Computational Investigation of the Potential and Limitations of Machine Learning with Neural Network Circuits Based on Synaptic Transistors.

Synaptic transistors have been proposed to implement neuron activation functions of neural networks (NNs). While promising to enable compact, fast, inexpensive, and energy-efficient dedicated NN circuits, they also have limitations compared to digital NNs (realized as codes for digital processors), including shape choices of the activation function using particular types of transistor implementation, and instabilities due to noise and other factors present in analog circuits. We present a computational study of the effects of these factors on NN performance and find that, while accuracy competitive with traditional NNs can be realized for many applications, there is high sensitivity to the instability in the shape of the activation function, suggesting that, when highly accurate NNs are required, high-precision circuitry should be developed beyond what has been reported for synaptic transistors to date.

N-DMBI Doping of Carbon Nanotube Yarns for Achieving High n-Type Thermoelectric Power Factor and Figure of Merit.

The application of carbon nanotube (CNT) yarns as thermoelectric materials for harvesting energy from low-grade waste heat including that generated by the human body, is attracting considerable attention. However, the lack of efficient n-type CNT yarns hinders their practical implementation in thermoelectric devices. This study reports efficient n-doping of CNT yarns, employing 4-(1, 3-dimethyl-2, 3-dihydro-1H-benzimidazole-2-yl) phenyl) dimethylamine (N-DMBI) in alternative to conventional n-dopants, with o-dichlorobenzene emerging as the optimal solvent. The small molecular size of N-DMBI enables highly efficient doping within a remarkably short duration (10 s) while ensuring prolonged stability in air and at high temperature (150 °C). Furthermore, Joule annealing of the yarns significantly improves the n-doping efficiency. Consequently, thermoelectric power factors (PFs) of 2800, 2390, and 1534 µW m-1  K-2 are achieved at 200, 150, and 30 °C, respectively. The intercalation of N-DMBI molecules significantly suppresses the thermal conductivity, resulting in the high figure of merit (ZT) of 1.69×10-2 at 100 °C. Additionally, a π-type thermoelectric module is successfully demonstrated incorporating both p- and n-doped CNT yarns. This study offers an efficient doping strategy for achieving CNT yarns with high thermoelectric performance, contributing to the realization of lightweight and mechanically flexible CNT-based thermoelectric devices.

Degeneration of kernel regression with Matern kernels into low-order polynomial regression in high dimension.

Kernel methods such as kernel ridge regression and Gaussian process regression with Matern-type kernels have been increasingly used, in particular, to fit potential energy surfaces (PES) and density functionals, and for materials informatics. When the dimensionality of the feature space is high, these methods are used with necessarily sparse data. In this regime, the optimal length parameter of a Matern-type kernel may become so large that the method effectively degenerates into a low-order polynomial regression and, therefore, loses any advantage over such regression. This is demonstrated theoretically as well as numerically in the examples of six- and fifteen-dimensional molecular PES using squared exponential and simple exponential kernels. The results shed additional light on the success of polynomial approximations such as PIP for medium-size molecules and on the importance of orders-of-coupling-based models for preserving the advantages of kernel methods with Matern-type kernels of on the use of physically motivated (reproducing) kernels.

A controlled study of the effect of deviations from symmetry of the potential energy surface (PES) on the accuracy of the vibrational spectrum computed with collocation.

Symmetry, in particular permutational symmetry, of a potential energy surface (PES) is a useful property in quantum chemical calculations. It facilitates, in particular, state labelling and identification of degenerate states. In many practically important applications, however, these issues are unimportant. The imposition of exact symmetry and the perception that it is necessary create additional methodological requirements narrowing or complicating algorithmic choices that are thereby biased against methods and codes that by default do not incorporate symmetry, including most off-the-shelf machine learning methods that cannot be directly used if exact symmetry is demanded. By introducing symmetric and unsymmetric errors into the PES of H2CO in a controlled way and computing the vibrational spectrum with collocation using symmetric and nonsymmetric collocation point sets, we show that when the deviations from an ideal PES are random, imposition of exact symmetry does not bring any practical advantages. Moreover, a calculation ignoring symmetry may be more accurate. We also compare machine-learned PESs with and without symmetrization and demonstrate that there is no advantage of imposing exact symmetry for the accuracy of the vibrational spectrum.

Machine learning of kinetic energy densities with target and feature smoothing: Better results with fewer training data.

