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Role of Spin Polarization and Dynamic Correlation in Singlet–Triplet Gap Inversion of Heptazine Derivatives
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Correlated atomic dynamics in liquid seen in real space and time
In liquids, the timescales for structure, diffusion, and phonon are all similar, of the order of a pico-second. This not only makes characterization of liquid dynamics difficult but also renders it highly questionable to describe liquids in these terms. In particular, the current definition of the structure of liquids by the instantaneous structure may need to be expanded because the liquid structure is inherently dynamic. Here, we advocate describing the liquid structure through the distinct-part of the Van Hove function, which can be determined by inelastic neutron and x-ray scattering measurements as well as by simulation. It depicts the dynamic correlation between atoms in space and time, starting with the instantaneous correlation function at t = 0. The observed Van Hove functions show that the atomic dynamics is strongly correlated in some liquids, such as water. The effect of atomic correlation on various transport properties of fluid, including viscosity and diffusivity, is discussed.
Data for "Observation of Real-Space Dynamic Electron Correlation in Beryllium"
We studied the electron dynamic correlation using inelastic X-ray scattering measurements. The data files contain a 2D array of numeric data that is used to produce the figures in the paper, "Observation of Real-space Dynamic Electron Correlation in Beryllium."
237 Np Mössbauer Isomer Shifts: A Lesson About the Balance of Static and Dynamic Electron Correlation in Heavy Element Complexes
A large set of neptunium compounds with different oxidation states (III to VII) was assembled to study the Mössbauer isomer shift by wave function calculations and better understand covalency in f-elements complexes. The contact density approach was used to calculate the isomer shift using complete active space self-consistent field (CASSCF) multiconfiguration wave functions, as well as matrix product states [from Density Matrix Renormalization Group (DMRG) algorithms] for large active spaces. Dynamic correlation effects for the isomer shifts were treated via CASPT2 energy derivatives with respect to the nuclear radius. The CASSCF calculations appear to produce different orbital overlocalization errors for low and high Np oxidation states. For compounds with low Np oxidation numbers, the errors can be attributed to the overlocalization of the 5f orbitals. For the compounds with high Np oxidation numbers, the main errors arise from an overlocalization of ligand orbitals and concomitant to weak donation bonding. Attempts to mitigate the overlocalization errors with large active spaces using DMRG were only partially successful, showing that explicit treatment of dynamic correlation is necessary for accurate predictions of Mössbauer isomer shifts. The CASPT2 calculations perform very satisfactorily. For a subset of Np compounds, both static and dynamic correlation effects were substantial. Furthermore, a rational active space selection based on orbital entanglement diagrams proved beneficial for determining the optimal reference wave function.
Dynamical electron correlation and the chemical bond. I. Covalent bonds in AH and AF (A = B–F)
Dynamical electron correlation has a major impact on the computed values of molecular properties and the energetics of molecular processes. This study focused on the effect of dynamical electron correlation on the spectroscopic constants ($R$ e , $ω$ e , $D$ e ), and potential energy curves, Δ$E$($R$), of the covalently bound AH and AF molecules, A = B–F. The changes in the spectroscopic constants (Δ$R$ e , Δ$ω$ e , Δ$D$ e ) caused by dynamical correlation are erratic and, at times, even surprising. These changes can be understood based on the dependence of the dynamical electron correlation energies of the AH and AF molecules as a function of the bond distance, i.e., Δ$E$ DEC ($R$). At large $R$, the magnitude of Δ$E$ DEC ($R$) increases nearly exponentially with decreasing $R$, but this increase slows as $R$ continues to decrease and, in many cases, even reverses at very short $R$. The changes in Δ$E$ DEC ($R$) in the region around $R$ e were as unexpected as they were surprising, e.g., distinct minima and maxima were found in the curves of Δ$E$ DEC ($R$) for the most polar molecules. The variations in Δ$E$ DEC ($R$) for $R$ ≲ $R$ e are directly correlated with major changes in the electronic structure of the molecules as revealed by a detailed analysis of the spin-coupled generalized valence bond wave function. In conclusion, the results reported here indicate that we have much to learn about the nature of dynamical electron correlation and its effect on chemical bonds and molecular properties and processes.
