Determination of geometry

Schleyer was the first to fully realize the sensitivity of calculated NMR chemical shifts with regard to molecular geometry and use this for ab im n o/IGLO/NMR-based structural determinations in many cases"6. Cremer and coworkers realized the usefulness of this approach for the determination of geometries of potentially homoaromatic compounds not amenable to experiment49-58. 

Apart from this, one could use the degree of pyramidalization at the central Si atom or geometrical distortions of solvent molecule(s) S or counterion(s) X interacting with R3Si+ in solution. However, direct determination of geometry and stability of an ion R3Si(S)+ in solution by experimental means is difficult. In... 

We have seen in the first section how important it is to have an accurate reference geometry for frequency calculations. Therefore, we start with the comparison of empirical and calculated geometries. For the determination of geometries we have used non-local corrections in the exchange correlation potential (LDA/NL). This geometry was used for the determination of LDA force field, and the non-zero forces were taken into account in the calculation of internal force constants and vibrational frequencies. Further, we compare the calculated and observed vibrational frequencies of the transition metal complexes. We also discuss the differences between forc constants of free and complexed small aromatic rings. 

Fortunately, determination of geometries and frequencies with B3LYP calculations are known to provide good results [141, 142, 143, 144, 145]. Part of the success of the G3MP2B3 methods is a result of the accuracy of the geometries and vibration frequency data. 

It should be noted that the hybrid quantum/classical schemes apply not only for determination of geometries, energies, and reaction mechanisms. The Monte Carlo [67, 68] and molecular dynamics (MD) [69-72] simulations are quite popular as frameworks for which various QM/MM procedures serve as subroutines . Before employing hybrid schemes the large-scale MD simulations were performed only with low-level approximations for force fields. The use of hybrid schemes extends significantly the scope of their application, improve precision of the results that allows to improve the understanding of statistical properties and dynamical processes in liquids and biopolymers. 

QM calculations represent the leading tool to study intrinsic molecular interactions in nucleic acids, such as base stacking and base pairing. However, the QM data should not be overinterpreted and any extrapolation to nucleic acids requires proper consideration of the gas phase nature of QM calculations. In addition, in order to obtain meaningful QM data, basic methodological requirements must be fulfilled. These include, in addition to the obvious selection of appropriate level of calculations, very careful selection or determination of geometries, which is discussed in detail in this chapter. 

LCAO-MO-SCF Calculations Using Gaussian Basic Functions. Ill Determination of Geometry by SCF Calculations, CFj . 

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