Density functional calculations of large systems containing heavy elements by means of the regionalization algorithm

The regionalized computational method is extended to the non-relativistic, scalar and 2-component relativistic density functional calculation of large systems containing transition series or heavy main-group metal elements. A large system is divided into several regions which can be considered as relatively independent quantum mechanical subsystems. Taking into account the Coulomb and exchange-correlation potentials as well as the Pauli repulsion exerted by the other subsystems, the Kohn-Sham equation related to subsystem K can be written as: \((F^K + F_P^K )C^K = S^K C^K \varepsilon ^K K = A,B,C \cdots ,\) where F ^K , C ^K , S ^K , ε ^K are the Fock matrix, the matrix of combination coefficients of orbitals, the overlap matrix of basis sets and the energy eigenvalue matrix, respectively. The matrix F ^K _K reflects the Pauli repulsion from the other subsystems. F ^K may be non-relativistic, scalar or 2-component relativistic Fock matrix determined by the theoretical method related to the density functional calculations. The other matrices are mated with F ^K . Solving the Kohn-Sham equation for every subsystem and combining the results from the subsystem calculations, the electronic structural information of the whole system is derived. The density functional calculation of several molecules containing transition metal Ni or heavy main-group metal TI or Bi is performed by the afore-mentioned regionalization algorithm. The obtained results for each molecule are compared with those from the density functional calculation of that molecule in its entirety in order to check the feasibility of the regionalization algorithm. It is found that with sufficiently large regional basis set in the subsystem calculation the accuracy of the results calculated by the regionalization algorithm is essentially the same as that from the calculation of the molecule in its entirety. With proper smaller regional basis sets the accuracy of the results calculated with the regionalization algorithm can still match the actual accuracy of the current approximate energy density functionals. Therefore, the regionalization algorithm is applicable to the non-relativistic, scalar and 2-component relativistic high accurate density functional calculation of large systems containing heavy elements.