Eleven density functionals are compared with regard to their performance for the lattice constants of solids. We consider standard functionals, such as the local-density approximation and the Perdew-Burke-Ernzerhof (PBE) generalized-gradient approximation (GGA), as well as variations of PBE GGA, such as PBEsol and similar functionals, PBE-type functionals employing a tighter Lieb-Oxford bound, and combinations thereof. Several of these variations are proposed here for the first time. On a test set of 60 solids we perform a system-by-system analysis for selected functionals and a full statistical analysis for all of them. The impact of restoring the gradient expansion and of tightening the Lieb-Oxford bound is discussed, and confronted with previous results obtained from other codes, functionals or test sets. No functional is uniformly good for all investigated systems, but surprisingly, and pleasingly, the simplest possible modifications to PBE turn out to have the most beneficial effect on its performance. The atomization energy of molecules was also considered and on a testing set of six molecules, we found that the PBE functional is clearly the best, the others leading to strong overbinding.
While Diffusion Monte Carlo (DMC) is in principle an exact stochastic method for \textit{ab initio} electronic structure calculations, in practice the fermionic sign problem necessitates the use of the fixed-node approximation and trial wavefunctions with approximate nodes (or zeros) must be used. This approximation introduces a variational error in the energy that potentially can be tested and systematically improved. Here, we present a computational method that produces trial wavefunctions with systematically improvable nodes for DMC calculations of periodic solids. These trial wavefunctions…
We systematically derive low-energy effective Hamiltonians for molecular solids $β^\prime$-$X$[Pd(dmit)$_{2}$]$_{2}$ ($X$ represents a cation) using ab initio density functional theory calculations and clarify how the cation controls the inter-dimer transfer integrals and the interaction parameters. The effective models are solved using the exact diagonalization method and the antiferromagnetic ordered moment is shown to be significantly suppressed around the spin-liquid candidate of $X$=EtMe$_{3}$Sb, which is reported in experiments. We also show that both the geometrical frustration and the …
The GaV$_4$S$_{8-y}$Se$_y$ $(y = 0$ to $8)$ family of materials have been synthesized in both polycrystalline and single crystal form, and their structural and magnetic properties thoroughly investigated. Each of these materials crystallizes in the $F\bar{4}3m$ space group at ambient temperature. However, in contrast to the end members GaV$_4$S$_8$ and GaV$_4$Se$_8$, that undergo a structural transition to the $R3m$ space group at 42 and 41 K respectively, the solid solutions $(y = 1$ to $7)$ retain cubic symmetry down to 1.5 K. In zero applied field the end members of the family order ferroma…
Quantum Monte Carlo (QMC) methods are some of the most accurate methods for simulating correlated electronic systems. We investigate the compatibility, strengths and weaknesses of two such methods, namely, diffusion Monte Carlo (DMC) and auxiliary-field quantum Monte Carlo (AFQMC). The multi-determinant trial wave functions employed in both approaches are generated using the configuration interaction using a perturbative selection made iteratively (CIPSI) technique. Complete basis set full configuration interaction (CBS-FCI) energies estimated with CIPSI are used as a reference in this compara…
Bi(1-x)R(x)FeO(3)(R=rare earth): a family of novel magnetoelectrics
得到了Bi（1-x）R（x）FeO（3）固溶体的晶体，这里R= La，Dy，Gd，x ≤ 0.7。当x从0增加到0.7时，所述稀土的固溶体具有相同的五种晶体结构序列（菱形C3 v 6、三斜晶系C11、正交晶系D2 6、正交晶系D2 5、正交晶系C2 v 9）。在T=810-560°C时，铁电-顺电转变发生在菱面体和三斜晶系晶体中。正交结构C2 v 9保持高达1180°C。铁电畴结构在所有类型的晶体中是独特的。在具有D2（222）对称性的正交晶体中没有检测到磁电效应。而mm ~ 2晶体既有二次效应，又有线性效应，二次效应值比线性效应值小得多。在晶体中发生磁电磁滞现象。从晶体对称性的角度分析了所得晶体的张量性质。
Functional and Density-Driven Errors in Density Functional Theory: Quantum Monte Carlo Benchmarks for Solids
Ruhr University Bochum（波鸿鲁尔大学）；Research Center Future Energy Materials and Systems of the University Alliance Ruhr（鲁尔大学联盟未来能源材料与系统研究中心）；Interdisciplinary Centre for Advanced Materials Simulation（先进材料模拟跨学科中心）
This chapter presents controlled approximations of Kohn-Sham density functional theory (DFT) that enable very large scale simulations. The work is motivated by the study of defects in crystalline solids, though the ideas can be used in other applications. The key idea is to formulate DFT as a minimization problem over the density operator, and to cast spatial and spectral discretization as systematically convergent approximations. This enables efficient and adaptive algorithms that solve the equations of DFT with no additional modeling, and up to desired accuracy, for very large systems, with …
The interaction between electronic and nuclear spins in the presence of external magnetic fields can be described by a spin Hamiltonian, with parameters obtained from first principles, electronic structure calculations. We describe an approach to compute these parameters, applicable to both molecules and solids, which is based on Density Functional Theory (DFT) and real-space, all-electron calculations using finite elements (FE). We report results for hyperfine tensors, zero field splitting tensors (spin-spin component) and nuclear quadrupole tensors of a series of molecules and of the nitroge…
