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** MO calculations theoretical methods **

** Theoretical Methods for Free Energy Calculations **

Figure Al.3.16. Reflectivity of silicon. The theoretical curve is from an empirical pseudopotential method calculation [25], The experimental curve is from [31], |

During the last decade, the progress in theoretical methods and the access to quantum-chemical calculations has become more available. Nowadays, the use of quantum-chemical calculations in the interpretation of experimental UPS valence band spectra is a common approach [26-29]. [Pg.388]

On the other hand, theoretical methods allow an insight into the structure of non-existent molecules like 2//-indazole (37) or the anion of indazole (38). INDO calculations have been performed by Palmer et al. on the anion of indazole (38) (75JCS(P1)1695). The optimized geometry obtained by them is shown in Figure 7. The N—N bond distance is longer in the [Pg.175]

Pd4oCu4oP2o, Pd5oCu3oP2o, and Pd6oCu2oP20 alloys were measured by resonant ultrasound spectroscopy (RUS). In this technique, the spectrum of mechanical resonances for a parallelepiped sample is measured and compared with a theoretical spectrum calculated for a given set of elastic constants. The true set of elastic constants is calculated by a recursive regression method that matches the two spectra [28,29]. [Pg.295]

The table on the next page indicates the relationship between problem size and resource requirements for various theoretical methods. Problem size is measured primarily as the total number of basis functions (N) involved in a calculation, which itself depends on both the system size and the basis set chosen some items depend also on the number of occupied and virtual (unoccupied) orbitals (O and V respectively), which again depend on both the molecular system and the basis set. The table lists both the formal, algorithmic dependence and the actual dependence as implemented in Gaussian (as of this writing), which may be somewhat better due to various computational techniques [Pg.122]

Calculation of thertnochetnical quantities like those we have just considered are a widely-used method for evaluating the accuracy of theoretical methods and models. In this section, we will look at the Gaussian-2 molecule set and then consider how well a variety of model chemistries perform on it. Note that our consideration of the G2 method itself will come later in this chapter. [Pg.144]

We also showed that the photoemission intensities of such a complex system as CusPts on a platinum substrate can be calculated in good agreement with experiments and this renders confidence into the power of the theoretical methods and the underlying principles. [Pg.250]

Although the recently observed discrepancy between the transition state structure predicted by theory and by interpreting the experimental KIEs using the traditional methods appears to favor the transition state structure predicted by theory, it is worth noting that none of the 39 theoretical methods calculated all six KIEs that were measured for the ethyl chloride-cyanide ion reaction within the experimental error. Obviously there is a need for further investigations of the relationship between observed KIEs and transition state structure. [Pg.267]

Recent theoretical studies have demonstrated that it is possible to calculate accurately adsorbate stmcture and energy levels, to explain trends with variations in metal composition, and to interpret and predict the influence of promoters and poisons on the adsorption of reactants. Additional efforts along these lines will contribute greatly to understanding how catalyst stmcture and composition influence catalyst-adsorbate interactions and the reactions of adsorbed species on a catalyst surface. With sufficient development of theoretical methods, it should be possible to predict the desired catalyst composition and stmcture to catalyze specific reactions prior to formulation and testing of new catalysts. [Pg.173]

In this chapter, we will consider the other half of a model chemistry definition the theoretical method used to model the molecular system. This chapter will serve as an introductory survey of the major classes of electronic structure calculations. The examples and exercises will compare the strengths and weaknesses of various specific methods in more detail. The final section of the chapter considers the CPU, memory and disk resource requirements of the various methods. [Pg.111]

Chapter 1, Computational Models and Model Chemistries, provides an overview of the computational chemistry field and where electronic structure theory fits within it. It also discusses the general theoretical methods and procedures employed in electronic structure calculations (a more detailed treatment of the underlying quantum mechanical theory is given in Appendix A). [Pg.316]

Only the structures of di- and trisulfane have been determined experimentally. For a number of other sulfanes structural information is available from theoretical calculations using either density functional theory or ab initio molecular orbital theory. In all cases the unbranched chain has been confirmed as the most stable structure but these chains can exist as different ro-tamers and, in some cases, as enantiomers. However, by theoretical methods information about the structures and stabilities of additional isomeric sul-fane molecules with branched sulfur chains and cluster-like structures was obtained which were identified as local minima on the potential energy hypersurface (see later). [Pg.108]

This chapter will try to cover some developments in the theoretical understanding of metal-catalyzed cycloaddition reactions. The reactions to be discussed below are related to the other chapters in this book in an attempt to obtain a coherent picture of the metal-catalyzed reactions discussed. The intention with this chapter is not to go into details of the theoretical methods used for the calculations - the reader must go to the original literature to obtain this information. The examples chosen are related to the different chapters, i.e. this chapter will cover carbo-Diels-Alder, hetero-Diels-Alder and 1,3-dipolar cycloaddition reactions. Each section will start with a description of the reactions considered, based on the frontier molecular orbital approach, in an attempt for the reader to understand the basis molecular orbital concepts for the reaction. [Pg.301]

Tliis interpretation is based only upon the structural and electronic properties of the pyridinium cations. Tire calculation of relative activation Ijarri-ers for the competing substitution reactions will give more reliable results —especially if solvent effects are included in the calculations. In order to assess the reliability of actual theoretical methods as applied to model sys- [Pg.196]

Let us illustrate this with the example of the bromination of monosubstituted benzene derivatives. Observations on the product distributions and relative reaction rates compared with unsubstituted benzene led chemists to conceive the notion of inductive and resonance effects that made it possible to explain" the experimental observations. On an even more quantitative basis, linear free energy relationships of the form of the Hammett equation allowed the estimation of relative rates. It has to be emphasized that inductive and resonance effects were conceived, not from theoretical calculations, but as constructs to order observations. The explanation" is built on analogy, not on any theoretical method. [Pg.170]

Optimize the structure of acetyl radical using the 6-31G(d) basis set at the HF, MP2, B3LYP and QCISD levels of theory. We chose to perform an Opt Freq calculation at the Flartree-Fock level in order to produce initial force constants for the later optimizations (retrieved from the checkpoint file via OptsReadFC). Compare the predicted spin polarizations (listed as part of the population analysis output) for the carbon and oxygen atoms for the various methods to one another and to the experimental values of 0.7 for the C2 carbon atom and 0.2 for the oxygen atom. Note that for the MP2 and QCISD calculations you will need to include the keyword Density=Current in the job s route section, which specifies that the population analysis be performed using the electron density computed by the current theoretical method (the default is to use the Hartree-Fock density). [Pg.130]

** MO calculations theoretical methods **

** Theoretical Methods for Free Energy Calculations **

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