Download Advances in Chemical Physics, Vol.125 (Wiley 2003) by I. Prigogine, Stuart A. Rice PDF

By I. Prigogine, Stuart A. Rice

Advances in Chemical Physics covers contemporary advances on the innovative of study relative to chemical physics. The sequence, Advances in Chemical Physics, presents a discussion board for severe, authoritative reviews of advances in each quarter of the self-discipline.

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Recently, there has been an ongoing experimental and theoretical search for doubly charged negative molecular dianions [12,127]. In contrast to atoms, large molecular systems can hold many extra electrons because the extra electrons can stay well-separated [128]. However, such systems are challenging from both theoretical and experimental points of view. Although several authors [129–132] have studied the problem of the stability of diatomic systems as a function of the two nuclear charges, Z1 and Z2 , there was no proof of the existence or absence of diatomic molecular dianions.

Critical charge parameters separating the regime of stable, metastable, and unstable binding were calculated using ab initio methods [134–137]. However, using the finite-size scaling approach, one can show that this critical charge is not a critical point [118]. But, without making use of the Born–Oppenheimer approximation the Hþ 2 -like system exhibits a critical point. For Hþ 2 -like systems, Eq. u. The ground-state eigenfunction can be expanded in the following basis set [138] Èðn;m;lÞ : Èðn;m;lÞ ðr1 ; r2 ; r12 Þ ¼ N0 fn ðxÞfm ðyÞfl ðzÞ ð92Þ finite-size scaling for atomic and molecular systems 47 where N0 is the normalization coefficient and fn ðxÞ is given in terms of Laguerre polynomials Ln ðxÞ: fn ðxÞ ¼ Ln ðxÞeÀx=2 ð93Þ The coordinates x; y; and z are expressed in the following perimetric coordinates [139]: y ðr1 þ r2 À r12 Þ kx y y ¼ ðÀr1 þ r2 þ r12 Þ ky y z ¼ ðr1 À r2 þ r12 Þ kz x¼ ð94Þ where kx ¼ 1 ¼ ky =2 ¼ kz =2 and y is an adjustable parameter that was chosen to be y ¼ 1:5.

Calculation of the critical charges for N-electron atoms is of fundamental importance in atomic physics since this will determine the minimum charge to bind N electrons. Already Kato [97] and Hunziker [124] show that an atom or ion has infinitely many discrete Rydberg states if Z > N À 1, and the results of Zhislin [125] show that a negative ion has only finitely many discrete states if Z N À 1. Because experiment has yet to find a stable doubly negative atomic ion, Morgan and co-workers [102] concluded that the critical charge obeys the finite-size scaling for atomic and molecular systems 45 following inequality: N À 2 Zc N À 1.

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