Lixin Lu

All Publications

• Non-Negative Least Squares Reweighting and Pruning of Quadrature Grids for Tensor Hypercontraction. Journal of chemical theory and computation Hillers-Bendtsen, A. E., Lu, L., Martínez, T. J. 2026; 22 (15): 7657-7666

  Abstract

  Tensor hypercontraction provides an attractive four-center two-electron repulsion integral format that can lower the scaling of many electronic structure methods while only requiring O(N2) memory. However, in its grid-based least-squares incarnation, tensor hypercontraction requires the tedious design of compact spatial quadrature grids to achieve efficiency and accuracy, representing a bottleneck for widespread application. To simplify grid generation, we devise a reweighting scheme in which the grid weights are optimized to ensure accurate reproduction of the atomic orbital overlap matrix by numerical integration. By casting this fitting task as a non-negative least-squares problem, we obtain a black-box methodology that not only yields robust grids for tensor hypercontraction as well as numerical integration of other integrals but also prunes the grids by zeroing quadrature weights for insignificant points.

  View details for DOI 10.1021/acs.jctc.6c00664

  View details for PubMedID 42579386

• Non-Negative LeastSquares Reweighting and Pruningof Quadrature Grids for Tensor Hypercontraction JOURNAL OF CHEMICAL THEORY AND COMPUTATION Hillers-Bendtsen, A., Lu, L., Martinez, T. J. 2026

  View details for DOI 10.1021/acs.jctc.6c00664

  View details for Web of Science ID 001837556400001

• Complete Active Space Self-Consistent Field with GPU-Accelerated Density Fitting. Journal of chemical theory and computation Wang, R., Wang, Y., Lu, L., Hait, D., Martínez, T. J. 2026

  Abstract

  The complete active space self-consistent field (CASSCF) method is essential for describing complex photochemical processes, but its application in ab initio molecular dynamics is often limited by the computational cost associated with four-center two-electron repulsion integrals (ERIs). We implement the atomic orbital (AO)-based GPU-accelerated density fitting (DF) approximation for CASSCF within the TeraChem software package. Validation on salicylaldimine demonstrates that the DF approximation introduces negligible errors in relative energies, yielding excitation energies accurate to within 10 microHartrees of the integral-direct reference. The DF-CASSCF implementation achieves significant computational speedups, accelerating total energy and gradient calculations by more than an order of magnitude for small- to medium-sized systems with large AO basis sets. We demonstrate the practical utility of this approach through ab initio multiple spawning dynamics simulations of excited-state intramolecular proton transfer (ESIPT). The DF-CASSCF trajectories reproduce the photodynamics of the reference simulations while reducing the total wall time (for a single GPU) by a factor of 3-30, depending on the choice of the basis set. This work significantly lowers the barrier for high-throughput, high-accuracy multireference simulations on modern GPU architectures.

  View details for DOI 10.1021/acs.jctc.5c02079

  View details for PubMedID 41854296

• Small tensor product distributed active space (STP-DAS) framework for relativistic and non-relativistic multiconfiguration calculations: Scaling from 10<SUP>9</SUP> on a laptop to 10<SUP>12</SUP> determinants on a supercomputer CHEMICAL PHYSICS REVIEWS Hu, H., Upadhyay, S., Lu, L., Jenkins, A. J., Zhang, T., Shayit, A., Knecht, S., Li, X. 2024; 5 (4)

  View details for DOI 10.1063/5.0227122

  View details for Web of Science ID 001345535500001

• Direct Probe of Conical Intersection Photochemistry by Time-Resolved X-ray Magnetic Circular Dichroism JOURNAL OF THE AMERICAN CHEMICAL SOCIETY Sun, S., Gu, B., Hu, H., Lu, L., Tang, D., Chernyak, V. Y., Li, X., Mukamel, S. 2024; 146 (29): 19863-19873

