Development Of Localized Orbitals Based First-principles Package

Density functional theory plays an important role in materials science. First-principles methods indicate methods, with which we can directly calculate the phys-ical properties of materials without any empirical parameters. Development of density functional theory based first-principles package is always a hot topic. On one hand, a well-established package can help more people to study the actual properties of all kinds of materials. On the other hand, a package is a necessary platform which can be used to develop new methods. There have been emerging many sophisticated pack-ages in Europe and US in the last twenty years, and they have always kept advancing. Though some of the Chinese group try to develop some kinds of first-principles meth-ods, still less effort has been made in China.During the last six years, the author tried to develop a first-principles package from zero, the package should be efficient and robust, and more importantly, has some unit character that others don’t have. During the past few years, the author started from developing the plane wave based first-principles package, then use the plane wave based package to develop methods that can generate systematically improvable opti-mized local orbitals. After that, the author developed a numerical atomic orbitals based package which can handle a system up to a thousand atoms. Notably, the author fo-cused on the development of local orbitals and have a series of publications. We still have several plans in the future, First, we would like to study linear scaling methods to study larger systems, we also have done some work, for example the implement of the sparse matrix and the series version of purification of density matrix methods. We also have deep understanding of the LS3DF method. Second, we would like to develop the hybrid functional methods, GW methods and random phase approximations. We also hope to have wide cooperations with other groups who have the interest in large system calculations or first-principles methods development.The achievement in the thesis are:1. We develop a method to construct transferable Wannier functions base setWe found the Wannier functions have high accuracy for a specific reference sys-tem, but don’t have good transferbility. We decompose the Wannier functions into the centers of several adjacents, and found this method reserves the transferbility.2. We develop a method to generate systematically improvable optimized atomic orbitals by using the spillage formulaWe use simulated annealing method to generate numerical atomic orbitals and have done a lot of tests. The results show the excellent accuracy of atomic orbitals and transferbility.3. We develop a method to generate numerical atomic orbitals for interpolat-ing the electronic structures of systemsWe use the spillage formula to generate higher angular momentum orbitals and more zeta functions for each angular momentum. The orbitals are used to interpolate the band structure of a series of materials, the accuracy can be controlled within10meV. We also use this method to test the optical properties. Our orbitals have transferbility which is good for perturbation calculations.4. We have developed a first-principles methods package based on numerical atomic orbitals.In the past few years, we have developed a series of localized orbitals based pro-grams, including program to search adjacent atoms for each atom, program for two center integrals, program to do real space grid integrals, program to calculate the force under atomic orbitals, program to generate sparse matrix form and the operations be-tween sparse matrix, program to diagonalize the Hamiltonian matrix, etc. We have done lots of tests to show the power of our package. Further development is still undergoing.