Soumi Haldar

One of the primary challenges in quantum chemistry is the accurate modeling of strong electron correlation. While multireference methods effectively capture such correlation, their steep scaling with system size prohibits their application to large molecules and extended materials. Quantum embedding offers a promising solution by partitioning complex systems into manageable subsystems. In this Review, we highlight recent advances in multireference density matrix embedding and localized active space self-consistent field approaches for complex molecules and extended materials. We discuss both classical implementations and the emerging potential of these methods on quantum computers. By extending classical embedding concepts to the quantum landscape, these algorithms have the potential to expand the reach of multireference methods in quantum chemistry and materials.

An octa-hydrated curium compound [Cm(H₂O)₈](Hdtp)(dtp)·H₂O (Cm1, H₂dtp = 2,3-di(tetrazol-5-yl)pyrazine) along with its lanthanide analogues [Ln(H₂O)₈](Hdtp)(dtp)·H₂O (Ln1, Ln³⁺ = La³⁺-Nd³⁺, Sm³⁺-Lu³⁺) were synthesized and characterized using single crystal X-ray diffraction and spectroscopic methods. Bond length analysis of ^VIIICm(III)-OH₂ (where ^VIII refers to the coordination number) was compared to ^VIIILn(III)-OH₂ (Ln³⁺ = Nd³⁺ and Sm³⁺), indicating similar ^VIIIM(III)-OH₂ bond lengths because of their similar eight-coordinate ionic radii of these ^VIIIM(III) cations. Owing to the reduced coordination number, the ^VIIICm(III)-OH₂ bond lengths were shorter than previously reported ^IXCm(III)-OH₂ bonds in [Cm(H₂O)₉](CF₃SO₃)₃. The octa-aquo complexes were also characterized by solid-state UV-vis-NIR spectroscopy in addition to variable-temperature and variable-pressure photoluminescence. Variable-pressure absorption spectra of Cm1 were compared with Ln1 and show that the Cm(III) f → f transitions have a stronger dependence on pressure than that observed in Ln1 (Ln³⁺ = Nd³⁺ and Sm³⁺). The experimental and computational analyses reveal that the monotonic decrease in the computed energy difference between the ground state and the first excited state corresponds to the observed red shift of the photoluminescence peak. This is accompanied by a gradual reduction in the average Cm(III)-OH₂ bond length and a delocalization of spin densities, alongside an intensified interaction involving the 5f orbitals under increasing pressure. These changes accommodate the new geometry and collectively modify the energy landscape, resulting in peak broadening and quenching.

The optical spectra of neutral oxygen vacancies (F⁰ centers) in the bulk MgO lattice are investigated using density matrix embedding theory. The impurity Hamiltonian is solved with the complete active space self-consistent field and second-order n-electron valence state perturbation theory (NEVPT2-DMET) multireference methods. To estimate defect-localized vertical excitation energies at the nonembedding and thermodynamic limits, a double extrapolation scheme is employed. The extrapolated NEVPT2-DMET vertical excitation energy value of 5.24 eV agrees well with the experimental absorption maxima at 5.03 eV, whereas the excitation energy value of 2.89 eV at the relaxed triplet defect-localized state geometry overestimates the experimental emission at 2.4 eV by only nearly 0.5 eV, indicating the involvement of the triplet-singlet decay pathway.

We investigate the negatively charged nitrogen-vacancy center in diamond using periodic density matrix embedding theory (pDMET). To describe the strongly correlated excited states of this system, the complete active space self-consistent field (CASSCF) followed by n-electron valence state second-order perturbation theory (NEVPT2) was used as the impurity solver. Since the NEVPT2-DMET energies show a linear dependence on the inverse of the size of the embedding subspace, we performed an extrapolation of the excitation energies to the nonembedding limit using a linear regression. The extrapolated NEVPT2-DMET first triplet-triplet excitation energy is 2.31 eV and that for the optically inactive singlet-singlet transition is 1.02 eV, both in agreement with the experimentally observed vertical excitation energies of ∼2.18 eV and ∼1.26 eV, respectively. This is the first application of pDMET to a charged periodic system and the first investigation of the NV^- defect using NEVPT2 for periodic supercell models.

We investigate the negatively charged nitrogen-vacancy center in diamond using periodic density matrix embedding theory (pDMET). To describe the strongly correlated excited states of this system, the complete active space self-consistent field (CASSCF) followed by n-electron valence state second-order perturbation theory (NEVPT2) was used as impurity solver. Since the NEVPT2-DMET energies show a linear dependence on the inverse of the size of the embedding subspace, we performed an extrapolation of the excitation energies to the non-embedding limit using linear regression. The extrapolated NEVPT2-DMET first triplet-triplet excitation energy is 2.31 eV and that for the optically inactive singlet-singlet transition is 1.02 eV, both in agreement with the experimentally observed vertical excitation energies of ~2.18 eV and ~1.26 eV, respectively. This is the first application of pDMET to a charged periodic system and the first investigation of the NV- defect using NEVPT2 for periodic supercell models.

The ground state molecular frame dipole moments of alkaline earth metal monofluorides and Group ІІB‐monohydrides have been computed using two analytic methods, namely the Z‐vector technique and the linear expectation value method within the four‐component relativistic coupled cluster singles and doubles framework. We have compared our results with the experimentally measured permanent dipole moments wherever available. It is found that the Z‐vector method, which is an energy‐derivative approach predicts the molecular permanent dipole moment more accurately than the linear expectation value approach in DZ and TZ quality basis set. Further, our study shows that the high‐energy virtual spinors seem to have almost no influence on the permanent dipole moment whereas the core electron correlation slightly affects this molecular property.

The ground state molecular frame permanent dipole moment of alkaline earth metal monofluorides and the group-IIB monohydrides have been calculated using two analytic methods: Z-vector method and the linear expectation value method. Results obtained from this methods have been compared with the experimental values and different contributing terms to the total permanent dipole moment have been discussed thoroughly.

We have presented a multi-layer implementation of the equation of motion coupled-cluster method for the electron affinity, based on local and pair natural orbitals. The method gives consistent accuracy for both localized and delocalized anionic states. It results in many fold speedup in computational timing as compared to the canonical and DLPNO based implementation of the EA-EOM-CCSD method. We have also developed an explicit fragment-based approach which can lead to even higher speed-up with little loss in accuracy. The multi-layer method can be used to treat the environmental effect of both bonded and non-bonded nature on the electron attachment process in large molecules.