The central role of density functional theory in the AI age

Periodic Single-Metal Site Catalysts: Creating Homogeneous and Ordered Atomic-Precision Structures

Heterogeneous single-metal-site catalysts (SMSCs), often referred to as single-atom catalysts (SACs), demonstrate promising catalytic activity, selectivity, and stability across a wide spectrum of reactions due to their rationally designed microenvironments encompassing coordination geometry, binding ligands, and electronic configurations. However, the inherent disorderliness of SMSCs at both atomic scale and nanoscale poses challenges in deciphering working principles and establishing the correlations between microenvironments and the catalytic performances of SMSCs. The rearrangement of randomly dispersed single metals into homogeneous and atomic-precisely structured periodic single-metal site catalysts (PSMSCs) not only simplifies the chaos in SMSCs systems but also unveils new opportunities for manipulating catalytic performance and gaining profound insights into reaction mechanisms. Moreover, the synergistic effects of adjacent single metals and the integration effects of periodic single-metal arrangement further broaden the industrial application scope of SMSCs. This perspective offers a comprehensive overview of recent advancements and outlines prospective avenues for research in the design and characterizations of PSMSCs, while also acknowledging the formidable challenges encountered and the promising prospects that lie ahead.

Ensemble Generalization of the Perdew-Zunger Self-Interaction Correction: A Way Out of Multiple Minima and Symmetry Breaking

The Perdew-Zunger (PZ) self-interaction correction (SIC) is an established tool to correct unphysical behavior in density functional approximations. Yet, the PZ-SIC is well-known to sometimes break molecular symmetries. An example of this is the benzene molecule, for which the PZ-SIC predicts a symmetry-broken electron density and molecular geometry, since the method does not describe the two possible Kekulé structures on an even footing, leading to local minima [Lehtola et al. J. Chem. Theory Comput. 2016, 12, 3195]. The PZ-SIC is often implemented with Fermi-Löwdin orbitals (FLOs), yielding the FLO-SIC method, which likewise has issues with symmetry breaking and local minima [Trepte et al. J. Chem. Phys. 2021, 155, 224109]. In this work, we propose a generalization of the PZ-SIC─the ensemble PZ-SIC (E-PZ-SIC) method─which shares the asymptotic computational scaling of the PZ-SIC (albeit with an additional prefactor). The E-PZ-SIC is straightforwardly applicable to various molecules, merely requiring one to average the self-interaction correction over all possible Kekulé structures, in line with chemical intuition. We showcase the implementation of the E-PZ-SIC with FLOs, as the resulting E-FLO-SIC method is easy to realize on top of an existing implementation of the FLO-SIC. We show that the E-FLO-SIC indeed eliminates symmetry breaking, reproducing a symmetric electron density and molecular geometry for benzene. The ensemble approach suggested herein could also be employed within approximate or locally scaled variants of the PZ-SIC and its FLO-SIC versions.

Boosting-Crystal Graph Convolutional Neural Network for Predicting Highly Imbalanced Data: A Case Study for Metal-Insulator Transition Materials

Applying machine-learning techniques for imbalanced data sets presents a significant challenge in materials science since the underrepresented characteristics of minority classes are often buried by the abundance of unrelated characteristics in majority of classes. Existing approaches to address this focus on balancing the counts of each class using oversampling or synthetic data generation techniques. However, these methods can lead to loss of valuable information or overfitting. Here, we introduce a deep learning framework to predict minority-class materials, specifically within the realm of metal-insulator transition (MIT) materials. The proposed approach, termed boosting-CGCNN, combines the crystal graph convolutional neural network (CGCNN) model with a gradient-boosting algorithm. The model effectively handled extreme class imbalances in MIT material data by sequentially building a deeper neural network. The comparative evaluations demonstrated the superior performance of the proposed model compared to other approaches. Our approach is a promising solution for handling imbalanced data sets in materials science.