Machine learning (ML) of kinetic energy functionals (KEFs), in particular kinetic energy density (KED) functionals, is a promising way to construct KEFs for orbital-free density functional theory (DFT). Neural networks and kernel methods including Gaussian process regression (GPR) have been used to learn Kohn-Sham (KS) KED from density-based descriptors derived from KS DFT calculations. The descriptors are typically expressed as functions of different powers and derivatives of the electron density. This can generate large and extremely unevenly distributed datasets, which complicates effective application of ML techniques. Very uneven data distributions require many training datapoints, can cause overfitting, and can ultimately lower the quality of an ML KED model. We show that one can produce more accurate ML models from fewer data by working with smoothed density-dependent variables and KED. Smoothing palliates the issue of very uneven data distributions and associated difficulties of sampling while retaining enough spatial structure necessary for working within the paradigm of KEDF. We use GPR as a function of smoothed terms of the fourth order gradient expansion and KS effective potential and obtain accurate and stable (with respect to different random choices of training points) kinetic energy models for Al, Mg, and Si simultaneously from as few as 2000 samples (about 0.3% of the total KS DFT data). In particular, accuracies on the order of 1% in a measure of the quality of energy-volume dependence B'=EV0-ΔV-2EV0+E(V0+ΔV)ΔV/V02 (where V0 is the equilibrium volume and ΔV is a deviation from it) are obtained simultaneously for all three materials.

Neural Network with Optimal Neuron Activation Functions Based on Additive Gaussian Process Regression.

Feed-forward neural networks (NNs) are a staple machine learning method widely used in many areas of science and technology, including physical chemistry, computational chemistry, and materials informatics. While even a single-hidden-layer NN is a universal approximator, its expressive power is limited by the use of simple neuron activation functions (such as sigmoid functions) that are typically the same for all neurons. More flexible neuron activation functions would allow the use of fewer neurons and layers and thereby save computational cost and improve expressive power. We show that additive Gaussian process regression (GPR) can be used to construct optimal neuron activation functions that are individual to each neuron. An approach is also introduced that avoids nonlinear fitting of neural network parameters by defining them with rules. The resulting method combines the advantage of robustness of a linear regression with the higher expressive power of an NN. We demonstrate the approach by fitting the potential energy surfaces of the water molecule and formaldehyde. Without requiring any nonlinear optimization, the additive-GPR-based approach outperforms a conventional NN in the high-accuracy regime, where a conventional NN suffers more from overfitting.

Nano-scale smooth surface of the compact-TiO2 layer via spray pyrolysis for controlling the grain size of the perovskite layer in perovskite solar cells.

The mechanism of perovskite film growth is critical for the final morphology and, thus, the performance of the perovskite solar cell. The nano-roughness of compact TiO2 (c-TiO2) fabricated via the spray pyrolysis method had a significant effect on the perovskite grain size and perovskite solar cell performance in this work. While spray pyrolysis is a low-cost and straightforward deposition technique suitable for large-scale application, it is influenced by a number of parameters, including (i) alcoholic solvent precursor, (ii) spray temperature, and (iii) annealing temperature. Among alcoholic solvents, 2-propanol and 1-butanol showed a smooth surface without any large TiO2 particles on the surface compared to EtOH. The lowest roughness of the c-TiO2 layer was obtained at 450 °C with an average perovskite grain size of around 300 nm. Increased annealing temperature has a positive effect on the roughness of TiO2. The highest efficiency of the solar cell was achieved by using 1-butanol as the solvent. The decrease in the nano roughness of c-TiO2 promoted larger perovskite grain sizes via a relative decrease in the nucleation rate. Therefore, controlling the spray pyrolysis technique used to deposit the c-TiO2 layer is a promising route to control the surface nanoroughness of c-TiO2, which results in an increase in the MAPbI3 grain size.

Surface engineering of two-dimensional hexagonal boron-nitride for optoelectronic devices.

Two-dimensional hexagonal boron nitride (2D h-BN) is being extensively studied in optoelectronic devices due to its electronic and photonic properties. However, the controlled optimization of h-BN's insulating properties is necessary to fully explore its potential in energy conversion and storage devices. In this work, we engineered the surface of h-BN nanoflakes via one-step in situ chemical functionalization using a liquid-phase exfoliation approach. The functionalized h-BN (F-h-BN) nanoflakes were subsequently dispersed on the surface of TiO2 to tune the TiO2/QDs interface of the optoelectronic device. The photoelectrochemical (PEC) devices based on TiO2/F-h-BN/QDs with optimized addition of carbon nanotubes (CNTs) and scattering layers showed 46% improvement compared to the control device (TiO2/QDs). This significant improvement is attributed to the reduced trap/carrier recombination and enhanced carrier injection rate of the TiO2-CNTs/F-h-BN/QDs photoanode. Furthermore, by employing an optimized TiO2-CNTs/F-h-BN/QDs photoanode, QDs-sensitized solar cells (QDSCs) yield an 18% improvement in photoconversion efficiency. This represents a potential and adaptability of our approach, and pathway to explore surface-engineered 2D materials to optimize the interface of solar energy conversion and other emerging optoelectronic devices.

