Medford group publications
A full list of publications is available via Prof. Medford's Google Scholar page.
Some selected publications are also highlighted below.
Gabriel S.Gusmão, Adhika P. Retnanto, Shashwati C. daCunha, Andrew J. Medford; Cat. Today (2022) doi: 10.1016/j.cattod.2022.04.002
Chemical kinetics and reaction engineering consists of the phenomenological framework for the disentanglement of reaction mechanisms, optimization of reaction performance and the rational design of chemical processes. Here, we utilize feed-forward artificial neural networks as basis functions to solve ordinary differential equations (ODEs) constrained by differential algebraic equations (DAEs) that describe microkinetic models (MKMs). We present an algebraic framework for the mathematical description and classification of reaction networks, types of elementary reaction, and chemical species. Under this framework, we demonstrate that the simultaneous training of neural nets and kinetic model parameters in a regularized multi-objective optimization setting leads to the solution of the inverse problem through the estimation of kinetic parameters from synthetic experimental data. We analyze a set of scenarios to establish the extent to which kinetic parameters can be retrieved from transient kinetic data, and assess the robustness of the methodology with respect to statistical noise. This approach to inverse kinetic ODEs can assist in the elucidation of reaction mechanisms based on transient data.
J. Phys. Chem. Lett. (2022) doi: 10.1021/acs.jpclett.2c02100
Machine-learning force fields have become increasingly popular because of their balance of accuracy and speed. However, a significant limitation is the use of element-specific features, leading to poor scalability with the number of elements. This work introduces the Gaussian multipole (GMP) featurization scheme that utilizes physically relevant multipole expansions of the electron density around atoms to yield feature vectors that interpolate between element types and have a fixed dimension regardless of the number of elements present. We combine GMP with neural networks and apply these models to the MD17 and QM9 data sets, revealing high computational efficiency, systematically improvable accuracy, and the ability to make reasonable predictions on elements not included in the training set. Finally, we test GMP-based models for the OCP data set, demonstrating comparable performance to graph-convolutional models. The results indicate that this featurization scheme fills a critical gap in the construction of efficient and transferable machine-learned force fields.
Schematic depicting the neural network used to predict exchange-correlation energy density from the electron density.
Xiangyun Lei and Andrew J. Medford, Phys. Rev. Materials (2019) doi:10.1103/PhysRevMaterials.3.063801
In this work we explore the potential of a data-driven approach to the design of exchange-correlation (xc) functionals. The approach, inspired by convolutional filters in computer vision and surrogate functions from optimization, utilizes convolutions of the electron density to form a feature space to represent local electronic environments and neural networks to map the features to the exchange-correlation energy density. These features are orbital free, and provide a systematic route to including information at various length scales. This work shows that convolutional descriptors are theoretically capable of an exact representation of the electron density, and proposes Maxwell-Cartesian spherical harmonic kernels as a class of rotationally invariant descriptors for the construction of machine learned functionals. The approach is demonstrated using data from the B3LYP functional on a number of small molecules containing C, H, O, and N along with a neural network regression model. The machine learned functionals are compared to standard physical approximations and the accuracy is assessed for the absolute energy of each molecular system as well as formation energies. The results indicate that it is possible to reproduce the exchange-correlation portion of B3LYP formation energies to within chemical accuracy using orbital-free descriptors with a spatial extent of 0.2 Å. The findings provide empirical insight into the spatial range of electron exchange, and suggest that the combination of convolutional descriptors and machine learning regression models is a promising framework for xc functional design, although challenges remain in obtaining training data and generating models consistent with pseudopotentials.
The proposed carbon-mediated catalytic cycle for photocatalytic nitrogen fixation. Surface-bound carbon radical species are generated by photo-oxidation of adventitous hydrocarbons on the surface of TiO2. These reactive carbon species efficiently bind dinitrogen, and subsequent reduction occurs through photo-generated electrons.
