First principles calculations computational procedure

By carrying out this combination of semi-empirical procedures and retreating from the pure Thomas-Fermi notion of a uniform electron gas it has actually been possible, somewhat surprisingly, to obtain computationally better results in many cases of interest than with conventional ab initio methods. True enough, calculations have become increasingly accurate but if one examines them more closely one realizes that they include considerable semi-empirical elements at various levels. From the purist philosophical point of view, or what I call "super - ab initio" this means that not everything is being explained from first principles. 

In the more fundamental ah initio methods, an attempt is made to calculate structures from first principles, using only the atomic numbers of the atoms present and their general arrangement in space. Such an approach is intrinsically more reliable than a semi-empirical procedure but it is much more demanding computationally. 

As I have said, Sekino and Bartlett [31] were the first to show how to proceed to calculate frequency-dependent hyperpolarizabilities within the TDCPHF approximation. They developed an infinite-order recursive procedure, using density matrices, and, by solving the equations iteratively at each order, could, in principle, calculate any non-linear optical property. Their first application was to H2, FH (the work on FH was analysed in detail in another paper [38]), CH4 and the fluoromethanes. The processes SHG, OR, dc-SHG, dc-OR, IDRI and THG were considered but not all hyperpolarizability components were computed (the assumption of Kleinman symmetry was made). 

Recent advances in computational chemistry have made it possible to calculate enthalpies of formation from quantum mechanical first principles for rather large unsaturated molecules, some of which are outside the practical range of combustion thermochemistry. Quantum mechanical calculations of molecular thermochemical properties are, of necessity, approximate. Composite quantum mechanical procedures may employ approximations at each of several computational steps and may have an empirical factor to correct for the cumulative error. Approximate methods are useful only insofar as the error due to the various approximations is known within narrow limits. Error due to approximation is determined by comparison with a known value, but the question of the accuracy of the known value immediately arises because the uncertainty of the comparison is determined by the combined uncertainty of the approximate quantum mechanical result and the standard to which it is compared. 

Other theoretical methods. In addition to the procedure described above, three other theoretical methods have been developed for calculating fractionation factors involving minerals. The first is based on computer simulation of crystal structures and first principles prediction of their thermodynamic properties (Patel et al. 1991 Dove et al. 

The solution of the Schrodinger equation only needs nuclear charge numbers and simulation environment parameters not involving any empirical parameters within the framework of the first-principles theory. The obtained results are eigenvalues and eigenfunctions of the systems studied, which can derive aU properties of the system from theory. Moreover, the simulated results agree better with the experiment due to the gradual improvement of the models and the calculation procedure as well as the promotion of computation precision. Therefore, the reliability of the... 

NMR is a powerful tool for the determination of structures from first principles and the chemical shift is the most important NMR parameter in structural analysis. For estimating the relationship between chemical structures and chemical shifts three possibilities exist the calculation of the chemical shift values by empirical methods [137], the computation by quantum chemical procedures, e.g., with the IGLO-method (Individual Gauge for Localized Orbitals [ 129]), or the use of large compilations of NMR spectra and the associated chemical structures. The access to relevant reference data for identical or similar compounds can facilitate the assignment process enormously. Reference data may assist by reducing the amount of experimental and/or interpretive effort required or increase confidence in the suggested structure. 

Theoretical calculations using modern quantum chemical methods provided an outstanding opportunity to make a valuable insight into the problem and allowed reliable description of reaction mechanisms in catalysis from the first principles. Application of informative and flexible computational procedures on numerous examples has demonstrated accurate computational modeling - often within the accuracy achieved in experimental measurements. 

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