Electronic Structures of Anti-Ferromagnetic Tetraradicals: <i>Ab Initio</i> and Semi-Empirical Studies

The energy relationships and electronic structures of the lowest-lying spin states in several anti-ferromagnetic tetraradical model systems are studied with high-level <i>ab initio</i> and semi-empirical methods. The Full-CI method (FCI), the complete active space second-order perturbation theory (CASPT2), and the <i>n</i>-electron valence state perturbation theory (NEVPT2) are employed to obtain reference results. By comparing the energy relationships predicted from the Heisenberg and Hubbard models with <i>ab initio</i> benchmarks, the accuracy of the widely used Heisenberg model for anti-ferromagnetic spin-coupling in low-spin polyradicals is cautiously tested in this work. It is found that the strength of electron correlation (|<i>U</i>/<i>t</i>|) concerning anti-ferromagnetically coupled radical centers could range widely from strong to moderate correlation regimes and could become another degree of freedom besides the spin multiplicity. Accordingly, the Heisenberg-type model works well in the regime of strong correlation, which reproduces well the energy relationships along with the wave functions of all the spin states. In moderately spin-correlated tetraradicals, the results of the prototype Heisenberg model deviate severely from those of multi-reference electron correlation <i>ab initio</i> methods, while the extended Heisenberg model, containing four-body terms, can introduce reasonable corrections and maintains its accuracy in this condition. In the weak correlation regime, both the prototype Heisenberg model and its extended forms containing higher-order correction terms will encounter difficulties. Meanwhile, the Hubbard model shows balanced accuracy from strong to weak correlation cases and can reproduce qualitatively correct electronic structures, which makes it more suitable for the study of anti-ferromagnetic coupling in polyradical systems

Hierarchical Mapping for Efficient Simulation of Strong System-Environment Interactions

Quantum dynamics (QD) simulation is a powerful tool for interpreting ultrafast spectroscopy experiments and unraveling their microscopic mechanism in out-of-equilibrium excited state behaviors in various chemical, biological, and material systems. Although state-of-the-art numerical QD approaches such as the time-dependent density matrix renormalization group (TD-DMRG) already greatly extended the solvable system size of general linearly coupled exciton–phonon models with up to a few hundred phonon modes, the accurate simulation of larger system sizes or strong system-environment interactions is still computationally highly challenging. Based on quantum information theory (QIT), in this work, we realize that only a small number of effective phonon modes couple to the excitonic system directly regardless of a large or even infinite number of modes in the condensed phase environment. On top of the identified small number of direct effective modes, we propose a hierarchical mapping (HM) approach through performing block Lanczos transformations on the remaining indirect modes, which transforms the Hamiltonian matrix to a nearly block-tridiagonal form and eliminates the long-range interactions. Numerical tests on model spin-boson systems and realistic singlet fission models in a rubrene crystal environment with up to 7000 modes and strong system-environment interactions indicate HM can reduce the system size by 1–2 orders of magnitude and accelerate the calculation by ∼80% without losing accuracy

Photoisomerization of Silyl-Substituted Cyclobutadiene Induced by σ → π* Excitation: A Computational Study

Photoinduced chemical processes upon Franck–Condon (FC) excitation in tetrakis­(trimethylsilyl)-cyclobutadiene (TMS-CBD) have been investigated through the exploration of potential energy surface crossings among several low-lying excited states using the complete active space self-consistent field (CASSCF) method. Vertical excitation energies are also computed with the equation-of-motion coupled-cluster model with single and double excitations (EOM-CCSD) as well as the multireference Møller–Plesset (MRMP) methods. Upon finding an excellent coincidence between the computational results and experimental observations, it is suggested that the Franck–Condon excited state does not correspond to the first π–π* single excitation state (<i>S</i>₁, 1¹<i>B</i>₁ state in terms of <i>D</i>₂ symmetry), but to the second ¹<i>B</i>₁ state (<i>S</i>₃), which is characterized as a σ–π* single excitation state. Starting from the Franck–Condon region, a series of conical intersections (CIs) are located along one isomerization channel and one dissociation channel. Through the isomerization channel, TMS-CBD is transformed to tetrakis­(trimethylsilyl)-tetrahedrane (TMS-THD), and this isomerization process could take place by passing through a “tetra form” conical intersection. On the other hand, the dissociation channel yielding two bis­(trimethylsilyl)-acetylene (TMS-Ac) molecules through further stretching of the longer C–C bonds might be more competitive than the isomerization channel after excitation into <i>S</i>₃ state. This mechanistic picture is in good agreement with recently reported experimental observations

Open-Shell Ground State of Polyacenes: A Valence Bond Study

Applying the density matrix renormalization group (DRMG) method to a nonempirical valence bond (VB) model Hamiltonian, we studied polyacene oligomers of different lengths in the strong electron correlation limit. Geometrical optimizations were performed for the lowest singlet and triplet states of oligomers up to [40]-acene, and a convergence of the bond lengths toward the polymer limit is observed in the interior of the oligomer. For large oligomers, as well as for the polymer, the ground state can be reasonably determined to be a singlet. Furthermore, a high similarity between the singlet geometries and triplet geometries suggests an open-shell character for the singlet ground state. A reasonable speculation of the soliton−antisoliton pair character of the singlet ground state was supported by a spin distribution analysis of the triplet state wave function of large oligomers, with each of the two solitons being broadly delocalized over the upper or bottom edge of the oligomers, respectively

