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Functionalized noble metal nanoparticles (NMNP), where the metal cluster is capped and stabilized by a layer of organic molecules, are an unmatched opportunity to create complex structures from simple building blocks and relatively straightforward manipulations.
Recently, adducts of NMNP have attracted attention of the scientific community due to the possibility to use them to modulate photophysical and magnetic properties, with respect to the isolated species, by controlling their distribution in space. This atom-like behavior determines the persistence of quantum effects still at the scale of 100 nm.
Assistance by computer simulations is therefore of fundamental importance.
The aim of this work is to develop a multiscale methodology in collaboration with other units of the HOMINO2012 project, in order to study larger and more complex systems.
First, we aim to apply ab initio (DFT) methods to investigate and probe the relationship between structural and electronic properties of NMNP.
Because these systems are made of hundred of atoms, a multiscale QM/QM' approach is going to be adopted to study the explicit effects of the organic ligands onto the NMNP.
This, combined with TD-DFT, would allow to model the NMNP-organic molecule interaction, as well as the relaxation in the excited states.
Magnetic properties (NMR and EPR) will also be calculated for a better comparison with experiments.
We have experience with Car-Parrinello molecular dynamics simulations and we plan to calculate transport and vibrational properties from these trajectories, both adopting standard methods based onto Fourier transform and Wavelet transform.
Moreover, we also plan to develop force fields to simulate these systems at the MM level in order to better sample the available phase space.
Eventually, aggregates of more NMNP will be investigated computationally.
Up to now, we investigated a (relatively) small gold-based nanocluster made up of a core of 11 Au atoms, itself coated by aromatic phosphines and thiols, whose structure has been experimentally resolved (below).
The testing consisted of a number of structural optimizations with the program Gaussian 09. The final structures have been compared with the starting experimental geometry. Accuracy has been checked computing the atom-averaged absolute value of the difference between metal-metal distances of the initial (exp ) and final (opt) geometries <δ>=<|r(opt)−r(exp)|>, where r represents the distance between two gold atoms. We tested many XCFs and BS/PPs on a simplified structure composed by the metal core and the atoms directly bonded to it (viz. P and S), with added hydrogen atoms to complete the connectivity of the latter. In particular, we employed 3 GGA (PBE, BPBE, BLYP), 1 meta-GGA (TPSS), 5 hybrid (B3LYP, PBE0, mPw1Pw91, M06, M06HF) and 4 long-range corrected hybrid (HSE06, cam-B3LYP, LC-BLYP, LC-PBE) functionals. All atoms have been set free to relax during the optimizations. Results of this testing are summarized in the following figure, but data for Lanl1-DZ are omitted since this BS/PP proved inadequate for the benchmarking (i.e. led to optimized structures very distorted with respect to the experimental one, with <δ> values exceeding 0.3 Å). As can be appreciated, the structural accuracy depends on both the XCF and BS/PP adopted. Apart from the Lanl1-DZ, the widely employed Lanl2-DZ BS/PP (blue bars) provides the worst results with most XCFs. Both modLanl2-DZ (cyan bars) and Lanl2-TZ (red bars) yield significantly better results, with just a slightly greater computational cost. Also semi-relativistic mWB60 (yellow bars) often gives satisfying results, but at the price of much more demanding computations. The full relativistic Dirac-Fock mDF60 (green bars), on the contrary, proves demanding as mWB60 but often provides inaccurate structures as Lanl2-DZ.
Most of the XCFs including PBE-like correlation (viz. PBE itself, BPBE, PBE0, HSE06, mPw1Pw91) provided the best results, with structural errors consistently below the 0.05 Å threshold when adopted in conjunction with modLanl2-DZ.
On these premises, we performed calculations on the complete nanocluster, including the organic coating. Due to the size of the particle (more than 280 atoms), we had to scale the level of theory of the inner and outer regions, following a rationale widely employed in computational chemistry. As XCF, we used BPBE and CAM-B3LYP, since they belong to different “families” but, at the same time, both yielded good optimized geometries for the bare metal core benchmarks. modLanl2-DZ has been used as BS/PP for gold atoms. Geometrical optimizations were performed both fixing the atoms of the outer layer (viz. C, H, and N) to their positions and leaving all the system free to relax.
The constrained calculations gave excellent results with both BPBE and CAM-B3LYP, yielding errors of ~0.05 Å when STO-3G basis set is used for the organic ligands, and ~0.03 Å when is adopted the larger 6-31G. However, the all-free-to-relax calculations gave larger errors, of ~0.11 Å and ~0.13 Å with STO-3G and 6-31G basis sets, respectively. Both XCFs, despite being very different and requiring different computational efforts (CAM-B3LYP is much more demanding), provided similar structures (differences in <δ> values less than 0.01 Å).
In conclusion, with these calculations we show that many GGA functionals (in particular, BPBE) can provide the same structural accuracy than much more complex XCFs for the hybrid organic-gold nanoparticle. modLanl2-DZ improves the accuracy with respect to the widely employed Lanl2-DZ without increasing the computational burden. These combinations of XCFs and PS/BBs can be used to correctly simulate both the metal core and the whole nanocluster, thus representing a good choice for investigations on larger particles and their excited states.
For the complete article, expanded to other 2 Au-based nanoclusters and many more XCFs, see JPC-C (link).
We are eager to start new collaborations both with experimental and computational groups, in order to either extend our competences or study new metal nano-systems.
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