Construction of Highly Accurate Machine Learning Potential Energy Surfaces for Excited-State Dynamics Simulations Based on Low-Level Data Sets

Machine learning is capable of effectively predicting the potential energies of molecules in the presence of high-quality data sets. Its application in the construction of ground- and excited-state potential energy surfaces is attractive to accelerate nonadiabatic molecular dynamics simulations of photochemical reactions. Because of the huge computational cost of excited-state electronic structure calculations, the construction of a high-quality data set becomes a bottleneck. In the present work, we first built two data sets. One was obtained from surface hopping dynamics simulations at the semiempirical OM2/MRCI level. Another was extracted from the dynamics trajectories at the CASSCF level, which was reported previously. The ground- and excited-state potential energy surfaces of ethylene-bridged azobenzene at the CASSCF computational level were constructed based on the former low-level data set. Although non-neural network machine learning methods can achieve good or modest performance during the training process, only neural network models provide reliable predictions on the latter external test data set. The BPNN and SchNet combined with the Δ-ML scheme and the force term in the loss functions are recommended for dynamics simulations. Then, we performed excited-state dynamics simulations of the photoisomerization of ethylene-bridged azobenzene on machine learning potential energy surfaces. Compared with the lifetimes of the first excited state (S1) estimated at different computational levels, our results on the E isomer are in good agreement with the high-level estimation. However, the overestimation of the Z isomer is unimproved. It suggests that smaller errors during the training process do not necessarily translate to more accurate predictions on high-level potential energies or better performance on nonadiabatic dynamics simulations, at least in the present case.

Identifying and embedding transferability in data-driven representations of chemical space

Transferability, especially in the context of model generalization, is a paradigm of all scientific disciplines. However, the rapid advancement of machine learned model development threatens this paradigm, as it can be difficult to understand how transferability is embedded (or missed) in complex models developed using large training data sets. Two related open problems are how to identify, without relying on human intuition, what makes training data transferable; and how to embed transferability into training data. To solve both problems for ab initio chemical modelling, an indispensable tool in everyday chemistry research, we introduce a transferability assessment tool (TAT) and demonstrate it on a controllable data-driven model for developing density functional approximations (DFAs). We reveal that human intuition in the curation of training data introduces chemical biases that can hamper the transferability of data-driven DFAs. We use our TAT to motivate three transferability principles; one of which introduces the key concept of transferable diversity. Finally, we propose data curation strategies for general-purpose machine learning models in chemistry that identify and embed the transferability principles.

A systematic theoretical study of CO2 hydrogenation towards methanol on Cu-based bimetallic catalysts: role of the CHO&CH3OH descriptor in thermodynamic analysis

The application of density functional theory (DFT) has enriched our understanding of methanol synthesis through CO2 hydrogenation on Cu-based catalysts. However, variations in catalytic performance under different metal doping conditions have hindered the development of universal catalytic principles. To address these challenges, we systematically investigated the scaling relationships of adsorption energy among different reaction intermediates on pure Cu, Au-Cu, Ni-Cu, Pt-Cu, Pd-Cu and Zn-Cu models. Additionally, by summing the respective adsorption energies of two separate species, we have developed a dual intermediate descriptor of CHO&CH3OH, capable of achieving computational accuracy on par with DFT results using the multiple linear regression method, all the while enabling the rapid prediction of thermodynamic properties at various stages of methanol synthesis. This method facilitates a better understanding of the coupling mechanisms between energy and linear expressions on copper-based substrates, and the universal linear criterion can be applied to other catalytic systems, with the aim of pursuing potential catalysts having both high efficiency and low cost.

Dataset for quantum-mechanical exploration of conformers and solvent effects in large drug-like molecules

We here introduce the Aquamarine (AQM) dataset, an extensive quantum-mechanical (QM) dataset that contains the structural and electronic information of 59,783 low-and high-energy conformers of 1,653 molecules with a total number of atoms ranging from 2 to 92 (mean: 50.9), and containing up to 54 (mean: 28.2) non-hydrogen atoms. To gain insights into the solvent effects as well as collective dispersion interactions for drug-like molecules, we have performed QM calculations supplemented with a treatment of many-body dispersion (MBD) interactions of structures and properties in the gas phase and implicit water. Thus, AQM contains over 40 global and local physicochemical properties (including ground-state and response properties) per conformer computed at the tightly converged PBE0+MBD level of theory for gas-phase molecules, whereas PBE0+MBD with the modified Poisson-Boltzmann (MPB) model of water was used for solvated molecules. By addressing both molecule-solvent and dispersion interactions, AQM dataset can serve as a challenging benchmark for state-of-the-art machine learning methods for property modeling and de novo generation of large (solvated) molecules with pharmaceutical and biological relevance.

