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

TL;DR

QCMaquis 4.0 delivers a versatile, open-source DMRG-based platform for general quantum chemistry, extending beyond electronic structure to anharmonic vibrational and vibronic dynamics, time-dependent processes, and multi-component nuclear–electronic treatment. The framework unifies MPS/MPO representations with a broad library of Hamiltonians (conventional and transcorrelated electronic, four-component relativistic, preBO, Watson and n-mode vibrational, Frenkel excitonic, and generic vibronic) and multiple excited-state and real-time propagation algorithms (ORTHO, IPI, FEAST, TD-DMRG). It introduces major capabilities such as transcorrelated DMRG, the n-mode vibrational Hamiltonian, Frenkel excitons, modal entanglement analyses, and Python bindings that interface with PySCF and OpenMolcas, enhancing automation and workflow integration. The paper demonstrates these features with representative calculations (e.g., Formic Acid Dimer, Benzoic Acid Dimer, rubrene exciton dynamics) and discusses practical aspects like AutoCAS active-space selection, RDM measurements, and robust I/O/checkpointing. Overall, QCMaquis 4.0 significantly broadens the applicability of DMRG in chemistry by enabling accurate treatment of strong correlation across electronic, vibrational, and vibronic landscapes, while offering scalable interfaces and automation for complex workflows.

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, multi-component (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.

Figures (19)

• Figure 1: Tensor diagram of the canonical vibrational lattice. Each site corresponds to a vibrational mode, indicated by the different colors of the tensor sites, with its corresponding bosonic harmonic oscillator creation and annihilation operators, $\hat{b}_i, \hat{b}^{\dagger}_i$, positioned above. The local basis $i$ is determined by the first $N_i$ vibrational states, given in curly brackets.
• Figure 2: Tensor diagram of the $n$-mode vibrational lattice, where each site corresponds to a modal basis function. The modals are color-coded according to their associated vibrational mode. The local dimension of each site is two, reflecting the occupancy of the modal, with the constraint that any single configuration only possesses a single occupied modal per normal mode. Shown above the tensor sites are their respective bosonic creation and annihilation operators.
• Figure 3: Tensor diagrams for the two lattices supported by QCMaquis for vibronic calculations. Sites are color-coded according to their electronic states, with corresponding vibrational modes shown in a lighter shade. Above each site tensor, the operators ($\hat{a}$ for fermionic and $\hat{b}$ for bosonic) corresponding to the degrees of freedom (DoF) are indicated, while the possible occupancy of these DoFs is listed below. The sequential lattice first includes sites related to the electronic, followed by the vibrational DoFs. In contrast, the intertwined lattice ordering groups all DoFs associated with the same electronic state.
• Figure 4: PESs of the first two electronic excited states in the benzoic acid dimer along the two normal modes that significantly mediate the energy transfer. The scatter and line plots depict the adiabatic and diabatic PESs, respectively. Deformations corresponding to the motion along these modes are indicated by the structures at the bottom.
• Figure 5: Population dynamics for the benzoic acid dimer obtained through TD-DMRG simulations of the vibronic model Hamiltonian. The dynamics are initiated from the ground vibrational state of the ground electronic state excited to the $S_1$ electronically excited state.