Part of a Molecular System

You can perform quantum mechanical calculations on a part of a molecular system, such as a solute, while using molecular mechanics for the rest of the system, such as the solvent surrounding the solute. This boundary technique is available in HyperChem for all quantum mechanical methods. It is somewhat less complete with ab initio calculations than with semi-empirical calculations, however. With ab initio calculations the boundary must occur between molecules rather than inside a molecule. 

Choose the region (single or multiple molecules) of interest for an ab initio calculation from the total molecular system. HyperChem performs the ab initio calculation for the selected region using the perturbation of an electrostatic potential arising from the net charges on the atoms of the un selected part. (For further details of this electrostatic potential perturbation implemented in HyperChem, please see the second part of this book. Theory and Methods). 

Choose the atoms of interest for the semi-empirical calculation, then use the Bttend to sp option on the Select menu to establish the appropriate atomic boundaries for the quantum mechanics calculation. HyperChem substitutes pararmeterized pseudo-fluorine atoms for the portions of the molecule not included directly in the calculation (see the second part of this book. Theory and Methods). 

The algorithms of the mixed classical-quantum model used in HyperChem are different for semi-empirical and ab mi/io methods. The semi-empirical methods in HyperChem treat boundary atoms (atoms that are used to terminate a subset quantum mechanical region inside a single molecule) as specially parameterized pseudofluorine atoms. However, HyperChem will not carry on mixed model calculations, using ab initio quantum mechanical methods, if there are any boundary atoms in the molecular system. Thus, if you would like to compute a wavefunction for only a portion of a molecular system using ab initio methods, you must select single or multiple isolated molecules as your selected quantum mechanical region, without any boundary atoms. 

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To limit an ab initio calculation to part of a molecular system, select the molecules of interest. Only the selected molecules move, but the frozen molecules influence the calculation. The ab initio... 

Electron transfer or redistribution is governed by the chemical potential of the electron cloud in different parts of a molecular system when reactants are brought close together or a molecule is subjected to an external field arising, for example, from interaction with another system. Although the chemical potentials dictate the direction of electron flow, the extent of charge transfer is controlled by another parameter, the chemical hardness. Both these concepts have been quantified through the theoretical framework of DET. ... 

In the most general terms a hybrid potential can be defined as any one that combines two or more potentials for the description of different parts of a molecular system. This definition is a very broad one and covers a wide range of possible combinations. In this review, therefore, we shall limit the discussion of a particular class of hybrid potentials that have found widespread use in the study of solute-solvent and protein-ligand systems. These types of potential were first introduced by Warshel and Levitt [15] with significant later enhancements by Singh and Kollman [16] and by Field et al [17]. In passing, we shall mention alternative potentials that have been developed for other applications. 

Obara-Saika or McMurchie-Davidson schemes. For more general charge distributions, representing, for example, a large part of a molecular system, it may be better to carry out the integration numerically, using Gaussian quadrature or some other numerical scheme. 

Amolecular dynamics simulation can have three distinct time and temperature periods heating, simulation (run), and cooling. If you want to measure equilibrium properties of a molecular system, you can divide the simulation period into two parts equilibration and data collection. 

Since the six carbons shown above have 10 additional bonds, the variety of substituents they carry or the structures they can be a part of is quite varied, making the Diels-Alder reaction a powerful synthetic tool in organic chemistry. A moment s reflection will convince us that a molecule like structure [XVI] is monofunctional from the point of view of the Diels-Alder condensation. If the Diels-Alder reaction is to be used for the preparation of polymers, the reactants must be bis-dienes and bis-dienophiles. If the diene, the dienophile, or both are part of a ring system to begin with, a polycyclic product results. One of the first high molecular weight polymers prepared by this synthetic route was the product resulting from the reaction of 2-vinyl butadiene [XIX] and benzoquinone [XX] ... 