Benjamin M. Comer, Yu-Hsuan Liu, Marm B. Dixit, Kelsey B. Hatzell , Yifan Ye, Ethan J. Crumlin , Marta C. Hatzell, and Andrew J. Medford, JACS (2018) doi:10.1021/jacs.8b08464
Photo-catalytic fixation of nitrogen by titania catalysts at ambient conditions has been reported for decades, yet the active site capable of adsorbing an inert N2 molecule at ambient pressure and the mechanism of dissociating the strong dinitrogen triple bond at room temperature remain unknown. In this work in situ near-ambient-pressure X-ray photo-electron spectroscopy and density functional theory calculations are used to probe the active state of the rutile (110) surface. The experimental results indicate that photon-driven interaction of N2 and TiO2 is observed only if adventitious surface carbon is present, and computational results show a remarkably strong interaction between N2 and carbon substitution (C*) sites that act as surface-bound carbon radicals. A carbon-assisted nitrogen reduction mechanism is proposed and shown to be thermodynamically feasible. The findings provide a molecular-scale explanation for the long-standing mystery of photo-catalytic nitrogen fixation on titania. The results suggest that controlling and characterizing carbon-based active sites may provide a route to engineering more efficient photo(electro)-catalysts and improving experimental reproducibility.
Andrew J. Medford, M. Ross Kunz, Sarah M. Ewing, Tammie Borders, and Rebecca Fushimi, ACS Catalysis (2018) doi:10.1021/acscatal.8b01708
Catalysis informatics is a distinct subfield that lies at the intersection of cheminformatics and materials informatics but with distinctive challenges arising from the dynamic, surface-sensitive, and multiscale nature of heterogeneous catalysis. The ideas behind catalysis informatics can be traced back decades, but the field is only recently emerging due to advances in data infrastructure, statistics, machine learning, and computational methods. In this work, we review the field from early works on expert systems and knowledge engines to more recent approaches utilizing machine-learning and uncertainty quantification. The data–information–knowledge hierarchy is introduced and used to classify various developments. The chemical master equation and microkinetic models are proposed as a quantitative representation of catalysis knowledge, which can be used to generate explanative and predictive hypotheses for the understanding and discovery of catalytic materials. We discuss future prospects for the field, including improved quantitative coupling of experiment/theory, advanced microkinetic models, and the development of open-source software tools. Ultimately, integration of existing chemical and physical models with emerging statistical and computational tools presents a promising route toward the automated design, discovery, and optimization of heterogeneous catalytic processes.
Free energies of nitrogen reduction intermediates for the associative mechanism on the rutile TiO2(110) surface calculated using density functional theory. The pristine surface, an oxygen vacancy defect, and iron substitution defect are investigated.
Benjamin C. Comer and Andrew J. Medford, ACS Sustainable Chemistry & Engineering (2018) doi:10.1021/acssuschemeng.7b03652
Photocatalytic nitrogen fixation provides a promising route to produce reactive nitrogen compounds at benign conditions. Titania has been reported as an active photocatalyst for reduction of dinitrogen to ammonia; however there is little fundamental understanding of how this process occurs. In this work the rutile (110) model surface is hypothesized to be the active site, and a computational model based on the Bayesian error estimation functional (BEEF-vdW) and computational hydrogen electrode is applied in order to analyze the expected dinitrogen coverage at the surface as well as the overpotentials for electrochemical reduction and oxidation. This is the first application of computational techniques to photocatalytic nitrogen fixation, and the results indicate that the thermodynamic limiting potential for nitrogen reduction on rutile (110) is considerably higher than the conduction band edge of rutile TiO2, even at oxygen vacancies and iron substitutions. This work provides strong evidence against the most commonly reported experimental hypotheses, and indicates that rutile (110) is unlikely to be the relevant surface for nitrogen reduction. However, the limiting potential for nitrogen oxidation on rutile (110) is significantly lower, indicating that oxidative pathways may be relevant on rutile (110). These findings suggest that photocatalytic dinitrogen fixation may occur via a complex balance of oxidative and reductive processes.
Andrew J. Medford and Marta C Hatzell, ACS Catalysis (2017) doi:10.1021/acscatal.7b00439
Over the last century the industrialization of agriculture and the consumption of fossil fuels have resulted in a significant imbalance and redistribution in nitrogen containing resources. This has sparked an interest in developing more sustainable and resilient approaches for producing nitrogen-containing commodities such as fertilizers and fuels. One largely neglected but emerging approach is photocatalytic nitrogen fixation. There is significant evidence that this process occurs spontaneously in terrestrial settings, and it has been demonstrated in numerous engineered systems. Yet many questions still remain unanswered regarding the rates, mechanisms and impacts of photocatalytically producing fixed nitrogen "out of thin air". This work reviews the fascinating history of the reaction and examines current progress toward understanding and improving photo-fixation of nitrogen. This is supplemented by a quantitative review of the thermodynamic considerations and limitations for various reaction mechanisms. Finally, future prospects and preliminary performance targets for photocatalytic nitrogen fixation are discussed.
“Essentially, all models are wrong, but some are useful.”