CAPÍTULO II MARCO TEÓRICO
PERITO CONTABLE JUDICIAL
3.5 Diseño de investigación
In this work, CASTEP10 (a first-principles DFT code) is used to optimise
the geometry of structural models and to perform NMR calculations, both using the GGA (PBE) functional. CASTEP also uses the GIPAW formalism,29 ultrasoft pseudopotentials30 and periodic boundary
conditions, with the latter reducing the cost of calculations on a infinite solid by recreating the three-dimensional structure from just one unit cell. Crystal structures were typically obtained from the Inorganic Crystal Structure Database (ICSD)11 or from the literature. The accuracy of
calculations is controlled through the choice of k-point spacing using a Monkhorst-Pack grid of k points and the planewave cutoff energy (Ecut).
These two parameters were converged as far as possible to obtain optimum values, using berlinite (AlPO4) for aluminophosphates and
yttrium stannate (Y2Sn2O7) for oxide pyrochlores ceramics. Typical
parameters used are 0.04 Å−1 and 50 Ry for the k-point spacing and cutoff
energy.
Calculations generate the absolute magnetic shielding tensor (σ) in the crystal frame. Diagonalisation of the symmetric part of σ yields three orthogonal principal components, σ11, σ22, and σ33. The principal
components of the chemical shift tensor, δ11, δ22, and δ33, are related by δii = − (σii − σref) / (1 − σref) ≈ −(σii − σref), where σref (assumed to be ≪1) is a
reference shielding. The isotropic shift, δiso, is given by δiso = (δ11 + δ22 +
δ33)/3. The quadrupolar coupling constant, CQ = eQVZZ/ħ and asymmetry
parameter, ηQ = (VXX − VYY)/VZZ are obtained from the principal
components of the electric field gradient (EFG) tensor, V, where Q is the nuclear quadrupole moment (for which a values of 146.6 and −25.58 mB was used for 27Al and 17O, respectively).31
Calculations were performed using the EaStCHEM Research Computing Facility at the University of St Andrews which consists of a 198-node (2376 core) Intel Westmere cluster with 2 GB memory per core and QCR Infiniband interconnect. Calculations were also carried out on a small, home-built cluster using commodity hardware. For further details, see the individual methods section in subsequent chapters.
3.10
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