CAPITULO II MARCO TEÓRICO Y CONCEPTUAL
3. MARCO CONCEPTUAL
Geometry optimisations of solid VOCl3 was performed using the planewave periodic
DFT code CPMD175 at the the BP86-‐D level, using the empirical dispersion correction
by Grimme.26 Modelling solid-‐state systems requires initial structural data, which for
metal complexes usually comes in the form of X-‐ray crystal structures. Two sets of crystal structures for VOCl3 were considered, by Galy et al. from 1983176, and by
Troyanov from 2005177. The latter has a slightly larger volume of the unit cell (by
2.5%) and a slightly lower R-‐value (reliability factor, a measure of how the model reproduces the diffraction data)178 than the former (3.2% vs. 4.9%). Single-‐point
energy computations found the Troyanov structure to be lower in energy and the Grimme dispersion correction was found to be crucial for a qualitatively correct cohesion energy.174 A supercell (crystallographic cell from Troyanov177 doubled along
the a-‐axes) with dimensions of 10x9x11 Å3 containing 8 molecules was calculated. As
optimisations of unit cell parameters are difficult, they were not attempted. Norm-‐ conserving Troullier-‐Martins pseudopotentials179 were used in the Kleinman-‐
Bylander form180 and Kohn-‐Sham MOs were expanded at the Γ-‐point in a basis of
plane waves with a cutoff of 80 Ry. These calculations were performed by Michael Bühl and more details are available in the published study.174
The accuracy of solid-‐state X-‐ray geometries vs. solid-‐state DFT-‐optimised
geometries in NMR calculations has been discussed in several studies.181-‐183 It seems
that due to resolution limitations of the X-‐ray structures, geometry optimisations are generally preferable, especially for hydrogen positions. The geometry from a periodic BP86-‐D calculation on the Troyanov structure was eventually chosen as the most reliable crystal structure of VOCl3 .
The Chemshell program v. 3.388,89 was used to create a large spherical MM cluster
with radius ~48 Å (90.0 au), from the DFT-‐optimised crystal structure, centered on the V atom of one VOCl3 molecule with all partial molecules at the surface deleted. A
simple Coulomb point charge force field for each MM atom type was defined by using atomic NPA charges from a single molecule calculated at the B3LYP/QZVPP level. Additional charges surrounding the cluster were added to simulate the electrostatic potential of the infinite periodic system, using a (now outdated) procedure in Chemshell named make_3d_corrected_covalent_cluster (superceded by the construct_cluster procedure, see later).
A simple scheme to iterate the MM point charges self-‐consistently was devised (similar as loop A in Chapter 3.5.1):
A quantum mechanical (QM) cluster (single VOCl3 unit or larger, see below) was
selected from the middle of the classical cluster, its charges deleted, thus resulting in coordinates for both the QM cluster and coordinates and charges for the MM atoms.
The coordinates and point charges of the entire cluster were subsequently used for single-‐point embedded QM calculations of the QM cluster, using the Gaussian 09 program. From these single-‐point embedded calculations, new NPA atomic charges were obtained that were used to update the Coulomb force field. This results in a cycle that was iterated until the charges were self-‐consistent. Single-‐point NMR calculations were performed with different density functionals using several different basis set combinations (basis set on metal/basis set on ligand): Wachters/6-‐31G* (AE1), QZVPP / 6-‐31G* and QZVPP/QZVPP as well as a combination of decontracted def2-‐QZVPP on metal and normal 6-‐31G* on ligand atoms.
Due to the small size of VOCl3, it was possible to increase the size of the QM cluster for
the single-‐point QM/MM calculations. This then allows one to probe how the chemical shift and EFG tensors are affected by the short-‐range quantum mechanical
polarisation (i.e. beyond the classical electrostatic effect by point charges). Three different cluster models were defined: a single molecule (I), this molecule with the 14 nearest neighbours (II) and finally a large cluster consisting of 65 molecules in total (III). The different cluster models are illustrated in Figure 8.
Figure 8 The three cluster models (from the top, clusters I, II and III) showing the different layers. Surrounding point charges not shown.
The single-‐point NMR calculations were performed with and without the surrounding point charges and subsequent charge updates. The charges converged quickly, only 2-‐ 3 iterations were necessary for the charges to stop changing more than 0.0001 e-‐.
Different basis set were used for the central molecule: (notation: basis set on V/basis set on O and Cl) Wachters/6-‐31G* (AE1) and def2-‐QZVPP/def2-‐QZVPP. Due to the size of cluster models II and III, smaller basis sets were used for the added molecules
in the two additional layers. For the second layer (14 molecules) in cluster model II and III, the surrounding molecules were all assigned the AE1 basis set. In cluster model III, the additional molecules in the third layer used the 6-‐31G* basis set (for V, O and Cl). As the outer layers only serve the purpose of polarising the density of the central molecule, on which the NMR parameters are calculated, the use of smaller basis sets on the outer layers seems justified. Decontraction of the basis set of the central molecule was also explored as well as different basis set combinations including effective core potentials (ECP) in the outer layers.