Fang Liu, Michael Filatov, and Todd J. Martínez. “Analytical Derivatives of the Individual State Energies in Ensemble Density Functional Theory Method: II. Implementation on Graphical Processing Units (GPUs).” chemrxiv.79856 (Preprint).

In Press

Fang Liu, Chenru Duan, and Heather Kulik. “Rapid Detection of Strong Correlation with Machine Learning for Transition Metal Complex High-Throughput Screening.” J. Phys. Chem. Lett. (In Press).


Chenru Duan, Fang Liu, Aditya Nandy, and Heather Kulik. “Semi-Supervised Machine Learning Enables the Robust Detection of Multireference Character at Low Cost.” J. Phys. Chem. Lett. no. 11 (2020): 6640–6648

Chenru Duan, Fang Liu, Aditya Nandy, and Heather Kulik. “Data-Driven Approaches Can Overcome Limitations in Multireference Diagnostics.” J. Chem. Theory Comput. 16, no. 7 (2020): 4373-4387.

Fang Liu and Heather Kulik. “Impact of Approximate DFT Density Delocalization Error on Potential Energy Surfaces in Transition Metal Chemistry.” J. Chem. Theory Comput. 6 (2020): 264.

Seritan, Stefan, Christoph Bannwarth, Bryan S. Fales, Edward G. Hohenstein, Christine M. Isborn, Sara I. L. Kokkila-Schumacher, Xin Li, Fang Liu, Nathan Luehr, James W. Snyder Jr. et al. “TeraChem: A graphical processing unit-accelerated electronic structure package for large-scale ab initio molecular dynamics.” WIREs Computational Molecular Science (2020): e1494.

Akash Bajaj, Fang Liu, and Heather Kulik. “Uncovering Alternate Pathways to Nafion Membrane Degradation in Fuel Cells with First-Principles Modeling.” The Journal of Physical Chemistry C 124, no. 28 (2020): 15094-15106.


Yao Wang, Juan Pablo Dehollain, Fang Liu, Uditendu Mukhopadhyay, Mark S. Rudner, Lieven M. K. Vandersypen, and Eugene Demler. “Ab Initio Exact Diagonalization Simulation of the Nagaoka Transition in Quantum Dots.” Phys. Rev. B 100 (2019): 155133.

Fang Liu, Tzuhsiung Yang, Jing Yang, Eve Xu, Akash Bajaj, and Heather Janine Kulik. “Bridging the homogeneous-heterogeneous divide: modeling spin and reactivity in single atom catalysis.” Front. Chem. 7 (2019): 219.

Jimmy Yu, Ruibinng Liang, Fang Liu, and Todd J. Martínez. “Characterization of the Elusive I Fluorescent State and the Ultrafast Photoisomerization of Retinal Protonated Schiff Base in Bacteriorhodopsin by Nonadiabatic Dynamics Simulation.” J. Am. Chem. Soc. 141 (2019): 18193.

Jon Paul Janet, Fang Liu, Aditya Nandy, Chenru Duan, Tzuhsiung Yang, Sean Lin, and Heather J. Kulik. “Designing in the Face of Uncertainty: Exploiting Electronic Structure and Machine Learning Models for Discovery in Inorganic Chemistry.” Inorg. Chem. 58 (2019): 10592.

Fang Liu, David M. Sanchez, Heather J. Kulik, and Todd J. Martínez. “Exploiting graphical processing units to enable quantum chemistry calculation of large solvated molecules with conductor-like polarizable continuum models.” Int. J. Quantum Chem. 119 (2019): e25760.

Chenru Duan, Jon Paul Janet, Fang Liu, Aditya Nandy, and Heather J. Kulik. “Learning from Failure: Predicting Electronic Structure Calculation Outcomes with Machine Learning Models.” J. Chem. Theory Comput. 15 (2019): 2331.

Ruibin Liang, Fang Liu, and Todd J. Martínez. “Nonadiabatic Photodynamics of Retinal Protonated Schiff Base in Channelrhodopsin 2.” J. Phys. Chem. Lett. 10 (2019): 2862.

Akash Bajaj, Fang Liu, and Heather J. Kulik. “Non-empirical, low-cost recovery of exact conditions with model-Hamiltonian inspired expressions in jmDFT.” J. Chem. Phys. 150 (2019): 154115.

Zhongyue Yang, Fang Liu, Adam H. Steeves, and Heather J. Kulik. “A Quantum Mechanical Description of Electrostatics Provides a Unified Picture of Catalytic Action Across Methyltransferases.” J. Phys. Chem. Lett. 10 (2019): 3779.


Margaux M. Pinney, Aditya Natarajan, Filip Yabukarski, David M. Sanchez, Fang Liu, Ruibin Liang, Tzanko Doukov, Jason P. Schwans, Todd J. Martínez, and Daniel Herschlag. “Structural coupling throughout the active site hydrogen bond networks of ketosteroid isomerase and photoactive yellow protein.” J. Am. Chem. Soc. 140 (2018): 9827.


Xin Li, Robert M. Parrish, Fang Liu, Sara I. L. Kokkila Schumacher, and Todd J. Martínez. “An ab initio exciton model including charge-transfer excited states.” J. Chem. Theory Comput. 13 (2017): 3493.

Michael Filatov, Fang Liu, and Todd J. Martínez. “Analytical derivatives of the individual state energies in ensemble density functional theory method. I. General formalism.” J. Chem. Phys. 147 (2017): 034113.

Shibdas Banerjee,§ Fang Liu,§ David M. Sanchez, Todd J. Martínez, and Richard N. Zare. “Pomeranz–Fritsch Synthesis of Isoquinoline: Gas-Phase Collisional Activation Opens Additional Reaction Pathways.” J. Am. Chem. Soc. 139 (2017): 14352-14355. [§ These two authors contribute equally]


Robert M. Parrish, Fang Liu, and Todd J. Martínez. “Communication: A difference density picture for the self-consistent field ansatz.” J. Chem. Phys. 144 (2016): 131101.

Michael Filatov, Fang Liu, Kwang S. Kim, and Todd J. Martínez. “Self-consistent implementation of ensemble density functional theory method for multiple strongly correlated electron pairs.” Journal Chem. Phys. 145 (2016): 244104.


Brendan D. Mar, Helena W. Qi, Fang Liu, and Heather J. Kulik. “Ab Initio screening approach for the discovery of lignin polymer breaking pathways.” J. Phys. Chem. A 119 (2015): 6551.

Fang Liu, Nathan Luehr, Heather J. Kulik, and Todd J. Martínez. “Quantum chemistry for solvated molecules on graphical processing units using polarizable continuum models.” J. Chem. Theory Comput. 11 (2015): 3131.


Lee-Ping Wang, Alexey Titov, Robert McGibbon, Fang Liu, Vijay S. Pande, and Todd J. Martínez. “Discovering chemistry with an ab initio nanoreactor.” Nat. Chem. 6 (2014): 1044.