Diagonal-corrected vibrational

Romelt, J. (1983). Prediction and interpretation of collinear reactive scattering resonances by the diagonal corrected vibrational adiabatic hyperspherical model, Chem. Phys. 79, 197-209. 

To clarify these questions we have studied the quantal and semiclassical theory of reactive resonances. In section II the Diagonal corrected Vibrational Adiabatic Hyperspherical (DIVAH) model 21, ) is reviewed. This theory was the first to provide quantitative predictions (with a typical accuracy of 0.1 kcal/mole) of collinear quantal resonance energies. Furthermore the DIVAH model led us to the new and very surprising phenomenon of vibrationally bonded molecules (29-41). The connection and interrelation with semiclassical RPO theory (25.30.42-47) which predicted and interpreted these results, is presented in section III. Having... 

Romelt [19,20] has prcsented an approximate method called the Diagonal corrected Vibrational Adiabatic Hypersi erical (DFVAH) model. In the DIVAH model all but the diagonal terms of P and Q are ignored. Now the coupled equations in Eq. (13) become a set of n uncoupled equations ... 

In the Bom-Oppenheimer picture the nuclei move on a potential energy surface (PES) which is a solution to the electronic Schrodinger equation. The PES is independent of the nuclear masses (i.e. it is the same for isotopic molecules), this is not the case when working in the adiabatic approximation since the diagonal correction (and mass polarization) depends on the nuclear masses. Solution of (3.16) for the nuclear wave function leads to energy levels for molecular vibrations (Section 13.1) and rotations, which in turn are the fundamentals for many forms of spectroscopy, such as IR, Raman, microwave etc. 

There have been a few recent studies of the corrections due to nuclear motion to the electronic diagonal polarizability (a ) of LiH. Bishop et al. [92] calculated vibrational and rotational contributions to the polarizability. They found for the ground state (v = 0, the state studied here) that the vibrational contribution is 0.923 a.u. Papadopoulos et al. [88] use the perturbation method to find a corrected value of 28.93 a.u. including a vibrational component of 1.7 a.u. Jonsson et al. [91] used cubic response functions to find a corrected value for of 28.26 a.u., including a vibrational contribution of 1.37 a.u. In all cases, the vibrational contribution is approximately 3% of the total polarizability. 

The results for the non-BO diagonal polarizability are shown in Table XIII. Our best—and, as it seems, well-converged—value of a, 29.57 a.u., calculated with a 244-term wave function, is slightly larger than the previously obtained corrected electronic values, 28.93 and 28.26 a.u. [88,91]. It is believed that the non-BO correction to the polarizability will be positive and on the order of less than 1 a.u. [92], but it is not possible to say if the difference between the value obtained in this work and the previous values for polarizability are due to this effect or to other effects, such as the basis set incompleteness in the BO calculations. An effective way of testing this would be to perform BO calculations of the electronic and vibrational components of polarizability using an extended, well-optimized set of explicitly correlated Gaussian functions. This type of calculation is outside of our current research interests and is quite expensive. It may become a possibility in the future. As such, we would like the polarizability value of 29.57 a.u. obtained in this work to serve as a standard for non-BO polarizability of LiH. 

The adiabatic correction is not always necessarily large. Consider the Cl+HCl- CIH+Cl exchange reaction on the extended LEPS surface of Ref. ( ). The coupling of the vibrational states is small, the adiabatic correction minor and the reaction proceeds nearly adiabatically. This statement can be easily verified from the reaction probabilities displayed in Fig. 3. The off-diagonal probabilities are small compared to the diagonal ones. Also the signature of resonance states in the th adiabatic surface U (r) is most noticeable in the Pp (E) or reaction probabilities... 

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