Neglecting intersite orbital overlap, one normalized real set of symmetry-adapted linear combinations is
(1)
The coefficient vectors are orthonormal. The first has equal phase at all three sites; the second opposes site to ; the third has zero amplitude at and opposite phases at . Any orthonormal rotation of the two functions is equally valid. With nonzero intersite orbital overlap, normalization must instead use the overlap matrix.
Figure 1.
Original coefficient-and-phase sketches of the three hydrogen symmetry orbitals in ammonia
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