Publications

1. Graph neural networks for predicting metal–ligand coordination of transition metal complexes (2024)
2. MOFs with the Stability for Practical Gas Adsorption Applications Require New Design Rules (2024)
3. Improving Predictions of Spin-Crossover Complex Properties through DFT Calculations with a Local Hybrid Functional (2024)
4. Caged AIEgens: Multicolor and White Emission Triggered by Mechanical Activation (2024)
5. Defect-Engineered Metal−Organic Frameworks as Bioinspired Heterogeneous Catalysts for Amide Bond Formation (2024)
6. Enzymatic synthesis of azide by a promiscuous N-nitrosylase (2024)
7. Tuning Metal-Organic Framework Linker Chemistry for Transition Metal Ion Separations (2024)
8. Mechanistic basis for the emergence of EPS1 as a catalyst in salicylic acid biosynthesis of Brassicaceae (2024)
9. Ligand Many-Body Expansion as a General Approach for Accelerating Transition Metal Complex Discovery (2024)
10. A Computational Investigation of the Role of Metal Center Identity in Cytochrome P450 Enzyme Model Reactivity (2024)
11. No Bridge Between Us: Two Distant Iron Ions Comprise the Active Site of Alkane Monooxygenase (AlkB) (2024)
12. CH−π Interactions Are Required for Human Galectin-3 Function (2024)
13. Designing membranes with specific binding sites for selective ion separations (2024)
14. The Energetic Landscape of CH–π Interactions in Protein–Carbohydrate Binding (2024)
15. Data-driven Screening and Discovery of Metal-organic Frameworks as C2 Adsorbents from Over 900 Experimental Isotherms (2024)
16. Reaction: The Challenge of Open-Shell Transition Metal Catalysis in "Systems Chemistry" (2024)
17. Computational Screening of Putative Catalyst Transition Metal Complexes as Guests in a Ga₄L₆⁻¹² Nanocage (2024)
18. Ligand-mediated Quantum Yield Enhancement in 1-Dimensional Silver Organothiolate Metal-Organic Chalcogenolates (2024)
19. Metal–Organic Framework Stability in Water and Harsh Environments from Data-Driven Models Trained on the Diverse WS24 Data Set (2024)
20. High-Throughput Discovery of Ferrocene Mechanophores with Enhanced Reactivity and Network Toughening (2024)
21. Isomer-Driven Polymerization, Depolymerization, and Reconstruction (2024)
22. Robust Chemiresistive Behavior in Conductive Polymer/MOF Composites (2024)
23. Visible light–mediated aza Paternò–Büchi reaction of acyclic oximes and alkenes to azetidines (2024)
24. Leveraging natural language processing to curate the tmCAT, tmPHOTO, tmBIO, and tmSCO datasets of functional transition metal complexes (2024)
25. The tension-activated carbon–carbon bond (2024)
26. Toughening polymer networks via chemo- and regioselective junction mechanochemistry (2024)
27. Dynamic Charge Distribution as a Key Driver of Catalytic Reactivity in an Artificial Metalloenzyme (2024)
28. Heterocyclic Modification Leading to Luminescent 0D Metal Organochalcogenide with Stable X-ray Scintillating Properties (2024)
29. Internal Catalysis in Dynamic Hydrogels with Associative Thioester Cross-links (2024)
30. Large Language Models are Catalyzing Chemistry Education (2024)
31. Insights into the catalytic promotion of propylene self-metathesis over silica-supported molybdenum oxide using substituted olefins (2024)
32. A semi-automated, high-throughput approach for the synthesis and identification of highly photo-cytotoxic iridium complexes (2024)
33. React-OT: Optimal Transport for Generating Transition State in Chemical Reactions (2024)
34. A Thermally Stable SO₂ Releasing Mechanophore: Facile Activation, Single-Event Spectroscopy, and Molecular Dynamic Simulations (2024)
35. Improving Gas Adsorption Modeling for MOFs by Local Calibration of Hubbard U Parameters (2024)
36. Self-Amplified HF Release and Polymer Deconstruction Cascades Triggered by Mechanical Force (2024)
37. Nested Non-covalent Interactions Expand the Functions of Supramolecular Polymer Networks (2024)
38. Angle-strained sila-cycloalkynes (2024)
39. How Do Differences in Electronic Structure Affect the Use of Vanadium Intermediates as Mimics in Nonheme Iron Hydroxylases? (2024)
40. Visible-Light-Mediated Macrocyclization for the Formation of Azetine-Based Dimers (2024)
