Quantum-Mechanical Assessment of the Energetics of Silver Decahedron Nanoparticles

Abstract

We present a quantum-mechanical study of silver decahedral nanoclusters and nanoparticles containing from 1 to 181 atoms in their static atomic configurations corresponding to the minimum of the ab initio computed total energies. Our thermodynamic analysis compares T = 0 K excess energies (without any excitations) obtained from a phenomenological approach, which mostly uses bulk-related properties, with excess energies from ab initio calculations of actual nanoclusters/nanoparticles. The phenomenological thermodynamic modeling employs (i) the bulk reference energy, (ii) surface energies obtained for infinite planar (bulk-related) surfaces and (iii) the bulk atomic volume. We show that it can predict the excess energy (per atom) of nanoclusters/nanoparticles containing as few as 7 atoms with the error lower than 3%. The only information related to the nanoclusters/nanoparticles of interest, which enters the phenomenological modeling, is the number of atoms in the nanocluster/nanoparticle, the shape and the crystallographic orientation(s) of facets. The agreement between both approaches is conditioned by computing the bulk-related properties with the same computational parameters as in the case of the nanoclusters/nanoparticles but, importantly, the phenomenological approach is much less computationally demanding. Our work thus indicates that it is possible to substantially reduce computational demands when computing excess energies of nanoclusters and nanoparticles by ab initio methods.Relative to the bulk, the {111} facet exhibits the highest density of atoms and the highest coordination number of surface atoms. The most stable structures of fcc nanoclusters include the icosahedron, cuboctahedron and decahedron [8]. Another energy contribution is that related to strain. The strain energy of the particle can be affected by many factors. As the ratio of surface to volume decreases, the effect of surface stress is more significant and leads to the compression of particles [8].Our study is focused on decahedral particles which have very interesting plasmonic and optical properties [16] as well as catalytic possibilities due to high strain energy [9]. The decahedron and icosahedron are inherently strained due to twinning and unfilled volume [17]. In particular, the decahedral nanoclusters are balancing the surface stability of five tetrahedrons (see Figure 1), which exhibit the {111} facets, against the strain energy related to an internal unfilled gap of 7.35 • and distortion induced by their twinned internal structure [9]. The actual shape of the studied nanoparticles can deviate from a prediction by the Wulff construction due to the influence of the internal strain and strain-associated strain energy (in particular in the case of intermediate states [18,19]).

Multiscale Modeling of Bio-Nano Interactions of Zero-Valent Silver Nanoparticles

“…For example, inconsistent estimates for the surface free energies for silver slabs in vacuum obtained at a different level of density functional theory approximation have been published. 79 − 81 …”

Best-Practice Aspects of Quantum-Computer Calculations: A Case Study of the Hydrogen Molecule

“…Quantum computing has recently emerged as a very promising alternative to conventional computational means. Conventional supercomputers, albeit versatile and remarkably reliable, seem to be outpaced by ever-increasing demand for computational power when developing new drugs [ 1 ], modeling nanoparticles [ 2 ], or assessing problems in materials science [ 3 ] and nuclear physics [ 4 , 5 ]. In contrast to the well-established conventional technologies, quantum computers are expected to provide exponentially growing computational power thanks to the their use of quantum effects [ 6 , 7 ], and the first indications of so-called quantum advantage/supremacy have already been demonstrated [ 8 , 9 , 10 ].…”

Multiscale modeling of bio-nano interactions of zero-valent silver nanoparticles.

“…In silico tools predicting those characteristics are available, but also susceptible to the same issues. For example, inconsistent estimates for the surface free energies for silver slabs in vacuum obtained at a different level of DFT approximation have been published [76][77][78] (Table 1).…”