一般化杂化轨函及夹角公式

CENERALIZED HYBRID ORBITAL AND ITS ABGLE FORMULA

量子力学应用到化学键方面最重要的成就之一就是从理论上说明键的角度和强度。作为现代化学键理论的一个重要组成部分,杂化轨道理论在阐明分子构型,成键性质及分子物性方面的成就是众所周知的。然而,迄今为止我们只见到了含f轨道的夹角公式,且缺少诸种杂化轨函之间关系的统一表达式,本文将讨论包括任意原子轨道在内的杂化轨道的一般化键函数和夹角公式。关于杂化键的强度问题,已另文专述。

According to the addation theorem of Legendre function and orthorgonality of the orbitals, ge neralized hybrid orbitals and their angle formula can be obtaied conveniently. The method of con- struction and the angle formula have been unified and generalized. It is shown that after an operation of rotational transformation, γ'(γ, θ',φ')-->γ'(γ, θ', φ') , the generalized hybrid orbital ψ_k=sum from l=0 to K((α_l)^(1/2)ψ_(nlo)), K=l_(max) has been transformed into ψ_k'=sum from l=0 to K sum from μ=0 to (?)(α_l/2l+1)A_l^(μ)(θ, φ)ψ_(nl)^(μ)(γ, θ, φ) where A_l^(μ) (θ, φ) is the angular function bormalized to 4π, the angle between ψ_k and ψ_k is 0 Then, the angle formula can be deduced as follows, or sum from l=0 to K (P_l (osθ)α_l=0 (equal-hybridization) sum from l=0 to K (P_l (Cosθ)(α_lα_l')^(1/2)=0 (unequal-hybridization).