Hybrid Density Functional Tight Binding (DFTB)─Molecular Mechanics Approach for a Low-Cost Expansion of DFTB Applicability.

The density functional-based tight binding (DFTB) method has seen a rise in adoption for materials modeling, as it offers significant improvement in scalability with accuracy comparable to the density functional theory (DFT) when good parameterizations exist. The cost reduction in DFTB compared to DFT is achieved by the pre-parameterization of the elements of the Hamiltonian matrix as well as the repulsion potential between all pairs of atoms. Parameterization for new systems with accuracies competitive with DFT in specific applications requires specialized manpower and computational resources. This prevents the application of the DFTB method to systems for which it was not parameterized. In this work, we explore an approach to address the problem of missing parameters of DFTB by modeling the interactions with missing Slater-Koster parameters with an interatomic interaction potential. When the distance between two atoms modeled at the force-field level is sufficiently large, the approach results in accurate structural and electronic properties. The resulting calculation is therefore a hybrid between DFTB and molecular mechanics, a pure DFTB for atoms with a complete set of interatomic parameterizations, and a mix between DFTB and molecular mechanics for atoms with a missing interatomic parameterization. The approach is expected to be particularly useful for hybrid materials and interfaces. The method is tested on the examples of 2D materials, mixed oxides, and a large-scale calculation of an oxide-oxide interface.

Clarifying the effects of nanoscale porosity of silicon on the bandgap and alignment: a combined molecular dynamics-density functional tight binding computational study.

Porous silicon (pSi) has been studied for its applications in solar cells, in particular in silicon-silicon tandem solar cells. It is commonly believed that porosity leads to an expansion of the bandgap due to nano-confinement. Direct confirmation of this proposition has been elusive, as experimental band edge quantification is subject to uncertainties and effects of impurities, while electronic structure calculations on relevant length scales are still outstanding. Passivation of pSi is another factor affecting the band structure. We present a combined force field-density functional tight binding study of the effects of porosity of silicon on its band structure. We thus perform electron structure-level calculations for the first time on length scales (several nm) that are relevant to real pSi, and consider multiple nanoscale geometries (pores, pillars, and craters) with key geometrical features and sizes of real porous Si. We consider the presence of a bulk-like base with a nanostructured top layer. We show that the bandgap expansion is not correlated with the pore size but with the size of the Si framework. Significant band expansion would require features of silicon (as opposed to pore sizes) to be as small as 1 nm, while the nanosizing of pores does not induce gap expansion. We observe a graded junction-like behavior of the band gap as a function of Si feature sizes as one moves from the bulk-like base to the nanoporous top layer.

Using Collocation to Solve the Schrödinger Equation.

We review the collocation approach to the solution of the Schrödinger equation and its uses in applications. Interrelations between collocation and other methods are highlighted. We also stress advantages and disadvantages of the rectangular collocation formulation. Using collocation makes it possible to use any, e.g. optimized, coordinates and basis functions, including nonintegrable basis functions, and provides a straightforward way of dealing with singularities in the potential. In addition, we stress that using collocation facilitates tuning the shape of basis functions and the placement of points, both of which can be done with machine-learning methods. Applications to electronic and vibrational problems are reviewed focusing on calculations for molecules on surfaces for which there are few variational calculations. Collocation has advantages when potential energy surfaces are unavailable, in particular, for molecule-surface systems, and for systems for which standard direct product quadrature grids, often used with variational methods, are costly.

The loss of the property of locality of the kernel in high-dimensional Gaussian process regression on the example of the fitting of molecular potential energy surfaces.

