Vibrational wave function interaction with rotation

The probability that J has a wave vector K relative to I in HD + is given by the momentum transform of the wave function for the vibrational and rotational interactions in HD +. The probability that I is captured by X with a wave vector k is given by the momentum transform of the wave function for the rotational and vibrational interactions in XI+. 

For a description of the induced transitions between rotovibrational levels vj) — v f) of H2, radial matrix elements, Eq. 4.17, are needed. Since the H-H interaction potential is well known, the vibrational wave-functions, (pVj(r), which depend on the rotational excitation j, can be computed with the help of digital computers [217], At fixed intermolecu-lar separations R, the AXt(r,R) are known at three vibrational spacings,... 

Wc). The initial wave function ) =, ) r) t) where the is the quantum number associated with the harmonic oscillator wave function for the strong molecular bond ( =i in fig. 10.7), is the rotational quantum number associated with the rotational wave function (not included in the one-dimensional picture of fig. 10.7), and is the quantum number associated with the vibrational wave function for the van der Waals bond ( Pv in fig. 10.7). A Morse potential is assumed for this latter interaction potential. For the final state, the wave function is f) = 4f) 7) t)> where f) is the quantum number associated with the final state of the strong bond ( I>v"=o fig- 10-7), the rotational quantum number, J, represents the rotational wave function (now a free... 

As we have suggested recently [68] the technique involving separation of the CM motion and representation of the wave function in terms of explicitly correlated gaussians is not only limited to non- adiabatic systems with coulombic interactions, but can also also extended to study assembles of particles interacting with different types of two- and multi-body potentials. In particular, with this approach one can calculate the vibration-rotation structure of molecules and clusters. In all these cases the wave function will be expanded as symmetry projected linear combinations of the explicitly correlated fa of eqn.(29) multiplied by an angular term, Y M. 

Our task is to find approximate solutions to the time-independent Schrodinger equation (Eq. (2)) subject to the Pauli antisymmetry constraints of many-electron wave functions. Once such an approximate solution has been obtained, we may extract from it information about the electronic system and go on to compute different molecular properties related to experimental observations. Usually, we must explore a range of nuclear configurations in our calculations to determine critical points of the potential energy surface, or to include the effects of vibrational and rotational motions on the calculated properties. For properties related to time-dependent perturbations (e.g., all interactions with radiation), we must determine the time development of the... 

The final form of the Born-Handy formula consists of three terms The first one represents the electron-vibrational interaction. I will not present the numerical details for H2, HD and D2 molecules here, it can be found in our previous work. The most important result here is that the electron-vibrational Hamiltonian is totally inadequate for the description of the adiabatic correction to the molecular groundstates its contribution differs almost in one decimal place from the real values acquired from the Born-Handy formula. In the case of concrete examples -H2, HD and D2 molecules - the first term contributes only with ca 20% of the total value. The dominant rest - 80% of the total contribution - depends of the electron-translational and electron-rotational interaction [22]. This interesting effect occurs on the one-particle level, and it justifies the use of one-determinant expansion of the wave function (28.2). Of course, we can calculate the corrections beyond the Hartree-Fock approximation by means of many-body perturbation theory, as it was done in our work [22], but at this moment it is irrelevant to further considerations. 

As for all the systems relegated to Section 2 the attenuation function for structural H2O in the microwave and far-infrared region, as well as that for free H2O, can be understood in terms of collision-broadened, equilibrium systems. While the average values of the relaxation times, distribution parameters, and the features of the far-infrared spectra for these systems clearly differ, the physical mechanisms descriptive of these interactions are consonant. The distribution of free and structural H2O molecules over molecular environments is different, and differs for the latter case with specific systems, as are the rotational dynamics which govern the relaxation responses and the quasi-lattice vibrational dynamics which determine the far-infrared spectrum. Evidence for resonant features in the attenuation function for structural H2O, which have sometimes been invoked (24-26,59) to play a role in the microwave and millimeter-wave region, is tenuous and unconvincing. 

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