Energy system with subsystem illustrating

Eigure 3 represents an illustrative biological application an Asp Asn mutation, carried out either in solution or in complex with a protein [25,26]. The calculation uses a hybrid amino acid with both an Asp and an Asn side chain. Eor convenience, we divide the system into subsystems or blocks [27] Block 1 contains the ligand backbone as well as the solvent and protein (if present) block 2 is the Asp moiety of the hybrid ligand side chain block 3 is the Asn moiety. We effect the mutation by making the Asn side chain gradually appear and the Asp side chain simultaneously disappear. We choose initially the hybrid potential energy function to have the form... 

If, on the other hand, the thermodynamic properties of the flow streams change with time in some.arbitrary way, the energy balance of Eq. 3.1-6 may not be useful since it may not be possible to evaluate the integral. The usual procedure, then, is to try to choose a new system (or subsystem) for the description of the process in which these time-dependent flows do not occur or are more easily handled (see Illustration 3.4-5). 

It is very attractive to couple the 3D-RISM method with the KS-DFT for the electronic structure to self-consistently obtain both classical and electronic properties of solutions and interfaces. The 3D-RISM approach using the 3D-FFT technique naturally combines with the KS-DFT in the planewave implementation. The planewave basis set is convenient for the simple representation of the kinetic and potential energy operators, and is frequently employed for large systems. The hybrid KS-DFT/3D-RISM method is illustrated below by the example of a metal slab immersed in aqueous solvent [28]. In a self-consistent field (SCF) loop the electronic structure of the metal solute in contact with molecular solvent is obtained from the KS-DFT equations modified for the presence of the solvent. The electron subsystem of the interface is assumed to be at the zeroth temperature, whereas its classical counterpart to have temperature T. The energy parameter of the KS-DFT is replaced by the Helmholtz free energy defined as... 

Fig. 13.10. Schematic illustration of arbitrariness behind the selection of subsystems within the total system. The total system under study is in the centre of the figure and can be divided into subsystems in many different ways. The isolated sub stems may differ from those incorporated in the total system (e.g., by shape). Of course, the sum of the energies of the isolated molecules depends on the choice made. The rest of the energy rcprc sents the interaction energy and depends on ehoiee too. A correct theory has to be invariant with respect to these ehoiees, which is an extreme eondition to fulfil- The problem is even mote eomplex. Using isolated subsystems does not tell us anything about the kind of complex they are going to make. We may imagine several stable aggregates (our system in the centre of the figure is only one of them). In this way we encounter the fundamental and so far unsolved problem of the most stable structure (cf. Chapter 7).

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