Calculation, 454 mentioned

Computational solid-state physics and chemistry are vibrant areas of research. The all-electron methods for high-accuracy electronic stnicture calculations mentioned in section B3.2.3.2 are in active development, and with PAW, an efficient new all-electron method has recently been introduced. Ever more powerfiil computers enable more detailed predictions on systems of increasing size. At the same time, new, more complex materials require methods that are able to describe their large unit cells and diverse atomic make-up. Here, the new orbital-free DFT method may lead the way. More powerful teclmiques are also necessary for the accurate treatment of surfaces and their interaction with atoms and, possibly complex, molecules. Combined with recent progress in embedding theory, these developments make possible increasingly sophisticated predictions of the quantum structural properties of solids and solid surfaces. 

The analytical data on CO2 in hydrothermal solutions and fluid inclusions and measured temperatures (Table 3.2) are consistent with the thermochemical calculations mentioned above. 

P. Hofmann, H. Heill, unpublished results. We have become aware of apparently similar EH model calculations mentioned in the abstract of a poster, which was presented at an ACS National Meeting (New York, April 1986) by V. Uma, J. A. Davies, K. Krogh-Jespersen. To our knowledge, no publication of these results has appeared. 

The trajectory calculations mentioned above also yield analytical expressions for the critical Stokes number... 

The ultimate goal of any titrimetric analysis is to determine the amount of the analyte in a sample. This involves the stoichiometry calculation mentioned in the Work the Data section of the analytical strategy flow chart in Figure 4.1. This amount of analyte is often expressed as a percentage, as it was for the gravimetric analysis examples in Chapter 3. This percentage is calculated via the basic equation for percent used previously for the gravimetric analysis examples ... 

A very important question in the context of dendrimers and their utility as host molecules relates to the existence of cavities within these macromolecules. The presence of internal voids in dendrimers is closely related to their conformational behaviour and to the degree of back-folding of the terminal branches into the interior of the dendrimer. The issue of back folding was already briefly touched upon in section 16.2.1. Next to the purely theoretical calculations mentioned there, several calculations have been performed on specific dendrimer types. 

Figure 4.9 illustrates the results of another of Phelan and Webb s [1, p 31, Table 13] calculations mentioned above. When we compare Figure 4.9 with Figure 4.5, the effect of soil type, as represented by the differing Kd values, becomes very apparent. 

Some of the calculations mentioned indicate a contribution from the wave-functions corresponding to the covalent structures of 1-2 per cent. In view of the very considerable number of assumptions in the mathematical treatment, magnitudes of this order should have no significance. 

The calculations mentioned [1] did not aim at obtaining quantitative results of the hydrogen bond energy or other characteristics but they were directed towards the dependence of the energy of the... 

NMR shielding tensors were calculated using the Gauge-Independent Atomic Orbital (GIAO) method as implemented in Gaussian 98 (44-46). The basis sets and level of theory are the same as used in the geometry optimizations and frequency calculations mentioned above. 

Among the alternative basis fimctions which have been used in SCF calculations, mention should be made of Gaussian orbitals, which by analogy with the Slater orbitals of (6.56) may be written... 

The transition state for BPR was given tetragonal-pyramidal symmetry, C4v in some recent calculations mentioned in footnotes 34 and 35 of Ref. 49. 

Both methods of absorption calculation mentioned are based on the fact that after absorption the drug/metabolites reach the central circulation. In case of oral administered drugs targeting the liver and being eliminated biliary instantly, it is obvious that both methods mentioned fail. In such a special case an absorption estimation might be possible via a biliary excretion study. 

The density functional theory calculations mentioned earlier also modeled the ring-opening of cyclobutane radical cation [87]. This reaction proceeded via a distorted trapezoid transition state with two shorter (142.2, 147.1 pm) and two longer bonds (187.7, 208.4 pm), forming the "anti -complex (one long bond 221.6 pm), similar to that calculated earlier [168]. 

Certainly detailed theoretical treatments of the stabilities, energetics, and electronic states of the doubly-charged negative ions, both monatomic and polyatomic, are now warranted. It was noted eariier that the EHT calculations employed here are only a zerot/i order approximation the results obtained, however, now justify an effort to employ more sophisticated approaches. The MINDO and LCAO-MO-SCF calculations mentioned above are a distinct improvement over the EHT calculations. Other calculational techniques should be brought to bear on an improved understanding of doubly-charged negative ions. 

Regioselectivity in the meta cycloaddition to substituted benzenes has been assumed to depend on charge polarization in the biradical intermediate shown in Scheme 21 (van der Hart et al., 1987). The theoretical calculations mentioned earlier, however, point out that in the early stage of the reaction the excited state has appreciable polar character that disappears as the reaction proceeds the biradical itself does not have any particular polarity. 

An almost identical conclusion was obtained analytically by way of the self-consistent field theory. Edward [23] showed Pcy j 9/5 for d = 3 in good accord with the numerical calculation mentioned above, together with the mean end-to-end distance that scales as... 

As far as we are aware, this type of calculation has been performed for lactim and lactam tautomers of both 2- and 4-oxopyridines [(2), (3)] and for formamide (6a) and formimidic acid (6b) only (Schlegel et al., 1982 Scanlan et al., 1983). Since the calculations mentioned are expensive, one estimates the S a b,> value by comparison of the electronic energies calculated in the HF approximation only [(HF)8EAliq)L and even this has often been done by means of semiempirical methods [(CNDO/2i8 A B,... 

In addition to MO calculations mentioned previously,380 382,383,396,423a others deal with energy levels within furan and similar nuclei either specializing in these424,425 or treating them in a more general context.426 427 All include discussions of ionization potentials the special case of the hydroxyfurans75,113 has also been mentioned (Sections III,A and B). Electrochemical one-electron oxidation is mentioned in Section VI,A1 (Part I). 

Contrary to formerly accepted opinion, the lack of any separation of the o and n levels into two bands with a gap between them has nothing to do with the question of the o—n separation as discussed in Sect. 3.1. In fact, all the calculations mentioned in this context were made in the framework of the independent-particle model and a fortiori in the frame of [Pg.46]

The calculations mentioned above draw their conclusion about the thermodynamic stability based on comparing free energy among a few candidate... 

We now turn to a consideration of the experimental data on the luminescence of closed-shell transition-metal complexes. It will be shown that the results of the calculations mentioned in this chapter are very helpful in the interpretation of the experimental results. 

Using the m.o. calculations mentioned in Sect. 2.2 it is possible to assign the levels in Figs. 25 and 26 to certain energy levels. Level 1 is the ground state Ajg. Level 4 consists of the Tju levels (one in tj tjg and one in tjy tjg). This is the level... 

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