arXiv subjects

Henrik R. Larsson

Publications and source records attributed to Henrik R. Larsson.

At least 19 recordsLinked to original sources

arXiv2026

Localized intrinsic bond orbitals decode correlated charge migration dynamics

For decades, scientists have studied the intricate charge migration dynamics, where after ionization a localized charge distribution ("hole") migrates across the molecule on a femtosecond timescale. This has the potential for controlling electrons in molecules, yet a comprehensive understanding of the many aspects of charge migration is still missing. In this work, we analyze charge migration using an extension of localized intrinsic bond orbitals (IBOs). These orbitals lead to a compact representation of the dynamics and map the complex, correlated many-electron charge migration to chemical concepts such as curly arrows and orbital-orbital interactions. By analyzing multiple challenging scenarios, we show how IBOs enable us to identify key mechanisms in charge migration. For example, we show that different mechanisms are responsible for converting a $π$-shaped hole to a $σ$-shaped hole and vice versa. We explain these in terms of hyperconjugation interactions and configurations that couple orbitals with different symmetries. We further demonstrate how IBOs can be used to find molecules with high charge migration efficiency. We carry out all simulations using an efficient set up of the time-dependent density matrix renormalization group (TDDMRG), correlating as many as 45 electrons in 50 orbitals. We believe that our results will be useful to design future experiments. The proposed IBO analysis is applicable to other types of real-time electron dynamics and spectroscopy.

physics.chem-ph↗

arXiv2026

Accurate, full-dimensional computations of thousands of complex vibrational eigenstates with tree tensor network states

Tree tensor network states (TTNSs) combined with the density matrix renormalization group (DMRG) are emerging as powerful tools for vibrational and vibronic structure simulations in molecules with strong coupling and fluxionality. In this Perspective, we discuss how TTNS methods enable accurate, full-dimensional computations of thousands of eigenstates for molecular systems ranging from quartic-force-field benchmarks to molecules with strong vibronic coupling and protonated water clusters as large as the 33-dimensional Eigen ion, H$_3$O$^+$$\cdot$(H$_2$O)$_3$. We emphasize the close connection and interoperability between DMRG-based TTNS methods and the multilayer multiconfiguration time-dependent Hartree method (ML-MCTDH), which share the same underlying ansatz. We also highlight practical challenges of predictive simulations, including robust error estimation, convergence of observables such as infrared intensities, and optimization of tensor network tree structures. Finally, we outline recent advances toward direct targeting of excited states and discuss opportunities for broader applications in molecular spectroscopy and quantum dynamics.

physics.chem-ph↗

arXiv2026

The Python Simulations of Chemistry Framework: 10 years of an open-source quantum chemistry project

Over the past decade, the Python-based Simulations of Chemistry Framework (PySCF) has developed into a widely used open-source platform for electronic structure theory and quantum chemical method development. This article reviews the major advances since the previous overview in 2020, covering new modules and methodology, infrastructure changes, and performance benchmarks.

physics.chem-ph↗

arXiv2025

Computing excited eigenstates using inexact Lanczos methods and tree tensor network states

To understand the dynamics of quantum many-body systems, it is essential to study excited eigenstates. While tensor network states have become a standard tool for computing ground states in computational many-body physics, obtaining accurate excited eigenstates remains a significant challenge. In this work, we develop an approach that combines the inexact Lanczos method, which is designed for efficient computations of excited states, with tree tensor network states (TTNSs). We demonstrate our approach by computing excited vibrational states for three challenging problems: (1) 122 states in two different energy intervals of acetonitrile (12-dimensional), (2) Fermi resonance states of the fluxional Zundel ion (15-dimensional), and (3) selected excited states of the fluxional and very correlated Eigen ion (33-dimensional). The proposed TTNS inexact Lanczos method is directly applicable to other quantum many-body systems.

physics.chem-ph↗

arXiv2025

Roadmap for Molecular Benchmarks in Nonadiabatic Dynamics

Simulating the coupled electronic and nuclear response of a molecule to light excitation requires the application of nonadiabatic molecular dynamics. However, when faced with a specific photophysical or photochemical problem, selecting the most suitable theoretical approach from the wide array of available techniques is not a trivial task. The challenge is further complicated by the lack of systematic method comparisons and rigorous testing on realistic molecular systems. This absence of comprehensive molecular benchmarks remains a major obstacle to advances within the field of nonadiabatic molecular dynamics. A CECAM workshop, Standardizing Nonadiabatic Dynamics: Towards Common Benchmarks, was held in May 2024 to address this issue. This Perspective highlights the key challenges identified during the workshop in defining molecular benchmarks for nonadiabatic dynamics. Specifically, this work outlines some preliminary observations on essential components needed for simulations and proposes a roadmap aiming to establish, as an ultimate goal, a community-driven, standardized molecular benchmark set.

physics.chem-ph↗

arXiv2025

Benchmarking vibrational spectra: 5000 accurate eigenstates of acetonitrile using tree tensor network states

