Describing Chemical Reactivity with Frontier Molecular Orbitalets

Locality in physical space is critical in understanding chemical reactivity in the analysis of various phenomena and processes in chemistry, biology, and materials science, as exemplified in the concepts of reactive functional groups and active sites. Frontier molecular orbitals (FMOs) pinpoint the locality of chemical bonds that are chemically reactive because of the associated orbital energies and thus have achieved great success in describing chemical reactivity, mainly for small systems. For large systems, however, the delocalization nature of canonical molecular orbitals makes it difficult for FMOs to highlight the locality of the chemical reactivity. To obtain localized molecular orbitals that also reflect the frontier nature of the chemical processes, we develop the concept of frontier molecular orbitalets (FMOLs) for describing the reactivity of large systems. The concept of orbitalets was developed recently in the localized orbital scaling correction method, which aims for eliminating the delocalization error in common density functional approximations. Orbitalets are localized in both physical and energy spaces and thus contain both orbital locality and energy information. The FMOLs are thus the orbitalets with energies highest among occupied orbitalets and lowest among unoccupied ones. The applications of FMOLs to hexadeca-1,3,5,7,9,11,13,15-octaene in its equilibrium geometry, inter- and intra-molecular charge-transfer systems, and two transition states of a bifurcating reaction demonstrate that FMOLs can connect quantum mechanical treatments of chemical systems and chemical reactivities by locating the reactive region of large chemical systems. Therefore, FMOLs extend the role of FMOs for small systems and describe the chemical reactivity of large systems with energy and locality insight, with potentially broad applications

Cerasus humilis Cherry Polyphenol Reduces High-Fat Diet-Induced Obesity in C57BL/6 Mice by Mitigating Fat Deposition, Inflammation, and Oxidation

This study aimed to determine the anti-obesity effects and mechanisms of Cerasus humilis polyphenol (CHP) in C57BL/6 obese mice and 3T3-L1 cells. High-performance liquid chromatography–electrospray ionization-tandem mass spectrometry was used for the qualitative and quantitative identification of CHP components. The obese mice, induced by feeding high-fat diet (HFD), were treated with CHP (250 mg/kg/day) by gavage for 12 weeks. Orlistat was gavaged at 15.6 mg/kg bw/day, as a positive control group. The analysis revealed that the main components of CHP were procyanidin B2, cyanidin-3-glucoside, and pelargonidin-3-glucoside. CHP dietary supplementation significantly reduced body weight and improved blood lipid measurements in HFD-fed mice (p < 0.01). Moreover, it inhibited mRNA expression of miR-122, Srebp-1c, and Cpt1a (p < 0.01) and reduced hepatic lipid deposition, as seen by hematoxylin and eosin staining. CHP downregulated the protein expression of PPARγ and C/EBPα in HFD-induced obese mice and inhibited adipocyte differentiation (p < 0.01). Compared with the HFD group, CHP supplementation had an obvious anti-inflammatory effect (decreased protein expression, such as TNF-α, IL-6, and MCP1), reducing leptin levels and TNF-α secretion in serum and cells (p < 0.01). CHP significantly inhibited the expression of miR-27a/b (53.3 and 29.9%, p < 0.01) in mice retroperitoneal white adipocytes, enhancing the expression of the target gene Prdm16 and significantly upregulating Sirt1 (105.5%, p < 0.01) compared with the HFD group. Moreover, CHP supplementation effectively improved oxidative stress (ROS, T-AOC, SOD, CAT, and GSH-Px) induced by HFD in obese mice (p < 0.01). Thus, CHP mitigates adipocyte differentiation, browning of white adipocytes, and reduction of inflammation and antioxidant activity to reduce obesity. Consequently, these results provide novel insights into the anti-obesity roles of CHP in HFD-induced obesity

Accurate Excitation Energies of Point Defects from Fast Particle–Particle Random Phase Approximation Calculations

