Optimized excitonic transport mediated by local energy defects: Survival of optimization laws in the presence of dephasing.

In an extended star with peripheral defects and a core occupied by a trap, it has been shown that exciton-mediated energy transport from the periphery to the core can be optimized [S. Yalouz et al., Phys. Rev. E 106, 064313 (2022)2470-004510.1103/PhysRevE.106.064313]. If the defects are judiciously chosen, then the exciton dynamics is isomorphic to that of an asymmetric chain and a speedup of the excitonic propagation is observed. Here we extend this previous work by considering that the exciton in both an extended star and an asymmetric chain is perturbed by the presence of a dephasing environment. Simulating the dynamics using a Lindblad master equation, two questions are addressed: How does the environment affect the energy transport on these two networks? and Do the two systems still behave equivalently in the presence of dephasing? Our results reveal that the timescale for the exciton dynamics strongly depends on the nature of the network. But quite surprisingly, the two networks behave similarly regarding the survival of their optimization law. In both cases, the energy transport can be improved using the same original optimal tuning of energy defects as long as the dephasing remains weak. However, for moderate or strong dephasing, the optimization law is lost due to quantum Zeno effect.

Modifications of Tanabe-Sugano d6 Diagram Induced by Radical Ligand Field: Ab Initio Inspection of a Fe(II)-Verdazyl Molecular Complex.

Quantum entanglement between the spin states of a metal center and radical ligands is suggested in an iron(II) [Fe(dipyvd)2]2+ compound (dipyvd = 1-isopropyl-3,5-dipyridil-6-oxoverdazyl). Wave function ab initio (Difference Dedicated Configuration Interaction, DDCI) inspections were carried out to stress the versatility of local spin states. We named this phenomenon excited state spinmerism, in reference to our previous work (see Roseiro et al., ChemPhysChem 2022, e202200478) where we introduced the concept of spinmerism as an extension of mesomerism to spin degrees of freedom. The construction of localized molecular orbitals allows for a reading of the wave functions and projections onto the local spin states. The low-energy spectrum is well-depicted by a Heisenberg picture. A 60 cm-1 ferromagnetic interaction is calculated between the radical ligands with the Stotal = 0 and 1 states largely dominated by a local low-spin SFe = 0. In contrast, the higher-lying Stotal = 2 states are superpositions of the local SFe = 1 (17%, 62%) and SFe = 2 (72%, 21%) spin states. Such mixing extends the traditional picture of a high-field d6 Tanabe-Sugano diagram. Even in the absence of spin-orbit coupling, the avoided crossing between different local spin states is triggered by the field generated by radical ligands. This puzzling scenario emerges from versatile local spin states in compounds which extend the traditional views in molecular magnetism.

Orthogonally Constrained Orbital Optimization: Assessing Changes of Optimal Orbitals for Orthogonal Multireference States.

The choice of molecular orbitals is decisive in configuration interaction calculations. In this letter, a democratic description of the ground and excited states follows an orthogonally constrained orbital optimization to produce state-specific orbitals. The approach faithfully recovers the excitation energy of a four-electron Hubbard trimer, whereas state-average calculations can miss the value by a factor 2.5. The method emphasizes the need for orbital optimization to reduce configuration interaction expansions and to reach spectroscopic accuracy.

Emergence of Spinmerism for Molecular Spin-Qubits Generation.

Molecular platforms are regarded as promising candidates in the generation of units of information for quantum computing. Herein, a strategy combining spin-crossover metal ions and radical ligands is proposed from a model Hamiltonian first restricted to exchange interactions. Unusual spin states structures emerge from the linkage of a singlet/triplet commutable metal centre with two doublet-radical ligands. The ground state nature is modulated by charge transfers and can exhibit a mixture of triplet and singlet local metal spin states. Besides, the superposition reaches a maximum for 2 K M = K 1 + K 2 ${2{K}_{M}={K}_{1}+{K}_{2}}$ , suggesting a necessary competition between the intramolecular K M ${{K}_{M}}$ and inter-metal-ligand K 1 ${{K}_{1}}$ and K 2 ${{K}_{2}}$ direct exchange interactions. The results promote spinmerism, an original manifestation of quantum entanglement between the spin states of a metal centre and radical ligands. The study provides insights into spin-coupled compounds and inspiration for the development of molecular spin-qubits.

Quantum embedding of multi-orbital fragments using the block-Householder transformation.

Recently, some of the authors introduced the use of the Householder transformation as a simple and intuitive method for embedding local molecular fragments [see Sekaran et al., Phys. Rev. B 104, 035121 (2021) and Sekaran et al., Computation 10, 45 (2022)]. In this work, we present an extension of this approach to the more general case of multi-orbital fragments using the block version of the Householder transformation applied to the one-body reduced density matrix, unlocking the applicability to general quantum chemistry/condensed matter physics Hamiltonians. A step-by-step construction of the block Householder transformation is presented. Both physical and numerical areas of interest of the approach are highlighted. The specific mean-field (noninteracting) case is thoroughly detailed as it is shown that the embedding of a given N spin-orbital fragment leads to the generation of two separated sub-systems: (1) a 2N spin-orbitals "fragment+bath" cluster that exactly contains N electrons and (2) a remaining cluster's "environment" described by so-called core electrons. We illustrate the use of this transformation in different cases of embedding scheme for practical applications. We particularly focus on the extension of the previously introduced Local Potential Functional Embedding Theory and Householder-transformed Density Matrix Functional Embedding Theory to the case of multi-orbital fragments. These calculations are realized on different types of systems, such as model Hamiltonians (Hubbard rings) and ab initio molecular systems (hydrogen rings).

Analytical Nonadiabatic Couplings and Gradients within the State-Averaged Orbital-Optimized Variational Quantum Eigensolver.

