publications

2026

1. Interpolative Separable Density-Fitting for Transcorrelated Hamiltonians

   Ke Liao, Yifan Cheng, Werner Dobrautz, and 2 more authors

   Jul 2026

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   The transcorrelated (TC) method dramatically accelerates the convergence of correlated calculations toward the complete-basis-set (CBS) limit by folding a Jastrow correlator into the Hamiltonian via a similarity transformation, incorporating the electron–electron cusp into the effective interaction. We make the TC framework practical for large systems and flexible, multi-center correlators by compressing the grid-evaluated TC integrals with the interpolative separable density-fitting (ISDF) approximation, combined with the effective two-body (xTC) treatment of the three-body operator. This low-rank representation reduces storage and integration costs by orders of magnitude, and a multi-GPU implementation with automatic differentiation of the correlator makes the construction routine for large basis sets. We demonstrate the resulting ISDF-xTC-CCSD method on the linear hydrogen chain, reaching the joint thermodynamic and CBS limits with basis sets up to cc-pV5Z in agreement with state-of-the-art many-body references to within about 1 mHa/atom, and on the benzene ground-state energy with up to 1200 orbitals (cc-pCV5Z), where the method attains state-of-the-art accuracy at the coupled cluster singles and doubles level and its CBS extrapolation is markedly more robust than that of conventional coupled-cluster methods.

2025

1. Energy-Filtered Excited States and Real-Time Dynamics Served in a Contour Integral

   Ke Liao

   J. Chem. Theory Comput., Jun 2025

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   It is observed that the Cauchy integral formula (CIF) can be used to represent holomorphic functions of diagonalizable operators on a finite domain. This forms the theoretical foundation for applying various operators in the form of a contour integral to a state, while filtering away eigen-components that are not included by the contour. As a special case, the identity operator in the integral form–the Riesz projector–is used to design a black-box algorithm for finding a given number of eigen-pairs whose energies are close to a specified value in the equation-of-motion coupled cluster singles and doubles (EOM-CCSD) framework, with applications to calculate core excited states of molecules which is relevant for the X-ray absorption spectroscopy (XAS). As a generalization, I showcase a novel real-time electron dynamics (RT-EOM-CCSD) algorithm based on the CIF form of the exponential time-evolution operator, which admits extremely large time steps while preserving accurate spectral information.

2024

1. What Can Quantum Information Theory Offer to Quantum Chemistry?

   Damiano Aliverti-Piuri, Kaustav Chatterjee, Lexin Ding, and 3 more authors

   Faraday Discuss., Apr 2024

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   It is the ultimate goal of this work to foster synergy between quantum chemistry and the flourishing field of quantum information theory. For this, we first translate quantum information concepts such as entanglement and correlation into the context of quantum chemical systems. In particular, we establish two conceptually distinct perspectives on correlation leading to a notion of orbital and particle correlation. We then demonstrate that particle correlation equals orbital correlation minimized with respect to all orbital reference bases. Accordingly, particle correlation resembles the minimal, thus intrinsic, complexity of many-electron wavefunctions while orbital correlation quantifies their complexity relative to a basis. We illustrate these novel concepts of intrinsic and extrinsic correlation complexity with analytic and numerical examples, which also demonstrates the crucial link between the two correlation pictures. Our results provide theoretical justification for the long-favored natural orbitals for simplifying electronic structures, and open new pathways for developing more efficient approaches towards the electron correlation problem.

2. Novel Perturbative and Variational Methods for Stronger Correlations: General Discussion

   Vibin Abraham, Kemal Atalar, Kenneth O. Berard, and 27 more authors

   Faraday Discuss., 2024

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3. Stochastic and Low-Scaling Techniques: General Discussion

   Ali Alavi, Marcus Allen, Kemal Atalar, and 45 more authors

   Faraday Discuss., 2024

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4. Stochastic and Low-Scaling Techniques/Extended Systems: General Discussion

   Ali Alavi, Kemal Atalar, Timothy C. Berkelbach, and 20 more authors

   Faraday Discuss., 2024

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5. Toward Real Chemical Accuracy on Current Quantum Hardware Through the Transcorrelated Method