  Abstract

  The direct probing of photochemical dynamics by detecting the electronic coherence generated during passage through conical intersections is an intriguing challenge. The weak coherence signal and the difficulty in preparing purely excited wave packets that exclude coherence from other sources make it experimentally challenging. We propose to use time-resolved X-ray magnetic circular dichroism to probe the wave packet dynamics around the conical intersection. The magnetic field amplifies the relative strength of the electronic coherence signal compared to populations through the magnetic field response anisotropy. More importantly, since the excited state relaxation through conical intersections involves a change of parity, the magnetic coupling matches the symmetry of the response function with the electronic coherence, making the coherence signal only sensitive to the conical intersection induced coherence and excludes the pump pulse induced coherence between the ground state and excited state. In this theoretical study, we apply this technique to the photodissociation dynamics of a pyrrole molecule and demonstrate its capability of probing electronic coherence at a conical intersection as well as population transfer. We demonstrate that a magnetic field can be effectively used to extract novel information about electron and nuclear molecular dynamics.

  View details for DOI 10.1021/jacs.4c03033

  View details for Web of Science ID 001276273200001

  View details for PubMedID 38989850

• Prediction of photodynamics of 200 nm excited cyclobutanone with linear response electronic structure and ab initio multiple spawning. The Journal of chemical physics Hait, D., Lahana, D., Fajen, O. J., Paz, A. S., Unzueta, P. A., Rana, B., Lu, L., Wang, Y., Kjønstad, E. F., Koch, H., Martínez, T. J. 2024; 160 (24)

  Abstract

  Simulations of photochemical reaction dynamics have been a challenge to the theoretical chemistry community for some time. In an effort to determine the predictive character of current approaches, we predict the results of an upcoming ultrafast diffraction experiment on the photodynamics of cyclobutanone after excitation to the lowest lying Rydberg state (S2). A picosecond of nonadiabatic dynamics is described with ab initio multiple spawning. We use both time dependent density functional theory (TDDFT) and equation-of-motion coupled cluster singles and doubles (EOM-CCSD) theory for the underlying electronic structure theory. We find that the lifetime of the S2 state is more than a picosecond (with both TDDFT and EOM-CCSD). The predicted ultrafast electron diffraction spectrum exhibits numerous structural features, but weak time dependence over the course of the simulations.

  View details for DOI 10.1063/5.0203800

  View details for PubMedID 38912674

• Attosecond-pump attosecond-probe x-ray spectroscopy of liquid water. Science (New York, N.Y.) Li, S., Lu, L., Bhattacharyya, S., Pearce, C., Li, K., Nienhuis, E. T., Doumy, G., Schaller, R. D., Moeller, S., Lin, M. F., Dakovski, G., Hoffman, D. J., Garratt, D., Larsen, K. A., Koralek, J. D., Hampton, C. Y., Cesar, D., Duris, J., Zhang, Z., Sudar, N., Cryan, J. P., Marinelli, A., Li, X., Inhester, L., Santra, R., Young, L. 2024: eadn6059

  Abstract

  Attosecond-pump/attosecond-probe experiments have long been sought as the most straightforward method to observe electron dynamics in real time. Although numerous successes have been achieved with overlapped near infrared femtosecond and extreme ultraviolet attosecond pulses combined with theory, true attosecond-pump/attosecond-probe experiments have been limited. We used a synchronized attosecond x-ray pulse pair from an x-ray free electron laser to study the electronic response to valence ionization in liquid water via all x-ray attosecond transient absorption spectroscopy (AX-ATAS). Our analysis showed that the AX-ATAS response is confined to the subfemtosecond timescale, eliminating any hydrogen atom motion and demonstrating experimentally that the 1b1 splitting in the x-ray emission spectrum is related to dynamics and is not evidence for two structural motifs in ambient liquid water.

