三中心エネルギー積分に関する研究I
1953 年 1953 巻 69 号 p. 205-216
詳細
1953 年 1953 巻 69 号 p. 205-216
The formula for the one-electron three-center molecular integral may be written
Kc;AB=∫xa(1) 1/rc1xb(1) dτ1≡ (xa|1/rc1|xb)
Using the slater-type as the AO's and expressing in terms of the fixed elliptical coordinates (ξc, ηc and φc) of the center C and the coordinates (ξ, η, φ) of the electron, in the conventional manner by the Neumann expansion, we obtain as follows.
Kc;AB=C∑Dτνw°njGντ (j : β) Rντ (n, α : ξc) Pντ (ηc) cosνφc sinνφc
where Gντ (j : β) =∫1-1ηje-ρηPντ (η) (1-η2) ν/2dη
Rντ (n, α : ξc) =∫∞1Qντ (ξ+) Pντ (ξ-) ξne-αξ (ξ2-1)ν/2dξ
(defined as Mτ (ξc, n, α) by H.Eyring)
R0τ (n, α : 1) =fτ (n, α)
(values tabulated by Prof.Kotani)
C=a constant