   Werner Dobrautz, Igor O. Sokolov, Ke Liao, and 4 more authors

   Journal of Chemical Theory and Computation, 2024

   PMID: 38723159

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   Quantum computing is emerging as a new computational paradigm with the potential to transform several research fields including quantum chemistry. However, current hardware limitations (including limited coherence times, gate infidelities, and connectivity) hamper the implementation of most quantum algorithms and call for more noise-resilient solutions. We propose an explicitly correlated Ansatz based on the transcorrelated (TC) approach to target these major roadblocks directly. This method transfers, without any approximation, correlations from the wave function directly into the Hamiltonian, thus reducing the resources needed to achieve accurate results with noisy quantum devices. We show that the TC approach allows for shallower circuits and improves the convergence toward the complete basis set limit, providing energies within chemical accuracy to experiment with smaller basis sets and, thus, fewer qubits. We demonstrate our method by computing bond lengths, dissociation energies, and vibrational frequencies close to experimental results for the hydrogen dimer and lithium hydride using two and four qubits, respectively. To demonstrate our approach’s current and near-term potential, we perform hardware experiments, where our results confirm that the TC method paves the way toward accurate quantum chemistry calculations already on today’s quantum hardware.

6. Quantum Information Orbitals (QIO): Unveiling Intrinsic Many-Body Complexity by Compressing Single-Body Triviality

   Ke Liao, Lexin Ding, and Christian Schilling

   J. Phys. Chem. Lett., Jun 2024

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   The simultaneous treatment of static and dynamical correlations in strongly-correlated electron systems is a critical challenge. In particular, finding a universal scheme for identifying a single-particle orbital basis that minimizes the representational complexity of the many-body wavefunction is a formidable and longstanding problem. As a substantial contribution towards its solution, we show that the total orbital correlation actually reveals and quantifies the intrinsic complexity of the wavefunction,once it is minimized via orbital rotations. To demonstrate the power of this concept in practice, an iterative scheme is proposed to optimize the orbitals by minimizing the total orbital correlation calculated by the tailored coupled cluster singles and doubles (TCCSD) ansatz. The optimized orbitals enable the limited TCCSD ansatz to capture more non-trivial information of the many-body wavefunction, indicated by the improved wavefunction and energy. An initial application of this scheme shows great improvement of TCCSD in predicting the singlet ground state potential energy curves of the strongly correlated C\_{}rm 2} and Cr\_{}rm 2} molecule.

2023

1. Density Matrix Renormalization Group for Transcorrelated Hamiltonians: Ground and Excited States in Molecules

   Ke Liao, Huanchen Zhai, Evelin Martine Christlmaier, and 4 more authors

   J. Chem. Theory Comput., Mar 2023

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   We present the theory of a density matrix renormalization group (DMRG) algorithm which can solve for both the ground and excited states of non-Hermitian transcorrelated Hamiltonians and show applications in molecular systems. Transcorrelation (TC) accelerates the basis set convergence rate by including known physics (such as, but not limited to, the electron–electron cusp) in the Jastrow factor used for the similarity transformation. It also improves the accuracy of approximate methods such as coupled cluster singles and doubles (CCSD) as shown by recent studies. However, the non-Hermiticity of the TC Hamiltonians poses challenges for variational methods like DMRG. Imaginary-time evolution on the matrix product state (MPS) in the DMRG framework has been proposed to circumvent this problem, but this is currently limited to treating the ground state and has lower efficiency than the time-independent DMRG (TI-DMRG) due to the need to eliminate Trotter errors. In this work, we show that with minimal changes to the existing TI-DMRG algorithm, namely, replacing the original Davidson solver with the general Davidson solver to solve the non-Hermitian effective Hamiltonians at each site for a few low-lying right eigenstates, and following the rest of the original DMRG recipe, one can find the ground and excited states with improved efficiency compared to the original DMRG when extrapolating to the infinite bond dimension limit in the same basis set. An accelerated basis set convergence rate is also observed, as expected, within the TC framework.

