Representation scheme of a system, S BF = S 1, containing two subsystems, S j, 1 ⊂ S 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.
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.
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.
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.
(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.
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.
Representation scheme of the mass-matrix M associated with parametrization shown in Fig. 1.
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
Examples of parametrization of the HONO molecule with Jacobi vectors (a) and with valence vectors (b).
Parametrization of H2CCH2 molecule with Valence vectors.
Parametrization of the benzopyran molecule in terms of subsystems (upper graph) and in terms of vectors (lower graph).
Mixed Jacobi/Valence vectors to parametrize the water protonated dimmer.
Numerical values of the coefficients C i , i = 1, …, 5, of the analytical expression given in Eq. (30).
Numerical values of the coefficients C i , i = 1, …, 9, of the analytical form shown in Eq. (31).
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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