Structural and electronic properties of CaCu3Ti4O12 have been calculated using density-functional theory within the local spin-density approximation. After an analysis of structural stability, zonecenter optical phonon frequencies are evaluated using the frozen-phonon method, and mode effective charges are determined from computed Berry-phase polarizations. Excellent agreement between calculated and measured phonon frequencies is obtained; calculated mode effective charges are in poorer agreement with experiment, although they are of the correct order of magnitude; and the lattice contribution to the static dielectric constant is calculated to be ∼40. On the basis of these results, various mechanisms are considered for the enormous dielectric response reported in recent experiments. No direct evidence is found for intrinsic lattice or electronic mechanisms, suggesting that increased attention should be given to extrinsic effects.

The spatial decay properties of Wannier functions and related quantities have been investigated using analytical and numerical methods. We find that the form of the decay is a power law times an exponential, with a particular power-law exponent that is universal for each kind of quantity. In one dimension we find an exponent of −3/4 for Wannier functions, −1/2 for the density matrix and for energy matrix elements, and −1/2 or −3/2 for different constructions of non-orthonormal Wannier-like functions.PACS: 71.15. Ap, A growing interest in localized real-space descriptions of the electronic structure of solids has been motivated by the development of computationally efficient "linearscaling" algorithms [1,2] and by the desirability of a local real-space mapping of chemical [3,4] and dielectric [5,6] properties. A primary avenue to such a description is the use of Wannier functions [7][8][9] (WFs), i.e., a set of localized wavefunctions w R (r) obtained from the Bloch functions ψ k (r) by a Fourier-like unitary transformation. A closely related approach is to represent the electronic structure in terms of the density matrix n(r, r ′ ). It is thus not surprising to find considerable recent interest in the localization properties of the WFs [3] and of the density matrix [10,11].In a classic 1959 paper, Kohn proved, for the case of a centrosymmetric crystal in one dimension (1D), that the WFs have an "exponential decay" w(x) ≈ e −hx , where h is the distance of a branch point from the real axis in the complex-k plane [8]. More precisely, lim x→∞ w(x) e qx = 0,The density matrix has a similar decay n(x, x ′ ) ≈ e −h|x−x ′ | . The exponential decay of the WFs has since been proven for the general 1D [12] and single-band 3D[13] cases, and that of the density matrix (more precisely, of the band projection operator) has been proven in general [12]. The energy matrix elements E(R) = w R |H|w 0 , with w R (x) = w(x − R) and R = la a lattice vector, are also expected to have a similar decay,The purpose of this Letter is to address two questions. First, Eq. (1) allows considerable freedom; in fact, it is consistent withfor any exponent α, i.e., a decay which could be faster (α > 0) or slower (α < 0) than pure exponential. Does such a power-law prefactor exist, and if so, what is the exponent α? Second, it has long been understood that relaxation of the orthogonality constraint w 0 |w R = δ 0,R can give "more localized" Wannier-like functions [14][15][16].In what sense are these more localized -a larger h, or a larger α for the same h, or only a smaller prefactor of the tail? We show that the power-law prefactors of Eq. (2) do exist, and that the various quantities have a common inverse decay length h but different exponents α. In 1D we find that α = 3/4 for usual (orthonormal) WFs, α = 1/2 for n(x, x ′ ) and E(R), and α = 1/2 or α = 3/2 for two different constructions of nonorthonormal Wannier-like functions (NWFs). The NWFs of superior decay (∼ x −3/2 e −hx ) can be constructed by a projection method as duals to a set of tria...

The large, temperature-independent, low-frequency dielectric constant recently observed in singlecrystal CaCu3Ti4O12 is most plausibly interpreted as arising from spatial inhomogenities of its local dielectric response. Probable sources of inhomogeneity are the various domain boundaries endemic in such materials: twin, Ca-ordering, and antiphase boundaries. The material in and neighboring such boundaries can be insulating or conducting. We construct a decision tree for the resulting six possible morphologies, and derive or present expressions for the dielectric constant for models of each morphology. We conclude that all six morphologies can yield dielectric behavior consistent with observations and suggest further experiments to distinguish among them.

We have investigated the interaction of oxygen vacancies and 180• domain walls in tetragonal PbTiO3 using density-functional theory. Our calculations indicate that the vacancies do have a lower formation energy in the domain wall than in the bulk, thereby confirming the tendency of these defects to migrate to, and pin, the domain walls. The pinning energies are reported for each of the three possible orientations of the original Ti-O-Ti bonds, and attempts to model the results with simple continuum models are discussed.

