United-atom approach

Some force fields use the so-called united atom approach where (for example) a methyl group is treated as a single pseudo-atom. They arose historically in order to save computer resource when dealing with large systems such as amino-acid chains. 

A modification of the united-atom approach, called the anisotropic united-atom (AUA) model was the focus of extensive work by Karabomi et al. [362-365]. As in the other models of hydrocarbon chains described so far, the AUA approach to monolayers was preceded by work on alkanes [367]. hi the AUA model the interaction site is located at the geometrical mean of the valence electrons of the atoms it represents, while the pseudoatom itself is located at the carbon atom position. The movement of each interaction center depends on the conformation of the molecule as a whole. 

Cui et al. performed similar analyses to fhose of Dupuis and co-workers. The side chain-side chain radial disfribufion functions (RDFs) reported by Cui et al. show remarkable qualitative deviation from fhose in Zhou et al. i It is of note that the united atom approach used by Cui and co-workers ignored electrostatic interactions between CP2 groups of the polymeric backbone. This can lead to a poor description of fhe hydrated structure in the regions close to the polymeric backbones, unlike the all-atom force field used in Zhou et al. ° For the sake of limited computational resources, Cui et al. used a relatively short representation of Nation ionomer chains consisting of three monomers as compared to the ten monomers used by Vishnyakov and Neimark or Urata et al. It can be expected that structural correlations will strongly depend on this choice. 

There are a number of different approaches to the description of molecular electronic states. In this section we describe molecular orbital theory, which has been by far the most significant and popular approach to both the qualitative and quantitative description of molecular electronic structure. In subsequent sections we will describe the theory of the correlation of molecular states to the Russell Saunders states of the separated atoms we will also discuss what is known as the united atom approach to the description of molecular electronic states, an approach which is confined to diatomic molecules. 

Molecular dynamics are time-consuming because the nonbonded interactions scale as n where n is the number of atoms. To save time, one may implement the united atom approach, substituting some atomistic detail with an imaginary entity that represents the essential features of what has been substituted. For example, it is common to substitute methylene groups with an imaginary spherical atom with mass 14. Therefore a polyethylene chain would look like a chain of spherical atoms, appropriately rescaled, terminated by similar entities with mass = 15 for the methyl groups. 

Eurther simplification may be achieved in force fields designed for treating macromolecules by not considering hydrogens explicitly, the so-called united atom approach (an option present in for example the AMBER, CHARMM, GROMOS and... 

With large molecules, the number of sites is often smaller than that of atoms and the multipoles are located at the center of groups of atoms. For instance, the site-site description of the interactions in hydrocarbons with, say, a LJ potential, can either place an interaction center on each nucleus or just on the carbon of CH3 or CH2 groups (united atom approach). From this point of view, different treatment may be applied to the interaction terms in multipolar expansions. 

Fig. 8 Schematic of coarse graining of an n-decane molecule. In the first level, the united atom approach lumps hydrogen and carbons into methyl and methylene groups (spheres). In the second level, lumping of five groups into two supergroups (lumps or coarse cells) is depicted.

In some force field models, even simpler representations are used than the united atom approach, with entire groups of atoms being modelled as single interaction points. For example, a benzene ring might be modelled as a single site with appropriately chosen parameters. 

Mulliken s interest in the electronic levels in molecules in the 1920s was stimulated by suggestions that their molecular spectra bore similarities to atomic spectra and definite relationships could be discerned for isosteric molecules. He found that the spectroscopic analogy between isosteric molecules could be extended to atoms with the same number of electrons, and this relatirmship was to lead subsequently to the united atom approach. He and Birge classified the electronic states in diatomic molecules using the same Russell-Saunders classification used previously for atomic states. Himd s theoretical analysis [ 149,162-166] of the nature of electronic states in molecules therefore proved to be timely for Mulliken and led him to publish [167-171] a summary of the theory and provide extra experimental evidence supporting it. In the molecular orbital theory Hund showed how the concept of atomic orbitals and the mathematical procedures developed to define them could... 

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