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A stereographic projection path integral study of the coupling between the orientation and the bending degrees of freedom of water
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10.1063/1.2925681
/content/aip/journal/jcp/128/20/10.1063/1.2925681
http://aip.metastore.ingenta.com/content/aip/journal/jcp/128/20/10.1063/1.2925681
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

A sketch of the geometric definition of the two coordinates used to map the bending manifold . The stereographic projection is obtained by finding the intersection point between the line that originates at , passes through the point on the circle at , and the tangent line that lays perpendicular to the line between the center and .

Image of FIG. 2.
FIG. 2.

The ratio as a function of the bending SPC. is the square root of the determinant of the metric in , mapped by center of mass, orientation, and all internal DF coordinates. is the square root of the determinant of the metric over the manifold. The units of the ratio are those of mass. is convenient for the fast computation of , the classical Jacobian in simulations.

Image of FIG. 3.
FIG. 3.

The Riemann Cartan curvature scalar of the manifold as a function of the SPC [cf. Eq. (62)].

Image of FIG. 4.
FIG. 4.

Graph of as a function of the SPC .

Image of FIG. 5.
FIG. 5.

Value of in the manifold [classical (white circles), quantum (white squares) labeled as “rigid”] compared to the values of computed with the manifold [classical , quantum ]. The quantum values are obtained with in both cases.

Image of FIG. 6.
FIG. 6.

Values of , the intramolecular potential along the bending coordinate computed at several temperatures for various values of .

Image of FIG. 7.
FIG. 7.

Values of , the total energy computed at several temperatures for various values of .

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/content/aip/journal/jcp/128/20/10.1063/1.2925681
2008-05-27
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: A stereographic projection path integral study of the coupling between the orientation and the bending degrees of freedom of water
http://aip.metastore.ingenta.com/content/aip/journal/jcp/128/20/10.1063/1.2925681
10.1063/1.2925681
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