Despite the availability of fast computers and efficient codes for accurate quantum chemistry calculations, it is not likely in the near future that we will be able to study chemical reactions in proteins taking all the proteins atoms into quantum mechanical calculations. Hybrid methods in which different parts of large molecular systems are treated by different theoretical levels of methods are likely to play a key role in such studies for the coming decade or more. The ONIOM method we have developed is a versatile hybrid method that allows combining different quantum mechanical methods as well as molecular mechanics method in multiple layers, some features of... 

Cyanine dyes have the common molecular formula R2N [CH=CH]nCH=N+R2 where the mono- or poly-methine chain is flanked by two nitrogen atoms that form part of a heterocyclic system (see Fig. 6.6). The most common cyanine derivatives used for labeling molecules are Cy3 and Cy5. These are symmetrical... 

In conclusion, by proper choice of a molecular system, specific bond breaking can be performed. By using an IET selective bond-breaking procedure, unnecessary parts of a molecule can be cleaved off and thereby active sites can be created. Such molecular fragments can be used as building blocks to join with other specifically tailored species to build a new molecule. 

Another way of performing calculations using the cluster model is the use of a hybrid method. It is a theoretical method, which uses different approaches for different parts of the molecular system. The ONIOM method is one of the hybrid methods developed quite recently to facilitate accurate ab initio calculations of large chemical species. The ONIOM method (n-layered integrated molecular orbital and molecular mechanics approach) [29] is a multi-level extrapolation method, in which the studied molecular system is divided into two or more parts or layers. The most important part of the system from the chemical point of view (the inner part, IP) is treated at a high" level of theory (the HL method - a high level of ab initio molecular orbital method) and the rest of the system is described by a computationally less demanding method (the LL method - the lowest ab initio approximation or even semiempirical or molecular mechanic approximations) [30]. 

Now we pass to the formal derivations of a hybrid method. We assume that the orbitals forming the basis for the entire molecular system may be ascribed either to the chemically active part of the molecular system (reactive or R-states) or to the chemically inactive rest of the system (medium or M-states). In the present context, the orbitals are not necessarily the basis AO, but any set of their orthonormal linear combinations thought to be distributed between the subsystems. The numbers of electrons in the R-system (chemically active subsystem) Nr and in the M-system (chemically inactive subsystem) NM = Ne — Nr, respectively, are good quantum numbers at least in the low energy range. We also assume that the orbital basis in both the systems is formed by the strictly local orbitals proposed in [59]. The strictly local orbitals are orthonormalized linear combinations of the AOs centered on a single atom. In that sense they are the classical hybrid orbitals (HO) ... 

In the generalized approach the probabilities p°a = [// j of the constituent inputs in the given externally decoupled (noncommunicating and non-bonded) subchannel a0 of the system "promolecular" reference M° = (a° j8°. ..) should thus exhibit the internal (intrasubsystem) normalization, Pa = we have denoted the externally closed status of each fragment in M° by separating it with the vertical solid lines from the rest of the molecule. Therefore, these subsystem probabilities are, in fact, conditional in character p = P(a a) = pa/Pa, calculated per unit input probability Pa = 1 of the whole subsystem a in the collection of the mutually nonbonded subsystems in the reference M°, that is, when this molecular fragment is not considered to be a part of a larger system. Indeed, the above summation over the internal orbital events then expresses the normalization of all such conditional probabilities in the separate (or isolated) subsystem a0 P(a a) = 1. 

The mechanical behaviour of a molecular system is most simply described within periods too short for perturbations to have much effect, so the behaviour of the correlation function over very short times is generally simple. Various forms of the dipole correlation function appear in the literature, some based on self-consistent simple models, others as convenient semi-empirical expressions. It is difScult to appreciate them vnthout working out at least some simple cases, and a good part of this chapter is devoted to such an exposition. Little attention will be given to the general theory, which is fully described in numerous reviews, but some vital results are summarized in an Appendix. 

The basis of the QM/MM approach (Figure 1) is that the process or subsystem of most interest is localized in a fairly small part of a larger system. The computational effort is therefore focused on this small region, which most requires a quantum mechanical description. The bulk of the system is treated more simply by a molecular mechanics potential function. The combination of... 

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