41. Protein3D: Enabling analysis and extraction of metal-containing sites from the Protein Data Bank with molSimplify (2024)
42. Large-scale Comparison of Fe and Ru Polyolefin C–H Activation Catalysts (2024)
43. Computational Discovery of Codoped Single-Atom Catalysts for Methane-to-Methanol Conversion (2024)
44. Benchmarking Nitrous Oxide Adsorption and Activation in Metal-Organic Frameworks Bearing Coordinatively Unsaturated Metal Centers (2024)
45. Machine Learning Prediction of the Experimental Transition Temperature of Fe(II) Spin-Crossover Complexes (2024)
46. Learning Design Rules for Catalysts through Computational Chemistry and Machine Learning (2024)
47. Section Introduction: Molecular Interactions and Catalysis (2024)
48. Uncertain of uncertainties? A comparison of uncertainty quantification metrics for chemical data sets (2023)
49. Accurate transition state generation with an object-aware equivariant elementary reaction diffusion model (2023)
50. Classification of Hemilabile Ligands Using Machine Learning (2023)
51. Discovering Molecular Coordination Environment Trends for Selective Ion Binding to Molecular Complexes Using Machine Learning (2023)
52. Why Nonheme Iron Halogenases Do Not Fluorinate C–H Bonds: A Computational Investigation (2023)
53. Polymer Networks with Cubic, Mixed Pd(II) and Pt(II) M₆L₁₂ Metal–Organic Cage Junctions: Synthesis and Stress Relaxation Behavior (2023)
54. Gas-Phase and Solid-State Electronic Structure Analysis and DFT Benchmarking of HfCO (2023)
55. Metal Identity Effects in the Fracture Behavior of Coordinatively Crosslinked Elastomers (2023)
56. Systematic Investigation of Silicon Substitution on Single Macromolecule Mechanics (2023)
57. Tailoring Dynamic Hydrogels by Controlling Associative Exchange Rates (2023)
58. Reversible O–O Bond Scission and O₂ Evolution at MOF-supported Tetramanganese Clusters (2023)
59. Unraveling Polymer–Ion Interactions in Electrochromic Polymers for their Implementation in Organic Electrochemical Synaptic Devices (2023)
60. Assessing the Performance of Approximate Density Functional Theory on 95 Experimentally Characterized Fe(II) Spin Crossover Complexes (2023)
61. Computational Discovery of Stable Metal-Organic Frameworks for Methane-to-Methanol Catalysis (2023)
62. Identifying Underexplored and Untapped Regions in the Chemical Space of Transition Metal Complexes (2023)
63. SESAMI APP: An Accessible Interface for Surface Area Calculation of Materials from Adsorption Isotherms (2023)
64. Synthesis and Ring-opening Metathesis Polymerization of a Strained trans-Silacycloheptene and Single Molecule Mechanics of its Polymer (2023)
65. A Database of Ultrastable MOFs Reassembled from Stable Fragments with Machine Learning Models (2023)
66. 1D Hybrid Semiconductor Silver 2,6-Difluorophenylselenolate (2023)
67. Emergence of a Proton Exchange-Based Isomerization and Lactonization Mechanism in the Plant Coumarin Synthase COSY (2023)
68. Mechanistic Insights Into Substrate Positioning Across Non-heme Fe(II)/Alpha-Ketoglutarate-Dependent Halogenases and Hydroxylases (2023)
69. A Transferable Recommender Approach for Selecting the Best Density Functional Approximations in Chemical Discovery (2023)
70. Insights into the deviation from piecewise linearity in transition metal complexes from supervised machine learning models (2023)
71. Remolding and Deconstruction of Industrial Thermosets via Carboxylic Acid-Catalyzed Bifunctional Silyl Ether Exchange (2023)
72. DFT-based Multireference Diagnostics in the Solid State: Application to Metal-organic Frameworks (2023)
73. Low-cost machine learning prediction of excited state properties of iridium-centered phosphors (2023)
74. Active Learning Exploration of Transition Metal Complexes to Discover Method-Insensitive and Synthetically Accessible Chromophores (2023)
75. Effects of MOF Linker Rotation and Functionalization on Methane Uptake and Diffusion (2023)
76. Fluids and Electrolytes under Confinement in Single-Digit Nanopores (2023)
77. Light Emission in 2D Silver Phenylchalcogenolates (2022)
