Geometry, derivatives, calculations with

To be able to determine the nature of the surrounding surface upon which we now find ourselves we will need to make more use of those force constants, and this is done by following the completed geometry optimization calculation with a vibrational frequency calculation, in which the fidl second derivatives are... 

Generally, a vibration analysis calculation should be performed after a geometry optim ization with th e sarn e meth od, Th is eri stires th at the ealeti laliori of second derivatives is perform ed at a eon figuration for which all first derivatives are zero. 

Some more recent software uses the tensor LEED approximation of Rous and Pen-dry which can save a substantial amount of computer time [2.268-2.270]. In tensor LEED the amplitudes (0) of all escaping electron waves (spots) are first calculated conventionally as described above for a certain reference geometry. Then the derivatives of these amplitudes 5Ag/5ri with respect to small displacements of each atom i in this reference geometry are calculated. These derivatives are the constituents of the "tensor". The wave amplitude for a modified model geometry where atom i is displaced by the vector Aq is then approximately given by ... 

It is often of interest to calculate force constants from observed vibrational frequencies. However, it is not generally possible to derive analytical expressions for the force constants as functions of the frequencies and the molecular geometry. The calculation is necessarily an iterative one. Starting with a set of assumed force constants - usually obtained by analogy with similar bonds in other molecules - the values are refined until a suitable set is found. The set that yields the best agreement between calculated and observed frequencies constitutes the accepted force field for die molecule. 

Modified intermediate neglect of differential overlap (MINDO/3) and modified neglect of differential overlap (MNDO) methods with full geometry optimization calculate triazol[4,5-, [l,2,3]triazole to possess antiaromatic structure with C h symmetry but not 1)2,5. In contrast, the aromatic structure with 1)2,5 symmetry is found advantageous for the 2,5-dioxide derivative <1991IZV1825>. 

Nowadays a wide variety of quantum-chemical programs are disposable, which permit to calculate with high accuracy the equilibrium geometry of the molecules and their energy of formation. Theoretical methods have been developed for analytical calculation of the first and second derivatives of energy [8,9], so that the force-constant matrix FHT and the harmonic frequencies can be extracted from the quantum-mechanical calculations. Since as a rule the molecular orbitals (MO) obtained by the quantum-mechanical methods are spread around the entire molecule, the corresponding quantum-mechanical force fields incorporate the important effects of the off-diagonal interactions. 

Optimizations of molecular geometries may be performed with a simpler basis set followed by a single-point Hartree-Fock (HF) calculation with a larger basis set for that derived geometry. This is indicated by double slashes, i.e. 6-31G //3-21G. 

---