Paving the road towards automated homogeneous catalyst design

In the past decade, computational tools have become integral to catalyst design. They continue to offer significant support to experimental organic synthesis and catalysis researchers aiming for optimal reaction outcomes. More recently, data-driven approaches utilizing machine learning have garnered considerable attention for their expansive capabilities. This Perspective provides an overview of diverse initiatives in the realm of computational catalyst design and introduces our automated tools tailored for high-throughput in silico exploration of the chemical space. While valuable insights are gained through methods for high-throughput in silico exploration and analysis of chemical space, their degree of automation and modularity are key. We argue that the integration of data-driven, automated and modular workflows is key to enhancing homogeneous catalyst design on an unprecedented scale, contributing to the advancement of catalysis research.

Progress in the Computer-Aided Analysis in Multiple Aspects of Nanocatalysis Research

Making the utmost of the differences and advantages of multiple disciplines, interdisciplinary integration breaks the science boundaries and accelerates the progress in mutual quests. As an organic connection of material science, enzymology, and biomedicine, nanozyme-related research is further supported by computer technology, which injects in new vitality, and contributes to in-depth understanding, unprecedented insights, and broadened application possibilities. Utilizing computer-aided first-principles method, high-speed and high-throughput mathematic, physic, and chemic models are introduced to perform atomic-level kinetic analysis for nanocatalytic reaction process, and theoretically illustrate the underlying nanozymetic mechanism and structure-function relationship. On this basis, nanozymes with desirable properties can be designed and demand-oriented synthesized without repeated trial-and-error experiments. Besides that, computational analysis and device also play an indispensable role in nanozyme-based detecting methods to realize automatic readouts with improved accuracy and reproducibility. Here, this work focuses on the crossing of nanocatalysis research and computational technology, to inspire the research in computer-aided analysis in nanozyme field to a greater extent.

Interlayer Interactions and Macroscopic Property Calculations of Squaric-Acid-Linked Zwitterionic Covalent Organic Frameworks: Structures, Photocatalytic Carrier Transport, and a DFT Study

Squaric-acid-linked zwitterionic covalent organic frameworks (Z-COFs), assembled through interlayer interactions, are emerging as potential materials in the field of photocatalysis. However, the study of their interlayer interactions has been largely overlooked. To address this, this work systematically calculated interlayer interactions via density functional theory (DFT) and analyzed the differences in interlayer interactions of different structures of Z-COFs through interlayer slippage, planarity, and an independent gradient model based on the Hirshfeld partition (IGMH). Furthermore, it revealed the relationship between the interactions and the macroscopic photocatalytic carrier transport performance of the material. The results indicated that both preventing interlayer slippage and enhancing planarity can enhance the interlayer interactions of Z-COFs, thereby improving their macroscopic carrier transport performance in photocatalysis.

TP-LMMSG: a peptide prediction graph neural network incorporating flexible amino acid property representation

Bioactive peptide therapeutics has been a long-standing research topic. Notably, the antimicrobial peptides (AMPs) have been extensively studied for its therapeutic potential. Meanwhile, the demand for annotating other therapeutic peptides, such as antiviral peptides (AVPs) and anticancer peptides (ACPs), also witnessed an increase in recent years. However, we conceive that the structure of peptide chains and the intrinsic information between the amino acids is not fully investigated among the existing protocols. Therefore, we develop a new graph deep learning model, namely TP-LMMSG, which offers lightweight and easy-to-deploy advantages while improving the annotation performance in a generalizable manner. The results indicate that our model can accurately predict the properties of different peptides. The model surpasses the other state-of-the-art models on AMP, AVP and ACP prediction across multiple experimental validated datasets. Moreover, TP-LMMSG also addresses the challenges of time-consuming pre-processing in graph neural network frameworks. With its flexibility in integrating heterogeneous peptide features, our model can provide substantial impacts on the screening and discovery of therapeutic peptides. The source code is available at https://github.com/NanjunChen37/TP_LMMSG.

A reactive neural network framework for water-loaded acidic zeolites

Under operating conditions, the dynamics of water and ions confined within protonic aluminosilicate zeolite micropores are responsible for many of their properties, including hydrothermal stability, acidity and catalytic activity. However, due to high computational cost, operando studies of acidic zeolites are currently rare and limited to specific cases and simplified models. In this work, we have developed a reactive neural network potential (NNP) attempting to cover the entire class of acidic zeolites, including the full range of experimentally relevant water concentrations and Si/Al ratios. This NNP has the potential to dramatically improve sampling, retaining the (meta)GGA DFT level accuracy, with the capacity for discovery of new chemistry, such as collective defect formation mechanisms at the zeolite surface. Furthermore, we exemplify how the NNP can be used as a basis for further extensions/improvements which include data-efficient adoption of higher-level (hybrid) references via Δ-learning and the acceleration of rare event sampling via automatic construction of collective variables. These developments represent a significant step towards accurate simulations of realistic catalysts under operando conditions.