78. Ligand Additivity Relationships Enable Efficient Exploration of Transition Metal Chemical Space (2022)
79. Highly Efficient Bromine Capture and Storage Using N-containing Porous Organic Cages (2022)
80. Chemical Design by Artificial Intelligence (2022)
81. Insights into the Stability of Engineered Mini-Proteins from Their Dynamic Electronic Properties (2022)
82. Non-Native Anionic Ligand Binding and Reactivity in Engineered Variants of the Fe(II)- and α-Ketoglutarate-Dependent Oxygenase, SadA (2022)
83. Endohedrally Functionalized Metal–Organic Cage-Cross-Linked Polymer Gels as Modular Heterogeneous Catalysts (2022)
84. Using Computational Chemistry to Reveal Nature's Blueprints for Single-Site Catalysis of C–H Activation (2022)
85. Mechanistic Studies of a Skatole-Forming Glycyl Radical Enzyme Suggest Reaction Initiation via Hydrogen Atom Transfer (2022)
86. Exploiting Ligand Additivity for Transferable Machine Learning of Multireference Character Across Known Transition Metal Complex Ligands (2022)
87. Machine learning models predict calculation outcomes with the transferability necessary for computational catalysis (2022)
88. Roadmap on Machine Learning in Electronic Structure (2022)
89. Influence of the Greater Protein Environment on the Electrostatic Potential in Metalloenzyme Active Sites: The Case of Formate Dehydrogenase (2022)
90. What's Left for a Computational Chemist To Do in the Age of Machine Learning? (2022)
91. Are Vanadium Intermediates Suitable Mimics in Non-Heme Iron Enzymes? An Electronic Structure Analysis (2022)
92. Audacity of huge: overcoming challenges of data scarcity and data quality for machine learning in computational materials discovery (2022)
93. Computational Modeling of Conformer Stability in Benenodin-1, a Thermally Actuated Lasso Peptide Switch (2022)
94. Computational Scaling Relationships Predict Experimental Activity and Rate Limiting Behavior in Homogenous Water Oxidation (2022)
95. Detection of multi-reference character imbalances enables a transfer learning approach for chemical discovery with coupled cluster accuracy at DFT cost (2022)
96. Eliminating Delocalization Error to Improve Heterogeneous Catalysis Predictions with Molecular DFT+U (2022)
97. Harder, better, faster, stronger: large-scale QM and QM/MM for predictive modeling in enzymes and proteins (2022)
98. Irreversible synthesis of an ultrastrong two-dimensional polymeric material (2022)
99. Large-scale Screening Reveals Geometric Structure Matters More than Electronic Structure in Bioinspired Catalyst Design of Formate Dehydrogenase Mimics (2022)
100. Ligand Additivity and Divergent Trends in Two Types of Delocalization Errors from Approximate Density Functional Theory (2022)
101. Machine Learning for the Discovery, Design, and Engineering of Materials (2022)
102. Machine Learning Reveals Key Ion Selectivity Mechanisms in Polymeric Membranes (2022)
103. Modeling the roles of rigidity and dopants in single-atom methane-to-methanol catalysts (2022)
104. MOFSimplify, machine learning models with extracted stability data of three thousand metal–organic frameworks (2022)
105. Molecular orbital projectors in non-empirical jmDFT recover exact conditions in transition-metal chemistry (2022)
106. New Strategies for Direct Methane-to-Methanol Conversion from Active Learning Exploration of 16 Million Catalysts (2022)
107. Probing the mechanism of isonitrile formation by a non-heme iron(II)-dependent oxidase/decarboxylase (2022)
108. Quantum-Mechanical/Molecular-Mechanical (QM/MM) Simulations for Understanding Enzyme Dynamics (2022)
109. Representations and Strategies for Transferable Machine Learning Improve Model Performance in Chemical Discovery (2022)
110. The Effect of Hartree-Fock Exchange on Scaling Relations and Reaction Energetics for C–H Activation Catalysts (2022)
111. Understanding the chemical bonding of ground and excited states of HfO and HfB with correlated wavefunction theory and density functional approximations (2022)
112. Advancing Discovery in Chemistry with Artificial Intelligence: From Reaction Outcomes to New Materials and Catalysts (2021)
113. Molecular DFT+U: A Transferable, Low-Cost Approach to Eliminate Delocalization Error (2021)
