The scattering unit of X-ray crystal structure analysis is changed from atoms to the subshell electrons by X-ray atomic orbital analysis (XAO). All the atoms in the unit cell are divided into groups of subshell electrons in the XAO analysis. Each subshell is treated as an independent pseudo-atom, which enables the atomic orbitals (AO's) and the electron population of each AO expressed as a linear combination of s/p/d/f orbitals in each subshell to be determined. When the environmental condition of the sample is varied, the electron transfer among the AO's in the crystal can be traced with XAO. It is applicable mainly to analyses of the electron-density distribution in ionic solids including those with a nonstoichiometric structure. The expansion coefficients of each AO are calculated with the perturbation theory putting a point charge on each atom in the unit cell. This automatically makes the perturbation potential have the point-group symmetry of the atom in the crystal field. Then the coefficients of each AO are refined to fit to the observed structure factors keeping the orthonormal relationships among the AO's. Complex basis functions with alpha or beta spin as well as real ones are employed for heavy atoms and the relationships among the coefficients for the AO's of an electron in the crystal fields of the 32 point-group symmetries are derived for p, d and f orbitals. The AO's thus derived can be applicable to an anti-symmetrized multi-electron system, although X-ray diffraction cannot specify the atomic terms occupied when the crystal symmetry permits the atom to have many terms.

X-ray atomic orbital (XAO) analysis revealed that at both temperatures the electrons are transferred from B 2p(x)(= p(y)) to Ce 5d and 4f orbitals. At 340 K 5d(j = 5/2)Gamma(8) orbitals are occupied partially, but 4f(j = 5/2)Gamma(8) orbitals are more populated than 4f(j = 5/2)Gamma(7) orbitals, in contrast to our observation at 430 K [Makita et al. (2007). Acta Cryst. B63, 683-692]. At 535 K the XAO analysis revealed clearly that the order of the energy levels of 4f(j = 5/2)Gamma(8) and Gamma(7) states reversed again and is the same as that at room temperature. It also limited the possible 5d configurations to three models among the nine possible ones. However, the XAO analysis could not decide which of the three models was the best with the present accuracy of the measurement. Two of them have partially and fully occupied 5d(j = 5/2)Gamma(7) orbitals and the remaining one has a fully occupied 5d(j = 3/2)Gamma(8) orbital. Since the lobes of 5d(j = 3/2)Gamma(8) or 5d(j = 5/2)Gamma(7) orbitals do not overlap with the 4f(j = 5/2)Gamma(8) orbitals as well as the 5d(j = 5/2)Gamma(8) orbitals, the order of the energy levels of the 4f(j = 5/2) orbitals became the same as that at room temperature. These results indicate that the crystal field varies with temperature due to the electron transfer from B 2p to Ce 5d orbitals. The difference densities after the spherical-atom refinement at the three temperatures clearly revealed the different combinations of 4f and 5d orbitals which are occupied. In the present study positive peaks due to the 4f electrons appear near the Ce nucleus and those due to 5d orbitals are found in the area outside the 4f peaks. Between the two areas there is a negative area distributed spherically at 340 K. The negative area produced by the contraction of 4f(j = 5/2)Gamma(8) orbitals seems to reduce the electron repulsion of the 5d(j = 5/2)Gamma(8) orbitals and helps the 4f(j = 5/2)Gamma(8) orbitals to remain as the ground state.

The 4f states of Ce in a typical Kondo crystal, CeB(6), are split into an excited state Gamma(7) and the ground state Gamma(8), with an excitation energy at 560 K. The electron-density distribution of the thermally excited state was measured at 430 K using a four-circle diffractometer equipped with a small furnace. In contrast to the previous results at lower temperature, electrons are transferred from B(6) to Ce at 430 K. X-ray atomic-orbital analysis revealed that the 5d-Gamma(8) orbitals (the energy level of which is similar to that of the B-2p orbitals) are fully occupied and the 4f-Gamma(7) orbitals are more populated than the 4f-Gamma(8) orbitals. Fully occupied 5d-Gamma(8) makes the 4f-Gamma(8) states unstable and the energy levels of 4f-Gamma(7) and 4f-Gamma(8) are inverted.

Neodymium strontium manganese oxide with ideal composition Nd0.5Sr0.5MnO3 was reported to have two different structure models. In one model, the x coordinate of an O atom is at x > 1/2, while in the other model the x-coordinate of this atom is at x < 1/2. Difference-density maps around this O atom obtained from the current redetermination clearly show that the structure with the O atom at x < 1/2 result in a more satisfactory model than that with x > 1/2. The title compound with a refined composition of Nd0.53 (5)Sr0.47 (5)MnO3 is a distorted perovskite-type structure with site symmetries 2mm for the statistically occupied (Nd, Sr) site and for the above-mentioned O atom, .2/m. for the Mn atom and ..2 for a second O-atom site. In contrast to previous studies, the displacement factors for all atoms were refined anisotropically.

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