Kinds of calculations

Tl le popularity of the MNDO, AMI and PM3 methods is due in large part to their implementation i n the MOPAC and AMP AC programs. The programs are able to perform many kinds of calculation and to calculate many different properties. 

With the current impressive CPU and main memory capacity of relatively inexpensive desktop PC s, non-direct SCF ab initio calculations involving 300-400 basis functions can be practical. However, to run these kinds of calculation, 20 GBytes of hard disk space might be needed. Such big disk space is unlikely to be available on desktop PCs. A direct SCF calculation can eliminate the need for large disk storage. 

Subsequent calculations at the MP2 level locate the two transition structures like those suggested. In this case, Intrinsic Reaction Coordinate (IRC) calculations were used to confirm that these transition structures do in fact connect the minima in question we ll look at this kind of calculation in detail later in this chapter. 

The spirit of this kind of calculation is to give a rough and ready visualization to the potential reactivity of a molecule. For example, Figure 16.3 is a contour map for aspirin. These maps look much better in colour, and it is often possible to spot the route that an approaching charged reagent would take. 

Example 16.2 illustrates the same kind of calculation for a different electrolyte the math is a bit more difficult, but the principle is the same. 

In semi-empirical methods, complicated integrals are set equal to parameters that provide the best fit to experimental data, such as enthalpies of formation. Semi-empirical methods are applicable to a wide range of molecules with a virtually limitless number of atoms, and are widely popular. The quality of results is very dependent on using a reasonable set of experimental parameters that have the same values across structures, and so this kind of calculation has been very successful in organic chemistry, where there are just a few different elements and molecular geometries. 

Levy (Chapter 6) has also explored the use of supercomputers to study detailed properties of biological macromolecule that are only Indirectly accessible to experiment, with particular emphasis on solvent effects and on the Interplay between computer simulations and experimental techniques such as NMR, X-ray structures, and vltratlonal spectra. The chapter by Jorgensen (Chapter 12) summarizes recent work on the kinetics of simple reactions In solutions. This kind of calculation provides examples of how simulations can address questions that are hard to address experimentally. For example Jorgensen s simulations predicted the existence of an Intermediate for the reaction of chloride Ion with methyl chloride In DMF which had not been anticipated experimentally, and they Indicate that the weaker solvation of the transition state as compared to reactants for this reaction In aqueous solution Is not due to a decrease In the number of hydrogen bonds, but rather due to a weakening of the hydrogen bonds. 

To show the logic of this kind of calculation, we apply the seven-step approach to problem solving. We are asked to calculate at 298 K for the Haber reaction. We visualize the process by remembering that there is a connection between free energy, A G reaction > and equilibrium,. eq. The problem provides only the balanced equation and the temperature. Any other necessary data will be found in tables and appendices. 

These kinds of calculations are easily done when a tree diagram is constructed for the plan. The Schreiber plan which proved the structure of the final target molecule has the highest degree of convergence since it has 3 points of convergence and 4 branches or paths in its tree diagram. 

The MaxEnt valence density for L-alanine has been calculated targeting the model structure factor phases as well as the amplitudes (the space group of the structure is acentric, Phlih). The core density has been kept fixed to a superposition of atomic core densities for those runs which used a NUP distribution m(x), the latter was computed from a superposition of atomic valence-shell monopoles. Both core and valence monopole functions are those of Clementi [47], localised by Stewart [48] a discussion of the core/valence partitioning of the density, and details about this kind of calculation, may be found elsewhere [49], The dynamic range of the L-alanine model... 

Finally, every kind of calculation shows that there is no substantial charge on the bromine atom of bromonium ions (Cioslowski et ai, 1990), in agreement with the conclusions from nmr spectra. This result is relevant to the possible reversibility of bromonium ion formation, as discussed later. 

It is clear that when the two substituents are identical, one does not need any kind of calculation in order to predict relative stabilities. A need for calculation arises only when the two substituents are nonidentical. Even in those cases, qualitative trends have emerged 392 Exceptions will be found when through space steric repulsion of the substituents in the 1,1-isomer plays a dominant role. This may be the case for pi acceptor substituents such as CN, COOR, C6H5, etc. 

DR. GLENN CROSBY (Washington State University) I really think that Dr. Schatz answer was correct the reason why you get away with this kind of calculation is precisely that higher electronic states are removed far enough that you can ignore... 

This kind of calculation is called a rating calculation (equipment size is fixed), as opposed to a design calculation in which equipment is sized. 

Such kind of calculations with a precise self-consistent account of crystal surrounding were performed by, at least, four scientific groups Baetzold [16], Das with coworkers [22,23], Winter etal. [28] and Ladik with coworkers [29]. Winter etal. [28] performed cluster calculation by restricted Hartree-Fock (RHF) method, so they did not take into account the electron correlation. The others groups used the umestricted Hartree-Fock (UHF) method for cluster calculations which allows to some extent the electron correlation. The strong covalent C-O bonding in planes and chains was revealed (in accordance with results obtained in Refs. [20,25,26]). For covalent systems,... 

The discussion presented in the subsequent parts of this chapter is based on the results of ab initio calculations of the electronic energy of molecular systems. Details about this kind of calculation are described in reference 11. In connection with this procedure, two major questions have to be addressed. The first is the choice of the wavefunction (basis set) to be used in the calculation, and the second whether or not to include electron correlation. 

The most basic type of DFT calculation is to compute the total energy of a set of atoms at prescribed positions in space. We showed results from many calculations of this type in Chapter 2 but have not said anything about how they actually are performed. The aim of this section is to show that this kind of calculation is in many respects just like the optimization problems we discussed above. 

Probability bounds analysis combines p-boxes together in mathematical operations such as addition, subtraction, multiplication, and division. This is an alternative to what is usually done with Monte Carlo simulations, which usually evaluate a risk expression in one fell swoop in each iteration. In probability bounds analysis, a complex calculation is decomposed into its constituent arithmetic operations, which are computed separately to build up the final answer. The actual calculations needed to effect these operations with p-boxes are straightforward and elementary. This is not to say, however, that they are the kinds of calculations one would want to do by hand. In aggregate, they will often be cumbersome and should generally be done on computer. But it may be helpful to the reader to step through a numerical example just to see the nature of the calculation. 

Alternatively, instead of looking for a significant truncation of the system of equations, one may try to perform multiple but simple calculations hoping for a favorable cancellation of errors. Thus, the idea tested was to start from a set of 2-TRDM s, corresponding to the eigenstates of 5, and then to apply the CLVNE in order to obtain a set of more accurate 1-TRDM s. This kind of calculation was not only carried out for the Beryllium atom but also for the LiH molecule (also with a double zeta basis set). Unfortunately, the results were not encouraging either. 

On Fig. 3 we plot the probabilities of different configurations versus the direct Coulomb interaction U. It can be seen that the system undergoes a metal-insulator transition for a sufficiently high value of U, close to 9. It is easy to perform the same kind of calculation in the case of triply degenerate... 

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