Novel computational methods for quantum modeling of materials in the exascale era: Applications to electrocatalysis

Faculty: Dr. Phani Motamarri (Department of Computational and Data Sciences) and Dr. Ananth Govind Rajan (Department of Chemical Engineering)

Quantum modelling of materials has been instrumental in providing crucial insights into materials’ structure and properties for various application areas. In particular, electronic density functional theory (DFT) calculations [1] have played a significant role in accurately predicting materials’ mechanical, chemical, electronic, and optical properties. In these calculations, a functional of the electron density is used to predict the potential energy of the system, which can ultimately be related to a variety of material properties. However, the asymptotic cubic scaling computational complexity with the number of electrons and the stringent accuracy requirements needed to compute meaningful properties demand enormous computational resources for DFT calculations. Hence, these calculations are routinely limited to bulk material systems with a few tens to hundred atoms using plane-wave based DFT codes and mostly remain in the high-throughput mode restricting the simulation domain to periodic boundary conditions. To address these challenges, recently, there has been an increasing thrust towards systematically improvable and scalable and real-space DFT discretization techniques. Among these real-space techniques, finite-element based methodologies provide several advantages over other widely used basis sets since they are systematically convergent for any material system, accommodate generic boundary conditions, and afford excellent parallel scalability due to the locality of the basis functions as shown in Dr. Phani Motamarri’s prior works [2,3]. An open-source code DFT-FE 1.0 [3] released recently and co-developed by Dr Phani Motamarri’s group inherits the above features while incorporating scalable and efficient solvers to solve the underlying DFT equations more efficiently than the widely used plane-wave-based codes. It has been demonstrated to run on massively parallel many-core CPU and hybrid CPUGPU systems with excellent scalability while simulating material systems as large as 600,000 electrons. These methodologies have been the backbone behind the ACM Gordon Bell Prize 2023. Additionally, recent works led by Dr. Phani Motamarri’s group [4,5] further reduce the computational cost by an order of magnitude compared to the current version of the DFT-FE code. However, state-of-the-art capabilities of finite-element-based methods for DFT have not yet been fully exploited for application problems involving electrocatalysis, and the current PhD proposal is towards this direction.

The conversion of renewable electricity into chemical energy via electrocatalysis is essential
to achieve the net-zero-carbon goals that have been set in response to the serious ongoing global
warming crisis. For instance, electrochemical water splitting to produce green hydrogen and oxygen [6], and electrochemical reduction of carbon dioxide (CO2) into valuable chemicals and fuels [7], such as ethylene and ethanol, have the potential to reduce the increasing levels of CO2 being emitted into the atmosphere. However, designing efficient catalytic materials for these applications has proven to be a challenge due to the requirement of finding materials that are both active as well as stable. Moreover, many of the cutting-edge catalysts are composed of noble metals, which greatly increases the cost of running such electrocatalytic processes. Thus, the ongoing endeavor in Dr. Ananth Govind Rajan’s group has been to use DFT calculations to discover new candidate electrocatalysts with high activity, low dissolution in electrolyte, and a low concentration of noble metals [8]. The DFT calculations of these systems are themselves fraught with challenges since these require the accurate multi-scale modeling of the electrode-electrolyte interface, where multiple phenomena such as surface reconstruction, ion adsorption, electric double-layer formation, and charge transfer take place under constant potential conditions [9]. While typical DFT simulations have assumed constant charge, vacuum conditions, increasing effort has been devoted to realistically simulate constant-potential, solvated conditions, so as to make accurate predictions [9]. With the above background and motivation in mind, the goal of the proposed PhD project is fourfold:

