A Model 2D Hamiltonian

The 2D model of the linear B- -H-A fragment, assuming a strong coupling between the proton (AH stretch) and low-frequency (B- -A stretch) coordinates, was introduced by Stepanov [9, 10]. It seems to be the simplest model enabling one to interpret the different specific features of H-bonded systems [11-16]. In terms of this model, the vibrational wave function of the H-bonded system is written as 

Here N is the number of degrees of freedom j q is a harmonic wave function, and P s,R) is the eigenfunction of the following 2D Hamiltonian  

Kinematic coupling is supposed to be nil and reduced masses are written as  

Here Mh, Ma and Mg stand for the mass of the corresponding particle. In the case of intramolecular H-bonds A and B may be treated as the terminal atoms, in the case of intermolecular H-bonds A and B may be considered as the heavy fragments. 

The 2D PES U(s,R) of the B -H-A fragment in a crystal can be obtained using DFT calculations with periodic boundary conditions (Section 9.3.2) or extracted from experimental data (Section 9.2.2). In the case of the model 2D PESs the equilibrium value of the B-A distance is usually defined by structural data. The barrier height along the proton coordinate Vq is the main control parameter whose variation allows one to reproduce the spectroscopic data. 

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