Eckart frame

From this expression one has to remove the center-of-mass motion. The corresponding Hamiltonian can then be rewritten in terms of the intrinsic variables and the Euler angles. The general form of the Hamiltonian operator is, in the Eckart frame,1... 

Rotation-Vibration Motion of Pyramidal XY3 Molecules Described in the Eckart Frame The Calculation of Intensities with Application to NH3... 

D. The Suppressing Effect of the Gauge Field Associated with the Eckart Frame VI. Concluding Remarks... 

The Eckart frame with respect to the reference configuration zSI for an arbitrary configuration psi is given by a proper rotation matrix R C SO(3) that satisfies... 

The rigorous dynamics in the internal space can be represented even in terms of the normal-mode coordinates by taking an appropriate account of in Eq. (11). Since / (v = S (v for the Eckart frame, Eq. (11) is written as... 

In Section IV, we have demonstrated that the gauge field associated with the Eckart frame has an effect of suppressing the reaction rate of M3. Here, we confirm that this suppressing effect is general and can be observed in the four-atom cluster M4. The total angular momentum of the system is again zero. 

The effect of the gauge field associated with the Eckart frame to suppress the reaction rate seems to be more general than is valid for M3 and M4. Indeed we have confirmed the similar effect of the gauge field in the isomerization... 

H. Wei and T. Carrington, Jr., The triatomic Eckart-frame kinetic energy operator in bond coordinates. J. Chem. Phys. 107, 9493-9501 (1997). 

The matrices x° and A° are the equilibrium values of these matrices. It should be noted that in an Eckart frame A° = 0. Moreover, if the Eckart frame corresponds to the principal axis frame in the equilibrium configuration, then Hr takes the familiar form of a Hamiltonian for rigid-body motion ... 

With the above approach we can combine the use of curvilinear normal coordinates with the Eckart frame. When we do so, the harmonic oscillator, rigid rotor, and, to lowest order, the Coriolis and centrifugal coupling contributions to H have exactly the same form as those found for the more commonly used Watson Hamiltonian (58). 

The meaning of the v) JKM) functions is different for different choices of the molecule-fixed (MF) frame and the size of the required basis depends on the definition of the MF frame. For many molecules an Eckart frame, designed to minimize Coriolis coupling close to a reference configmation, is a good choice. When normal coordinates are used it is easy to use an Eckart frame [1, 61], however, the Eckart... 

There exists a moving frame, called the Eckart frame, relative to which the molecule moves without rotation, but the frame depends on a choice of the molecular motion and is not unique for any molecular configuration. For this reason, the Eckart frame is not suitable for describing motions of a nonrigid molecule (Ref.69). 

We accomplished this by assigning the zero rotational angular momentum part of the Coriolis Hamiltonian (expressed in the usual Eckart frame) to the vibrational Hamiltonian and the remainder to the rotational Hamiltonian. This partitioning causes some variations in both vibrational and rotational energies with time, but test calculations indicate that this time dependence is usually weak. 

Gabriel et al. [35] computed ab initio DMSs of H2O with highly correlated coupled electron pair CEPA-1 method, which were then represented by polynomials as in Eq. (31) using the Eckart-frame. Based on these DMSs absorption band and line intensities at 298 K were computed, which showed good agreement with experiment. The very good quality of these DMSs demonstrated was shown later by Lynasgray et al. [36]. 

Eckart frame [53]. Here i =1,2 labels the outer oxygen atoms Oi and O2, with O3 as the central atom. Because of the symmetry of the dipole moment components the expansion coefficients satisfy and D... 

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