We present an efficient particle–particle random phase approximation (ppRPA) approach that predicts accurate excitation energies of point defects, including the nitrogen-vacancy (NV–) and silicon-vacancy (SiV0) centers in diamond and the divacancy center (VV0) in 4H silicon carbide, with errors of ±0.2 eV compared with experimental values. Starting from the (N + 2)-electron ground state calculated with density functional theory (DFT), the ppRPA excitation energies of the N-electron system are calculated as the differences between the two-electron removal energies of the (N + 2)-electron system. We demonstrate that the ppRPA excitation energies converge rapidly with a few hundred canonical active-space orbitals. We also show that active-space ppRPA has weak DFT starting-point dependence and is significantly cheaper than the corresponding ground-state DFT calculation. This work establishes ppRPA as an accurate and low-cost tool for investigating excited-state properties of point defects and opens up new opportunities for applications of ppRPA to periodic bulk materials

Linear Scaling Calculations of Excitation Energies with Active-Space Particle–Particle Random-Phase Approximation

We developed an efficient active-space particle–particle random-phase approximation (ppRPA) approach to calculate accurate charge-neutral excitation energies of molecular systems. The active-space ppRPA approach constrains both indexes in particle and hole pairs in the ppRPA matrix, which only selects frontier orbitals with dominant contributions to low-lying excitation energies. It employs the truncation in both orbital indexes in the particle–particle and the hole–hole spaces. The resulting matrix, whose eigenvalues are excitation energies, has a dimension that is independent of the size of the systems. The computational effort for the excitation energy calculation, therefore, scales linearly with system size and is negligible compared with the ground-state calculation of the (N – 2)-electron system, where N is the electron number of the molecule. With the active space consisting of 30 occupied and 30 virtual orbitals, the active-space ppRPA approach predicts the excitation energies of valence, charge-transfer, Rydberg, double, and diradical excitations with the mean absolute errors (MAEs) smaller than 0.03 eV compared with the full-space ppRPA results. As a side product, we also applied the active-space ppRPA approach in the renormalized singles (RS) T-matrix approach. Combining the non-interacting pair approximation that approximates the contribution to the self-energy outside the active space, the active-space GRSTRS@PBE approach predicts accurate absolute and relative core-level binding energies with the MAEs around 1.58 and 0.3 eV, respectively. The developed linear scaling calculation of excitation energies is promising for applications to large and complex systems

LibSC: Library for Scaling Correction Methods in Density Functional Theory

In recent years, a series of scaling correction (SC) methods have been developed in the Yang laboratory to reduce and eliminate the delocalization error, which is an intrinsic and systematic error existing in conventional density functional approximations (DFAs) within density functional theory (DFT). On the basis of extensive numerical results, the SC methods have been demonstrated to be capable of reducing the delocalization error effectively and producing accurate descriptions for many critical and challenging problems, including the fundamental gap, photoemission spectroscopy, charge transfer excitations, and polarizability. In the development of SC methods, the SC methods were mainly implemented in the QM4D package that was developed in the Yang laboratory for research development. The heavy dependency on the QM4D package hinders the SC methods from access by researchers for broad applications. In this work, we developed a reliable and efficient implementation, LibSC, for the global scaling correction (GSC) method and the localized orbital scaling correction (LOSC) method. LibSC will serve as a lightweight and open-source library that can be easily accessed by the quantum chemistry community. The implementation of LibSC is carefully modularized to provide the essential functionalities for conducting calculations of the SC methods. In addition, LibSC provides simple and consistent interfaces to support multiple popular programing languages, including C, C++, and Python. In addition to the development of the library, we also integrated LibSC with two popular and open-source quantum chemistry packages, the Psi4 package and the PySCF package, which provides immediate access for general users to perform calculations with SC methods

Results of ordinal logistic regression on the main travel purpose influence the rental time of UGB and UGA.

Results of ordinal logistic regression on the main travel purpose influence the rental time of UGB and UGA.</p

Research data.

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Scatter diagram of user clusters.

Scatter diagram of user clusters.</p

Auto clustering information of rented car usage.

Auto clustering information of rented car usage.</p

Questionnaires.

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