Dynamical electron correlation and the chemical bond. II. Recoupled pair bonds in the $a$ 4 Σ - states of CH and CF
We extended our studies of the effect of dynamical electron correlation on the covalent bonds in the AH and AF series (A = B–F) to the recoupled pair bonds in the excited $a$ 4 Σ - states of the CH and CF molecules. Dynamical correlation is energetically less important in the $a$ 4 Σ - states than in the corresponding X 2 Π states for both molecules, which is reflected in smaller changes in bond energies ($D$ e ). Changes in the equilibrium bond distance ($R$ e ) and vibrational frequency ($ω$ e ), on the other hand, are influenced by the changes in the slope and curvature of the dynamical electron correlation energy as a function of the internuclear distance $R$, $E$ DEC ($R$). In the CH($a$ 4 Σ - ) state, these changes are much smaller than in the CH(X 2 Π) state, but in the CF($a$ 4 Σ - ) state, they are larger, reflecting a significant difference in the shapes of $E$ DEC ($R$) curves. At large $R$, the shape of $E$ DEC ($R$) curves for covalent and recoupled pair bonds is similar although different in magnitude. For the CH($a$ 4 Σ - ) state, $E$ DEC ($R$) has a minimum at $R$ = $R$ e + 0.72 Å as the orbitals associated with the formation of the recoupled pair bond switch places. $E$ DEC (R) for the CF($a$ 4 Σ - ) state decreases continuously throughout the bound region of the potential energy curve because the dynamical correlation energy associated with the electrons in the lone pair orbitals is increasing. In conclusion, these results support our earlier conclusion that we still have much to learn about the nature of dynamical electron correlation in molecules.
On the role of dynamic electron correlation in non-orthogonal configuration interaction with fragments
Two different approaches have been implemented to include the effect of dynamic electron correlation in the Non-Orthogonal Configuration Interaction for Fragments (NOCI-F) method. The first is based on shifting the diagonal matrix elements of the NOCI matrix, while the second incorporates the dynamic correlation explicitly in the fragment wave functions used to construct the many-electron basis functions of the NOCI. The two approaches are illustrated for the calculation of the electronic coupling relevant in singlet fission and the coupling of spin moments in organic radicals. Comparison of the calculated diabatic couplings, the NOCI energies and wave functions shows that dynamic electron correlation is not only efficiently but also effectively incorporated by the shifting approach and can largely affect the coupling between electronic states. Additionally, it brings the NOCI coupling of the spin moments in close agreement with benchmark calculations.
Electronic structure of strongly correlated systems: recent developments in multiconfiguration pair-density functional theory and multiconfiguration nonclassical-energy functional theory
Strong electron correlation plays an important role in transition-metal and heavy-metal chemistry, magnetic molecules, bond breaking, biradicals, excited states, and many functional materials, but it provides a significant challenge for modern electronic structure theory. The treatment of strongly correlated systems usually requires a multireference method to adequately describe spin densities and near-degeneracy correlation. However, quantitative computation of dynamic correlation with multireference wave functions is often difficult or impractical. Multiconfiguration pair-density functional theory (MC-PDFT) provides a way to blend multiconfiguration wave function theory and density functional theory to quantitatively treat both near-degeneracy correlation and dynamic correlation in strongly correlated systems; it is more affordable than multireference perturbation theory, multireference configuration interaction, or multireference coupled cluster theory and more accurate for many properties than Kohn–Sham density functional theory. This perspective article provides a brief introduction to strongly correlated systems and previously reviewed progress on MC-PDFT followed by a discussion of several recent developments and applications of MC-PDFT and related methods, including localized-active-space MC-PDFT, generalized active-space MC-PDFT, density-matrix-renormalization-group MC-PDFT, hybrid MC-PDFT, multistate MC-PDFT, spin–orbit coupling, analytic gradients, and dipole moments. We also review the more recently introduced multiconfiguration nonclassical-energy functional theory (MC-NEFT), which is like MC-PDFT but allows for other ingredients in the nonclassical-energy functional. We discuss two new kinds of MC-NEFT methods, namely multiconfiguration density coherence functional theory and machine-learned functionals.
