Interbond coupling

Summary of interbond couplings in linear tetratomic molecules... 

In the LM model, molecular vibrations are treated as motions of individual anharmonic bonds [38] (usually Morse oscillators). They therefore include anharmonicity, but not coupling between bonds, thus requiring inclusion of interbond coupling for obtaining a better description. For the case of t identical Morse oscillators, the energy levels related to the LM Hamiltonian are given by... 

Consider first = < 4 H Xi - Let one of the bond orbitals from the Bloch sum for the wave function on the right be the orbital labelled 3 in the center of Fig. 6-2. There arc then matrix elements with nearest-neighbor bonds of type 4 lying above and below the central orbital 3 in the figure, and both of these have phase factors e" the same as the phase factor for the central orbital (that is, for this choice of wave number). One is coupled through an atom of type A and one through an atom of type C we call these interbond matrix elements B and respectively. Thus if we retain only nearest-neighbor matrix elements, we obtain immediately... 

The geometrical structure of gaseous PH2 in its X Ai ground state appears to be similar to that of ground-state PH2 (with an internuclear distance of r=1.42 A and an interbond angle of a = 92° see p. 72). This was inferred from a sharp increase of the photodetachment cross section at threshold, measured by ion cyclotron resonance [2, 3] and from the predominance of the (0, 0, 0)<-(0, 0, 0) transition in the PH2, X Bi PH, X A photoelectron spectrum [4]. r=1.34 0.05 A and a = 92 5 were taken from the isoelectronic H2S molecule (and used to calculate the thermodynamic functions of PH, see p. 109) [5]. r and a have also been theoretically calculated by several ab initio MO methods, i.e., at an MP2 [6, 7], a CEPA (coupled electron pair approximation) [8], and an HF level [9 to 15]. r was also obtained from a united-atom approximation [16] a was also calculated by a semiempirical (CNDO/2) method [17] and estimated by extended Huckel calculations [18]. 

Finally, a few comments shall be made on the concept of local modes as compared to normal modes [3,33-35], The main idea of the local mode model is to treat a molecule as if it were made up of a set of equivalent diatomic oscillators, and the reason for the local mode behavior at high energy (>8000 cm ) may be understood qualitatively as follows. As the stretching vibrations are excited to high energy levels, the anharmonicity term / vq (Equation (2.9)) tends, in certain cases, to overrule the effect of interbond coupling and the vibrations become uncoupled vibrations and occur as local modes. ... 

From an extension of the ideas presented above for V(P-P), we may expect a coupling V(P-E-P) to depend on the oxidation states of the phosphorus atoms, the electronegativity and steric bulk of their substituents, and the degree of rotation about the P-E bonds. Any n bonding between P and E and the interbond angles at E could also be important. The most extensively studied case is where E = N. ° ... 

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