In approximate density functional theory (DFT), the self-interaction error is an electron delocalization anomaly associated with underestimated insulating gaps. It exhibits a predominantly quadratic energy-density curve that is amenable to correction using efficient, constraint-resembling methods such as DFT + Hubbard $U$ (DFT+$U$). Constrained DFT (cDFT) enforces conditions on DFT exactly, by means of self-consistently optimized Lagrange multipliers, and while its use to automate error corrections is a compelling possibility, we show that it is limited by a fundamental incompatibility with constraints beyond linear order. We circumvent this problem by utilizing separate linear and quadratic correction terms, which may be interpreted either as distinct constraints, each with its own Hubbard $U$ type Lagrange multiplier, or as the components of a generalized DFT+$U$ functional. The latter approach prevails in our tests on a model one-electron system, $H_2^+$, in that it readily recovers the exact total-energy while symmetry-preserving pure constraints fail to do so. The generalized DFT+$U$ functional moreover enables the simultaneous correction of the total-energy and ionization potential or the correction of either together with the enforcement of Koopmans condition. For the latter case, we outline a practical, approximate scheme by which the required pair of Hubbard parameters, denoted as U1 and U2, may be calculated from first-principles.
Finite-Temperature Thermally-Assisted-Occupation Density Functional Theory, Ab Initio Molecular Dynamics, and Quantum Mechanics/Molecular Mechanics Methods
National Taiwan University（台湾大学）；Department of Physics, National Taiwan University（台湾大学物理系）；Center for Theoretical Physics and Center for Quantum Science and Engineering, National Taiwan University（台湾大学理论物理中心与量子科学与工程中心）；Physics Division, National Center for Theoretical Sciences（国家理论科学中心物理组）
Anharmonic Infrared Spectra of Thermally Excited Pyrene(C$_{16}$H$_{10}$): the combined view of DFT-based GVPT2 with AnharmonicCaOs and approximate DFT molecular dynamics with DemonNano
NeuralNEB -- Neural Networks can find Reaction Paths Fast
DTU Compute, Technical University of Denmark (DTU)（丹麦技术大学（DTU）计算系）；DTU Energy, Technical University of Denmark (DTU)（丹麦技术大学（DTU）能源系）；Department of Biology, University of Copenhagen (UCph)（哥本哈根大学（UCph）生物系）；Genomic Medicine, Copenhagen University Hospital, Rigshospitalet（哥本哈根大学医院（Rigshospitalet）基因组医学部）
Extending orbital-optimized density functional theory to L-edge XPS and beyond: Spin-orbit coupling via non-orthogonal quasi-degenerate perturbation theory
Construction of a general semilocal exchange-correlation hole model: Application to nonempirical meta-GGA functionals
利用逆向工程的方法，我们构造了一个具有普遍适用性的亚广义梯度近似（meta-GGA）角平均交换关联空穴模型。它满足已知的精确空穴约束条件，并且可以精确地恢复任何合理的元GGA交换相关能量泛函的交换相关能量密度，该交换相关能量泛函满足一组最小的精确性质。将空穴模型应用于几个非经验元GGA泛函：Tao-Perdew-Staroverov-Scuseria（TPSS）、修正的TPSS（revTPSS）和最近L.A.康斯坦丁，E. Fabiano和F. Della Sala，（J. Chem. Theory Comput. 9，2256（2013））。还考虑了经验M06-L meta-GGA泛函。真实空间的原子和离子的分析，以及波矢量分析的凝胶表面能，表明元GGA孔模型，特别是BLOC的，是非常现实的，可以重现许多功能的基准XC孔。此外，BLOC空穴模型还可用于小原子和离子的库仑空穴半径的精确估算。因此，所提出的元GGA孔模型提供了一个有价值的工具，以详细验证现有的元GGA泛函，并可以进一步用于DFT方法的发展超越半局部理论水平。
