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Valence-Shell Electron-Pair Repulsion (VSEPR) Model

Deviations from Ideal Geometry

The bond angles described in the introduction to the VSEPR Model are associated with ideal geometries. Some molecules possess very high symmetry and the experimental bond angles coincide with those of the ideal geometry. Carbon dioxide, for example, is found to be a perfectly linear molecule, consistent with the prediction of the VSEPR Model. In other cases, however, the experimental bond angles differ from those of the ideal geometry. Water has NEG = 4 and NB = 2. The ideal bond angle is cos-1(-1/3) = 109.5°, but the experimental bond angle is 104.5°.

Fortunately, such deviations are easily anticipated on the basis of the considerations described below. Note that the VSEPR Model does not allow quantitative prediction of nonideal bond angles. The predictions are qualitative.

Lone Pairs Occupy More Space than Bonding Pairs

When a pair of electrons is confined to a sigma bonding orbital, the electron density is concentrated in the region between the bonded atoms and is drawn close to the line connecting the atoms. A lone pair of electrons, however, is drawn to a single atom and the electron density greatly expands as one moves away from the atom. Because a lone pair of electrons requires more space than a bonding pair, the molecular geometry distorts to afford the lone pair greater space, with the result that bond angles are smaller than those of the ideal geometry.

In the case of water, the two lone pairs push the bonding pairs closer together, yielding a smaller bond angle. The white lines in the virtual reality display shown below are at the ideal 109.5° angle. The experimental HOH bond angle is only slightly smaller, but the effect is noticable.

The VSEPR Model does not allow one to predict how much smaller the bond angle will be, but one can predict the HOH bond angle is < 109.5°.

water

Ideal Bond Angle: 109.5° (white lines)
Experimental Bond Angle: 104.5°

This effect is clearly observed by comparison of the F-P-F bond angles in PF3 and OPF3. In PF3 the lone pair on the phosphorus pushes the P-F bonding electrons away from itself, resulting in a F-P-F bond angle of 97.8°, which is appreciably smaller than the ideal bond angle of 109.5°.

In OPF3, the lone pair is replaced with a P-O bond, which occupies less space than the lone pair in PF3. Thus there is less distortion of the P-F bonds, and the F-P-F bond angle is 101.3°.

One might ask: Why aren't the bond angles in OPF3 all exactly 109.5°? Oxygen and fluorine are similar in size, but the P-O has some pi bonding character, which increases its size relative to the pure sigma character of the P-F bonds. (In this case, the P-F bonds do not reside exclusively in the nodal plane of the P-O pi bond.)

phosphorus trifluoride

Ideal F-P-F Bond Angle: 109.5° (white lines)
Experimental F-P-F Bond Angle: 97.8°
phosphoryl fluoride

Ideal F-P-F Bond Angle: 109.5° (white lines)
Experimental F-P-F Bond Angle: 101.3°

Avoid 90° Interactions with Lone Pairs

Among the various Electron Group geometries, the trigonal bipyramidal geometry is unique, because not all sites are equivalent. The three positions that are coplanar with the central atom are called the equitorial sites. The other two positions, forming a straight line with the central atom, are called the axial sites. The equitorial and axial sites are obviously not equivalent. In PCl5 all five positions are occupied by chlorine atoms, giving the trigonal bipyramidal molecular geometry, shown below at the left.

SF4 also has NEG = 5, but in this case NB = 4 with the remaining position occupied by a lone pair. Should the lone pair be placed in an axial or equitorial site?

The answer is to place the lone pair in the site that will provide the least repulsion with adjacent pairs. Placed in an equitorial position, the lone pair will be a 90° angles with two bonding pairs and at 120° angles with two other bonding pairs. In the axial position, the one pair will be at 90° angles with three bonding pairs. The key concept is that 90° interactions are significant, as the two pairs of electrons are forced into close proximity. On the other hand, 120° interactions between electron pairs involves little repulsions, because the two pairs are oriented in significantly different positions. Thus the lone pair in the SF4 molecule is best placed in an equitorial position, giving rise to a "see-saw" geometry, as shown below at the righ. As described above, the lone pair will occupy more than its fair share of space, forcing the atoms somewhat closer together than would be the case with perfect trigonal bipyramidal Electron Group geometry.

In general, lone pairs occupy equitorial positions in the trigonal bipyramidal geometry.

phosphorus pentachloride

Equitorial-Equitorial Cl-P-Cl Bond Angle: 120°
Equitorial-Axial Cl-P-Cl Bond Angle: 90°
sulfur tetrafluoride

Experimental Equitorial-Equitoral F-P-F Bond Angle: 103.8°
Experimental Equitorial-Axial F-P-F Bond Angle: 88.4°

Not All Hybrid Orbitals are Created Equal

The most basic hybridization scheme for ammonia (NH3) is that the nitrogen atomic 2s, 2px, 2py, and 2pz orbitals are mixed to yield a new set of sp3 atomic orbitals. Each orbital is equivalent and oriented at the corners of a tetrahedron. One can think of a sp3 hybrid orbital as having 25.0% s character and 75.0% p character.

There is no reason, however, why one need to make each of the hybrid orbitals equivalent or that the s and p orbitals need be combined in integer proportions. (Recall that hybrid orbitals are just linear combinations of basic atomic s and p orbitals.) For a molecule like CH4, it makes sense that each hybrid orbital is identical, since each hybrid orbital is involved in an identical C-H bond. But for NH3, it would make sense that the hybrid orbital accommodating the lone pair has a different composition than the hybrid orbitals accommodating the N-H bonds. As the formulation of the hybrid orbitals differ from sp3, the geometries of the orbitals differ from tetrahedral.

Ab initial quantum mechanical calculations (mp2/cc-pTVZ) for NH3 are shown in the table below. The hybrid orbitals for both the bonding and lone pairs are each very close to sp3, which predicts a trigonal pyramidal geometry with 109.5° bond angles. Note, though, that the nitrogen lone pair has slightly more s character and slighly less p character than the sigma bonding orbitals, consistent with the lone pair occuping more space than a sigma bonding pair. Recall that an s orbital is spherical and occupied considerable space. The p orbitals are directional and occupy less space. Thus an sp hybrid orbital occupied more space than the corresponding sp3 hybrid orbital. (See the discussion of hybridization.)

 NH3PH3AsH3
Bond
Hybridization
s character25.2%15.8%14.4%
p character74.7%83.2%85.0%
hybridizationsp2.97sp5.25sp5.91
Lone Pair
Hybridization
s character24.5%52.4%56.8%
p character74.7%83.2%85.0%
hybridizationsp3.09sp0.91sp0.76
Bond
Length (Å)
calculated1.0111.4121.500
experimental1.0151.421.519
Bond
Angle
calculated105.9°93.7°92.8°
experimental106.6°93.8°91.83°

Interestingly, as the central atom is changed from nitrogen to phosphorus to arsenic, the hybrid orbitals for bonding have increasing p character and less s character, resulting in more directional orbitals. Conversely, the lone pair is accommodated in a hybrid orbital has has increasing s character, decreasing p character. The implications for the molecular geometry are that the bond angles become closer to 90° (the bond angle for pure p character) and the lone pair occupies an increasingly large amount of space. This behavior is actually plausible when one considers the small size of the hydrogen atom (and hence bonds to it) and the fact that P and As are appreciably larger than N. The molecular geometries are all trigonal pyramidal, but the bond angles narrow considerably for the large As atom, as shown by the space-filling structures below.

ammonia

H-N-H Bond Angle: 106.6°
phosphine

H-P-H Bond Angle: 93.8°
arsine

H-As-H Bond Angle: 91.83°

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