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- W1528528036 abstract "Quantum-mechanical calculations of molecular properties and reactions require the introduction of atomic orbitals (AO's) that are centered on the nuclei of the different atoms of the investigated molecule or molecular complex. Each atomic orbital is a certain mathematical function of the coordinates of one electron with respect to a coordinate system that has its origin in the nucleus of the considered atom. The main difficulties of quantum-mechanical theories are because of operators that may be considered as special cases of irregular solid spherical harmonics. The formulas derived to describe the transformation properties of solid spherical harmonics under rotations and translations have been found useful for the calculation of molecular integrals. The chapter describes the solid spherical harmonics and presents certain relations that are to be used in the sequel. The behavior of spherical harmonics under rotations is discussed to obtain a set of uniform formulas useful for subsequent considerations. The derivation of the transformation of solid spherical harmonics under translations is facilitated by the translation of general functions and by deriving some auxiliary identities needed in the sequel." @default.
- W1528528036 created "2016-06-24" @default.
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- W1528528036 date "1973-01-01" @default.
- W1528528036 modified "2023-10-16" @default.
- W1528528036 title "Rotation and Translation of Regular and Irregular Solid Spherical Harmonics" @default.
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- W1528528036 doi "https://doi.org/10.1016/s0065-3276(08)60558-4" @default.
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