Research in the Kulik group

Research in the Kulik group harnesses first-principles electronic structure in transition-metal chemistry and large-scale enzymology to understand fundamental phenomena in chemical bonding for catalyst and materials design. Our broader research goals are delineated by the following three research areas:

Automated molecular design and discovery. Computational discovery techniques have become integral in identifying new compounds from among many possible candidates in vast regions of chemical space. Transition metal complexes have many desirable characteristics in bonding and reactivity or electronic properties for functional materials, but strategies for their efficient design are much less well-developed in comparison to the discovery of simple organic molecules or ordered solid state materials. We develop new software tools that merge what works from therapeutic drug design and the machine learning communities with knowledge we’ve developed about transition metal chemistry to enable efficient and informed traversal of chemical space to discover new compounds. We’ve applied these ideas across materials science – from redesigning the building blocks of quantum dots to the discovery of new functionalizations for electrochemically active polymers for ion separation. Many of these advances hinge on our open-source code molSimplify, which enables automated discovery of transition metal complexes by interfacing with large chemical or user-built databases. More recently, we’ve introduce the first artificial neural network capable of predicting both spin-state and geometry of transition metal complexes to molSimplify, enabling prediction of transition metal complex properties at a fraction of the computational cost of typical DFT studies, enabling high-throughput screening.

Large-scale quantum phenomena in enzymes and the condensed phase. Knowledge of the mechanism by which enzymes accelerate reaction rates is the cornerstone of fundamental understanding in health and disease. Despite strides in understanding enzyme mechanism, guiding principles for the role of the greater protein environment in this rate enhancement remain under debate. Computational atomistic force field and first-principles simulation have emerged as crucial tools to augment experimentally-derived mechanistic understanding, as highlighted by the 2013 Nobel Prize for the development of mixed quantum-mechanical/molecular-mechanics (QM/MM) multiscale methods. First-principles, QM methods are essential to treat the charge transfer, polarization, and bond rearrangements in enzyme catalysis, albeit at much higher computational cost than MM methods. Our group has developed new quantitative methods to identify electronic contributions to enzyme properties. We’re now using these tools to reveal electronic contributions to rate enhancement, identify interactions that give rise to substrate specificity, and guide our understanding of where strong quantum mechanical interactions may reveal new structure-function relationships.

Electronic structure for transition metal chemistry and catalysis. Approximate density functional theory (DFT) is an essential tool for computational materials and catalysis discovery initiatives, owing to its balance of computational cost and accuracy, yet the accuracy of DFT is eroded proportionately to the novelty of the materials being studied (e.g., correlated electrons in transition metals). In order both for discovery efforts to become predictive and large-scale electronic structure in enzymes to provide meaningful results, these errors must be both understood and corrected. Presently available DFT functionals suffer from a mixture of errors, and standard corrections (e.g., DFT+U and range-separated hybrid functionals) improve one facet (e.g., delocalization error) while worsening another (e.g., static correlation error). Further, although energetic errors may be corrected, density errors may worsen or not improve sufficiently. We are currently developing novel correction schemes that simultaneously alleviate numerous errors by separately treating fractional spin concavity and fractional charge convexity. We also address uncertainty in DFT through an artificial neural network that can predict the sensitivity of key electronic properties to changes in functional choice.

Read more about recent papers and projects in the group below!

Ligand-only descriptors for catalyst design

We present a detailed study of nearly 70 Zn molecular catalysts for CO2 hydration from four diverse ligand classes ranging from well-studied carbonic anhydrase mimics (e.g., cyclen) to new structures we obtain by leveraging diverse hits from large organic libraries. Using microkinetic analysis and establishing linear free energy relationships, we confirm that turnover is sensitive to the relative thermodynamic stability of reactive hydroxyl and bound bicarbonate moieties.

Discovering inorganic complexes with an ANN

Machine learning (ML) has emerged as a powerful complement to simulation for materials discovery by reducing time for evaluation of energies and properties at accuracy competitive with first-principles methods. In this work, we take our recently developed artificial neural network (ANN) that can predict spin-state ordering to within 3 kcal/mol of DFT training data and use it for chemical exploration.