Kernel-based methods, including Gaussian process regression (GPR) and generally kernel ridge regression, have been finding increasing use in computational chemistry, including the fitting of potential energy surfaces and density functionals in high-dimensional feature spaces. Kernels of the Matern family, such as Gaussian-like kernels (basis functions), are often used which allow imparting to them the meaning of covariance functions and formulating GPR as an estimator of the mean of a Gaussian distribution. The notion of locality of the kernel is critical for this interpretation. It is also critical to the formulation of multi-zeta type basis functions widely used in computational chemistry. We show, on the example of fitting of molecular potential energy surfaces of increasing dimensionality, the practical disappearance of the property of locality of a Gaussian-like kernel in high dimensionality. We also formulate a multi-zeta approach to the kernel and show that it significantly improves the quality of regression in low dimensionality but loses any advantage in high dimensionality, which is attributed to the loss of the property of locality.

Machine learning in computational chemistry: interplay between (non)linearity, basis sets, and dimensionality.

Machine learning (ML) based methods and tools have now firmly established themselves in physical chemistry and in particular in theoretical and computational chemistry and in materials chemistry. The generality of popular ML techniques such as neural networks or kernel methods (Gaussian process and kernel ridge regression and their flavors) permitted their application to diverse problems from prediction of properties of functional materials (catalysts, solid state ionic conductors, etc.) from descriptors to the building of interatomic potentials (where ML is currently routinely used in applications) and electron density functionals. These ML techniques are assumed to have superior expressive power of nonlinear methods, and are often used "as is", with concepts such as "non-parametric" or "deep learning" used without a clear justification for their need or advantage over simpler and more robust alternatives. In this Perspective, we highlight some interrelations between popular ML techniques and traditional linear regressions and basis expansions and demonstrate that in certain regimes (such as a very high dimensionality) these approximations might collapse. We also discuss ways to recover the expressive power of a nonlinear approach and to help select hyperparameters with the help of high-dimensional model representation and to obtain elements of insight while preserving the generality of the method.

The Role of Local DFT+U Minima in the First-Principles Modeling of the Metal-Insulator Transition in Vanadium Dioxide.

The DFT+U method is frequently employed to improve the first-principles description of strongly correlated materials. However, it is prone to deliver metastable electronic minima. While these local minima of the DFT+U method are often considered to be computational artifacts, their physical meaning and relationship to true excited states remains unclear. In this work, the possibility of theoretically modeling transformations in the solid state that require thermal or optical excitations of electrons is explored, taking into account the metastable states of the computationally undemanding DFT+U formalism. For this purpose, we choose to examine the example of the VO2 metal-insulator transition. Metastable states that are located on different electronic potential energy surfaces are found to correspond to experimentally observed VO2 phases. The identified metastable electronic states can be used to model the collapse of the VO2 band gap at elevated temperatures and upon photoexcitation as well as other monoclinic-monoclinic phase transformations. The results suggest that local DFT+U minima can indeed carry physical meaning, while they remain under-reported in theoretical literature on transition metal oxides like VO2.

Computational vibrational spectroscopy of molecule-surface interactions: what is still difficult and what can be done about it.

Interactions of molecules with solid surfaces are responsible for key functionalities in a range of currently actively pursued technologies, including heterogeneous catalysis for synthesis or decomposition of molecules, sensitization, surface functionalization and molecular doping, etc. Modeling of such interactions is important, in particular, for the assignment of species and assignment and design of reaction pathways and ultimately for rational design of better functional materials for a range of applications. Key types of calculations involve calculations of adsorption structures and energies, electronic structures, charge transport, vibrational and optical spectra, and reaction dynamics. While some of these calculations are routinely doable for small-size models, other types of calculations, including anharmonic vibrational spectroscopy, accurate optical spectroscopy, quantum reaction dynamics, and calculations on large systems, are still too difficult to be routinely doable. In this Perspective, we specifically focus on issues related to computing accurate vibrational spectra including quantum effects and anharmonicity and coupling of key degrees of freedom. Vibrational spectroscopies are widely used for species assignment on surfaces but computations of vibrational spectra are still dominated by the harmonic approximation. We discuss approaches that can make accurate quantum anharmonic computational spectroscopy easier and enable its wider deployment in applications. We describe advantages and disadvantages of different techniques including perturbation theory, variational, vibrational self-consistent field and vibrational configuration interaction, as well as collocation which we argue has significant potential in this application, allowing computing accurate spectra directly from non-expensive ab initio data and with modest CPU cost. Examples of applications of anharmonic techniques to molecule-surface systems are given.

Density-Based Descriptors of Redox Reactions Involving Transition Metal Compounds as a Reality-Anchored Framework: A Perspective.