Predicting the Stability and Loading for Electrochemical Preparation of Single-Atom Catalysts

Underpotential electrochemical deposition is a convenient approach for precisely controlling the fabrication process of single-atom catalysts (SACs). In achieving a balance between raising the loading of SACs and suppressing the aggregation of the adsorbates, the working electrode potential should be deliberately optimized, for which the adsorption isotherm of the loading of atomically dispersed adsorbates versus electric potential is of crucial importance in performance tuning. We report an integrated theoretical scheme for simulating the adsorption isotherm, which can enormously accelerate the evaluation of the adsorption energy for large model systems by combining our recently proposed constant-potential calculation scheme with the cluster expansion (CE) model, as well as accurately estimate the configurational effect through a thermodynamic integration (TI) computation based on Monte Carlo (MC) simulations. With the established simulation scheme, the surface map of the adsorption free energy as a function of deposition coverage and electric potential is computed for atomically dispersed copper on 1T′-MoS2, which is further employed to reasonably estimate the equilibrium coverage of the deposit at varying electric potentials and predict the feature of the adsorbate distribution pattern, as well as simulate the cyclic voltammogram (CV). Besides, based on the study of nine metal/transition-metal dichalcogenide (TMD) systems, we demonstrate that the well-characterized potential-related metal–substrate and metal–metal interactions provide rational criteria for evaluating the stability of SACs against aggregation under electrochemical conditions

Spin-Adapted Externally Contracted Multireference Configuration Interaction Method Based on Selected Reference Configurations

As one kind of approximation of the full configuration interaction solution, the selected configuration interaction (sCI) methods have been shown to be valuable for large active spaces. However, the inclusion of dynamic correlation beyond large active spaces is necessary for more quantitative results. Since the sCI wave function can provide a compact reference for multireference methods, previously, we proposed an externally contracted multireference configuration interaction method using the sCI reference reconstructed from the density matrix renormalization group wave function [J. Chem. Theory Comput. 2018, 14, 4747–4755]. The DMRG2sCI-EC-MRCI method is promising for dealing with more than 30 active orbitals and large basis sets. However, it suffers from two drawbacks: spin contamination and low efficiency when using Slater determinant bases. To solve these problems, in this work, we adopt configuration state function bases and introduce a new algorithm based on the hybrid of tree structure for convenient configuration space management and the graphical unitary group approach for efficient matrix element calculation. The test calculation of naphthalene shows that the spin-adapted version could achieve a speed-up of 6.0 compared with the previous version based on the Slater determinant. Examples of dinuclear copper­(II) compound as well as Ln­(III) and An­(III) complexes show that the sCI-EC-MRCI can give quantitatively accurate results by including dynamic correlation over sCI for systems with large active spaces and basis sets

Benzo[<i>g</i>]quinoxaline-Based Complexes [Ir(pbt)₂(dppn)]Cl and [Ir(pt)₂(dppn)]Cl: Modulation of Photo-Oxidation Activity and Light-Controlled Luminescence

Based on benzo­[i]­dipyrido­[3,2-a:2′,3′-c]­phenazine (dppn) with photo-oxidation activity, complexes [Ir­(pbt)2(dppn)]Cl (1) and [Ir­(pt)2(dppn)]Cl (2) have been synthesized (pbtH = 2-phenylbenzothiazole, and ptH = 2-phenylthiazole), with two aims, including studying the influence of the cyclometalating ligands (pbt– in 1, pt– in 2) on the photo-oxidation activity of these complexes and exploring their photo-oxidation-induced luminescence. Both 1H nuclear magnetic resonance (NMR) and electrospray (ES) mass spectrometry indicate that the benzo­[g]­quinoxaline moiety in complex 1 can be oxidized at room temperature upon irradiation with 415 nm light. Thus, this complex in CH2Cl2 shows photo-oxidation-induced turn-on yellow luminescence. In contrast, complex 2 reveals significant structural decomposition during the process of photo-oxidation due to incorporating a cyclometalating ligand pt– instead of pbt– in complex 1. In this paper, we report the photo-oxidation behaviors and the related luminescence modulation in 1 and 2 and discuss the relationship between structure and photo-oxidation activity in these complexes

Visualization of electron density changes along chemical reaction pathways

We propose a simple procedure for visualising the electron density changes (EDC) during a chemical reaction, which is based on a mapping of rectangular grid points for a stationary structure into (distorted) positions around atoms of another stationary structure. Specifically, during a small step along the minimum energy pathway (MEP), the displacement of each grid point is obtained as a linear combination of the motion of all atoms, with the contribution from each atom scaled by the corresponding Hirshfeld weight. For several reactions (identity SN2, Claisen rearrangement, Diels-Alder reaction, [3+2] cycloaddition, and phenylethyl mercaptan attack on pericosine A), our EDC plots showed an expected reduction of electron densities around severed bonds (or those with the bond-order lowered), with the opposite observed for newly-formed or enhanced chemical bonds. The EDC plots were also shown for copper triflate catalyzed N2O fragmentation, where the N–O bond weakening initially occurred on a singlet surface, but continued on a triplet surface after reaching the minimum-energy crossing point (MECP) between the two potential energy surfaces.</p