114. Protein Dynamics and Substrate Protonation State Mediate the Catalytic Action of Trans-4-Hydroxy-L-Proline Dehydratase (2021)
115. Molecular basis of C-S bond cleavage in the glycyl radical enzyme isethionate sulfite-lyase (2021)
116. Navigating Transition-Metal Chemical Space: Artificial Intelligence for First-Principles Design (2021)
117. Biochemical and crystallographic investigations into isonitrile formation by a nonheme iron-dependent oxidase/decarboxylase (2021)
118. Computational Discovery of Transition-Metal Complexes: From High-throughput Screening to Machine Learning (2021)
119. Deciphering Cryptic Behavior in Bimetallic Transition Metal Complexes with Machine Learning (2021)
120. Machine learning to tame divergent density functional approximations a new path to consensus materials design principles (2021)
121. Mapping the Origins of Surface- and Chemistry-Dependent Doping Trends in III-V Quantum Dots with Density Functional Theory (2021)
122. Putting Density Functional Theory to the Test in Machine-Learning-Accelerated Materials Discovery (2021)
123. Quantifying the Long-Range Coupling of Electronic Properties in Proteins with Ab Initio Molecular Dynamics (2021)
124. Quantum Chemistry Common Driver and Databases (QCDB) and Quantum Chemistry Engine (QCEngine): Automation and interoperability among computational chemistry programs (2021)
125. Spectroscopically Guided Simulations Reveal Distinct Strategies for Positioning Substrates to Achieve Selectivity in Nonheme Fe(II)/α-Ketoglutarate-Dependent Halogenases (2021)
126. Using Machine Learning and Data Mining to Leverage Community Knowledge for the Engineering of Stable Metal-Organic Frameworks (2021)
127. When are two hydrogen bonds better than one? Accurate first-principles models explain the balance of hydrogen bond donors and acceptors found in proteins (2021)
128. Ionization behavior of nanoporous polyamide membranes (2020)
129. Why Conventional Design Rules for C–H Activation Fail for Open-Shell Transition-Metal Catalysts (2020)
130. Rapid Detection of Strong Correlation with Machine Learning for Transition-Metal Complex High-Throughput Screening (2020)
131. Semi-supervised Machine Learning Enables the Robust Detection of Multireference Character at Low Cost (2020)
132. Understanding the diversity of the metal-organic framework ecosystem (2020)
133. Data-Driven Approaches Can Overcome the Cost–Accuracy Trade-Off in Multireference Diagnostics (2020)
134. Uncovering Alternate Pathways to Nafion Membrane Degradation in Fuel Cells with First-Principles Modeling (2020)
135. Both Configuration and QM Region Size Matter: Zinc Stability in QM/MM Models of DNA Methyltransferase (2020)
136. Machine Learning in Chemistry (2020)
137. Accurate Multiobjective Design in a Space of Millions of Transition Metal Complexes with Neural-Network-Driven Efficient Global Optimization (2020)
138. Seeing Is Believing: Experimental Spin States from Machine Learning Model Structure Predictions (2020)
139. Enumeration of de novo inorganic complexes for chemical discovery and machine learning (2020)
140. Impact of Approximate DFT Density Delocalization Error on Potential Energy Surfaces in Transition Metal Chemistry (2020)
141. Large-scale comparison of 3d and 4d transition metal complexes illuminates the reduced effect of exchange on second-row spin-state energetics (2020)
142. Making machine learning a useful tool in the accelerated discovery of transition metal complexes (2020)
143. Critical Knowledge Gaps in Mass Transport through Single-Digit Nanopores: A Review and Perspective (2019)
144. Machine Learning Accelerates the Discovery of Design Rules and Exceptions in Stable Metal–Oxo Intermediate Formation (2019)
145. Reply to “Comment on ‘Evaluating Unexpectedly Short Non-covalent Distances in X-ray Crystal Structures of Proteins with Electronic Structure Analysis’” (2019)
146. Stable Surfaces That Bind Too Tightly: Can Range-Separated Hybrids or DFT+U Improve Paradoxical Descriptions of Surface Chemistry? (2019)
147. Designing in the Face of Uncertainty: Exploiting Electronic Structure and Machine Learning Models for Discovery in Inorganic Chemistry (2019)