Description of redox reactions is critically important for understanding and rational design of materials for electrochemical technologies, including metal-ion batteries, catalytic surfaces, or redox-flow cells. Most of these technologies utilize redox-active transition metal compounds due to their rich chemistry and their beneficial physical and chemical properties for these types of applications. A century since its introduction, the concept of formal oxidation states (FOS) is still widely used for rationalization of the mechanisms of redox reactions, but there exists a well-documented discrepancy between FOS and the electron density-derived charge states of transition metal ions in their bulk and molecular compounds. We summarize our findings and those of others which suggest that density-driven descriptors are, in certain cases, better suited to characterize the mechanism of redox reactions, especially when anion redox is involved, which is the blind spot of the FOS ansatz.

Structural Geometry Variation of 1,4-Naphthalene-Based Co-Polymers to Tune the Device Performance of PVK-Host-Based OLEDs.

Blue-color-emitting organic semiconductors are of significance for organic light-emitting diodes (OLEDs). In this study, through Suzuki coupling polymerization, three 1,4-naphthalene-based copolymers-namely, PNP(1,4)-PT, PNP(1,4)-TF, and PNP(1,4)-ANT-were designed and synthesized. The variation of comonomers, phenothiazine (PT), triphenylamine substituted fluorene (TF), and anthanthrene (ANT), effectively tuned the emitting color and device performance of poly(9-vinyl carbazole) (PVK)-based OLEDs. Especially, the polymer PNP(1,4)-TF, bearing perpendicular aryl side groups, showed a most twisted structural geometry, which enabled an ultra-high thermal stability and a best performance with blue emitting in PVK-host-based OLEDs. Overall, in this work, we demonstrate a promising blue-color-emitting polymer through structural geometry manipulation.

Materials Design and Optimization for Next-Generation Solar Cell and Light-Emitting Technologies.

We review some of the most potent directions in the design of materials for next-generation solar cell and light-emitting technologies that go beyond traditional solid-state inorganic semiconductor-based devices, from both the experimental and computational standpoints. We focus on selected recent conceptual advances in tackling issues which are expected to significantly impact applied literature in the coming years. Specifically, we consider solution processability, design of dopant-free charge transport materials, two-dimensional conjugated polymeric semiconductors, and colloidal quantum dot assemblies in the fields of experimental synthesis, characterization, and device fabrication. Key modeling issues that we consider are calculations of optical properties and of effects of aggregation, including recent advances in methods beyond linear-response time-dependent density functional theory and recent insights into the effects of correlation when going beyond the single-particle ansatz as well as in the context of modeling of thermally activated fluorescence.

Synergistic Effect of Dielectric Property and Energy Transfer on Charge Separation in Non-Fullerene-Based Solar Cells.

In non-fullerene-based photovoltaic devices, it is unclear how excitons efficiently dissociate into charge carriers under small driving force. Here, we developed a modified method to estimate dielectric constants of PM6 donor and non-fullerene acceptors. Surprisingly, most non-fullerene acceptors and blend films showed higher dielectric constants. Moreover, they exhibited larger dielectric constants differences at the optical frequency. These results are likely bound to reduced exciton binding energy and bimolecular recombination. Besides, the overlap between the emission spectrum of donor and absorption spectra of non-fullerene acceptors allowed the energy transfer from donor to acceptors. Hence, based on the synergistic effect of dielectric property and energy transfer resulting in efficient charge separation, our finding paves an alternative path to elucidate the physical working mechanism in non-fullerene-based photovoltaic devices.

One-step direct oxidation of fullerene-fused alkoxy ethers to ketones for evaporable fullerene derivatives.

Ketones are widely applied moieties in designing functional materials and are commonly obtained by oxidation of alcohols. However, when alcohols are protected/functionalized, the direct oxidation strategies are substantially curbed. Here we show a highly efficient copper bromide promoted one-step direct oxidation of benzylic ethers to ketones with the aid of a fullerene pendant. Mechanistic studies unveil that fullerene can serve as an electron pool proceeding the one-step oxidation of alkoxy group to ketone. In the absence of the fullerene pendant, the unreachable activation energy threshold hampers the direct oxidation of the alkoxy group. In the presence of the fullerene pendant, generated fullerene radical cation can activate the neighbour C-H bond of the alkoxy moiety, allowing a favourable energy barrier for initiating the direct oxidation. The produced fullerene-fused ketone possesses high thermal stability, affording the pin-hole free and amorphous electron-transport layer with a high electron-transport mobility.