Predicting molecular properties (e.g., atomization energy) is an essential issue in quantum chemistry, which could speed up much research progress, such as drug designing and substance discovery. Traditional studies based on density functional theory (DFT) in physics are proved to be time-consuming for predicting large number of molecules. Recently, the machine learning methods, which consider much rule-based information, have also shown potentials for this issue. However, the complex inherent quantum interactions of molecules are still largely underexplored by existing solutions. In this paper, we propose a generalizable and transferable Multilevel Graph Convolutional neural Network (MGCN) for molecular property prediction. Specifically, we represent each molecule as a graph to preserve its internal structure. Moreover, the well-designed hierarchical graph neural network directly extracts features from the conformation and spatial information followed by the multilevel interactions. As a consequence, the multilevel overall representations can be utilized to make the prediction. Extensive experiments on both datasets of equilibrium and off-equilibrium molecules demonstrate the effectiveness of our model. Furthermore, the detailed results also prove that MGCN is generalizable and transferable for the prediction.

We describe how to apply the recently developed pole expansion and selected inversion (PEXSI) technique to Kohn-Sham density function theory (DFT) electronic structure calculations that are based on atomic orbital discretization. We give analytic expressions for evaluating the charge density, the total energy, the Helmholtz free energy and the atomic forces (including both the Hellman-Feynman force and the Pulay force) without using the eigenvalues and eigenvectors of the Kohn-Sham Hamiltonian. We also show how to update the chemical potential without using Kohn-Sham eigenvalues. The advantage of using PEXSI is that it has a much lower computational complexity than that associated with the matrix diagonalization procedure. We demonstrate the performance gain by comparing the timing of PEXSI with that of diagonalization on insulating and metallic nanotubes. For these quasi-1D systems, the complexity of PEXSI is linear with respect to the number of atoms. This linear scaling can be observed in our computational experiments when the number of atoms in a nanotube is larger than a few hundreds. Both the wall clock time and the memory requirement of PEXSI is modest. This makes it even possible to perform Kohn-Sham DFT calculations for 10,000-atom nanotubes with a sequential implementation of the selected inversion algorithm. We also perform an accurate geometry optimization calculation on a truncated (8,0) boron-nitride nanotube system containing 1024 atoms. Numerical results indicate that the use of PEXSI does not lead to loss of accuracy required in a practical DFT calculation.

We present a first-principles computer code package (ABACUS) that is based on density functional theory and numerical atomic basis sets. Theoretical foundations and numerical techniques used in the code are described, with focus on the accuracy and transferability of the hierarchial atomic basis sets as generated using a scheme proposed by Chen, Guo and He [J. Phys.:Condens.Matter 22, 445501 (2010)]. Benchmark results are presented for a variety of systems include molecules, solids, surfaces, and defects. All results show that the ABACUS package with its associated atomic basis sets is an efficient and reliable tool for simulating both small and large-scale materials.

Bismuth (Bi) has been demonstrated as a promising anode for Na-ion batteries (NIBs) because it has high gravimetry (386 mA h g–1) and volumetric capacity (3800 mA h cm–3). However, Bi suffers from large volume expansion during sodiation, leading to poor electrochemical performance. The construction of a nanostructure with sufficient void space to accommodate the volume change has been proven effective for achieving prolonged cycling stability. However the excessive void space will definitely decrease the volumetric energy density of the battery. Herein, we design optimized Bi@Void@C nanospheres (Bi@Void@C-2) with yolk–shell structure that exhibit the best cycling performance and enhanced volumetric energy density. The optimized void space not only could buffer the volume change of the Bi nanosphere but also could keep the high volumetric energy density of the battery. The Bi@Void@C-2 shows an excellent rate capacity of 173 mA h g–1 at ultrahigh current density of 100 A g–1 and long-cycle life (198 mA h g–1 at 20 A g–1 over 10 000 cycles). The origin of the superior performance is achieved through in-depth fundamental studies during battery operation using in situ X-ray diffraction (XRD) and in situ transmission electron microscope (TEM), complemented by theoretical calculations and ex situ TEM observation. Our rational design provides insights for anode materials with large volume variation, especially for conversion type and alloying type mechanism materials for batteries (i.e., Li-ion batteries, Na-ion batteries).