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The emerging field of polaritonic chemistry explores the behavior of molecules under strong coupling with cavity modes. Despite recent developments in ab initio polaritonic methods for simulating polaritonic chemistry under electronic strong coupling, their capabilities are limited, especially in cases where the molecule also features strong electronic correlation. To bridge this gap, we have developed a novel method for cavity QED calculations utilizing the Density Matrix Renormalization Group (DMRG) algorithm in conjunction with the Pauli-Fierz Hamiltonian. Our approach is applied to investigate the effect of the cavity on the S0 -S1 transition of n-oligoacenes, with n ranging from 2 to 5, encompassing 22 fully correlated {\pi} orbitals in the largest pentacene molecule. Our findings indicate that the influence of the cavity intensifies with larger acenes. Additionally, we demonstrate that, unlike the full determinantal representation, DMRG efficiently optimizes and eliminates excess photonic degrees of freedom, resulting in an asymptotically constant computational cost as the photonic basis increases.

In this work we integrate the variational quantum eigensolver (VQE) with the adiabatic connection (AC) method for efficient simulations of chemical problems on near-term quantum computers. Orbital optimized VQE methods are employed to capture the strong correlation within an active space and classical AC corrections recover the dynamical correlation effects comprising electrons outside of the active space. On two challenging strongly correlated problems, namely the dissociation of N$_2$ and the electronic structure of the tetramethyleneethane biradical, we show that the combined VQE-AC approach enhances the performance of VQE dramatically. Moreover, since the AC corrections do not bring any additional requirements on quantum resources or measurements, they can literally boost the VQE algorithms. Our work paves the way towards quantum simulations of real-life problems on near-term quantum computers.

The new generation of proposed light-emitting molecules for OLEDs has raised a considerable research interest due to its exceptional feature-a negative singlet-triplet (ST) gap violating the Hund's multiplicity rule in the excited S1 and T1 states. We investigate the role of spin polarization in the mechanism of ST gap inversion. Spin polarization is associated with doubly excited determinants of certain types, whose presence in the wavefunction expansion favors the energy of the singlet state more than that of the triplet. Using a perturbation theory-based model for spin polarization, we propose a simple descriptor for prescreening of candidate molecules with negative ST gaps and prove its usefulness for heptazine-type molecules. Numerical results show that the quantitative effect of spin polarization is approximately inverse-proportional to the HOMO-LUMO exchange integral. Comparison of single- and multireference coupled- cluster predictions of ST gaps shows that the former methods provide good accuracy by correctly balancing the effects of doubly excited determinants and dynamic correlation. We also show that accurate ST gaps may be obtained using a complete active space model supplemented with dynamic correlation from multireference adiabatic connection theory.

A multiconfigurational adiabatic connection (AC) formalism is an attractive approach to computing dynamic correlation within CASSCF and DMRG models. Practical realizations of AC have been based on two approximations: i) fixing one- and two-electron reduced density matrices (1- and 2-RDMs) at the zero-coupling constant limit and ii) extended random phase approximation (ERPA). This work investigates the the effect of removing the "fixed-RDM" approximation in AC. The analysis is carried out for two electronic Hamiltonian partitionings: the group product function- and the Dyall-Hamiltonians. Exact reference AC integrands are generated from the DMRG FCI solver. Two AC models are investigated, employing either exact 1- and 2-RDMs or their second-order expansions in the coupling constant in the ERPA equations. Calculations for model molecules indicate that lifting the fixed-RDM approximation is a viable way toward improving accuracy of the existing AC approximations.

The quantum chemical version of the density matrix renormalization group (DMRG) method has established itself as one of the methods of choice for calculations of strongly correlated molecular systems. Despite its great ability to capture strong electronic correlation in large active spaces, it is not suitable for computations of dynamical electron correlation. In this work, we present a new approach to the electronic structure problem of strongly correlated molecules, in which DMRG is responsible for a proper description of the strong correlation, whereas dynamical correlation is computed via the recently developed adiabatic connection (AC) technique, which requires only up to two-body active space reduced density matrices. We report encouraging results of this approach on typical candidates for DMRG computations, namely the $n$-acenes ($n = 2 \rightarrow 7$), Fe(II)-porphyrin, and Fe$_3$S$_4$ cluster.

Iron-sulfur clusters comprise an important functional motif of the catalytic centers of biological systems, capable of enabling important chemical transformations at ambient conditions. This remarkable capability derives from a notoriously complex electronic structure that is characterized by a high density of states that is sensitive to geometric changes. The spectral sensitivity to subtle geometric changes has received little attention from fully-correlated calculations, owing partly to the exceptional computational complexity for treating these large and correlated systems accurately. To provide insight into this aspect, we report the first Complete Active Space Self Consistent Field (CASSCF) calculations for different geometries of cubane-based clusters using two complementary, fully-correlated solvers: spin-pure Adaptive Sampling Configuration Interaction (ASCI) and Density Matrix Renormalization Group (DMRG). We find that the previously established picture of a double-exchange driven magnetic structure, with minute energy gaps (< 1 mHa) between consecutive spin states, has a weak dependence on the underlying geometry. However, the spin gap between the lowest singlet and the highest spin states is strongly geometry dependent, changing by an order of magnitude upon slight deformations that are still within biologically relevant parameters. The CASSCF orbital optimization procedure, using active spaces as large as 86 electrons in 52 orbitals, was found to reduce this gap by a factor of two compared to typical mean-field orbital approaches. Our results clearly demonstrate the need for performing highly correlated calculations to unveil the challenging electronic structure of these complex catalytic centers., Comment: 16 pages, 7 figures, 6 tables plus SI (12 pages, 3 figures, 9 tables)

Fe(II)-porphyrins (FeP) play an important role in many reactions relevant to material science and biological processes, due to their closely lying spin states. However, this small energetic separation also makes it challenging to establish the correct spin state ordering. Although the prevalent opinion is that these systems posses the triplet ground state, the recent experiment on Fe(II)-phthalocyanine under conditions matching those of an isolated molecule points toward the quintet ground state. We present a thorough study of FeP model by means of the density functional theory and density matrix renormalization group based tailored coupled clusters, in which we address all previously discussed correlation effects. We examine the importance of geometrical parameters, the Fe-N distances in particular, and conclude that the system possesses the quintet ground state, which is in our calculations well-separated from the triplet state.