148. Quantum Mechanical Description of Electrostatics Provides a Unified Picture of Catalytic Action Across Methyltransferases (2019)
149. The Protein’s Role in Substrate Positioning and Reactivity for Biosynthetic Enzyme Complexes: The Case of SyrB2/SyrB1 (2019)
150. Evaluating Unexpectedly Short Non-covalent Distances in X-ray Crystal Structures of Proteins with Electronic Structure Analysis (2019)
151. Learning from Failure: Predicting Electronic Structure Calculation Outcomes with Machine Learning Models (2019)
152. Non-empirical, low-cost recovery of exact conditions with model-Hamiltonian inspired expressions in jmDFT (2019)
153. A quantitative uncertainty metric controls error in neural network-driven chemical discovery (2019)
154. Anthracene as a Launchpad for a Phosphinidene Sulfide and for Generation of a Phosphorus–Sulfur Material Having the Composition P2S, a Vulcanized Red Phosphorus That Is Yellow (2019)
155. Bridging the Homogeneous-Heterogeneous Divide: Modeling Spin for Reactivity in Single Atom Catalysis (2019)
156. Coding solvation: challenges and opportunities (2019)
157. Exploiting graphical processing units to enable quantum chemistry calculation of large solvated molecules with conductor-like polarizable continuum models (2019)
158. Protection of tissue physicochemical properties using polyfunctional crosslinkers (2019)
159. Revealing quantum mechanical effects in enzyme catalysis with large-scale electronic structure simulation (2019)
160. Electronic Structure Origins of Surface-Dependent Growth in III–V Quantum Dots (2018)
161. Strategies and Software for Machine Learning Accelerated Discovery in Transition Metal Chemistry (2018)
162. When Is Ligand pKa a Good Descriptor for Catalyst Energetics? In Search of Optimal CO2 Hydration Catalysts (2018)
163. Accelerating Chemical Discovery with Machine Learning: Simulated Evolution of Spin Crossover Complexes with an Artificial Neural Network (2018)
164. Understanding and Breaking Scaling Relations in Single-Site Catalysis: Methane to Methanol Conversion by FeIV═O (2018)
165. Where Does the Density Localize in the Solid State? Divergent Behavior for Hybrids and DFT+U (2018)
166. Large-scale QM/MM free energy simulations of enzyme catalysis reveal the influence of charge transfer (2018)
167. Modeling Mechanochemistry from First Principles (2018)
168. Communication: Recovering the flat-plane condition in electronic structure theory at semi-local DFT cost (2017)
169. Quantifying Electronic Effects in QM and QM/MM Biomolecular Modeling with the Fukui Function (2017)
170. Resolving Transition Metal Chemical Space: Feature Selection for Machine Learning and Structure–Property Relationships (2017)
171. Unifying Exchange Sensitivity in Transition-Metal Spin-State Ordering and Catalysis through Bond Valence Metrics (2017)
172. Leveraging Cheminformatics Strategies for Inorganic Discovery: Application to Redox Potential Design (2017)
173. Density functional theory for modelling large molecular adsorbate–surface interactions: a mini-review and worked example (2017)
174. Harnessing Organic Ligand Libraries for First-Principles Inorganic Discovery: Indium Phosphide Quantum Dot Precursor Design Strategies (2017)
175. Ligand-Field-Dependent Behavior of Meta-GGA Exchange in Transition-Metal Complex Spin-State Ordering (2017)
176. Systematic Quantum Mechanical Region Determination in QM/MM Simulation (2017)
177. Depolymerization Pathways for Branching Lignin Spirodienone Units Revealed with ab Initio Steered Molecular Dynamics (2017)
178. Predicting electronic structure properties of transition metal complexes with neural networks (2017)
179. Where Does the Density Localize? Convergent Behavior for Global Hybrids, Range Separation, and DFT+U (2016)
180. How Large Should the QM Region Be in QM/MM Calculations? The Case of Catechol O-Methyltransferase (2016)
181. Computational Discovery of Hydrogen Bond Design Rules for Electrochemical Ion Separation (2016)
182. Computational Investigation of the Interplay of Substrate Positioning and Reactivity in Catechol O-Methyltransferase (2016)
