Anharmonicity corrections from Coriolis coupling constants

Ananthakrishnan, T. R.; Aruldhas, G.

doi:10.1071/ch9752727

Aust. J. Chem.

1975

DOI: 10.1071/ch9752727

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Anharmonicity corrections from Coriolis coupling constants

T. R. Ananthakrishnan¹,

G. Aruldhas²

Abstract: A new method is suggested for calculating the ratios of harmonic frequencies for certain types of molecules and their isotopic forms by making use of Coriolis coupling constants. The method applies to cases where there are two distinct degenerate vibrations with the same species. The anharmonicity constants for these vibrations can then be evaluated.

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“…As an illustration, the method is applied to XY 2 bend symmetric systems. A parametric approach developed by Ananthakrishnan et al [3][4][5][6] to analyse vibrational problems in molecules basically involves splitting up of the L matrix into the form…”

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confidence: 99%

Dependence of Potential Energy on Inter-bond Angles in Simple Molecules

Indira¹,

Warier

Ananthakrishnan³

et al. 1992

Zeitschrift Für Naturforschung A

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A method is developed to investigate the variation of potential energy contributions (F stretch , F bend , ^stretch-bend an d Ktretch-stretch) > n simple molecules when their inter-bond angles 6 are varied arbitrarily. Applied to XY 2 bend symmetric systems, the V-6 plots suggest that the actual equilibrium configuration in these molecules lies in the premises of minimum F bend and zero F stretch . bend .In terms of internal symmetry coordinates, the average potential energy of a vibrating molecule may be written as [1] <2 V)=ZF ij Z ij .(1)Here the matrices F and I define the intramolecular force field and the mean square amplitudes of vibration, respectively. They are given byThe elements A x and A i of the diagonal matrices A and A can easily be calculated from the values of the vibrational frequencies. The elements of the L matrix are significant in the sense that they relate the normal coordinates Q, to the internal symmetry coordinates S, in the form S = LQ. The evaluation of the L matrix is a basic problem in molecular dynamics, since one has to determine n 2 elements using the n vibrational frequencies as the input data. One most useful condition in this context has been provided by Wilson [2] as LL=G, (4) where G is the inverse kinetic energy matrix obtainable from the molecular geometry and atomic masses. Thus the potential energy of a vibrating molecule depends on its vibrational frequencies and geometry.It will be of fundamental interest to investigate the variation of the potential energy with the geometry of Reprint requests to Dr. M. K. R. Warier, Department of Physics, Maharajas College, Kochi 682011, Indien. a molecule since every molecule has its own preferential geometry for stability. A mathematical formalism for this kind of investigation is developed here. As an illustration, the method is applied to XY 2 bend symmetric systems. A parametric approach developed by to analyse vibrational problems in molecules basically involves splitting up of the L matrix into the formHere L 0 is written in the lower triangular form and is easily calculated using (4). C is an orthogonal matrix of the n(n -1)/2 parameters associated with each vibrational species of order n. Many simple molecules of types XY 2 bend symmetric, XY 3 planar, XY 3 pyramidal and XY 4 tetrahedral possess vibrational species of order n = 2, and in such cases the orthogonal matrix C of (5) can be written asAlong with (5), the invariance of the F matrix under isotopic substitution enables us to write (2) asHere the asterisk refers to the case after isotopic substitution. Since C^ is orthogonal,This reduces to a simple quadratic equation of the form pc 2 + qc + r = 0 .0932-0784 / 92 / 0600-781 $ 01.30/0. -Please order a reprint rather than making your own copy. Unauthenticated Download Date | 5/13/18 12:22 AM

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mentioning

confidence: 99%

Dependence of Potential Energy on Inter-bond Angles in Simple Molecules

Indira¹,

Warier

Ananthakrishnan³

et al. 1992

Zeitschrift Für Naturforschung A

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Use ofD J, DJK constants for the unique fixing of intramolecular forces inXY 3 pyramidal molecules

1977

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Anharmonicity corrections from Coriolis coupling constants

Cited by 2 publications

References 0 publications

Dependence of Potential Energy on Inter-bond Angles in Simple Molecules

Dependence of Potential Energy on Inter-bond Angles in Simple Molecules

Use ofD J, DJK constants for the unique fixing of intramolecular forces inXY 3 pyramidal molecules

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