TROPOMI unravels transboundary transport pathways of atmospheric carbon monoxide in Tibetan Plateau.

Numerous studies have reported in situ monitoring and source analysis in the Tibetan Plateau (TP), a region crucial for climate systems. However, a gap remains in understanding the comprehensive distribution of atmospheric pollutants in the TP and their transboundary pollution transport. Here, we analyzed the high-resolution satellite TROPOMI observations from 2018 to 2023 in Tibet and its surrounding areas.

Reproducibility of Hybrid Density Functional Calculations for Equation-of-State Properties and Band Gaps.

Hybrid density functional (HDF) approximations usually deliver higher accuracy than local and semilocal approximations to the exchange-correlation functional, but this comes with drastically increased computational cost. Practical implementations of HDFs inevitably involve numerical approximations─even more so than their local and semilocal counterparts due to the additional numerical complexity arising from treating the exact-exchange component. This raises the question regarding the reproducibility of the HDF results yielded by different implementations.

Efficient Hybrid Density Functional Calculations for Large Periodic Systems Using Numerical Atomic Orbitals.

We present an efficient, linear-scaling implementation for building the (screened) Hartree-Fock exchange (HFX) matrix for periodic systems within the framework of numerical atomic orbital (NAO) basis functions. Our implementation is based on the localized resolution of the identity approximation by which two-electron Coulomb repulsion integrals can be obtained by only computing two-center quantities-a feature that is highly beneficial to NAOs. By exploiting the locality of basis functions and efficient prescreening of the intermediate three- and two-index tensors, one can achieve a linear scaling of the computational cost for building the HFX matrix with respect to the system size.

Accuracy of Localized Resolution of the Identity in Periodic Hybrid Functional Calculations with Numerical Atomic Orbitals.

We present an implementation of hybrid density functional approximations for periodic systems within a pseudopotential-based, numerical atomic orbital (NAO) framework. The two-electron Coulomb repulsion integrals (ERIs) are evaluated using the localized resolution-of-the-identity (LRI) approximation. The accuracy of the LRI approximation is benchmarked unambiguously against independent reference results obtained via a computational scheme whereby the ERIs are accurately evaluated by expanding the products of NAOs in terms of plane waves.