183. Global and local curvature in density functional theory (2016)
184. Predicting the Stability of Fullerene Allotropes Throughout the Periodic Table (2016)
185. Adapting DFT+U for the Chemically Motivated Correction of Minimal Basis Set Incompleteness (2016)
186. Direct Observation of Early-Stage Quantum Dot Growth Mechanisms with High-Temperature Ab Initio Molecular Dynamics (2016)
187. Anion-Selective Redox Electrodes: Electrochemically Mediated Separation with Heterogeneous Organometallic Interfaces (2016)
188. molSimplify: A toolkit for automating discovery in inorganic chemistry (2016)
189. Discovering Amorphous Indium Phosphide Nanostructures with High-Temperature ab Initio Molecular Dynamics (2015)
190. Quantum Chemistry for Solvated Molecules on Graphical Processing Units Using Polarizable Continuum Models (2015)
191. Towards quantifying the role of exact exchange in predictions of transition metal complex properties (2015)
192. Ab Initio Screening Approach for the Discovery of Lignin Polymer Breaking Pathways (2015)
193. Mediation of donor–acceptor distance in an enzymatic methyl transfer reaction (2015)
194. Perspective: Treating electron over-delocalization with the DFT+U method (2015)
195. Mechanically triggered heterolytic unzipping of a low-ceiling-temperature polymer (2014)
196. Developing an approach for first-principles catalyst design: application to carbon-capture catalysis (2014)
197. Substrate Placement Influences Reactivity in Non-heme Fe(II) Halogenases and Hydroxylases (2013)
198. Ab Initio Quantum Chemistry for Protein Structures (2012)
199. Probing the Structure of Salt Water under Confinement with First-Principles Molecular Dynamics and Theoretical X-ray Absorption Spectroscopy (2012)
200. Accurate potential energy surfaces with a DFT+U(R) approach (2011)
201. Transition-metal dioxides: A case for the intersite term in Hubbard-model functionals (2011)
202. Designing small-molecule catalysts for CO2 capture (2011)
203. Modeling, synthesis and characterization of zinc containing carbonic anhydrase active site mimics (2011)
204. Spatially Extended Kondo State in Magnetic Molecules Induced by Interfacial Charge Transfer (2010)
205. Systematic study of first-row transition-metal diatomic molecules: A self-consistent DFT+U approach (2010)
206. Local Effects in the X-ray Absorption Spectrum of Salt Water (2010)
207. Electronic Structure and Reactivity of Transition Metal Complexes (2010)
208. Ab initio investigation of high multiplicity Σ+–Σ+ optical transitions in the spectra of CN and isoelectronic species (2009)
209. First-Principles Study of Non-heme Fe(II) Halogenase SyrB2 Reactivity (2009)
210. A self-consistent Hubbard U density-functional theory approach to the addition-elimination reactions of hydrocarbons on bare FeO+ (2008)
211. Density Functional Theory in Transition-Metal Chemistry: A Self-Consistent Hubbard U Approach (2006)

Posts

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• Ab initio steered molecular dynamics with TeraChem
• Quick tips: More about U
• Geometries from strings with SMILES and OpenBabel
• Theoretical Infrared Spectroscopy
• Ten research tools and shortcuts
• Building slab geometries for catalysis with VESTA
• Quick tip: Choosing how to parallelize your jobs
• Job management 101
• Quick tip: Maximally localized Wannier functions
• Reader's Choice: X-ray absorption spectroscopy
• Reader's Choice: DFT+U
• Quick-tip: Building molecules with Molden
• Quickstart with xmgrace
• Convergence 101
• Visualizing trajectories with PyMOL
• Including Hubbard U variations with DFT+U(R)
• Population analysis and PDOS
• Vibrational properties of molecules
• More visualization with VMD & PyMOL
• Visualizing with VMD & rendering with POV-Ray
• Calculating Hubbard U for periodic systems
• Converging and comparing multiple electronic states
• The right Hubbard U for any element
• Troubleshooting common problems with DFT+U
• Low-lying electronic states
• Nudged elastic band
• Quick tip: Constraining molecular coordinates
• Hubbard U for multiple sites
• Visualizing molecular orbitals
• Calculating the Hubbard U