Dynamical electron correlation and the chemical bond. III. Covalent bonds in the A 2 molecules (A = C–F)
The behavior of the dynamical electron correlation energy is remarkably complex at short internuclear distances: Δ E DEC (Δ R ) = E DEC (Δ R ) − E DEC ( R = ∞) with Δ R = R − R e .
Benchmarking an Embedded Adaptive Sampling Configuration Interaction Method for Surface Reactions: H 2 Desorption from and CH 4 Dissociation on Cu(111)
Embedded (emb-) correlated wavefunction (CW) theory enables accurate assessments of both ground- and excited-state reaction mechanisms involved in heterogeneous catalysis. Embedded multireference second-order perturbation theory (emb-MRPT2) based on reference wavefunctions generated via embedded complete active space self-consistent field (emb-CASSCF) theory is currently state-of-the-art. However, the factorial scaling of CASSCF limits the size of active space and the complexity of systems that can be studied. In this work, we assess the efficacy of an alternative CW method, adaptive sampling configuration interaction (ASCI)–which enables large active spaces to be used–for studying surface reactions. We couple ASCI with density functional embedding theory (DFET) and benchmark its performance for two reactions: H 2 desorption from and CH 4 dissociation on the Cu(111) surface. Unlike embedded complete active space second-order perturbation theory (emb-CASPT2) that accurately reproduces a measured H 2 desorption barrier, embedded ASCI, using a very large active space (though one that still comprises a small portion of the full set of orbitals) fails to do so. Adding an extra correlation term from embedded Møller–Plesset second-order perturbation theory (emb-MP2) improves the desorption barrier and endothermicity predictions. Thus, the inaccuracy of embedded ASCI comes from the missing dynamic correlation from the many other electrons and orbitals not included in the active space. For CH 4 dissociation, again embedded ASCI overestimates the dissociation barrier compared to emb-CASPT2 predictions. Adding dynamic correlation from emb-MP2 helps correct the barrier. However, this composite approach suffers from double counting of correlation within embedded ASCI followed by emb-MP2 calculations. We therefore conclude that the state-of-the-art emb-MRPT2 based on reference wavefunctions generated via emb-CASSCF remains the method of choice for studying surface reactions. emb-ASCI is useful when large active spaces beyond the limit of emb-CASSCF are essential, such as to study complex surface reactions with significant multiconfigurational character (static correlation) but weak dynamic correlation.
Dynamical Ion Correlations in Polymer and Membrane Electrolytes: Recent Advances and Open Questions
Ion transport in polymer and membrane electrolytes is often described using uncorrelated models like the Nernst–Einstein (NE) approximation, which link conductivity, transference number, and salt diffusivity to individual ion mobilities. However, growing evidence shows that dynamical ion correlations─arising from ion pairing, polymer-mediated coupling, confinement, and electrostatic interactions─can substantially alter macroscopic transport properties. The Onsager transport formalism offers a rigorous framework to quantify these effects via cross-correlated ionic displacements. This Perspective highlights how such correlations manifest across dry and hydrated systems, including salt-doped polymers, block copolymers, hydrogels, and ion-exchange membranes. Here, we examine key physical origins, the influence of salt chemistry and polymer structure, and open questions in measuring and controlling correlated motion. Embracing correlation-aware design enables new pathways to optimize conductivity, transference number, and selectivity─shifting the focus from individual ion mobility to engineered collective dynamics for next-generation electrolytes in energy storage and separations.
