One of the biggest problems of the LDA theory is the underestimation of the band gap for insulators. However, there remains a quite justified concern about how far the LDA can be pushed. As a matter of fact, LDA theory has been routinely applied to obtain excited states of many different systems, and in many cases, achieved very satisfactory results. Comparison of calculated and measured spectra can shed much light on the important question as to whether the LDA is an appropriate or adequate theory to explore the excited state of a crystal, since it is based on the approximation to the ground state of the electron system. It can be used as a benchmark to test the accuracy of a calculation since experimental studies on optical properties are quite abundant. The calculation of interband optical transition provides an opportunity for investigating the excited states of the system.

A very important application of LDA beyond the usual electronic structure calculation is the optical properties of solids.

The LDA theory gives the formal theoretical justification in using the one-electron approach in solving a complicated many body problem. In the past two decades, the density functional theory (DFT)1,2, in the local density approximation (LDA) has proved to be an extremely successful approach in studying physical properties of many molecules and solids, including bulk metals, semiconductors, insulators as well as surfaces and interfaces3–5. Our findings shed light on the elastic-plastic transition controversy of Si and provide new knowledge about the nanoplasticity of Si. Moreover, a large indenter promotes a sharp pop-in singularity in the load-penetration depth curve but a small indenter gives rise to a gentle and difficult-to-detect pop-in singularity. All the observed dislocations are the shuffle dislocation loops in the slip system emitted from the high-pressure phases/dc-Si interface. In fact, the larger the indenter, the more prevailing are the dislocations. However, for a large indenter, HPPT alone can no longer relieve the mechanical load and dislocations are activated synchronously. When a small indenter is used, the high-pressure phase transformation (HPPT) is exclusively responsible for the elastic-plastic transition and subsequent incipient plasticity, giving rise to the strain-induced HPPT from the cubic diamond structure Si (dc-Si) to the β-Si and bct5 phases. Our results predict an interesting indenter-size-dependent transition for the nanoplasticity of Si. Herein, molecular dynamics simulation is performed to reveal the nanoplasticity of Si at room temperature during nanoindentation with indenter diameters in the range of 20 nm to 100 nm. However, the origin of its nanoplasticity is still controversial and it is not certain whether the elastic-plastic transition is determined by phase transformation or dislocation. Silicon (Si) is commonly used in microelectronic devices and micro/nanoelectromechanical systems (MEMS/NEMS) and the mechanical behavior of nanoscale silicon is very important.

In phase combination of atomic orbitals