How does solid state density localize? (Ed Choice)

Widely employed approximate density functional theory (DFT) suffers from delocalization errors. DFT+U and hybrid functionals are widely employed methods to correct energetic delocalization errors, but their effect on the density is less well known. Our recent work demonstrated that in transition metal complexes both methods localize density away from the metal and onto surrounding ligands, regardless of metal or ligand identity, in a similar fashion.

Scaling relations in single-site catalysis

Computational catalyst screening is limited primarily by the efficiency with which accurate predictions can be made. In bulk heterogeneous catalysis, linear free energy relationships (LFERs) accelerate screening by relating catalytic activity back to the adsorption energies of key intermediates, but their applicability to single-site catalysts remains unclear, in view of the directional, covalent metal-ligand bonds and the broader chemical space of accessible ligand scaffolds.

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Recovering exact conditions in semilocal DFT

Widely employed semi-local DFT suffers from well-known errors that prevent its robust predictio, e.g. in materials and catalyst design. This failure in semi-local DFT can be traced to the violation of exchange-correlation approximations of key exact conditions. The flat-plane condition is the union of two exact constraints in electronic structure theory: (i) energetic piecewise linearity with fractional electron removal or addition and (ii) invariant energetics with change in electron spin in a half filled orbital.

Inorganic features for machine learning

Machine learning models can accelerate the discovery of new materials by allowing rapid screening of potential candidates, but depend on the way the molecule is represented. For transition metal complexes, accurate calculations are computationally costly and available training data sets are small, so finding the correct representation becomes a critical ingredient for model predictive accuracy.

Unifying sensitivity in catalysis and spin states

Open-shell single-site transition metal (TM) complexes are efficient catalysts, but challenging to screen computationally because of 1) the need to simultaneously predict spin-splitting energies, activation barriers and reaction energies, and 2) well-known challenges of approximate DFT for these predictions that manifest as strong sensitivity to the amount of exact exchange in the functional. Hence, advancing DFT-based screening requires understanding how computed energetics are sensitive to exact exchange.

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Conceptual DFT for systematic modeling

Multi-scale quantum-mechanical/molecular-mechanical (QM/MM) and large-scale QM simulation provide valuable insight into enzyme mechanism and structure-property relationships. Analysis of the electron density afforded through these methods can enhance our understanding of how the enzyme environment modulates reactivity at the enzyme active site. From this perspective, tools from conceptual density functional theory to interrogate electron densities can provide added insight into enzyme function.

Predicting electronic structure with ANNs

Direct density functional theory (DFT) simulation is the critical bottleneck in high-throughput computational screening for inorganic materials and molecular transition metal complexes. These calculations are computationally costly and the calculated properties are sensitive to the exchange–correlation functional employed. Screening efforts for molecular inorganic systems are complicated by the uncertain spin-state ordering of hypothetical complexes and difficulty in obtaining good initial guess geometries.

Discovering chemistry from large databases

Using our recently developed inorganic discovery toolkit, molSimplify code, candidate molecules were obtained from the ChEMBL-19 database (> 1M molecules) to address a critical outstanding challenge in materials science. These databases of bioactive organic molecules are typically employed for discovery of therapeutic drug-like molecules; we instead demonstrated their power as a tool to discover design rules for inorganic complexes while maintaining realism (i.e., stable, synthetically accessible substituents) and providing diversity in functional groups.

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About Us

The Kulik group focuses on the development and application of new electronic structure methods and atomistic simulations tools in the broad area of catalysis.

Our Interests

We are interested in transition metal chemistry, with applications from biological systems (i.e. enzymes) to nonbiological applications in surface science and molecular catalysis.

Our Focus

A key focus of our group is to understand mechanistic features of complex catalysts and to facilitate and develop tools for computationally driven design.

Contact Us

Questions or comments? Let us know! Contact Dr. Kulik: