Advanced methods for larger molecules

This chapter is the most complicated and formal in the book. Looking back to Chapter 4 we can obtain an idea of what is needed in general. In this chapter we  

outline the theoiy of the permutation (symmetric) groups and their algebras. The goal here is the special, factored form for the antisymmetrizer of Section 5.4.10, since, in this form the influence of the spin state on the spatial functions is especially transparent  

show how the resultant spatial functions allow an optimal algorithm for the evaluation of matrix elements of the Hamiltonian, which is given  

show the way to generate HLSP functions from the previous treatment. 

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The concept of immunoassay was first described in 1945 when Landsteiner suggested that antibodies could bind selectively to small molecules (haptens) when they were conjugated to a larger carrier molecule. This hapten-specific concept was explored by Yalow and Berson in the late 1950s, and resulted in an immunoassay that was applied to insulin monitoring in humans. This pioneering work set the stage for the rapid advancement of immunochemical methods for clinical use. 

Thanks mainly to improved methods and advances in computer technology, but aided by hard work, persistence, adaptability, optimism, and patience, computational chemists became able to answer research questions better and faster. Computers became easier to use, quicker, and capable of handling larger molecules. One of the aspects that experimentalists had a particular trouble accepting was the need for computational chemists to use simplified models of the structures they computed. Computational chemists could readily understand that replacing computationally irrelevant side chains with hydrogens would have no material effect on the outcome of the calculations of, say, the electronic structure of the core of the molecule. However,... 

DFT computations can be extended to considerably larger molecules than advanced ab initio methods and are being used extensively in the prediction and calculation of molecular properties. A recent study, for example, examined the energy required for ionization of very strong acids in the gas phase. Good correlations with experimental values were observed and predictions were made for several cases that have not been measured experimentally, as shown in Table 1.14. 

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