2. Block2 : A Comprehensive Open Source Framework to Develop and Apply State-of-the-Art DMRG Algorithms in Electronic Structure and Beyond

   Huanchen Zhai, Henrik R. Larsson, Seunghoon Lee, and 10 more authors

   J. Chem. Phys., Dec 2023

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   BLOCK2 is an open source framework to implement and perform density matrix renormalization group and matrix product state algorithms. Out-of-the-box it supports the eigenstate, time-dependent, response, and finite-temperature algorithms. In addition, it carries special optimizations for ab initio electronic structure Hamiltonians and implements many quantum chemistry extensions to the density matrix renormalization group, such as dynamical correlation theories. The code is designed with an emphasis on flexibility, extensibility, and efficiency and to support integration with external numerical packages. Here, we explain the design principles and currently supported features and present numerical examples in a range of applications.

2021

1. Towards Efficient and Accurate Ab Initio Solutions to Periodic Systems via Transcorrelation and Coupled Cluster Theory

   Ke Liao, Thomas Schraivogel, Hongjun Luo, and 2 more authors

   Phys. Rev. Research, Jul 2021

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   We propose a streamlined combination of the transcorrelation (TC) and coupled cluster (CC) theory, which not only increases the convergence rate with respect to the basis set but also extends the applicability of the lowest-order CC approximations to strongly correlated systems. Using the three-dimensional uniform electron gas as a model for real periodic solids and highly accurate ground-state energies from the state-of-the-art quantum Monte Carlo methods as benchmark, we show that, with the correct physical insights incorporated, our TC-CC methods gain drastic improvements in accuracy compared with canonical CC methods, and the errors of our methods remain \textpm0.001 Hartree per electron (Ha/electron) across a wide range of densities. With the greatly improved efficiencies and the balanced and accurate performances at both low and high densities, our methods present great promise for applications on real solids with weak and strong correlations.

2. Structural and Electronic Properties of Solid Molecular Hydrogen from Many-Electron Theories

   Ke Liao, Tong Shen, Xin-Zheng Li, and 2 more authors

   Phys. Rev. B, Feb 2021

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   We study the structural and electronic properties of phase III of solid hydrogen using accurate many-electron theories and compare the results to state-of-the-art experimental findings. The atomic structures of phase III modeled by C2/c-24 crystals are fully optimized on the level of second-order perturbation theory, demonstrating that previously employed structures optimized on the level of approximate density functionals exhibit errors in the H2 bond lengths that cause significant discrepancies in the computed quasiparticle band gaps and vibrational frequencies compared to experiment. Using these optimized atomic structures, we study the band gap closure and change in vibrational frequencies as a function of pressure. Our findings are in good agreement with recent experimental observations and may prove useful in resolving long-standing discrepancies between experimental estimates of metallization pressures possibly caused by disagreeing pressure calibrations.

3. Ab Initio Studies of Solid Phase Diagrams with Quantum Chemical Theories

   Ke Liao

   2021

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2019

1. A Comparative Study Using State-of-the-Art Electronic Structure Theories on Solid Hydrogen Phases under High Pressures

   Ke Liao, Xin-Zheng Li, Ali Alavi, and 1 more author

   npj Comput. Mater., Dec 2019

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2018

1. Applying the Coupled-Cluster Ansatz to Solids and Surfaces in the Thermodynamic Limit

   Thomas Gruber, Ke Liao, Theodoros Tsatsoulis, and 2 more authors

   Phys. Rev. X., May 2018

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2016

1. Communication: Finite Size Correction in Periodic Coupled Cluster Theory Calculations of Solids

   Ke Liao and Andreas Grüneis

   J. Chem. Phys., Oct 2016

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   We present a method to correct for finite size errors in coupled cluster theory calculations of solids. The outlined technique shares similarities with electronic structure factor interpolation methods used in quantum Monte Carlo calculations. However, our approach does not require the calculation of density matrices. Furthermore we show that the proposed finite size corrections achieve chemical accuracy in the convergence of second-order Møller-Plesset perturbation and coupled cluster singles and doubles correlation energies per atom for insulating solids with two atomic unit cells using 2 \texttimes 2 \texttimes 2 and 3 \texttimes 3 \texttimes 3 k-point meshes only.