Moseley Law for Atomic Orbital Exponents

The piecewise linear dependence of orbital exponents \(\xi \) characterizing either nonorthogonal Slater or orthogonal minimum atomic parameters/Moscow–Aachen–Paris (MAP) radial parts of atomic orbitals is theoretically derived from a plausible model of electronic subshell energy and compared with their values derived from a pragmatic Koga basis set covering the elements from H to Lr ( \(Z = 103\) ). So derived values of exponents as well follow piecewise linear laws as functions of the nuclear charge \(Z\) . The linear branches of the \(\xi \) vs. \(Z\) fairly follow the structure of the Periodic Table being specific for the segments of the \(Z\) values corresponding to p-, d- and f-elements, respectively. In details, however, the parameters of the theoretical linear dependencies of orbital exponents \(\xi \) on \(Z\) and those derived from the pragmatic basis set (referred to as experimental) differ from each other which will be addressed elsewhere.