We introduce several technical and analytical extensions to our recent state-averaged orbital-optimized variational quantum eigensolver (SA-OO-VQE) algorithm (see Yalouz et al. Quantum Sci. Technol. 2021, 6, 024004). Motivated by the limitations of current quantum computers, the first extension consists of an efficient state-resolution procedure to find the SA-OO-VQE eigenstates, and not just the subspace spanned by them, while remaining in the equi-ensemble framework. This approach avoids expensive intermediate resolutions of the eigenstates by postponing this problem to the very end of the full algorithm. The second extension allows for the estimation of analytical gradients and nonadiabatic couplings, which are crucial in many practical situations ranging from the search of conical intersections to the simulation of quantum dynamics, in, for example, photoisomerization reactions. The accuracy of our new implementations is demonstrated on the formaldimine molecule CH2NH (a minimal Schiff base model relevant for the study of photoisomerization in larger biomolecules), for which we also perform a geometry optimization to locate a conical intersection between the ground and first-excited electronic states of the molecule.

Extended star graph as a light-harvesting-complex prototype: Excitonic absorption speedup by peripheral energy defect tuning.

We study the quantum dynamics of a photoexcitation uniformly distributed at the periphery of an extended star network (with N_{B} branches of length L_{B}). More specifically, we address here the question of the energy absorption at the core of the network and how this process can be improved (or not) by the inclusion of peripheral defects with a tunable energy amplitude Δ. Our numerical simulations reveal the existence of optimal value of energy defect Δ^{*} which depends on the network architecture. Around this value, the absorption process presents a strong speedup (i.e., reduction of the absorption time) provided that L_{B}≤L_{B}^{*} with L_{B}^{*}≈12.5/ln(N_{B}). Analytical and numerical developments are then conducted to interpret this feature. We show that the origin of this speedup takes place in the hybridization of two upper-band excitonic eigenstates. This hybridization is important when L_{B}≤L_{B}^{*} and vanishes almost totally when L_{B}>L_{B}^{*}. These structural rules we draw here could represent a potential guide for the practical design of molecular nanonetwork dedicated to the realization of efficient photoexcitation absorption.

Continuous-time quantum walk on an extended star graph: Disorder-enhanced trapping process.

Using a tight binding model, we investigate the dynamics of an exciton on a disordered extended star graph whose central site acts as an energy trap. When compared with what happens in an ordered network, our results reveal that the disorder drastically improves the excitonic absorption that becomes complete. Moreover, we show the occurrence of an optimal disorder for which the absorption time is strongly minimized, a surprising effect that originates in a disorder-induced restructuring process of the exciton eigenstates. Finally, we also show the existence of an optimal value of the absorption rate that reduces even more the absorption time. The resulting superoptimized trapping process is interpreted as a positive interplay between both the disorder and the so-called superradiance transition.

Continuous-time quantum walk on an extended star graph: Trapping and superradiance transition.

A tight-binding model is introduced for describing the dynamics of an exciton on an extended star graph whose central node is occupied by a trap. On this graph, the exciton dynamics is governed by two kinds of eigenstates: many eigenstates are associated with degenerate real eigenvalues insensitive to the trap, whereas three decaying eigenstates characterized by complex energies contribute to the trapping process. It is shown that the excitonic population absorbed by the trap depends on the size of the graph, only. By contrast, both the size parameters and the absorption rate control the dynamics of the trapping. When these parameters are judiciously chosen, the efficiency of the transfer is optimized resulting in the minimization of the absorption time. Analysis of the eigenstates reveals that such a feature arises around the superradiance transition. Moreover, depending on the size of the network, two situations are highlighted where the transport efficiency is either superoptimized or suboptimized.

Exciton-phonon dynamics on complex networks: Comparison between a perturbative approach and exact calculations.

A method combining perturbation theory with a simplifying ansatz is used to describe the exciton-phonon dynamics in complex networks. This method, called PT^{*}, is compared to exact calculations based on the numerical diagonalization of the exciton-phonon Hamiltonian for eight small-sized networks. It is shown that the accuracy of PT^{*} depends on the nature of the network, and three different situations were identified. For most graphs, PT^{*} yields a very accurate description of the dynamics. By contrast, for the Wheel graph and the Apollonian network, PT^{*} reproduces the dynamics only when the exciton occupies a specific initial state. Finally, for the complete graph, PT^{*} breaks down. These different behaviors originate in the interplay between the degenerate nature of the excitonic energy spectrum and the strength of the exciton-phonon interaction so that a criterion is established to determine whether or not PT^{*} is relevant. When it succeeds, our study shows the undeniable advantage of PT^{*} in that it allows us to perform very fast simulations when compared to exact calculations that are restricted to small-sized networks.

Exciton-phonon system on a star graph: A perturbative approach.

Based on the operatorial formulation of the perturbation theory, the properties of an exciton coupled with optical phonons on a star graph are investigated. Within this method, the dynamics is governed by an effective Hamiltonian, which accounts for exciton-phonon entanglement. The exciton is dressed by a virtual phonon cloud whereas the phonons are clothed by virtual excitonic transitions. In spite of the coupling with the phonons, it is shown that the energy spectrum of the dressed exciton resembles that of a bare exciton. The only differences originate in a polaronic mechanism that favors an energy shift and a decay of the exciton hopping constant. By contrast, the motion of the exciton allows the phonons to propagate over the graph so that the dressed normal modes drastically differ from the localized modes associated to bare phonons. They define extended vibrations whose properties depend on the state occupied by the exciton that accompanies the phonons. It is shown that the phonon frequencies, either red shifted or blue shifted, are very sensitive to the model parameter in general, and to the size of the graph in particular.