Hydrogen angular term

There is some debate over whether or not angular terms should be included in the potential. The three deviations from linearity that have been discussed involve the angle around the hydrogen atom (D-H...A 6), the angle around the hydrogen acceptor (H... A-R /, see Fig. 2.13) and the out-of-plane deformation around the acceptor A co, involving A, H and two selected atoms in the substituent R of... 

An important observation is that experimental structures may be reproduced satisfactorily with and without the angular terms involved in the hydrogen bonding interaction1481. Thus, irrespective of the fundamental reason for the deviation from linearity, the angular dependence may be modeled accurately either by van der Waals repulsion or by lone-pair directionality. 

There is some debate over whether or not angular terms should be included in the hydrogen-bonding potential. The three deviations from linearity that have been discussed involve the angle around the hydrogen atom (D 0), the angle... 

MM3(89). Contains an explicit hydrogen bond term but no angular terms. 

MM3(94) or later. Contains an explicit hydrogen bond term with an H-bond linearity function ( -. 3 angular term). MM3 distances are rg values. 

MM4. Contains an explicit hydrogen bond term with both H-bond linearity and lone-pair directional functions (0h-a-b and 0h-bb-b angular terms). MM4 distances are tg values. 

Despite the complication due to the interdependence of orbital and spin angular momenta, the Dirac equation for a central field can be separated in spherical polar coordinates [63]. The energy eigenvalues for the hydrogen atom (V(r) = e2/r, in electrostatic units), are equivalent to the relativistic terms of the old quantum theory [64]... 

The solutions of the angular dependent part are the spherical harmonics, Y, known to most chemists as the mathematical expressions describing shapes of (hydrogenic) atomic orbitals. It is noted that Y is defined only in terms of a central field and not for atoms in molecules. 

The GUGA-Cl wavefunctions are spatial and spin symmetry-adapted, thus the projections of total orbital angular momentum and total spin of a hydrogen molecule in a particular electronic state are conserved for all the values of R. Therefore, the term remains constant for an electronic state, and it causes a... 

Atomic density functions are expressed in terms of the three polar coordinates r, 6, and multipole formalism, the density functions are products of r-dependent radial functions and 8- and -dependent angular functions. The angular functions are the real spherical harmonic functions ytm (8, ), but with a normalization suitable for density functions, further discussed below. The functions are well known as they describe the angular dependence of the hydrogenic s, p, d,f... orbitals. 

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