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Automatic computer procedure for generating exact and analytical kinetic energy operators based on the polyspherical approach
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10.1063/1.3675163
/content/aip/journal/jcp/136/3/10.1063/1.3675163
http://aip.metastore.ingenta.com/content/aip/journal/jcp/136/3/10.1063/1.3675163

Figures

Image of FIG. 1.
FIG. 1.

Representation scheme of a system, S BF = S 1, containing two subsystems, S j, 1S 1, j = 1, 2. According to the notation discussed below, F(1) is the global BF frame attached to the system, S 1. It is oriented with respect to the space-fixed frame, SF. We have assumed that F(1) is defined such that the -axis and the half plane are parallel to the vectors, and , respectively.

Image of FIG. 2.
FIG. 2.

Case 1: . Since is not involved in the definition of the F(r)-frame, the orientation F(j, r) with respect to F(r)-frame is characterized by two Euler angles.

Image of FIG. 3.
FIG. 3.

Case 2: The vectors and are chosen to define the F(j, r)-frame. Its orientation with respect to the F(r)-frame is characterized by the three Euler angles.

Image of FIG. 4.
FIG. 4.

Case 3: and the vector is involved in the definition of the F (r)-frame. In such situation, the orientation is characterized by one Euler angle.

Image of FIG. 5.
FIG. 5.

(Case 4: Orientation of the F(1, r)-frame with respect to the F(r)-frame when the vector is involved in the definition of the F(r)-frame and . The orientation is characterized by the two Euler angles.

Image of FIG. 6.
FIG. 6.

Characterization by the spherical angles of a vector which is not involved in the definition of the F(j, r)-frame as described by Case 4.

Image of FIG. 7.
FIG. 7.

Representation scheme of the mass-matrix M associated with parametrization shown in Fig. 1.

Image of FIG. 8.
FIG. 8.

Computation scheme of for a given subsystem S j, r . It is assumed that all are already computed by the same procedure. The total KEO is computed from the recursion equation, Eq. (20). The mass-matrix M is computed from TNUM.18

Image of FIG. 9.
FIG. 9.

Examples of parametrization of the HONO molecule with Jacobi vectors (a) and with valence vectors (b).

Image of FIG. 10.
FIG. 10.

Parametrization of H2CCH2 molecule with Valence vectors.

Image of FIG. 11.
FIG. 11.

Parametrization of the benzopyran molecule in terms of subsystems (upper graph) and in terms of vectors (lower graph).

Image of FIG. 12.
FIG. 12.

Mixed Jacobi/Valence vectors to parametrize the water protonated dimmer.

Tables

Generic image for table
Table I.

Numerical values of the coefficients C i , i = 1, …, 5, of the analytical expression given in Eq. (30).

Generic image for table
Table II.

Numerical values of the coefficients C i , i = 1, …, 9, of the analytical form shown in Eq. (31).

Generic image for table
Table III.

Numerical values of the coefficients C i of Eq. (B1) that corresponds to the analytical expression of the KEO of the HONO molecule in a non-orthogonal parametrization.

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/content/aip/journal/jcp/136/3/10.1063/1.3675163
2012-01-17
2014-04-25
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Automatic computer procedure for generating exact and analytical kinetic energy operators based on the polyspherical approach
http://aip.metastore.ingenta.com/content/aip/journal/jcp/136/3/10.1063/1.3675163
10.1063/1.3675163
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