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Proposals that utilize established theoretical and modeling approaches to solve problems in chemistry without significant theoretical or methodological development, or that focus on the development of biology or materials design, may be more appropriate for other programs in either the Chemistry Division or in other NSF Divisions or Directorates. Display additional information.

Contact Help Search search. Search search. Email Print Share. Display additional information News. E E D. However, as soon as we retrain Model 1 on four additional MD snapshots each of PE with double and triple bonds we immediately observe a sharp improvement in the predictive capabilities of the new model referred to as Model 2 as depicted in Fig.

A single model is capable of capturing vastly different bonding environments highlighting that although an initial model may not be general enough, the prediction capability can be systematically improved. Model 1 , trained on eight molecular dynamics snapshots of pristine PE, is unable to accurately predict the charge density in the vicinity of the defects. Model 2 , trained on four additional snapshots each of PE with double and triple bonds is able to accurately capture the charge density for unseen snapshots containing such defects.

The neural network models were trained and implemented for prediction in a graphical processing unit GPU -based computing system. As depicted in Fig. DFT calculations on equivalent materials systems, performed on 48 cores of a more expensive central processing unit CPU node, are orders of magnitude slower and also scale quadratically. Moreover, as shown in Table S3 , traditional DFT algorithms are memory intensive and cannot handle more than a few thousand atoms. Computational time and scaling of density functional theory DFT vs machine learning ML for electronic structure predictions.

DFT shows near-quadratic scaling, whereas the ML prediction algorithm shows perfect linear-scaling and is orders of magnitude faster than DFT. We note, however, that direct comparison between DFT and ML computing times is difficult as the computations were performed on different architectures. Since modern DFT codes scale at best quadratically, the relative cost and time benefit of the proposed ML prediction scheme is enhanced tremendously for large system sizes of tens of thousands of atoms.

The details of the scaling tests are shown in Table S3. As a final comment, we mention that the predicted total DOS and charge density can be utilized to directly obtain the total energy E of the system. In Eq.


Hence, the ML-enabled prediction of the DOS and charge density allows us to directly access the total energy, circumventing the computationally expensive Kohn-Sham equation. In Section 2 of the Supplementary material we have provided preliminary results on how the charge density predicted using ML can be used to obtain highly accurate total energies when used as a starting point for a non-self-consistent calculation. A more comprehensive investigation of obtaining the total energy from the charge density and DOS using Eq. Once trained on past one-time DFT results , the ML models can predict the electronic charge density and DOS given just the atomic configuration information.

In contrast to recent works, 40 we have demonstrated a direct grid-based learning and prediction scheme as opposed to the learning of a certain basis representation of the local electronic properties.

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A brief discussion of the merits and limitations of both methods is provided in Section 1 of the Supplementary material. We mention here that standard DFT calculations involve thousands or even millions of grid-points. The exceptional accuracy obtained using this grid-based approach thus comes at the cost of greater computational effort. Moreover, the learning of the grid-based LDOS is memory intensive since it requires multiple partial charge density files for every for every energy-window. Nonetheless, by taking advantage of modern GPU architectures and parallelized batch-wise training and prediction schemes, our algorithm is linear-scaling and has been shown to be several orders of magnitude faster than the parent DFT code that created the training data in the first place.

Large systems, containing several tens of thousands of atoms, inaccessible to traditional DFT computations, can be routinely handled; this capability may thus be interfaced with MD software, which can then produce electronic structure results along the molecular trajectory. Other derived properties, such as energy, forces, dipole moments, etc.

Going forward, we hope to benchmark our method using large, diverse, and well-curated datasets such as the QM9 dataset. Slabs are used for data generation rather than bulk structures so as to obtain energy values with respect to the vacuum level. The LDOS is defined as the density of eigenvalues in a particular energy interval at a given grid-point. Four PE polymer chains were constructed with the chain direction along the z -axis. Each polymer chain consisted of 10 carbon and 20 hydrogen atoms atoms in the entire supercell.

A six-atomic layer-thick Al slab was constructed with atoms as depicted in Figure S1 a. Ten structures were then chosen at random from the generated trajectory to be included in the dataset.

Theoretical and Computational Chemistry

The scalar fingerprint, S k , is already rotationally invariant. The rotationally invariant form of the vector fingerprint is,. The width of the narrowest Gaussian utilized was 0. Therefore, 16 Gaussians of widths ranging from 0. Prior to the training phase, each fingerprint column was scaled to a mean of zero and variance of one.

28. Modern Electronic Structure Theory: Basis Sets

Our initial convergence tests indicate as depicted in the inset of Figure S4 that 16 Gaussians are more than sufficient to model both Al and PE systems. However, a more in depth system-dependent analysis of the range and number of Gaussians would likely reduce the error even further. The high-level neural network API, Keras, was utilized to build the models. We used the mean-squared-error as the loss function and employed the ADAM stochastic optimization method for gradient descent. The convergence of the neural network hyperparameters is indicated in Figure S5. A batch size of grid-points was used during the training phase.

Ten recurrent neurons were linked to each of the final energy windows. In all neural networks, the RelU activation function was utilized. LeCun, Y. Deep learning. Nature , Geiger, A. Are we ready for autonomous driving? Mueller, T. Machine learning in materials science: recent progress and emerging applications. Huo, H. Unified representation for machine learning of molecules and crystals. Gaussian approximation potentials: the accuracy of quantum mechanics, without the electrons.

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Hands-On DFT and Beyond: Frontiers of Advanced Electronic Structure and Molecular Dynamics Methods

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