First principles calculations previous studies

The question of methanol protonation was revisited by Shah et al. (237, 238), who used first-principles calculations to study the adsorption of methanol in chabazite and sodalite. The computational demands of this technique are such that only the most symmetrical zeolite lattices are accessible at present, but this limitation is sure to change in the future. Pseudopotentials were used to model the core electrons, verified by reproduction of the lattice parameter of a-quartz and the gas-phase geometry of methanol. In chabazite, methanol was found to be adsorbed in the 8-ring channel of the structure. The optimized structure corresponds to the ion-paired complex, previously designated as a saddle point on the basis of cluster calculations. No stable minimum was found corresponding to the neutral complex. Shah et al. (237) concluded that any barrier to protonation is more than compensated for by the electrostatic potential within the 8-ring. 

The available first-principle calculations of the electronic properties of DNA molecules, reviewed in the previous section, are complemented by the so-called model Hamiltonian studies [122-125]. The latter typically grasp... 

In this subsection we will analyze results of first-principle calculations of the electron distribution of the rutile (100) and (110) surfaces. This analysis enables us to study the consequences of the fact that the octahedra in TiOa not isolated, as we implicitly supposed in the previous section, but connected. Ti atomic orbitals in one octahedron interact with Ti atomic orbitals in another octahedron by way of the connecting oxygen orbitals. Similarly oxygen orbitals interact via connecting Ti atoms. These interactions cause a broadening of levels discrete in isolated octahedra. The analysis presented in the previous section is only useful if the main characteristics of the electron distribution remain the same in the extended system. 

Ni-Mo-Jf (X = V, Ta, Al, W, Cr) alloys by transmission electron microscopy (TEM) and the first-principles calculations. They discussed influences of the alloying elements on the ordering behavior in terms of the effective atomic interactions, electronic structures of the ordered compounds and so on. In these previous studies, however, the ordering behavior was interpreted based on the mean-field approximation even for the SRO and imperfectly ordered states. Thus, the following points about the atomistic ordering process are not clear (i) Do Ni-based 1 1/2 0 alloys form similar SRO structures in atomic level (ii) How do the various LRO structures develop from the 1 1/2 0 type SRO state (iii) What governs the SRO-LRO transition process in Ni-based 1 1/2 0 alloys ... 

The purpose of this chapter is to present an overview of the computational methods that are utilized to study solvation phenomena in NMR spectroscopy. We limit the review to first-principle (ab initio) calculations, and concentrate on the most widespread solvation model the polarizable continuum model (PCM), which has been largely described in the previous chapter of this book. 

The reactor model presented above has been used in two versions as a conventional model (CM) and as a hybrid model (HM), respectively. In the conventional model the reaction rates r j appearing in the balance equations of Eq. 7 have been calculated following the expressions for Langmuir-Hinshelwood kinetics [13] derived in our previous studies. In the hybrid first principles-neural network model (HM) the conventional kinetic subroutines in the CM algorithm have been replaced by the neural network, so in the HM the reaction rates r- have been supplied by the trained network. 

Recent dramatic advances in computational techniques and computer power have enabled us to simulate crystalline structures from first-principles by means of the electronic structure calculation of the whole system within the density functional theory. Even liquid and vitreous silica have come to be studied by the ab initio MD method or so-called Car-Parrinello method [59]. Thus the application of the classical MD method is to be shifted to study of dynamics with a larger system size and longer simulation time. For example, the simulation of the oxygen diffusivity mentioned in the previous section needs accumulation of positions of five hundred atoms over 120 ps at each pressure, for which the ab initio MD is too inefficient. On the other hand, a local structural deformation relevant for the diffusion could be simulated with a smaller cell and a shorter time scale. It is obviously fruitful to make proper use ofthese approaches, i.e. the classical MD supported by first-principles cluster calculations and the ab initio MD, in each problem of materials science. 

Recent advances in first-principles molecular dynamics (MD) calculations, which follow the Newtonian dynamics of classically treated nuclei, have made electronic-structure calculations applicable to the study of large systems where previously only classical simulations were possible. Examples of quantum-mechanical (QM) simulation methods are Born-Oppenheimer molecular dynamics (BOMD), Car-Parrinello molecular dynamics (CPMD), tight-binding molecular dynamics (TBMD), atom-centered density matrix propagation molecular dynamics (ADMPMD), and wavepacket ab idtb molecular dynamics (WPAIMD). 

The final step in the unified theory of the ground electronic state of solids is the calculation of the restoring forces for any of the degrees of freedom of the nuclei in the solid. For small displacements from equilbrium, this may be considered in the harmonic approximation and described completely in terms of the phonon eigenfrequencies and eigenvectors. This is an area of the theory of solids which was studied very much in previous years but suffered from the situation that there was no firm theoretical approach to calculate these properties from first-principles (except for simple metals) and the impossibility to determine uniquely the desired relation of forces to displacements from the experimental information on the eigenfrequencies. 

First, we shall explore a conceptual relation between kinetics and thermodynamics that allows one to draw certain conclusions about the kinetics of the reverse reaction, even when it has itself not been studied. Second, we shall show how the thermodynamic state functions for the transition state can be defined from kinetic data. These are the previously mentioned activation parameters. If their values for the reaction in one direction have been determined, then the values in the other can be calculated from them as well as the standard thermodynamic functions. The implications of this calculation will be explored. Third, we shall consider a fundamental principle that requires that the... 

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