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Eckart constraint

A new trajectory with coordinates Y,- - - 8Y, j j then satisfies the Eckart constraints. [Pg.395]

There are 3N + 7 coordinates on the right sides of Eq. (3.4), Le., the 3N vibrational displacements the three coordinates of the center of mass, the three Euler angles 0, x and the angle p. Since there are 3N coordinates/ /a (i = 1,2,.., N ot=x,y, z) on the left sides of Eq. (3.4), the 3N vibrational displacements are subject to seven constraint equations which further specify the molecule-fixed axis system. We shall use the following set of Eckart and Sayvetz conditions for these constraint equations ... [Pg.66]

Let the n 1 three-dimensional vectors zSi (i = 1,1) be the mass-weighted Jacobi vectors for a reference molecular configuration. The reference configuration is usually set to be a local equilibrium structure of the molecule oriented to a certain orientation. The Eckart subspace is defined as a (3n — 6)-dimensional subspace in the (3n — 3)-dimensional translation-reduced configuration space, which is parameterized by Jacobi vectors pf (/ = 1,..., m - 1) with three additional constraint conditions called the Eckart conditions,... [Pg.107]

The vibration-rotation interaction is the effect arising from coupling terms between angular and vibrational momenta as well as from the dependence of the rotational G-matrix elements (the /u-tensor) on the internal coordinates. The importance of this effect may to some extent be reduced provided an appropriate axis convention is used. The axis convention is the set of rules defining the orientation of the molecular axes, eg, g = x,y, z, relative to an arbitrary configuration as given by the position vectors, Ra, a. = 1, 2,... N. These rules can be expressed in three relations between the rag components, similar to the center of mass conditions(2.4). We shall refer to these relations as the axial constraints . Usually Eckart-condi-tions39 are imposed, but other possibilities may be considered. [Pg.103]

The two sets of rotational s-vectors are easily expressed using the corresponding constraint vectors of the Eckart conditions as described in Sect. 2.2.3.2.2,... [Pg.129]

As rotational constraints we retain the three Eckart conditions and the corresponding constraint vectors [Eq. (2.68) or (3.35)], here depending on p. These constraints have been discussed by Hougen17) as well. [Pg.134]

The function = (6S/SY,) depends on the distances (Eq. [32]), which are computed as norms in Cartesian space. Therefore, it is important to remove overall translations and rotations from the structures along the trajectory, which can be done by imposing linear constraints using the Eckart conditions ... [Pg.395]

These constraints secure that the motion is described relative to the center of mass of the system. The next three constraints are due to Eckart ... [Pg.1597]

The Eckart Sayvetz conditions imply that, if during the vibration a small translation of the center of masses is invoked, the origin of the Cartesian reference system is displaced so that no linear momentum is produced. The second Sayvetz condition, expressed in the last diree equations of (2.8), imposes the constraint that, during vibrational displacements, no angular momentum is produced. Eq. (2.8) implies that the reference Cartesian system translates and rotates with the molecule in such a way that the displacement coordinates Ax, Ay and Az reflect pure vibrational distortions. It is evident that through Eq. (2.8) certain mass-dependency is imposed on the atomic Cartesian displacement coordinates. [Pg.30]


See other pages where Eckart constraint is mentioned: [Pg.503]    [Pg.611]    [Pg.611]    [Pg.1597]    [Pg.503]    [Pg.611]    [Pg.611]    [Pg.1597]    [Pg.2349]    [Pg.335]    [Pg.134]    [Pg.2349]    [Pg.26]    [Pg.335]    [Pg.136]    [Pg.85]   
See also in sourсe #XX -- [ Pg.395 ]




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