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3). In the London description, a 1s orbital is centered on each of the three hydrogen atoms denoted by A, B, and C, respectively. This gives Slater determinants like 1sA α(1) 1sA α(2) 1sA α(3) 1 ψVB (1, 2, 3) = √ 1sB α(1) 1sB α(2) 1sB α(3) 3! 34) where all three electrons have identical spin in this example. There are 23 = 8 such Slater determinants, corresponding to the two possible spin states of each electron. The London equation for the three hydrogen atoms is based on a variational calculation that involves these eight electronic (spin) configurations.

Computer programs that solve this equation and that can locate saddle Fig. 5 A potential energy surface for a direct unimolecular reaction without a saddle point. The surface corresponds to a reaction like H2 O → H + OH for dissociation along a fixed bond angle, where only two internuclear coordinates are required in order to specify the configuration. ) Molecular electronic energies, analytical results 41 Fig. 6 Contour plot of the potential energy surface of Fig. 5. 5◦ and the inner contours correspond to the lowest energies.

C. T. Lee, J. Chem. Phys. 82, 3045 (1985) and M. Faubel, L. Rusin, S. Schlemmer, F. Sondermann, U. P. Toennies, J. Chem. Phys. 101, 2106 (1994)]. It is found that the total reaction cross-section increases with collision 3 The 4π indicates that integration is over the full unit sphere, dΩ = sin θdθdφ, with θ ∈ [0, π] and φ ∈ [0, 2π]. Cross-sections and rate constants 25 Fig. 2 A beam of molecules incident on a rectangle of area A. The ratio of the total cross-section (σR (ij, v|l)) to the area of the rectangle (A) is, according to Eq.

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A Guide To Entropy And The Second Law Of Thermodynamics (Princeton) by Jakob Yngvason, Elliott H.Lieb

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