Valence-bond theory of compounds of transition metals

1976

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confidence: 99%

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Angles between orthogonal spd bond orbitals with maximum strength

1976

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“…Sci. USA 74 (1977) in organic chemistry, with the increased complexity associated with the increase from quadricovalence to enneacovalence and from one stable bond angle' the tetrahedral angle 109.470, to two, the best spd angles 73.150 and 133.62° (2,3). Application of the theory should accelerate progress in the transition-metal field.…”

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confidence: 99%

Structure of transition-metal cluster compounds: Use of an additional orbital resulting from the f, g character of spd bond orbitals

1977

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A general theory of the structure of complexes of the transition metals is developed on the basis of the enneacovalence of the metals and the requirements of the electroneutrality principle. An extra orbital may be provided through the small but not negligible amount of fand g character of spd bond orbitals, and an extra electron or electron air may be accepted in this orbital for a single metal or a c uster to neutralize the positive electric charge resulting from the partial ionic character of the bonds with ligands, suc-h as the carbonyl group. Examples of cluster compounds of cobalt, ruthenium, rhodium, osmium, and gold are discussed. The composition and structure of a great many compounds of transition metals correspond well to the assumption that transition-metal atoms can use their set of nine hybrid sp3d5 bond orbitals in forming bonds (1-4). For example, cobalt has nine outer electrons and accordingly can form nine bonds, as in the molecule hydridotetracarbonylcobalt, HCo(CO)4, in which a single bond is formed with a hydrogen atom and double bonds are formed with each of the four carbon atoms. Another example is the enneahydridorhenate anion, [ReHg]2-, in which the rhenium atom, which has increased its number of valence electrons from 7 to 9 by transfer of 2 from an electropositive metal (potassium in K2ReHg), forms single bonds with each of 9 hydrogen atoms. A few complexes are known, however, for which the composition and structure indicate that an additional stable orbital, which can serve as a bond orbital, is present. The explanation of this deviation from the predictions of the simple hybrid-orbital theory of chemical bonds has not been obvious. I have now found that consideration of the f, and to some extent the g, character of spd bond orbitals leads to the conclusion that some transition-metal atoms or clusters of them are provided with an additional bond orbital by the release of some spd character through the contribution of a small amount of f and g character by the relatively unstablef and g orbitals. Hybrid bond orbitalsIn the simple theory of hybrid bond orbitals (5, 6) the bond strength S, equal to the value of the angular part of the wave function in the bond direction, is taken as a measure of the bond-forming power of the orbital. The values of S for the best hybrid sp, spd, and spdf bond orbitals are 2, 3, and 4, respectively. The carbon atom is usually described as forming bonds in the four tetrahedral directions by using a set of four best Sp3 bond orbitals, each with strength 2. It has been pointed out, however, that the bond orbitals have some d and f character,The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked "advertisement" in accordance with 18 U. S. C. §1734 solely to indicate this fact. estimated at about 4 and 2%, respectively, which increases the value of S to about 2.76, thus making the bonds significantly stronger (ref. 6, p. 126). The spectral term values for potassium, rub...

“…According to the simple theory of hybrid bond orbitals, in which only the angular dependence of the orbitals is taken into account, the strongest spd single bonds can be formed at angles 73.150 and 133.620 (1)(2)(3)(4). The favored angles between a double bond and a single bond or between a pair of double bonds can be found from these angles by assuming the axis of a double bond to lie midway between the axes of the two single bonds that by bending constitute the double bond.…”

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

1978

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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]