Delocalized, asynchronous, closed-loop discovery of organic laser emitters

Contemporary materials discovery requires intricate sequences of synthesis, formulation, and characterization that often span multiple locations with specialized expertise or instrumentation. To accelerate these workflows, we present a cloud-based strategy that enabled delocalized and asynchronous design-make-test-analyze cycles. We showcased this approach through the exploration of molecular gain materials for organic solid-state lasers as a frontier application in molecular optoelectronics. Distributed robotic synthesis and in-line property characterization, orchestrated by a cloud-based artificial intelligence experiment planner, resulted in the discovery of 21 new state-of-the-art materials. Gram-scale synthesis ultimately allowed for the verification of best-in-class stimulated emission in a thin-film device. Demonstrating the asynchronous integration of five laboratories across the globe, this workflow provides a blueprint for delocalizing-and democratizing-scientific discovery.

Quantum Monte Carlo Simulations of the Vibrational Wavefunction of the Aromatic Cyclo[10]carbon Using a Full Dimensional Permutationally Invariant Potential Energy Surface

New experimental measurements [Sun et al., Nature 2023, 623, 972] of the cyclic C10 reveal a cumulenic pentagon-like D5h structure at ∼5 K. However, the long-standing presumption that a large zero-point vibrational energy combined with an extremely flat D5h ↔ D10h ↔ D5h isomerization pathway washes out the pentagonal D5h structure and yields a symmetric D10h decagon remains at odds with the experiment. We resolve this issue with our fitting approach based on a bond-order charge-density matrix expressed in permutationally invariant polynomials. We train the model on τHCTH/cc-pVQZ data morphed to reproduce a relativistic all-electron CCSDT(Q)/CBS D5h-D10h potential energy barrier (benchmarked previously by others). Large scale diffusion Monte Carlo simulations in full dimensionality show that the vibrational ground state of C10 has compositional character of more than 96% D5h, fully reflecting the experimental imaging data. Quantum mechanical variational calculations in 1-D further suggest persistence of the D5h symmetry structure at higher temperatures.

The Enigma of Methanol Synthesis by Cu/ZnO/Al2O3-Based Catalysts

The activity and durability of the Cu/ZnO/Al2O3 (CZA) catalyst formulation for methanol synthesis from CO/CO2/H2 feeds far exceed the sum of its individual components. As such, this ternary catalytic system is a prime example of synergy in catalysis, one that has been employed for the large scale commercial production of methanol since its inception in the mid 1960s with precious little alteration to its original formulation. Methanol is a key building block of the chemical industry. It is also an attractive energy storage molecule, which can also be produced from CO2 and H2 alone, making efficient use of sequestered CO2. As such, this somewhat unusual catalyst formulation has an enormous role to play in the modern chemical industry and the world of global economics, to which the correspondingly voluminous and ongoing research, which began in the 1920s, attests. Yet, despite this commercial success, and while research aimed at understanding how this formulation functions has continued throughout the decades, a comprehensive and universally agreed upon understanding of how this material achieves what it does has yet to be realized. After nigh on a century of research into CZA catalysts, the purpose of this Review is to appraise what has been achieved to date, and to show how, and how far, the field has evolved. To do so, this Review evaluates the research regarding this catalyst formulation in a chronological order and critically assesses the validity and novelty of various hypotheses and claims that have been made over the years. Ultimately, the Review attempts to derive a holistic summary of what the current body of literature tells us about the fundamental sources of the synergies at work within the CZA catalyst and, from this, suggest ways in which the field may yet be further advanced.

Deep Mind 21 functional does not extrapolate to transition metal chemistry

The development of density functional approximations stands at a crossroads: while machine-learned functionals show potential to surpass their human-designed counterparts, their extrapolation to unseen chemistry lags behind. Here we assess how well the recent Deep Mind 21 (DM21) machine-learned functional [Science, 2021, 374, 1385-1389], trained on main-group chemistry, extrapolates to transition metal chemistry (TMC). We show that DM21 demonstrates comparable or occasionally superior accuracy to B3LYP for TMC, but consistently struggles with achieving self-consistent field convergence for TMC molecules. We also compare main-group and TMC machine-learning DM21 features to shed light on DM21's challenges in TMC. We finally propose strategies to overcome limitations in the extrapolative capabilities of machine-learned functionals in TMC.

