Directed Valence in P4 and As4

It has been reported that three best spd hybrid bond orbitals may be constructed at mutual angles of 73°9′ and 133°37′, but these bond orbitals have not been adapted to actual molecules. We can obtain trigonal pyramid bond orbitals which have mutual angles of 73°9′ and strength 3. When an angle between the directions of three equivalent bond orbitals is introduced as a parameter to these bond functions, variation of strength of these bond orbitals with the angle may be illustrated. These hybrid bond orbitals may be adapted to P4 and As4. It is reported that P4 and As4 molecules have bond angle 60°, the four atoms lying at the tetrahedron corners and the bonds along the tetrahedron edges. Hultgren has applied pd hybrid bond orbitals to such a configuration. Assuming that the s orbital is used in hybridization, we can obtain stronger bond orbitals than that by pd hybridization. Such spd trigonal pyramid bond orbitals have strength 2.970 (only slightly less than that of the best spd hybrid bond orbital) at bond angle 60°. It seems to be more probable that spd hybrid orbitals are used in the bond formation in P4 and As4 molecules; the unshared pair occupies the fourth hybrid orbital (containing all of the residual s parts) which has 76.5 percent s character at bond angle 60°.