Out-of-plane bending

To ensure that the arrangement of four atoms in a trigonal planar environment (e.g., a sp -hybridized carbon atom) remains essentially planar, a quadratic term like V(0) = (fe/2) is used to achieve the desired geometry. By calculating the angle 9 between a bond from the central atom and the plane defined by the central 

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 

Consider the following situation involving an atom X that is sp hybridized 

The dihedral angle or torsional energy interaction in MM-t is of the general form of equation (12) on page 175 but explicitly includes n=l, 2, and 3 with a phase angle (j) =0  

The values of VI, V2, and V3, in kcal/mol, are listed in mmp-tor.txt(dbf). The MM-t force field uses special values for the torsional force constants when the atoms are in a four-member ring. 

The MMh- van der Waals interactions do not use a Lennard-Jones potential but combine an exponential repulsion with an attractive 

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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... 

I h e -M. l+ 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 th at cen tral atom is used if a specific parameter is n ot foiin d. 

Various other ways to incorporate the out-of-plane bending contribution are possible. For e3angle 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... 

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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