  View details for DOI 10.1126/science.adn6059

  View details for PubMedID 38359104

• Correlated Dirac-Coulomb-Breit multiconfigurational self-consistent-field methods JOURNAL OF CHEMICAL PHYSICS Hoyer, C. E., Lu, L., Hu, H., Shumilov, K. D., Sun, S., Knecht, S., Li, X. 2023; 158 (4): 044101

  Abstract

  The fully correlated frequency-independent Dirac-Coulomb-Breit Hamiltonian provides the most accurate description of electron-electron interaction before going to a genuine relativistic quantum electrodynamics theory of many-electron systems. In this work, we introduce a correlated Dirac-Coulomb-Breit multiconfigurational self-consistent-field method within the frameworks of complete active space and density matrix renormalization group. In this approach, the Dirac-Coulomb-Breit Hamiltonian is included variationally in both the mean-field and correlated electron treatment. We also analyze the importance of the Breit operator in electron correlation and the rotation between the positive- and negative-orbital space in the no-virtual-pair approximation. Atomic fine-structure splittings and lanthanide contraction in diatomic fluorides are used as benchmark studies to understand the contribution from the Breit correlation.

  View details for DOI 10.1063/5.0133741

  View details for Web of Science ID 000931509500008

  View details for PubMedID 36725503

• Relativistic Kramers-Unrestricted Exact-Two-Component Density Matrix Renormalization Group JOURNAL OF PHYSICAL CHEMISTRY A Hoyer, C. E., Hu, H., Lu, L., Knecht, S., Li, X. 2022; 126 (30): 5011-5020

  Abstract

  In this work we develop a variational relativistic density matrix renormalization group (DMRG) approach within the exact-two-component (X2C) framework (X2C-DMRG), using spinor orbitals optimized with the two-component relativistic complete active space self-consistent field. We investigate fine-structure splittings of p- (Ga, In, Tl) and d-block (Sc, Y, La) atoms and excitation energies of monohydride molecules (GeH, SnH, and TlH) with X2C-DMRG calculations using an all-electron relativistic Hamiltonian in a Kramers-unrestricted basis. We find that X2C-DMRG yields accurate 2P and 2D splittings compared to multireference configuration interaction with singles and doubles (MRCISD). We also investigated the degree of symmetry breaking in the atomic multiplets and convergence of electron correlation in the total energies. Symmetry breaking can be large in some cases (∼30 meV); however, increasing the number of renormalized block states m for the DMRG optimization recovers the symmetry breaking by several orders of magnitude. Encouragingly, we find the convergence of electron correlation to be close to MRCISDTQ5 quality. Relativistic X2C-DMRG approaches are important for cases where spin-orbit coupling is significant and the underlying reference wave function requires a large determinantal space. We are able to obtain quantitatively correct fine-structure splittings for systems up to 1019 number of determinants with traditional CI approaches, which are currently unfeasible to converge for the field.

  View details for DOI 10.1021/acs.jpca.2c02150

  View details for Web of Science ID 000894525000001

  View details for PubMedID 35881436

• Exact-Two-Component Relativistic Multireference Second-Order Perturbation Theory JOURNAL OF CHEMICAL THEORY AND COMPUTATION Lu, L., Hu, H., Jenkins, A. J., Li, X. 2022; 18 (5): 2983-2992

  Abstract

  As the relativistic corrections become stronger for late-row elements, the fully perturbative treatment of spin-orbit coupling and dynamic correlation may become inadequate for accurate descriptions of chemical properties. In this work, we introduce a determinant-based Kramers-unrestricted exact-two-component multireference second-order perturbation (X2C-MRPT2) method which variationally includes relativistic corrections with a perturbative dynamic correlation. The restricted active space partitioning scheme is employed to provide an adjustable correlation space for the second-order perturbation treatment. The multistate perturbation theory is also developed to improve the descriptions of ground and excited states. Benchmark studies of atomic fine-structure splittings and spectroscopic constants of molecular monohydrides using X2C-MRPT2 are compared to the other perturbative and variational approaches. The results suggest that X2C-MRPT2 is a highly accurate alternative to the fully variational multireference configuration interaction method at only a small fraction of the computational cost.

