Inversion symmetry momentum density

Eq. (5.34). However, it is possible to construct approximate wavefunctions that lead to electron momentum densities that do not have inversion symmetry. Within the Born-Oppenheimer approximation, the total electronic system must be at rest the at-rest condition... 

Taking both the symmetry of the nuclear configuration and the inversion symmetry described above into account, it follows that the symmetry of the momentum density II(p) is (g) If contains the inversion operation i, then (g) However, if does not contain i, then the symmetry of the... 

Hybrids constructed from hydrogenic eigenfunctions are examined in their momentum-space representation. It is shown that the absence of certain cross-terms that cause the breaking of symmetry in position space, cause inversion symmetry in the complementary momentum representation. Analytical expressions for some simple hybrids in the momentum representation are given, and their nodal and extremal structure is examined. Some rather unusual features are demonstrated by graphical representations. Finally, special attention is paid to the topology at the momentum-space origin and to the explicit form of the moments of the electron density in both spaces. 

Consequently the momentum density of any mol ule will have inversion symmetry, even if p(r) does not. It can be useful to take advantage of this inversion symmetry when integrating functions of p(p such as the generalised overlaps to be described in Sect. 3. 

The one-electron momentum density for bound states of atoms and molecules always has inversion symmetry as a consequence of time-reversal symmetry or the principle of microreversibility [42,43] ... 

When the geometrical and inversion symmetries are considered together, it follows that the symmetry of the momentum density IT(p) is If does not contain the... 

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