R-CCS Cafe 第226回 第3部

In order to calculate the electronic structure of atoms in the entire periodic table uniformly and with high accuracy, it is essential to take relativistic effects into account. In fact, the relativistic molecular orbital method and the relativistic density functional theory, which are electronic structure theories that incorporate relativistic effects, have contributed greatly to the understanding of the properties of heavy and super-heavy elements. However, the current relativistic electronic structure theory needs to be further improved in two point.

The first is high calculation cost of two-electron relativistic effects. The relativistic correction of the electron interaction potential can be treated by the relativistic four-component method or the two-component method with the transformation of the two-electron term.

The problem with these methods is that the computational cost of the two-electron integral is much larger than that of the non-relativistic calculation. In addition, the four-component method has some large differences from non-relativistic programs and is expensive to implement.

The second is that there are some effects associated with relativistic effects that are not fully incorporated. For example, the relativistic electronic structure theory is based on relativistic quantum mechanics, but relativistic quantum mechanics has been developed into quantum electrodynamics (QED) in order to solve the problem of anti-particles. On the other hand, relativistic quantum mechanics has been developed into QED in order to solve antiparticle problems, etc. Therefore, relativistic electronic structure theory also should be rewritten to QED level theory, but the conventional QED formulation is not compatible with electronic structure theory. It is necessary to perform this reformulation and incorporate the QED effect ab initio into the electronic structure theory. In addition, relativistic effects cause the shrinkage of core orbitals, which is strongly affected them by the charge distribution of nuclei in heavy atoms. In order to calculate polyatomic systems including heavy atoms with high accuracy and efficiency, it is necessary to develop a new function that analytical nuclear attractive integrals available for multi-center systems and describe realistic nuclear charge distributions.

In this talk, I will introduce a new methods developed by the speaker to solve these problems.