1. To develop finite-element (FE) based computational methodologies for incorporating implicit solvation models [10], a continuum-equation strategy to incorporate the effect of solvents to simulate solid-liquid interfaces in conjunction with the existing DFT-FE framework.
2. Extend this formalism to develop a real-space FE based computational methodology for “joint” density functional theory calculations [11], a theory that allows one to combine the electronic DFT problem with the free energy functional associated with the solvent in one functional.
3. Finally, to develop a computational methodology for grand-canonical DFT [11], i.e.,
   constant electrochemical potential, DFT building on the joint DFT framework.
4. To leverage the developed computational methods in conjunctional with AI techniques to address challenging problems in electrocatalysis, e.g., potential-dependent kinetic modeling of the water splitting mechanism on iron-doped nickel oxyhydroxide and the CO₂ reduction mechanism on copper-based single-atom alloys of transition metals. This will allow the accurate prediction of the effect of applied potential, pH, temperature, and pressure on the current density of the electrolyzer and the selectivity of the desired hydrocarbon product.

Background and Skills Required:

• Strong foundations in Linear Algebra, Numerical methods, Excellent programming
  skills,
• Strong interest in Chemical Engineering/Mechanical Engineering/Physics/Materials
• Knowledge in finite-element methods is a bonus.

Basic qualifications: B.E/B.Tech/M.E/MTech in Chemical Engineering, Mechanical Engineering, Computational Science or BS/MS in Physics, Mathematics, Chemistry.

References

1. W. Kohn and L. J. Sham. Self-consistent equations including exchange and correlation
   effects. Phys. Rev., 140:A1133–A1138, Nov 1965.
2. P. Motamarri, S. Das, Shiva Rudraraju, Krishnendu Ghosh, Denis Davydov, Vikram
   Gavini: DFT-FE — A massively parallel adaptive finite-element code for large-scale
   density functional theory calculations, Computer Physics Communications, 246 (2020)
   106853.
3. S. Das, P. Motamarri, Vishal Subramanian, David M. Rogers, and Vikram Gavini.
   DFT-FE 1.0: A massively parallel hybrid CPU-GPU density functional theory code
   using finite-element discretization. Computer Physics Communications, page 108473,
   2022.
4. K. Ramakrishnan, S. Das, P. Motamarri: Fast and scalable finite-element-based
   approach for density functional theory calculations using projector-augmented wave
   method, Physical Review B, 111, 035101 (2025).
5. N. Kodali, P. Motamarri: Finite-element based methods for non-collinear magnetism
   and spin-orbit coupling in real-space pseudopotential density functional theory
   calculations (accepted in Physical Review B).
6. A. Govind Rajan, J. M. P. Martirez, and E. A. Carter, “Why Do We Use the Material
   and Operating Conditions We Use for Heterogeneous (Photo)Electrochemical Water
   Splitting?,” ACS Catal. 2020, 10, 19, 11177–11234.
7. A. John, A. M. Verma, M. Shaneeth, and A. Govind Rajan, “Discovering a Single‐
   Atom Catalyst for CO2 Electroreduction to C1 Hydrocarbons: Thermodynamics and
   Kinetics on Aluminum‐Doped Copper,” ChemCatChem 2023, 15, 14, e202300188.
8. A. K. Verma, S. Atif, A. Padhy, T. S. Choksi, P. Barpanda, and A. Govind Rajan,
   “Robust Oxygen Evolution on Ni-Doped MoO3: Overcoming Activity-Stability Trade-
   Off in Alkaline Water Splitting,” Chem Bio Eng. 2025.
9. R. Rajagopalan, S. Chaturvedi, N. Chaudhary, A. Gogoi, T. S. Choksi, and A. Govind
   Rajan, “Advances in CO2 reduction on bulk and two-dimensional electrocatalysts:
   From first principles to experimental outcomes,” Curr. Opin. Electrochem. 2025, 51,
   101668.
10. S. Ringe, N. G. Hörmann, H. Oberhofer, and K. Reuter, “Implicit Solvation Methods
    for Catalysis at Electrified Interfaces,” Chem. Rev. 2022, 122, 12, 10777–10820.
11. R. Sundararaman, W. A. Goddard, and T. A. Arias, “Grand canonical electronic
    density-functional theory: Algorithms and applications to electrochemistry,” J. Chem.
    Phys. 2017, 146, 11, 114104.