Out-of-plane bends

The MMh- force field assigns default values for out of plane bending terms around an sp2 center. If a central atom has some out of plane parameters, then the first out of plane parameter involving that central atom is used if a specific parameter is not found. 

The functional form for default torsions is the MM-t form with three torsional constants VI, V2, and V3 for 1-fold, 2-fold, and 3-fold contributions. The default values for these constants depend on the particular chemical situation associated with the bond 

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Now, consider the subgroup C3 of D3 , (since no out-of-plane bending is possible for a triatomic system, and hence the subgroup C3 may be used for the discussion). Then, Eq. (E. 15) contains only four symmetry types of electronic operators Iia, Iia, h, and hy. The direct product decompositions for C3 may then be shown (see Table 57 of [28]) to assume the fomi... 

Various other ways to incorporate the out-of-plane bending contribution are possible. For e3plane bend involves a cakulation of the angle between a bond from the central atom and the plane defined by I he central atom and the other two atoms (Figure 4.10). A value of 0° corresponds to all four atoms being coplanar. A third approach is to calculate the height of the central atom above a plane defined by the other three atoms (Figure 4.10). With these two definitions the deviation of the out-of-plane coordinate (be it an angle or a distance) can be modelled Lt ing a harmonic potential of the form... 

An atom that has sp hybridization tends to be coplanar with its attached atoms. This effect is accounted for by improper torsions in other force fields and by out-of-plane-bending interactions in... 

Commonly used descriptions for these vibrations are (i) symmetric CH-stretch, (ii) antisymmetric CH-stretch, (iii) CH2-scissors, (iv) CH2-rock, (v) CO-stretch, (vi) out-of-plane bend. 

It is common to use the symbols v(X-Y), i5(X-Y) and y(X-Y) for stretching, in-plane bending and out-of-plane bending, respectively, in the X-Y group. In addition, the word deformation is often used to imply a bending motion. 

The A A2 X Ai, n -n system of formaldehyde (see Section 7.3.1.2) is also electronically forbidden since A2 is not a symmetry species of a translation (see Table A.l 1 in Appendix A). The main non-totally symmetric vibration which is active is Vq, the hj out-of-plane bending vibration (see Worked example 4.1, page 90) in 4q and d transitions. 

Note also that different analytical forms are used for some of the terms (angles harmonic in cos 0 rather than 0, cosine expansions for dihedrals, r or exp(—yfr,y) instead of repulsions, etc.). Some force fields also have cross-terms between different degrees of freedom. Additional terms may be present for out-of-plane bendings, hydrogen bonds, etc. 

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