Abstract
We suggest a new grid-free approach for the local exchange-correlation (XC) calculation using Cholesky Decomposition (CD) in density functional theory (DFT). The conventional grid-based method for the XC calculation involves numerical approximations because of the complexity of the XC functional, and it may causes numerical instabilities. On the other hand, a grid-free approach, which uses matrix representation of the density and matrix operations to represent any density functional, can describe the XC term to avoid these instabilities in the grid-based approach. However, in order to get the matrix representation of the density, the four-center overlap integrals require much computational resource, which becomes the bottleneck of the grid-free method. Meanwhile, it attracts much attention to apply the CD method into the electron repulsion integral calculations of the Coulomb and exchange Fock matrices, recently. Thus, in order to solve the difficulty of the grid-free XC calculation, we introduced the CD method into the four-center overlap integrals of a grid-free XC calculation. The suggested method is expected to realize the practically analytical integral of XC calculation and perform effectively in large system.