  View details for DOI 10.1021/acs.jctc.2c00171

  View details for Web of Science ID 000801046200020

  View details for PubMedID 35481362

• Two-Component Multireference Restricted Active Space Configuration Interaction for the Computation of L-Edge X-ray Absorption Spectra JOURNAL OF CHEMICAL THEORY AND COMPUTATION Jenkins, A. J., Hu, H., Lu, L., Frisch, M. J., Li, X. 2022; 18 (1): 141-150

  Abstract

  X-ray absorption spectroscopy is a powerful probe of local electronic and nuclear structures, providing insights into chemical processes. The theoretical prediction and interpretation of metal L-edge X-ray absorption spectra are complicated by both relativistic effects, including spin-orbit coupling and the multiconfigurational nature of the states involved. This work details an exact two-component multireference restricted active space (RAS) configuration interaction scheme that uses an exact two-component state-averaged complete active space self-consistent-field method, which includes the spin-orbit coupling in a variational manner, for the accurate description of the electronic structure before using a RAS configuration interaction method to describe the core excited states of the X-ray spectrum. Benchmark calculations are presented for a series of iron-containing complexes, with results showing key features of the spectrum being reproduced, including ligand-to-metal charge transfer and shake-up excitations.

  View details for DOI 10.1021/acs.jctc.1c00564

  View details for Web of Science ID 000733779300001

  View details for PubMedID 34908414

• Defect-Induced Magnetic Skyrmion in a Two-Dimensional Chromium Triiodide Monolayer JACS AU Beck, R. A., Lu, L., Sushko, P., Xu, X., Li, X. 2021; 1 (9): 1362-1367

  Abstract

  Chromium iodide monolayers, which have different magnetic properties in comparison to the bulk chromium iodide, have been shown to form skyrmionic states in applied electromagnetic fields or in Janus-layer devices. In this work, we demonstrate that spin-canted solutions can be induced into monolayer chromium iodide by select substitution of iodide atoms with isovalent impurities. Several concentrations and spatial configurations of halide substitutional defects are selected to probe the coupling between the local defect-induced geometric distortions and orientation of chromium magnetic moments. This work provides atomic-level insight into how atomically precise chemical doping can be used to create and control complex magnetic patterns in chromium iodide layers and lays out the foundation for investigating the field- and geometric-dependent magnetic properties in similar two-dimensional materials.

  View details for DOI 10.1021/jacsau.1c00142

  View details for Web of Science ID 000703333000007

  View details for PubMedID 34604846

  View details for PubMedCentralID PMC8479765

• The "Hole" Story in Ionized Water from the Perspective of Ehrenfest Dynamics JOURNAL OF PHYSICAL CHEMISTRY LETTERS Lu, L., Wildman, A., Jenkins, A. J., Young, L., Clark, A. E., Li, X. 2020; 11 (22): 9946-9951

  Abstract

  The radiolysis of liquid water and the radiation-matter interactions that happen in aqueous environments are important to the fields of chemistry, materials, and environmental sciences, as well as the biological and physiological response to extreme conditions and medical treatments. The initial stage of radiolysis is the ultrafast response, or hole dynamics, that triggers chemical processes within complex energetic landscapes that may include reactivity. A fundamental understanding necessitates the use of theoretical methods that are capable of simulating both ultrafast coherence and non-adiabatic energy transfer pathways. In this work, we carry out an ab initio Ehrenfest dynamics study to provide a more complete description of the ultrafast dynamics and reactive events initiated by photoionization of water. After sudden ionization, a range of processes, including hole trapping and transfer, large OH oscillations, proton transfer and subsequent relay, formation of the metastable Zundel complex, and long-lived coherence, are identified and new insight into their driving forces is elucidated.

  View details for DOI 10.1021/acs.jpclett.0c02987

  View details for Web of Science ID 000592959100059

  View details for PubMedID 33170721

• Spectroscopic Signatures of the B and H₄ Polyatomic Nitrogen Aggregates in Nanodiamond JOURNAL OF PHYSICAL CHEMISTRY C Beck, R. A., Lu, L., Petrone, A., Ong, A. C., Pauzauskie, P. J., Li, X. 2020; 124 (33): 18275-18283

  View details for DOI 10.1021/acs.jpcc.0c03106

  View details for Web of Science ID 000563746200046