On the numerical evaluation of the Stokes’ stream function

Greenspan, Donald

doi:10.1090/s0025-5718-1957-0090128-3

Cited by 2 publications

(1 citation statement)

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“…It was shown previously that pairing is essential for a semiclassical, dynamical simulation of H, [20]. To test the importance of pairing in the present study, we ran the second example of Section 5 but without pairing for 2 billion time steps.…”

Section: Remarksmentioning

confidence: 98%

A semiclassical, dynamical model of the water molecule

Greenspan

1996

Phys. Scr.

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A model of the ground state water molecule is formulated dynamically and studied by computer simulations. Excellent approximations of NMR determined bond angles and bond lengths are achieved through electron pairing and simulation of ice f. l. Introduction. The past 75 years has seen an immense amount of research directed at the most fundamental molecule in living matter, the water molecule (1-3). And yet, from both the classical and quanhrm mechanical points of view, msny fundamentd questions reurain unanswered (1-1). For a single water molecule, only static models are available, and thesc include those of Bader; Bernal; Duncan and Pople; Ellison and Shull; Gllespie; Heath and Linnett; Rowlinson; and Vernay (1'5'6)' Since a dynamical simulation of the water molecule quantum mechanically would require the exact or approximate solution of Schrodingels equation for a wave function in 39 space dimensions and one time dimensioq we will begn more simply in this paper by studying a semiclassical model. The keys to our excellent results will be the introduction of electron pairing and the use of a crystalline state. 2. General Model Formulation. Consider a ground state water molecule M1 t'hose o)ryg€n rucleus is denoted by 0r. l*t M2, Ms, Mt, Mb, with respective orygen rrue'lei &, Q,0r,0r, bc fotr neighboring molecules of Mt. Aselme tlnt Mr-Msar€ water molecules in ice f, thus allowing us to avoid the complex motions of the {gya state urd allowing the introduction of available experimental rezults into the model (r'r'7). For the crystal structure of ice I., we assume that 02-0s are at the vertices of a regular tetrahedron with 0r at the centroid as shown in Figure 2.1. In each Mi, let the ttro nyatogen nuclei be H;i, i-!,2, g, 4, 5; i = 1, 2. Experimentally (lp'3'7)' the-rr" the distance from 0r to each of 02, 0s, 01, 0r is 2.?6 A and on each line joining 01 to 02, 03, 0r, 0r there is oractly one H6, one possible srch arrangement being that shown in ltigure 2.t. It will be important to recall that the ground state enerry E of Mlit (8'e'10) E-(3333.04)10-12erg.

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Section: Remarksmentioning

confidence: 98%