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1. The valence and Rydberg states of dienes

   https://doi.org/10.1039/c9cp06952f  

   Ning, Jiaxin ; Truhlar, Donald G. ( March 2020 , Physical Chemistry Chemical Physics)

   The molecules 1,4-cyclohexadiene (unconjugated 1,4-CHD) and 1,3-cyclohexadiene (conjugated 1,3-CHD) both have two double bonds, but these bonds interact in different ways. These molecules have long served as examples of through-bond and through-space interactions, respectively, and their electronic structures have been studied in detail both experimentally and theoretically, with the experimental assignments being especially complete. The existence of Rydberg states interspersed with the valence states makes the quantum mechanical calculation of their spectra a challenging task. In this work, we explore the electronic excitation energies of 1,4-CHD and 1,3-CHD for both valence and Rydberg states by means of complete active space second-order perturbation theory (CASPT2), extended multi-state CASPT2 (XMS-CASPT2), and multiconfiguration pair-density functional theory (MC-PDFT); it is shown by comparison to experiment that MC-PDFT yields the most accurate results. We found that the inclusion of Rydberg orbitals in the active space not only enables the calculation of Rydberg excitation energies but also improves the accuracy of the valence ones. A special characteristic of the present analysis is the calculation of the second moments of the excited-state orbitals. Because we find that the CASPT2 densities agree well with the CASSCF ones and since the MC-PDFT methods gets accurate excitation energies based onmore »the CASSCF densities, we believe that we can trust these moments as far as giving a more accurate picture of the diffuseness of the excited-state orbitals in these prototype molecules than has previously been available.« less
2. Electronic structure of strongly correlated systems: recent developments in multiconfiguration pair-density functional theory and multiconfiguration nonclassical-energy functional theory

   https://doi.org/10.1039/d2sc01022d  

   Zhou, Chen ; Hermes, Matthew R. ; Wu, Dihua ; Bao, Jie J. ; Pandharkar, Riddhish ; King, Daniel S. ; Zhang, Dayou ; Scott, Thais R. ; Lykhin, Aleksandr O. ; Gagliardi, Laura ; et al ( July 2022 , Chemical Science)

   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 themore »nonclassical-energy functional. We discuss two new kinds of MC-NEFT methods, namely multiconfiguration density coherence functional theory and machine-learned functionals.« less
3. Global perspectives of the bulk electronic structure of URu ₂ Si ₂ from angle-resolved photoemission

   https://doi.org/10.1088/2516-1075/ac4315  

   Denlinger, J. D. ; Kang, J-S ; Dudy, L. ; Allen, J. W. ; Kim, Kyoo ; Shim, J-H ; Haule, K. ; Sarrao, J. L. ; Butch, N. P. ; Maple, M. B. ( January 2022 , Electronic Structure)

   Previous high-resolution angle-resolved photoemission (ARPES) studies of URu₂Si₂have characterized the temperature-dependent behavior of narrow-band states close to the Fermi level (E_F) at low photon energies near the zone center, with an emphasis on electronic reconstruction due to Brillouin zone folding. A substantial challenge to a proper description is that these states interact with other hole-band states that are generally absent from bulk-sensitive soft x-ray ARPES measurements. Here we provide a more globalk-space context for the presence of such states and their relation to the bulk Fermi surface (FS) topology using synchrotron-based wide-angle and photon energy-dependent ARPES mapping of the electronic structure using photon energies intermediate between the low-energy regime and the high-energy soft x-ray regime. Small-spot spatial dependence,f-resonant photoemission, Si 2pcore-levels, x-ray polarization, surface-dosing modification, and theoretical surface slab calculations are employed to assist identification of bulk versus surface state character of theE_F-crossing bands and their relation to specific U- or Si-terminations of the cleaved surface. The bulk FS topology is critically compared to density functional theory (DFT) and to dynamical mean field theory calculations. In addition to clarifying some aspects of the previously measured high symmetry Γ,ZandXpoints, incommensurate 0.6a* nested Fermi-edge states located alongZ–N–Zare found to be distinctlymore »different from the DFT FS prediction. The temperature evolution of these states aboveT_HO, combined with a more detailed theoretical investigation of this region, suggests a key role of theN-point in the hidden order transition.

