Bond angles in transition-metal tricarbonyl compounds: A test of the theory of hybrid bond orbitals

Abstract

The theory of hybrid bond orbitals is used to calculate equations giving the value of the bond angle 0C M-CO in relation to the bond number of the metal-carbonyl bond for tricarbonyl groups in which the transition-metal atom is enneacovalent or octacovalent and the group has approximate trigonal symmetry. (3,5), the tetragonal antiprism with cap (3). and the trigonal prism with three lateral caps (3). For these structures the smaller bond angles usually lie in the range from 670 to 80°a nd the larger in the range from 120°to 1400. The prediction of bond angles is made somewhat uncertain because of this effect of the geometry of space. In the following discussion, except where noted, the axes of the bond orbitals are placed at the angle 73.15°with one another.The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked "advertisemnent" in accordance with 18 U. S. C. §1734 solely to indicate this fact.I consider groups M(CO)3 with a threefold axis. Three single bonds can be formed with bond angles all equal to 73.15°. In the three best arrangements of nine bonds the coordination polyhedrons have nearly equilateral triangles as most of their faces, and for these triangular faces, which would be appropriate to the M(CO)3 group, the average bond angle is 72.20.The difference between this value and the ideal value 73.150 suggests that the predicted values are uncertain by a degree or two.To make a calculation for three double bonds we need three more orbitals. These may be the three equatorial bonds of the trigonal prism with three caps; that is, with ) = 900 and k = 600, There is some uncertainty in the calculation of the bond angle for resonance of two single bonds and one double bond among the three positions (n = 1.33) or of one single bond and two double bonds (n = 1.67). For n = 1.5, however, there is no uncertainty; symmetry requirements fix the bond angle at 900. The three calculated points are shown in Fig. 1, together with a curve through them. This curve is given by the equation: Tricarbonyl bond angle (v = 9) = 73.150 + 38.70(n -1) -100(n-1)2 [1] in which v is covalence.For octacovalence a different equation is needed. From symmetry considerations we see that the OC-M-CO bond angle for M(CO)3 with three double bonds is the tetrahedral angle 109.470. The upper curve in Fig. 1 has been drawn as a straight line passing through the points for n = 1 and n = 2:Tricarbonyl bond angle (v = 8) = 73.150 + 36.30(n -1). [2]

Ionic Bonding, Partial Ionic Character, and Electronegativity

“…Thus, they assume C +4 tances in ionic crystals. 20 It will be shown that the theoretical radii account satisfactorily for the experimental results not only for normal crystals, but also for those deviating from additivity (through mutual contact of the anions or through the action of double repulsion), and that furthermore they permit the theoretical prediction of the relative stabilities of the fluorite and the rutile (and anatase) structure, and of the sodium chloride and the sphalerite (and wurzite) structure. The Alkali Halides.-In Table V are given the experimental interatomic distances for the alkali halides with the sodium chloride structure, together with the sum of the radii of Table II.…”

“…This requirement is fulfilled for the chloride, bromide and iodide of lithium. In Table VI are given radii 20 Huggins, who has particularly emphasized the fact that different atomic radii are required for different crystals, has recently [Phys. Rev., 28, 1086 (1926)] suggested a set of atomic radii based upon his ideas of the location of electrons in crystals.…”