We present a new hybrid multiconfigurational method based on the concept of range-separation that combines the density matrix renormalization group approach with density functional theory. This new method is designed for the simultaneous description of dynamical and static electron-correlation effects in multiconfigurational electronic structure problems.

We present here the coupling of a polarizable embedding (PE) model to the recently developed multiconfiguration short-range density functional theory method (MC-srDFT), which can treat multiconfigurational systems with a simultaneous account for dynamical and static correlation effects. PE-MC-srDFT is designed to combine efficient treatment of complicated electronic structures with inclusion of effects from the surrounding environment. The environmental effects encompass classical electrostatic interactions as well as polarization of both the quantum region and the environment. Using response theory, molecular properties such as excitation energies and oscillator strengths can be obtained. The PE-MC-srDFT method and the additional terms required for linear response have been implemented in a development version of Dalton. To benchmark the PE-MC-srDFT approach against the literature data, we have investigated the low-lying electronic excitations of acetone and uracil, both immersed in water solution. The PE-MC-srDFT results are consistent and accurate, both in terms of the calculated solvent shift and, unlike regular PE-MCSCF, also with respect to the individual absolute excitation energies. To demonstrate the capabilities of PE-MC-srDFT, we also investigated the retinylidene Schiff base chromophore embedded in the channelrhodopsin protein. While using a much more compact reference wave function in terms of active space, our PE-MC-srDFT approach yields excitation energies comparable in quality to CASSCF/CASPT2 benchmarks.

Charge transfer excitations can be described within Time-Dependent Density Functional Theory (TD-DFT), not only by means of the Coulomb Attenuated Method (CAM) but also with a combination of wave function theory and TD-DFT based on range separation. The latter approach enables a rigorous formulation of multi-determinantal TD-DFT schemes where excitation classes, which are absent in conventional TD-DFT spectra (like for example double excitations), can be addressed. This paper investigates the combination of both the long-range Multi-Configuration Self-Consistent Field (MCSCF) and Second Order Polarization Propagator Approximation (SOPPA) ansätze with a short-range DFT (srDFT) description. We find that the combinations of SOPPA or MCSCF with TD-DFT yield better results than could be expected from the pure wave function schemes. For the Time-Dependent MCSCF short-range DFT ansatz (TD-MC-srDFT) excitation energies calculated over a larger benchmark set of molecules with predominantly single reference character yield good agreement with their reference values, and are in general comparable to the CAM-B3LYP functional. The SOPPA-srDFT scheme is tested for a subset of molecules used for benchmarking TD-MC-srDFT and performs slightly better against the reference data for this small subset. Beyond the proof-of-principle calculations comprising the first part of this contribution, we additionally studied the low-lying singlet excited states (S1 and S2) of the retinal chromophore. The chromophore displays multireference character in the ground state and both excited states exhibit considerable double excitation character, which in turn cannot be described within standard TD-DFT, due to the adiabatic approximation. However, a TD-MC-srDFT approach can account for the multireference character, and excitation energies are obtained with accuracy comparable to CASPT2, although using a much smaller active space.

We present a detailed derivation of Multi-Configuration Self-Consistent Field (MCSCF) optimization and linear response equations within the polarizable embedding scheme: PE-MCSCF. The MCSCF model enables a proper description of multiconfigurational effects in reaction paths, spin systems, excited states, and other properties which cannot be described adequately with current implementations of polarizable embedding in density functional or coupled cluster theories. In the PE-MCSCF scheme the environment surrounding the central quantum mechanical system is represented by distributed multipole moments and anisotropic dipole-dipole polarizabilities. The PE-MCSCF model has been implemented in DALTON. As a preliminary application, the low lying valence states of acetone and uracil in water has been calculated using Complete Active Space Self-Consistent Field (CASSCF) wave functions. The dynamics of the water environment have been simulated using a series of snapshots generated from classical Molecular Dynamics. The calculated shifts from gas-phase to water display between good and excellent correlation with experiment and previous calculations. As an illustration of another area of potential applications we present calculations of electronic transitions in the transition metal complex, [Fe(NO)(CN)5](2-) in a micro-solvated environment. This system is highly multiconfigurational and the influence of solvation is significant.