Fragment-Based Deep Learning for Simultaneous Prediction of Polarizabilities and NMR Shieldings of Macromolecules and Their Aggregates

Simultaneous prediction of the molecular response properties, such as polarizability and the NMR shielding constant, at a low computational cost is an unresolved issue. We propose to combine a linear-scaling generalized energy-based fragmentation (GEBF) method and deep learning (DL) with both molecular and atomic information-theoretic approach (ITA) quantities as effective descriptors. In GEBF, the total molecular polarizability can be assembled as a linear combination of the corresponding quantities calculated from a set of small embedded subsystems in GEBF. In the new GEBF-DL(ITA) protocol, one can predict subsystem polarizabilities based on the corresponding molecular wave function (thus electron density and ITA quantities) and DL model rather than calculate them from the computationally intensive coupled-perturbed Hartree-Fock or Kohn-Sham equations and finally obtain the total molecular polarizability via a linear combination equation. As a proof-of-concept application, we predict the molecular polarizabilities of large proteins and protein aggregates. GEBF-DL(ITA) is shown to be as accurate enough as GEBF, with mean absolute percentage error <1%. For the largest protein aggregate (>4000 atoms), GEBF-DL(ITA) gains a speedup ratio of 3 compared with GEBF. It is anticipated that when more advanced electronic structure methods are used, this advantage will be more appealing. Moreover, one can also predict the NMR chemical shieldings of proteins with reasonably good accuracy. Overall, the cost-efficient GEBF-DL(ITA) protocol should be a robust theoretical tool for simultaneously predicting polarizabilities and NMR shieldings of large systems.

Why neural functionals suit statistical mechanics

We describe recent progress in the statistical mechanical description of many-body systems via machine learning combined with concepts from density functional theory and many-body simulations. We argue that the neural functional theory by Sammülleret al(2023Proc. Natl Acad. Sci.120e2312484120) gives a functional representation of direct correlations and of thermodynamics that allows for thorough quality control and consistency checking of the involved methods of artificial intelligence. Addressing a prototypical system we here present a pedagogical application to hard core particle in one spatial dimension, where Percus' exact solution for the free energy functional provides an unambiguous reference. A corresponding standalone numerical tutorial that demonstrates the neural functional concepts together with the underlying fundamentals of Monte Carlo simulations, classical density functional theory, machine learning, and differential programming is available online athttps://github.com/sfalmo/NeuralDFT-Tutorial.

Can simple 'molecular' corrections outperform projector augmented-wave density functional theory in the prediction of 35 Cl electric field gradient tensor parameters for chlorine-containing crystalline systems?

Many-body expansion (MBE) fragment approaches have been applied to accurately compute nuclear magnetic resonance (NMR) parameters in crystalline systems. Recent examples demonstrate that electric field gradient (EFG) tensor parameters can be accurately calculated for 14 N and 17 O. A key additional development is the simple molecular correction (SMC) approach, which uses two one-body fragment (i.e., isolated molecule) calculations to adjust NMR parameter values established using 'benchmark' projector augmented-wave (PAW) density functional theory (DFT) values. Here, we apply a SMC using the hybrid PBE0 exchange-correlation (XC) functional to see if this can improve the accuracy of calculated 35 Cl EFG tensor parameters. We selected eight organic and two inorganic crystal structures and considered 15 chlorine sites. We find that this SMC improves the accuracy of computed values for both the 35 Cl quadrupolar coupling constant (CQ ) and the asymmetry parameter ( η Q ) by approximately 30% compared with benchmark PAW DFT values. We also assessed a SMC that offers local improvements not only in terms of the quality of the XC functional but simultaneously in the quality of the description of relativistic effects via the inclusion of spin-orbit effects. As the inorganic systems considered contain heavy atoms bonded to the chlorine atoms, we find further improvements in the accuracy of calculated 35 Cl EFG tensor parameters when both a hybrid functional and spin-orbit effects are included in the SMC. On the contrary, for chlorine-containing organics, the inclusion of spin-orbit relativistic effects using a SMC does not improve the accuracy of computed 35 Cl EFG tensor parameters.

