A machine-learning-based exchange-correlation functional is proposed for general-purpose density functional theory calculations. It is built upon the long-range-corrected Becke–Lee–Yang–Parr (LC–BLYP) functional, along with an embedded neural network which determines the value of the range-separation parameter μ for every individual system. The structure and the weights of the neural network are optimized with a reference data set containing 368 highly accurate thermochemical and kinetic energies. The newly developed functional (LC–BLYP–NN) achieves a balanced performance for a variety of energetic properties investigated. It largely improves the accuracy of atomization energies and heats of formation on which the original LC–BLYP with a fixed μ performs rather poorly. Meanwhile, it yields a similar or slightly compromised accuracy for ionization potentials, electron affinities, and reaction barriers, for which the original LC–BLYP works reasonably well. This work clearly highlights the potential usefulness of machine-learning techniques for improving density functional calculations.

Being an important biomimetic model catalyst for water oxidation, the dimanganese molecular complex [H2O(terpy)MnIII(μ-O)2MnIV(terpy)OH2]3+ (complex 1, terpy = 2,2′:6′,2″-terpyridine) has been investigated extensively by experimentalists. By carrying out density functional theory calculations, we explore theoretically the oxygen evolution mechanisms of complex 1. On the basis of understandings of the geometric and electronic structural features of complex 1, we explore the possibility of improving its catalytic efficiency through a rational design of ligands coordinated to the manganese ions. Recognizing that the rate-determining step of oxygen evolution is the formation of an O–O bond at a high-valent manganese center, we design a new complex, [H2O(2-bpnp)MnIII(μ-O)2MnIV(2-bpnp)OH2]3+ (complex 2, 2-bpnp = 2-([2,2′-bipyridin]-6-yl)-1,8-naphthyridine). It is verified that the proton-accepting 2-bpnp ligand leads to stabilized hydrogen bonding with surrounding water molecules, and hence, the barrier height associated with O–O bond formation is substantially reduced. Moreover, despite its larger size, the 2-bpnp ligand does not cause steric hindrance for the release of molecular oxygen. Consequently, the proposed complex 2 is expected to outperform the existing complex 1 regarding catalytic efficiency. This work highlights the potential usefulness of rational design toward reaching the high efficiency of the oxygen evolution center in photosystem II.

Delocalization error associated with the presently used density functional approximations is one of the main sources of errors which plague density functional theory calculations. In this paper, we give a comprehensive review on scaling correction (SC) approaches developed recently for reducing the delocalization error. The global and local SC approaches impose the rigorous Perdew-Parr-Levy-Balduz condition that the total electronic energy should scale linearly between integer electron numbers, on systems involving global and local fractional electron distributions, respectively. After presenting the theoretical background and mathematical formulation of scaling corrections, we demonstrate that they lead to universal alleviation of delocalization error. This is exemplified by the substantial improvement for the prediction of a wide range of electronic properties, including Kohn-Sham frontier orbital energies and band gaps, dissociation behavior of molecules, reaction barriers, electric polarizabilities, and charge-transfer species. The encouraging performances of SC approaches highlight their practicality and usefulness, and also affirm that an explicit treatment of fractional electron distributions is essentially important for reducing the intrinsic delocalization error. The existing limitations, the remaining challenges, and the future perspectives of SC are also discussed. Moreover, the SC approaches are compared with some existing methods attempting to remove the self-interaction error, such as the Perdew-Zunger self-interaction correction, the local hybrid hyper-generalized gradient approximations, and the rangeseparated density functional approximations. The unique advantages of SC suggest that it could open a novel and potentially paradigm-changing route for advancing density functional theory methods towards chemical accuracy.

Time-dependent density-functional theory (TDDFT) has been successfully applied to predict excited-state properties of isolated and periodic systems. However, it cannot address a system coupled to an environment or whose number of electrons is not conserved. To tackle these problems, TDDFT needs to be extended to accommodate open systems. This paper provides a comprehensive account of the recent developments of TDDFT for open systems (TDDFT-OS), including both theoretical and practical aspects. The practicality and accuracy of a latest TDDFT-OS method is demonstrated with two numerical examples: the time-dependent electron transport through a series of quasi-one-dimensional atomic chains, and the real-time electronic dynamics on a two-dimensional graphene surface. The advancement of TDDFT-OS may lead to promising applications in various fields of chemistry, including energy conversion and heterogeneous catalysis.

Density-functional theory calculations are carried out for a biomimetic dimanganese complex, [H2O(terpy)MnIII(μ-O)2MnIV(terpy)OH2]3+(1, terpy = 2,2′:6′,2″-terpyridine), which is a structural model for the oxygen evolving center of photosystem II. Theoretical investigations aim at elucidating the asymmetry features in the geometric and electronic structures of complex 1, as well as their influences on the chemical functions of the two manganese centers, in the presence of water solvent. With the insight gained from the first-principles calculations, we study the oxidation state of complex 1 in the acetate buffer solution. Both the thermodynamic and kinetic aspects are explored in detail, and the structural and chemical asymmetry of the two manganese centers is fully considered. It is found that the larger steric repulsion associated with the Mn(IV) center plays a decisive role, which leads to the predominant acetate coordination at the Mn(III) ion. This thus resolves the existing controversy on the preferential acetate binding to complex 1.

As a promising candidate of a proton conductor under reducing atmosphere, La2Ce2O7 has attracted considerable research interest. However, the thermodynamically stable structure of bulk La2Ce2O7 has remained rather unclear. In this paper, first-principles calculations are carried out to resolve this issue. It is found that the lattice of La2Ce2O7 is substantially stabilized by the formation of anion Frenkel defects, i.e., oxygen atoms displaced from their original sites to interstitial regions. Consequently, the bulk La2Ce2O7 favors disordered fluorite configurations over pyrochlore structure. Our calculation results are consistent with the previously reported neutron diffraction patterns. In addition, partial disordering of cations is also likely under experimental conditions. We then explore the possible proton transfer pathways inside bulk La2Ce2O7. It is revealed that the partial disordering in La2Ce2O7 increases the energy barriers of proton transfer pathways.

We present the time-dependent holographic electron density theorem (TD-HEDT), which lays the foundation of time-dependent density-functional theory (TDDFT) for open electronic systems. For any finite electronic system, the TD-HEDT formally establishes a one-to-one correspondence between the electron density inside any finite subsystem and the time-dependent external potential. As a result, any electronic property of an open system in principle can be determined uniquely by the electron density function inside the open region. Implications of the TD-HEDT on the practicality of TDDFT are also discussed.

We present the time-dependent holographic electron density theorem (TD-HEDT), which lays the foundation of time-dependent density-functional theory (TDDFT) for open electronic systems. For any finite electronic system, the TD-HEDT formally establishes a one-to-one correspondence between the electron density inside any finite subsystem and the time-dependent external potential. As a result, any electronic property of an open system in principle can be determined uniquely by the electron density function inside the open region. Implications of the TD-HEDT on the practicality of TDDFT are also discussed.