Foreword to the special issue on ab initio and density functional methods for Raman wavenumbers and intensities
✍ Scribed by Anne B. Myers
- Publisher
- John Wiley and Sons
- Year
- 1998
- Tongue
- English
- Weight
- 97 KB
- Volume
- 29
- Category
- Article
- ISSN
- 0377-0486
No coin nor oath required. For personal study only.
✦ Synopsis
Vibrational wavenumbers of molecules are sensitive to both the equilibrium geometry and the interatomic forces that act to maintain that geometry, and thus contain valuable information about the molecular structure and bonding. However, interpreting vibrational wavenumbers of polyatomic molecules is rarely trivial because most vibrations are at least somewhat delocalized, and each wavenumber depends on a number of force constants and geometric parameters. Raman intensities are also highly informative in principle, but they are at least equally non-trivial to interpret. Whether excited far from electronic resonance, where the intensities depend on the derivatives of the molecular polarizability along the vibrational normal coordinates, or on resonance, where they depend on the changes in equilibrium geometry and force constants between the ground and resonant states, experimental Raman intensities depend in a sensitive manner on both the electronic properties and the detailed form of the vibrational normal modes.
Most small-amplitude molecular vibrations can be described fairly well by solving the classical equations of motion for a multi-dimensional harmonic oscillator and then imposing quantization to Ðnd the allowed spectroscopic transitions. This is a straightforward, if sometimes messy, procedure given the masses and equilibrium positions of the atoms and the force constants accompanying displacements from equilibrium. The difficult part is how to determine the geometry and force constants in the Ðrst place. Even if the geometry is known (e.g. from an x-ray crystal structure), there are almost always far fewer experimental wavenumbers than there are independent force constants. Thus many distinct force Ðelds, often very di †erent from one another, are equally consistent with the data, making it difficult to draw any deÐnitive conclusions about bonding from Ðtting of empirical force Ðelds to experimental wavenumbers. The problem is further exacerbated if the equilibrium geometry is not known and/or is part of the information being sought.
The dependence of the electronic energy on nuclear positions, i.e. the equilibrium geometry and force Ðeld, can be formulated straightforwardly from quantum mechanical fundamentals, but not until recently was it possible to solve the resulting equations with reasonable accuracy for any but the smallest molecules. Early semiempirical electronic structure methods compensated for lack of computational power by replacing many of the integrals that occur in the complete quantum mechanical expressions by empirical parameters. These methods are still widely used and often give good results for the classes of molecules on which they have been parameterized, but are ultimately only as good as the data on which the parameterization was based. Fortunately, rapid advances in the power of readily available computers have now made fully ab initio calculations, in which no