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4. Evaluation of molecular photophysical and photochemical properties using linear response time-dependent density functional theory with classical embedding: Successes and challenges

   https://doi.org/10.1063/5.0088271  

   Liang, WanZhen ; Pei, Zheng ; Mao, Yuezhi ; Shao, Yihan ( June 2022 , The Journal of Chemical Physics)

   Time-dependent density functional theory (TDDFT) based approaches have been developed in recent years to model the excited-state properties and transition processes of the molecules in the gas-phase and in a condensed medium, such as in a solution and protein microenvironment or near semiconductor and metal surfaces. In the latter case, usually, classical embedding models have been adopted to account for the molecular environmental effects, leading to the multi-scale approaches of TDDFT/polarizable continuum model (PCM) and TDDFT/molecular mechanics (MM), where a molecular system of interest is designated as the quantum mechanical region and treated with TDDFT, while the environment is usually described using either a PCM or (non-polarizable or polarizable) MM force fields. In this Perspective, we briefly review these TDDFT-related multi-scale models with a specific emphasis on the implementation of analytical energy derivatives, such as the energy gradient and Hessian, the nonadiabatic coupling, the spin–orbit coupling, and the transition dipole moment as well as their nuclear derivatives for various radiative and radiativeless transition processes among electronic states. Three variations of the TDDFT method, the Tamm–Dancoff approximation to TDDFT, spin–flip DFT, and spin-adiabatic TDDFT, are discussed. Moreover, using a model system (pyridine–Ag 20 complex), we emphasize that caution is needed tomore »properly account for system–environment interactions within the TDDFT/MM models. Specifically, one should appropriately damp the electrostatic embedding potential from MM atoms and carefully tune the van der Waals interaction potential between the system and the environment. We also highlight the lack of proper treatment of charge transfer between the quantum mechanics and MM regions as well as the need for accelerated TDDFT modelings and interpretability, which calls for new method developments.« less
5. Analytical gradients for nuclear–electronic orbital multistate density functional theory: Geometry optimizations and reaction paths

   https://doi.org/10.1063/5.0085344  

   Yu, Qi ; Schneider, Patrick E. ; Hammes-Schiffer, Sharon ( March 2022 , The Journal of Chemical Physics)

   Hydrogen tunneling plays a critical role in many biologically and chemically important processes. The nuclear–electronic orbital multistate density functional theory (NEO-MSDFT) method was developed to describe hydrogen transfer systems. In this approach, the transferring proton is treated quantum mechanically on the same level as the electrons within multicomponent DFT, and a nonorthogonal configuration interaction scheme is used to produce delocalized vibronic states from localized vibronic states. The NEO-MSDFT method has been shown to provide accurate hydrogen tunneling splittings for fixed molecular systems. Herein, the NEO-MSDFT analytical gradients for both ground and excited vibronic states are derived and implemented. The analytical gradients and semi-numerical Hessians are used to optimize and characterize equilibrium and transition state geometries and to generate minimum energy paths (MEPs), for proton transfer in the deprotonated acetylene dimer and malonaldehyde. The barriers along the resulting MEPs are lower when the transferring proton is quantized because the NEO-MSDFT method inherently includes the zero-point energy of the transferring proton. Analysis of the proton densities along the MEPs illustrates that the proton density can exhibit symmetric or asymmetric bilobal character associated with symmetric or slightly asymmetric double-well potential energy surfaces and hydrogen tunneling. Analysis of the contributions to the intrinsic reactionmore »coordinate reveals that changes in the C–O bond lengths drive proton transfer in malonaldehyde. This work provides the foundation for future reaction path studies and direct nonadiabatic dynamics simulations of a wide range of hydrogen transfer reactions.

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