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arXiv:2505.01405 · The Journal of Physical Chemistry A

QCMaquis 4.0: Multipurpose Electronic, Vibrational, and Vibronic Structure and Dynamics Calculations with the Density Matrix Renormalization Group

Kalman Szenes, Nina Glaser, Mihael Eraković, Valentin Barandun, Maximilian Mörchen, Robin Feldmann, Stefano Battaglia, Alberto Baiardi, Markus Reiher

Published Aug 1, 2025• 6 citations
arXivHTMLPDF

Abstract

QCMaquis is a quantum chemistry software package for general molecular structure calculations in a matrix product state/matrix product operator formalism of the density matrix renormalization group (DMRG). It supports a wide range of features for electronic structure, multicomponent (pre-Born-Oppenheimer), anharmonic vibrational structure, and vibronic calculations. In addition to the ground and excited state solvers, QCMaquis allows for time propagation of matrix product states based on the tangent-space formulation of time-dependent DMRG. The latest developments include transcorrelated electronic structure calculations, very recent vibrational and vibronic models, and a convenient Python wrapper, facilitating the interface with external libraries. This paper reviews all the new features of QCMaquis and demonstrates them with new results.

DOI
10.1021/acs.jpca.5c02970

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QCMaquis is a quantum chemistry software package for general molecular structure calculations in a matrix product state/matrix product operator formalism of the density matrix renormalization group (DMRG). It supports a wide range of features for electronic structure, multicomponent (pre-Born-Oppenheimer), anharmonic vibrational structure, and vibronic calculations. In addition to the ground and excited state solvers, QCMaquis allows for time propagation of matrix product states based on the tangent-space formulation of time-dependent DMRG. The latest developments include transcorrelated electronic structure calculations, very recent vibrational and vibronic models, and a convenient Python wrapper, facilitating the interface with external libraries. This paper reviews all the new features of QCMaquis and demonstrates them with new results.
In the past two decades, the density matrix renormalization group (DMRG) has emerged as an innovative new method in quantum chemistry relying on a theoretical framework very different from that of traditional electronic structure approaches. The development of the quantum chemical DMRG has been remarkably fast: it has already become one of the reference approaches for large-scale multiconfigurational calculations. This perspective discusses the major features of DMRG, highlighting its strengths and weaknesses also in comparison with other novel approaches. The method is presented following its historical development, starting from its original formulation up to its most recent applications. Possible routes to recover dynamical correlation are discussed in detail. Emerging new fields of applications of DMRG are explored, such as its time-dependent formulation and the application to vibrational spectroscopy.
High Resolution Image Download MS PowerPoint Slide Theoretical predictions of photochemical processes are essential for interpreting and understanding spectral features. Reliable quantum dynamics calculations of vibronic systems require precise modeling of anharmonic effects in the potential energy surfaces and off-diagonal nonadiabatic coupling terms. In this work, we present the n -mode quantization of all vibronic Hamiltonian terms comprised of general high-dimensional model representations. We expand the existing vibrational DMRG formalism by applying the n -mode quantization to all potential energy surfaces entering the Hamiltonian as well as to all off-diagonal coupling terms. This is accompanied by the introduction of a novel matrix product state architecture employing tailored local site operators, which allow an effective encoding of the vibronic wave function in a tensor-train format. This results in a second-quantized framework for accurate vibronic calculations employing the density matrix renormalization group algorithm. We demonstrate the accuracy and reliability of this approach by calculating the excited-state quantum dynamics of maleimide. We analyze convergence and the choice of parameters of the underlying time-dependent density matrix renormalization group algorithm for the n -mode vibronic Hamiltonian, demonstrating that it enables accurate calculations of complex photochemical dynamics.
Recent advances in experimental techniques have enabled precise characterization of fundamental nonadiabatic and even electronic dynamics in molecules, on ultrafast time scales reaching femtosecond to attosecond resolution. However, accurate theoretical simulation of these ultrafast chemical dynamics processes in large systems remains challenging, largely due to the overwhelming number of degrees of freedom (DoFs) and the pronounced many-body correlations. In recent years, by leveraging efficient decomposition schemes for high-dimensional wave function and operator tensors, the time-dependent density matrix renormalization group (TD-DMRG) has emerged as a powerful and accurate quantum dynamics method for simulating nonadiabatic and electron dynamics in large chemical systems, in conjunction with realistic electron/exciton-vibration/phonon models or ab initio quantum chemistry many-electron Hamiltonians. This review outlines the fundamentals of TD-DMRG for chemical dynamics, covering matrix product state/operator (MPS/MPO) frameworks and algorithms from ground-state calculations to time evolution. We discuss thermal/environmental effects and compare TD-DMRG with other tensor network methods such as multiconfiguration time-dependent Hartree (MCTDH) and multilayer MCTDH (ML-MCTDH). Demonstrated applications include simulations of pyrazine absorption, singlet fission in rubrene crystal, and charge migration in chloroacetylene cation. These show TD-DMRG’s capability for modeling complex ultrafast processes from femtoseconds to attoseconds with controlled accuracy.
Dynamical electronic- and vibrational-structure theories have received a growing interest in the past few years due to their ability to simulate spectra recorded with ultrafast experimental techniques. The exact time evolution of a molecular system can, in principle, be obtained from the time-dependent version of full configuration interaction. Such an approach is, however, limited to few-atom systems due to the exponential increase of its cost with the system dimension. In the present work, we overcome this unfavorable scaling by employing the time-dependent density matrix renormalization group (TD-DMRG) which parametrizes the time-dependent wave function as a matrix product state. The time-dependent Schrödinger equation is then integrated with a sweep-based algorithm, as in standard time-independent DMRG. Unlike other TD-DMRG approaches, the one presented here leads to a set of coupled equations that can be integrated exactly. The resulting theory enables us to study real- and imaginary-time evolutions of Hamiltonians comprising more than 20 degrees of freedom that are challenging for current state-of-the-art quantum dynamics algorithms. We apply our algorithm to the simulation of quantum dynamics of models of increasing complexity, ranging from simple excitonic Hamiltonians to more complex ab initio vibronic ones.
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.
Recent advances in high-resolution spectroscopy and cavity quantum technologies have driven growing interest in multicomponent quantum chemistry, where electronic degrees of freedom are treated on an equal footing with other quantum particles. Here, we present a unified symmetry-aware density matrix renormalization group (DMRG) framework for multicomponent quantum chemistry. By decoupling physical model specification from tensor-network representation and numerical optimization, new multicomponent models are introduced through symmetry quantum numbers, local basis, and operators, without modifying the underlying tensor algorithms. Built upon a mature tensor infrastructure, the framework provides a reusable symmetry-aware numerical engine, allowing new models to be implemented through concise Python-level specifications while fully reusing the optimized computational backend. The framework is demonstrated through symmetry-adapted nuclear-electronic orbital (NEO) and cavity quantum electrodynamics (CQED) DMRG calculations, yielding accurate electronic structures, excited-state energies, and polaritonic properties. This work establishes a reusable and extensible computational framework for symmetry-aware multicomponent quantum chemistry.