Search arXiv⌕ Search

arXiv · cond-mat/0306332

Vibrational properties of a sodium tetrasilicate glass: Ab initio versus Classical Force Fields

Abstract

We have determined the vibrational properties of a sodium tetrasilicate (Na$_{2}$Si$_{4}$O$_{9}$) glass model generated by molecular dynamics simulations. The study has been carried out using a classical valence force fields approach as well as an {\it ab initio} approach in the framework of the density functional theory. The total and partial vibrational densities of states (VDOS) are presented, as well as some characteristics of the vibrational modes (participation ratios, correlation lengths). For the low-frequency bands below 500 cm${}^{-1}$, we find that the shapes of the two calculated VDOS as well as those of their corresponding partial VDOS are quite similar. For the intermediate- and high-frequency ranges, we observe larger discrepancies between the two calculations. Using the eigenmodes of the dynamical matrix we also calculate the polarized Raman spectra within the bond-polarizability approximation. We find an overall agreement between the calculated parallel polarized (VV) Raman spectra and the corresponding experimental spectrum. Regarding the perpendicular depolarized (VH) Raman spectrum, the comparison of the calculated spectra to the experimental data indicates a need for an adjustment of the VH bond-polarizability parameters.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

S. Ispas, N. Zotov, S. De Wispelaere, W. Kob. 2003-11-17. Vibrational properties of a sodium tetrasilicate glass: Ab initio versus Classical Force Fields. https://arxiv.org/abs/cond-mat/0306332

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Deep-layered machines have a built-in Occam's razor

Many complex systems map vast numbers of microscopic descriptions onto far fewer macroscopic outcomes. Surprisingly, these input-output maps strongly favor simple outputs. In an exactly solvable deep-layered machine, we prove that simplicity bias strengthens with every layer. The probability of an output function $F$ approaches $\Pr(F)\propto 2^{-K(F)}$, where $K$ is the Kolmogorov complexity. Our results show that hierarchical composition alone can generate an intrinsic Occam's razor, suggesting a general mechanism for simplicity bias in learning and evolution.

cond-mat.dis-nn↗

Neural Networks with Exciton-Polariton Waveguides

We propose and numerically study a scheme for neural networks using exciton-polariton waveguide meshes. These enable arbitrary programmable interlayer couplings suited to a restricted Boltzmann machine architecture where polariton phases act as stochastic network variables. We show that such a network can be trained using unsupervised Hebbian and anti-Hebbian updates. This allows the implementation of an associative memory, where the network recovers learned patterns from imperfect inputs.

cond-mat.dis-nn↗

Finite-width shift of the edge of chaos in deep neural networks

Deep neural networks train best when they are initialised at the edge of chaos, the critical line in the plane of weight and bias variances on which the distance between two inputs neither grows nor shrinks with depth. The line is known for infinitely wide networks; at finite width it moves, and how it moves has been disputed. We treat the logarithm of the distance between two inputs through a network of width $N$ as a random walk and compute its drift and variance to order $1/N$. The edge of chaos moves to a larger weight variance, by $Δσ_w^2=-a_1/(N\,\partial_{σ_w^2}\lnχ_1)$, about $8/N$ for $\tanh$ networks at a bias variance of $0.05$, confirmed by simulations of the exact finite-width recursion. The shift describes a typical network; the average over many networks is dominated by rare networks in which the distance grows, and its critical point moves the other way, which explains why calculations and simulations have disagreed. Backpropagation follows the same random walk, so the shift applies to gradients unchanged. Along the edge of chaos, the information about the similarity of two inputs is constant until the compression over the depth exceeds about one nat, which fixes where to sit on the line. The results give an initialisation rule, Crinit, that places a network on its finite-width edge of chaos without a search. On MNIST and Fashion-MNIST at width $64$ it is more accurate than the standard rules at their usual settings, by a small margin in shallow networks and a large one in deep networks, where most standard rules fail; it trains in fewer steps, and it matches or beats the standard rules with a tuned gain.

cond-mat.dis-nn↗