Correlated conformational dynamics of the human GluN1-GluN2A type N-methyl-D-aspartate (NMDA) receptor
N-Methyl-D-aspartate receptors (NMDARs) are glutamate-gated ion channels found in the nerve cell membranes. As a result of overexcitation of NMDARs, neuronal death occurs and may lead to diseases such as epilepsy, stroke, Alzheimer’s disease, and Parkinson’s disease. In this study, human GluN1- GluN2A type NMDAR structure is modeled based on the X-ray structure of the Xenopus laevis template and missing loops are added by ab-initio loop modeling. The final structure is chosen according to two different model assessment scores. To be able to observe the structural changes upon ligand binding, glycine and glutamate molecules are docked into the corresponding binding sites of the receptor. Subsequently, molecular dynamics simulations of 1.3 μs are performed for both apo and ligand-bound structures. Structural parameters, which have been considered to show functionally important changes in previous NMDAR studies, are monitored as conformational rulers to understand the dynamics of the conformational changes. Moreover, principal component analysis (PCA) is performed for the equilibrated part of the simulations. Additionally, from these analyses, the differences in between apo and ligand-bound simulations can be summarized as the following: The girdle right at the beginning of the pore loop, which connects M2 and M3 helices of the ion channel, partially opens. Ligands act like an adhesive for the ligand-binding domain (LBD) by keeping the bi-lobed structure together and consequently this is reflected to the overall dynamics of the protein as an increased correlation of the LBD with especially the amino-terminal domain (ATD) of the protein.
Strongly Correlated Ion Dynamics in Plastic Ionic Crystals and Polymerized Ionic Liquids
Understanding the mechanisms controlling ionic conductivity is critical for the development of the next generation of batteries and supercapacitors. This paper discusses the significant role played by ionic correlations in conductivity of concentrated ionic systems. Our studies of an organic ionic plastic crystal reveal that correlations in ions dynamics suppress conductivity by 25–100 times in comparison to the expected uncorrelated ionic conductivity estimated from the Nernst–Einstein relationship. Furthermore, additional analysis also demonstrates that ionic correlations suppress conductivity in polymerized ionic liquids and gel by ~10 times. Thus, ionic correlations, usually neglected in many studies, play a very important role in conductivity of concentrated ionic systems. These results cannot be explained by a diffusion of ion pairs because all these systems are essentially single ion conductors. In contrast, strongly correlated motions of mobile ions with the same charge (cation–cation or anion–anion correlations) are the major mechanism suppressing the ionic conductivity in these systems. Finally, on the basis of these results, we emphasize that charge transport rather than ion diffusion is critical for electrolyte performance and suggest the potential design of plastic crystals and polymer electrolytes with enhanced ionic conductivity.
Dynamic electron correlations with charge order wavelength along all directions in the copper oxide plane
In strongly correlated systems the strength of Coulomb interactions between electrons, relative to their kinetic energy, plays a central role in determining their emergent quantum mechanical phases. We perform resonant x-ray scattering on Bi 2 Sr 2 CaCu 2 O 8+δ , a prototypical cuprate superconductor, to probe electronic correlations within the CuO 2 plane. We discover a dynamic quasi-circular pattern in the x-y scattering plane with a radius that matches the wave vector magnitude of the well-known static charge order. Along with doping- and temperature-dependent measurements, our experiments reveal a picture of charge order competing with superconductivity where short-range domains along x and y can dynamically rotate into any other in-plane direction. This quasi-circular spectrum, a hallmark of Brazovskii-type fluctuations, has immediate consequences to our understanding of rotational and translational symmetry breaking in the cuprates. We discuss how the combination of short- and long-range Coulomb interactions results in an effective non-monotonic potential that may determine the quasi-circular pattern.
Role of effective mass and long-range interactions in the band-gap renormalization of photoexcited semiconductors
Understanding how to control changes in the electronic structure and related dynamical renormalizations by external driving fields is the key for understanding ultrafast spectroscopy and applications in electronics. Here, we focus on the band gap's modulation by external electric fields and uncover the effect of band dispersion on the gap renormalization. We employ the Green's function formalism using the real-time Dyson expansion to account for dynamical correlations induced by photodoping. The many-body formalism captures the dynamics of systems with long-range interactions, carrier mobility, and variable electron and hole effective mass. We also demonstrate that mean-field simulations based on the Hartree-Fock Hamiltonian, which lacks dynamical correlations, yields a qualitatively incorrect picture of band-gap renormalization. We find the trend that increasing effective mass, thus decreasing mobility, leads to as much as a 6% enhancement in band-gap renormalization. Further, the renormalization is strongly dependent on the degree of photodoping. As the screening induced by free electrons and holes effectively reduces any long-range and interband interactions for highly excited systems, we show that there is a specific turnover point with a minimal band gap. Here, we further demonstrate that the optical gap renormalization follows the same trend though its magnitude is altered by the Moss-Burstein effect.