Physical Chemistry Third Edition

868 21 The Electronic Structure of Polyatomic Molecules

21.1 The BeH 2 Molecule and thespHybrid Orbitals

Beryllium hydride, BeH 2 , is the simplest triatomic molecule. This substance has

apparently not been shown experimentally to exist, but calculations indicate that it

should be a bound linear molecule with two equal Be–H bond distances. We assume

this equilibrium conformation and apply the Born–Oppenheimer approximation. We

place the molecule in a Cartesian coordinate system with the Be atom at the origin and

with the H atoms on thezaxis, as shown in Figure 21.1. We denote one of the H atoms

by Haand the other by Hb. The molecule possesses the same symmetry operations as

H+ 2 :E,i,σh,C∞z, and infinitely manyσvandC 2 operations perpendicular to the bond

axis.

We seek a wave function that is a product of LCAOMOs. Table 21.1 shows the

first three optimized LCAOMOs from a Hartree–Fock–Roothaan calculation using a

minimal basis set of Slater-type orbitals: 1s,2s, and 2pzon the Be atom and the two 1s

orbitals on the hydrogens. The six basis functions give six independent LCAOMOs, but

y

Hb

Be

z

x

Ha

Figure 21.1 The BeH 2 molecule.

Table 21.1 Results of a Hartree–Fock–Roothaan Calculation for the BeH 2

Ground-State at a Be–H Bond Distance of 134 pm

MO c 1 sBe c 2 sBe c 2 pzBe c 1 sHa c 1 sHb

1 σg 0.99718 0.01597 0.00000 − 0. 00163 − 0. 00163

2 σg 0.17095 − 0. 40852 0.00000 0.45033 0.45033

3 σu 0.00000 0.00000 0.44253 0.44126 − 0. 44126

From R. G. A. R. Maclagan and G. W. Schnuelle,J. Chem. Phys., 55 , 5431 (1971).