Equilibrium geometries

Sohlegel H B 1987 Optimization of equilibrium geometries and transition struotures/tdv. Chem. Phys. 67 249-86 My own ooworkers and I have also oontributed to finding transition states, in partioular. See, for example ... 

Schlegel H B 1987 Optimization of equilibrium geometries and transition structures Adv. Chem. Phys. 67 249... 

Pulay P 1969 Ab initio calculation of force constants and equilibrium geometries in polyatomic molecules. I. Theory/Wo/. Phys. 17 197... 

Schlegel H B 1982 Optimization of equilibrium geometries and transition states J. Comput. Chem. 3 214... 

Nayak S K, Khanna S N, Rao B K and Jena P 1997 Physics of nickel clusters energetics and equilibrium geometries J. Phys. Chem. A 101 1072... 

Figure Cl.3.7. Equilibrium geometries of some water clusters from ah initio calculations. (Taken from 1621.)...

The situation in singlet A electronic states of triatomic molecules with linear equilibrium geometry is presented in Figme 2. This vibronic structure can be interpreted in a completely analogous way as above for n species. Note that in A electronic states there is a single unique level for K =, but for each other K 0 series there are two levels with a unique character. 

Now, we discuss briefly the situation when one or both of the adiabatic electronic states has/have nonlinear equilibrium geometry. In Figures 6 and 7 we show two characteristic examples, the state of BH2 and NH2, respectively. The BH2 potential curves are the result of ab initio calculations of the present authors [33,34], and those for NH2 are taken from [25]. 

Unfortunately, the approach of determining empirical potentials from equilibrium data is intrinsically limited, even if we assume complete knowledge of all equilibrium geometries and their energies. It is obvious that statistical potentials cannot define an energy scale, since multiplication of a potential by a positive, constant factor does not alter its global minimizers. But for the purpose of tertiary structure prediction by global optimization, this does not not matter. 

The next step in iin proving a basis set could be to go to triple zeta, quadruple zeta, etc. Ifone goes in this direction rather than adding functions of higher angular quantum number, the basis set would not be well balanced. With a large number of s and p functions only, one finds, for example, that the equilibrium geometry of am monia actually becomes planar. The next step beyond double z.ela n sit ally in voices addin g polarization fn n ciion s, i.e.. addin g d-... 

An undesirable side-effect of an expansion that includes just a quadratic and a cubic term (as is employed in MM2) is that, far from the reference value, the cubic fimction passes through a maximum. This can lead to a catastrophic lengthening of bonds (Figure 4.6). One way to nci iimmodate this problem is to use the cubic contribution only when the structure is ,utficiently close to its equilibrium geometry and is well inside the true potential well. MM3 also includes a quartic term this eliminates the inversion problem and leads to an t". . 11 better description of the Morse curve. 

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