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

By I. Prigogine, Stuart A. Rice

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

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Extra resources for Advances in Chemical Physics, Vol.125 (Wiley 2003)

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Kato [97] showed that these series have a nonzero radius of convergence. This radius is determined by the distance from the origin to the nearest singularity in the complex plane là . The study of the radius of convergence, là , and whether or not this is the same as the critical value of lc , has a long history with controversial results [98–101]. Recently, Morgan and co-workers [102] have performed a 401-order perturbation calculation to resolve this controversy over the radius of convergence of the l ¼ 1=Z expansion for the ground-state energy.

15. The crossing points between two different sizes N and N þ 1 give a series for flðNÞ g. By systematically increasing the order N, one can reach a critical point lc ¼ 1:2286 Æ 0:0005. Here lc and the error are estimated using the final minimum and maximum values and their difference over 48 < N < 60. This value is in agreement with the calculation using the first-order method [11]. For the critical exponent a, starting from the series faðNÞ ðlÞg and following the direct approach of finite-size scaling Eq.

The ratio between the ground-state energy and the second lowest eigenvalue of the two-electron atom raised to a power N as a function of l for N ¼ 6; 7; . . ; 13. As expected, the second derivative will develop a delta-function-like behavior as N is getting larger, as shown in Fig. 8c. The behavior of the ground-state energy and its first and second derivatives resembles the behavior of the free energy at a first-order phase transition. For the two-electron atoms, when l < lc the nuclear charge is large enough to bind two electrons; this situation remains until the system reaches a critical point lc , which is the maximum value of l for which the Hamiltonian has a bound state or the minimum charge necessary to bind two electrons.

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