Electronic structure computations anharmonic force field

A major difficulty in the experimental determination of anharmonic force fields is the burgeoning number of force constants at higher-orders (Table 4, vide infra) compared with the extent of accessible data. As a consequence, reliable experimental anharmonic force fields are available for only a small number of simple molecules. Within the last decade, determination of harmonic and anharmonic molecular force fields by methods of molecular electronic structure theory has become one of the most successful applications of computational quantum chemistry. In Table 1 those species are indicated (without references given to the original publications) for which full force fields have been determined, at least at the HE level of theory and at least up to quartic force constants. 

The procedure and pertinent issues one has to consider when determining anharmonic force fields by methods of electronic structure theory may be described as follows. Once the definition of molecular force constants involving selection of an appropriate coordinate system is clear, one may need to identify all unique force (potential) constants to be determined. Then selection of the reference geometry follows, which affects precision of the force field determined and how the theoretical force field can be transformed from one coordinate system (representation) to another. Given that an appropriate basis set and level of electronic structure theory are chosen for the actual computations, the necessary quantum chemical calculations can be performed after one has carefully considered how to obtain the high-order force constants from low-order analytic information without much loss of precision. Last but not least one needs to understand the potential uses and misuses of anharmonic molecular force fields. 

Since in computations of electronic structure theory derivatives of the total energy of molecular systems with respect to geometrical coordinates are best obtained in Cartesian coordinates, transformation of these derivatives to coordinate systems of more spectroscopic use, e.g., internal or normal coordinates, needs to be discussed. Furthermore, it is noted that, due to the lack of analytic higher-derivative methods at correlated levels of computational quantum chemistry, in practice higher-order force constants are usually determined first in a convenient set of internal coordinates. Then, in order to employ varia-tional or perturbational approaches utilizing anharmonic force fields they may n6ed to be expressed in normal coordinates, never known a priori to the calculation. It is thus clear that these usually nonlinear and somewhat complicated transformation equations occupy a central role in anharmonic force field studies. 

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