Integrating experimental and computational approaches for deep eutectic solvent-catalyzed glycolysis of post-consumer polyethylene terephthalate

To achieve a sustainable and circular economy, developing effective plastic recycling methods is essential. Despite advances in the chemical recycling of plastic waste, modern industries require highly efficient and sustainable solutions to address environmental problems. In this study, we propose an efficient glycolysis strategy for post-consumer polyethylene terephthalate (PET) using deep eutectic solvents (DESs) to produce bis(2-hydroxyethyl) terephthalate (BHET) with high selectivity. Choline chloride (ChCl)- and urea-based DESs were synthesized using various metal salts and were tested for the glycolysis of PET waste; ChCl-Zn(OAc)2 exhibited the best performance. The DES-containing solvent system afforded a complete PET conversion, producing BHET at a high yield (91.6%) under optimal reaction conditions. The degradation mechanism of PET and its interaction with DESs were systematically investigated using density functional theory-based calculations. Furthermore, an intuitive machine learning model was developed to predict the PET conversion and BHET selectivity for different DES compositions. Our findings demonstrate that the DES-catalyzed glycolysis of post-consumer PET could enable the development of a sustainable chemical recycling process, providing insights to identify the new design of DESs for plastic decomposition.

Going against the Grain: Atomistic Modeling of Grain Boundaries in Solid Electrolytes for Solid-State Batteries

Atomistic modeling techniques, including density functional theory and molecular dynamics, play a critical role in the understanding, design, discovery, and optimization of bulk solid electrolyte materials for solid-state batteries. In contrast, despite the fact that the atomistic simulation of microstructural inhomogeneities, such as grain boundaries, can reveal essential information regarding the performance of solid electrolytes, such simulations have so far only been limited to a relatively small selection of materials. In this Perspective, the fundamental properties of grain boundaries in solid electrolytes that can be determined and manipulated through state-of-the-art atomistic modeling are illustrated through recent studies in the literature. The insights and examples presented here will inspire future computational studies of grain boundaries with the aim of overcoming their often detrimental impact on ion transport and dendrite growth inhibition in solid electrolytes.

Evolutionary Monte Carlo of QM Properties in Chemical Space: Electrolyte Design

Optimizing a target function over the space of organic molecules is an important problem appearing in many fields of applied science but also a very difficult one due to the vast number of possible molecular systems. We propose an evolutionary Monte Carlo algorithm for solving such problems which is capable of straightforwardly tuning both exploration and exploitation characteristics of an optimization procedure while retaining favorable properties of genetic algorithms. The method, dubbed MOSAiCS (Metropolis Optimization by Sampling Adaptively in Chemical Space), is tested on problems related to optimizing components of battery electrolytes, namely, minimizing solvation energy in water or maximizing dipole moment while enforcing a lower bound on the HOMO-LUMO gap; optimization was carried out over sets of molecular graphs inspired by QM9 and Electrolyte Genome Project (EGP) data sets. MOSAiCS reliably generated molecular candidates with good target quantity values, which were in most cases better than the ones found in QM9 or EGP. While the optimization results presented in this work sometimes required up to 106 QM calculations and were thus feasible only thanks to computationally efficient ab initio approximations of properties of interest, we discuss possible strategies for accelerating MOSAiCS using machine learning approaches.

How important is the amount of exact exchange for spin-state energy ordering in DFT? Case study of molybdenum carbide cluster, Mo4C2

Since the form of the exact functional in density functional theory is unknown, we must rely on density functional approximations (DFAs). In the past, very promising results have been reported by combining semi-local DFAs with exact, i.e. Hartree-Fock, exchange. However, the spin-state energy ordering and the predictions of global minima structures are particularly sensitive to the choice of the hybrid functional and to the amount of exact exchange. This has been already qualitatively described for single conformations, reactions, and a limited number of conformations. Here, we have analyzed the mixing of exact exchange in exchange functionals for a set of several hundred isomers of the transition metal carbide, Mo4C2. The analysis of the calculated energies and charges using PBE0-type functional with varying amounts of exact exchange yields the following insights: (1) The sensitivity of spin-energy splitting is strongly correlated with the amount of exact exchange mixing. (2) Spin contamination is exacerbated when correlation is omitted from the exchange-correlation functional. (3) There is not one ideal value for the exact exchange mixing which can be used to parametrize or choose among the functionals. Calculated energies and electronic structures are influenced by exact exchange at a different magnitude within a given distribution; therefore, to extend the application range of hybrid functionals to the full periodic table the spin-energy splitting energies should be investigated.