Quantum mechanical model hierarchy

The first attempt to explain the characteristic properties of molecular spectra in terms of the quantum mechanical equation of motion was undertaken by Born and Oppenheimer. The method presented in their famous paper of 1927 forms the theoretical background of the present analysis. The discussion of vibronic spectra is based on a model that reflects the discovered hierarchy of molecular energy levels. In most cases for molecules, there is a pattern followed in which each electronic state has an infrastructure built of vibrational energy levels, and in turn each vibrational state consists of rotational levels. In accordance with this scheme the total energy, has three distinct components of different orders of magnitude,... 

Figure 13.2 Multi-scale modelling hierarchy [35], showing the approximate regimes of time and length scales over which atomistic modelling techniques (quantum and molecular mechanics) can usefully be applied and how these link with process methods via mesoscale modelling.

The computations required for accurate modeling and simulation of large-scale systems with atomistic resolution involve a hierarchy of levels of theory quantum mechanics (QM) to determine the electronic states force fields to average the electronics states and to obtain atom based forces (FF), molecular dynamics (MD) based on such an FF mesoscale or coarse grain descriptions that average or homogenize atomic motions and finally continuum level descriptions (see Fig. 1). 

The disparate time and length scales that control heterogeneous catalytic processes make it essentially impossible to arrive at a single method to treat the complex structural behavior, reactivity and dynamics. Instead, a hierarchy of methods have been developed which can can be used to model different time and length scales. Molecular modeling of catalysis covers a broad spectrum of different methods but can be roughly categorized into either quantum-mechanical methods which track the electronic structure or molecular simulations which track the atomic structme (see the Appendix). 

In this respect, chemistry does not differ from other sciences. Contemporary chemical research is organized around a hierarchy of models that aid its practitioners in their everyday quest for the understanding of natural phenomena. The building blocks of the language of chemistry, including the representations of molecules in terms of structural formulae [1], occupy the very bottom of this hierarchy. Various phenomenological models, such as reaction types and mechanisms, thermodynamics and chemical kinetics, etc. [2], come next. Quantum chemistry, which at present is the supreme theory of electronic structures of atoms and molecules, and thus of the entire realm of chemical phenomena, resides at the very top. 

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