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General Diatomic and Polyatomic Molecular Ions and Molecules
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e 0.72698 (13.380) The nucleus of the H atom and the nucleus of the N atom comprise the foci of the H 2 -type ellipsoidal MO. The parameters of the point of intersection of each H 2 -type ellipsoidal MO and the N 2 px , N 2 p y , or N 2 pz AO are given by Eqs. (13.84-13.95),
(13.261-13.270), and (13.261-13.270). Using Eqs. (13.375-13.377) and (13.379-13.380), the polar intersection angle ' given by Eq. (13.261) with rn r7 0.93084a0 is ' 115.89 (13.381) Then, the angle N 2 pAO the radial vector of the N 2 px , N 2 p y , or N 2 pz AO makes with the internuclear axis is
N 2 pAO 180 115.89 64.11
(13.382)
as shown in Figure 13.5. The parametric angle H 2 MO given by Eqs. (13.264-13.265), (13.379), and (13.382) is
H MO 64.83 2
(13.383)
Then, the distance d H 2 MO along the internuclear axis from the origin of H 2 -type ellipsoidal MO to the point of intersection of the orbitals given by Eqs. (13.267), (13.375), and (13.383) is (13.384) d H 2 MO 0.57314a0 3.03292 X 1011 m The distance d N 2 pAO along the internuclear axis from the origin of the N atom to the point of intersection of the orbitals given by Eqs. (13.269), (13.376), and (13.384) is (13.385) d N 2 pAO 0.40647a0 2.15093 X 1011 m As shown in Eq. (13.370), in addition to the p -orbital charge-density modulation, the uniform charge-density in the px , p y , and pz orbitals is increased by a factor of 0.25 and the H atoms are each decreased by a factor of 0.25. Using the orbital composition of NH 3 (Eq. (13.370)), the radii of N1s 0.14605a0 (Eq. (10.51)), N 2 s 0.69385a0 (Eq. (10.62)), and N 2 p 0.93084a0 (Eq. (10.142)) shells, and the parameters of the NH 3 MO given by Eqs. (13.3-13.4) and (13.375-13.385), the charge-density of the NH 3 MO comprising the linear combination of three N H -bond MOs ( NH -type ellipsoidal MOs given in the Energies of NH section) according to Eq. (13.370) is shown in Figure 13.8. Each N H -bond MO comprises a H 2 -type ellipsoidal MO and an N 2 p AO having the dimensional diagram shown in Figure 13.5. Figu r e 13.8. NH 3 MO comprising the linear combination of three N H -bonds. Each N H -bond MO comprises the
superposition of a H 2 -type ellipsoidal MO and the N 2 px , N 2 p y , or N 2 pz AO with a relative charge-density of 0.75 to 1.25; otherwise, the N 2 p orbitals are the same as those of the nitrogen atom. The each internuclear axis of one N H bond is perpendicular to the bonding p orbital. (A) Color scale, translucent view of the charge-density of the NH 3 MO shown obliquely from the top. For each N H bond, the ellipsoidal surface of each H 2 -type ellipsoidal MO transitions to a N 2 p AO. The N 2 p shell, the N 2 s shell, the N1s shell, and the nuclei (red, not to scale) are shown. (B) Off-center cut-away view showing the complete inner most N1s shell, and moving radially, the cross section of the N 2 s shell, the N 2 p shell, and the H 2 -type ellipsoidal MO that transitions to a N 2 p AO for each N H bond. Bisector current not shown. (C)-(E) Color scale, side-on, top, and bottom translucent views of the charge-density of the NH 3 MO, respectively.