Confining potential anharmonicity

The anharmonicity of the confining potential can be controlled by changing the depth of the Gaussian potential D with respect to >z and ojxy, respectively. The parameters coz and coxy represent the frequency of the harmonic-oscillator potential characterizing the strength of confinement of... 

Introducing anharmonicity is important for simulating realistic confining potentials [23,24]. 

In infrared spectroscopy of diatomic molecules, the vibrational motion is generally limited to the first two vibrational states of a diatomic molecule whereby the displacement of the bond is near the minimum (i.e. small values of s). As a result, it is reasonable as a first approximation to confine the anharmonicity to the third order term of Equation 6-37. The potential can be represented by a third order polynomial such that the first term is the same as in the harmonic oscillator model problem. 

The anharmonic modes for both the a symmetric and 67 asymmetric CH stretching vibrations have been explored. In order to perform a reasonable anharmonic treatment, we had to take into account the stretching of the bonds to larger elongations than for the harmonic description where displacements can be confined close to the equilibrium geometry. Consequently, correlation effects were included in the determination of the potential surface. The electronic calculations were carried out at the MP2 level, which insures a good description of the CH bond potential towards dissociation. A double zeta... 

In principle, one can induce and control unimolecular reactions directly in the electronic ground state via intense IR fields. Note that this resembles traditional thermal unimolecular reactions, in the sense that the dynamics is confined to the electronic ground state. High intensities are typically required in order to climb up the vibrational ladder and induce bond breaking (or isomerization). The dissociation probability is substantially enhanced when the frequency of the field is time dependent, i.e., the frequency must decrease as a function of time in order to accommodate the anharmonicity of the potential. Selective bond breaking in polyatomic molecules is, in addition, complicated by the fact that the dynamics in various bond-stretching coordinates is coupled due to anharmonic terms in the potential. 

The anharmonic potential energy is usually easier to represent in internal coordinates than in normal mode coordinates. However, what restricts the use of internal coordinates is the complicated expression for the vibrational/rotational kinetic energy in these coordinates (Pickett, 1972). It is difficult to write a general expression for the vibrational/rotational kinetic energy in internal coordinates and, instead, one usually considers Hamiltonians for specific molecules. For a bent triatomic molecule confined to rotate in a plane, the internal coordinate Hamiltonian is (Blais and Bunker, 1962) ... 

In Section 10.3.4, the dynamics were treated of two harmonically-confined ions having small amplitudes of oscillation around the equilibrium positions of the ions. More specifically, in deriving Equations 10.10 and 10.13 (for z = zjit was assumed that the change of the ion distance is small compared to the equilibrium distance Az, such that the Coulomb interaction energy can be approximated by a harmonic potential. For large changes in the ion-ion distance, additional terms in the Coulomb energy lead to an anharmonic interaction and, hence, to an amplitude-dependent oscillation frequency. 

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