Energy, Stretch-Bend

At the end of run, various energies (stretch, bend, torsion, van der Waals, and dipole-dipole) and total energy is displayed (Figure 14.5). 

Terms in the energy expression that describe how one motion of the molecule affects another are called cross terms. A cross term commonly used is a stretch-bend term, which describes how equilibrium bond lengths tend to shift as bond angles are changed. Some force fields have no cross terms and may compensate for this by having sophisticated electrostatic functions. The MM4 force field is at the opposite extreme with nine different types of cross terms. 

D. Frequencies Molecules vibrate (stretch, bend, twist) even if they are cooled to 0 K. This is the basis of infrared/Raman spectroscopy, where absorption of energy occurs when the frequency of molecular... 

Usually the constants involved in these cross terms are not taken to depend on all the atom types involved in the sequence. For example the stretch/bend constant in principle depends on all three atoms. A, B and C. However, it is usually taken to depend only on the central atom, i.e. = k , or chosen as a universal constant independent of atom type. It should be noted that cross tenns of the above type are inherently unstable if the geometry is far from equilibrium. Stretching a bond to infinity, for example, will make str/bend go towards — oo if 0 is less than If the bond stretch energy itself is harmonic (or quartic) this is not a problem as it approaches +oo faster, however, if a Morse type potential is used, special precautions will have to be made to avoid long bonds in geometry optimizations and simulations. 

Carbon dioxide absorbs infrared energy during bending or stretching motions that are accompanied by a change in dipole moment (from zero). Which of the transitions pictured in Fig. 2b... 

The number and type of cross terms vary among different force fields. Thus, AMBER2 contains no cross terms, MM23 uses stretch-bend interactions only and MM34 uses stretch-bend, bend-bend and stretch-torsion interactions. Cross terms are essential for an accurate reproduction of vibrational spectra and for a good treatment of strained molecular systems, but have only a small effect on conformational energies. 

The stretch-bend energy allows for the i-j and j-k bonds to stretch when the angle between them (i-j-k) closes and is given by... 

When a molecule absorbs light at a certain frequency, it means that a specific bond is stretching, bending, or vibrating. The frequency where each bond absorbs light energy to stretch, bend, or vibrate is very specific. The absorption results in a decrease in intensity of the light transmitted, as measured by the sensor. This is how an infrared... 

These potential energy terms and their attendant empirical parameters define the force field (FF). More complicated FFs which use different and/or more complex functional forms are also possible. For example, the simple harmonic oscillator expression for bond stretching can be replaced by a Morse function, Euorse (3), or additional FF terms may be added such as the stretch-bend cross terms, Estb, (4) used in the Merck molecular force field (MMFF) (7-10) which may be useful for better describing vibrations and conformational energies. 

---