Accurate vibrational spectra are essential for understanding how molecules behave, yet their computation remains challenging and benchmark data to reliably compare different methods are sparse. Here, we present high-accuracy eigenstate computations for the six-atom, 12-dimensional acetonitrile molecule, a prototypical, strongly coupled, anharmonic system. Using a density matrix renormalization group (DMRG) algorithm with a tree-tensor-network-state (TTNS) ansatz, a refinement using TTNSs as basis set, and reliable procedures to estimate energy errors, we compute up to 5,000 vibrational states with error estimates below 0.0007 $\mathrm{cm}^{-1}$. Our analysis reveals that previous works underestimated the energy error by up to two orders of magnitude. Our data serve as a benchmark for future vibrational spectroscopy methods and our new method offers a path toward similarly precise computations of large, complex molecular systems.

physics.chem-ph↗

arXiv2024

Simulating real-time molecular electron dynamics efficiently using the time-dependent density matrix renormalization group

Compared to ground state electronic structure optimizations, accurate simulations of molecular real-time electron dynamics are usually much more difficult to perform. To simulate electron dynamics, the time-dependent density matrix renormalization group (TDDMRG) has been shown to offer an attractive compromise between accuracy and cost. However, many simulation parameters significantly affect the quality and efficiency of a TDDMRG simulation. So far, it is unclear whether common wisdom from ground state DMRG carries over to the TDDMRG, and a guideline on how to choose these parameters is missing. Here, in order to establish such a guideline, we investigate the convergence behavior of the main TDDMRG simulation parameters, such as time integrator, the choice of orbitals, and the choice of matrix-product-state representation for complex-valued non-singlet states. In addition, we propose a method to select orbitals that are tailored to optimize the dynamics. Lastly, we showcase the TDDMRG by applying it to charge migration ionization dynamics in furfural, where we reveal a rapid conversion from an ionized state with a $σ$ character to one with a $π$ character within less than a femtosecond.

physics.chem-ph↗

arXiv2024

2500 vibronic eigenstates of the NO$_3$ radical

The nitrate radical NO$_3$ plays an important role in atmospheric chemistry, yet many aspects of its coupled and anharmonic vibronic structure remain elusive. Here, using an accurate, coupled full-dimensional diabatic potential that includes five electronic states, we revisit the vibronic spectrum associated with the electronic $\tilde X ^2A_2'$ state. Using recently developed tensor network state methods, we are able to compute more than 2500 vibronic states, thereby increasing the number of computed full-dimensional states by a factor of 50, compared to previous work. While we obtain good agreement with experiment for most of the assigned vibronic levels, for several others, we observe striking disagreement. Further, for the antisymmetric bending motion we find remarkably large symmetry-induced level splittings that are larger than the zero-order reference. We discuss non-negligible nonadiabatic effects and show that the Born-Oppenheimer approximation leads to significant errors in the spectrum.

physics.chem-ph↗

arXiv2024

A tensor network view of multilayer multiconfiguration time-dependent Hartree methods

The multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method and the density matrix renormalization group (DMRG) are powerful workhorses applied mostly in different scientific fields. Although both methods are based on tensor network states, very different mathematical languages are used for describing them. This severely limits knowledge transfer and sometimes leads to re-inventions of ideas well known in the other field. Here, we review ML-MCTDH and DMRG theory using both MCTDH expressions and tensor network diagrams. We derive the ML-MCTDH equations of motions using diagrams and compare them with time-dependent and time-independent DMRG algorithms. We further review two selected recent advancements. The first advancement is related to optimizing unoccupied single-particle functions in MCTDH, which corresponds to subspace enrichment in the DMRG. The second advancement is related to finding optimal tree structures and on highlighting similarities and differences of tensor networks used in MCTDH and DMRG theories. We hope that this contribution will foster more fruitful cross-fertilization of ideas between ML-MCTDH and DMRG.

physics.chem-ph↗

arXiv2023

Block2: a comprehensive open source framework to develop and apply state-of-the-art DMRG algorithms in electronic structure and beyond

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.

physics.chem-ph↗

arXiv2022

State-resolved infrared spectrum of the protonated water dimer: Revisiting the characteristic proton transfer doublet peak

The infrared (IR) spectra of protonated water clusters encode precise information on the dynamics and structure of the hydrated proton. However, the strong anharmonic coupling and quantum effects of these elusive species remain puzzling up to the present day. Here, we report unequivocal evidence that the interplay between the proton transfer and the water wagging motions in the protonated water dimer (Zundel ion) giving rise to the characteristic doublet peak is both more complex and more sensitive to subtle energetic changes than previously thought. In particular, hitherto overlooked low-intensity satellite peaks in the experimental spectrum are now unveiled and mechanistically assigned. Our findings rely on the comparison of IR spectra obtained using two highly accurate potential energy surfaces in conjunction with highly accurate state-resolved quantum simulations. We demonstrate that these high-accuracy simulations are important for providing definite assignments of the complex IR signals of fluxional molecules.

physics.chem-ph↗

arXiv2022

The chromium dimer: closing a chapter of quantum chemistry

The complex electronic structure and unusual potential energy curve of the chromium dimer have fascinated scientists for decades, with agreement between theory and experiment so far elusive. Here, we present a new ab initio simulation of the potential energy curve and vibrational spectrum that significantly improves on all earlier estimates. Our data support a shift in earlier experimental assignments of a cluster of vibrational frequencies by one quantum number. The new vibrational assignment yields an experimentally derived potential energy curve in quantitative agreement with theory across all bond lengths and across all measured frequencies. By solving this long-standing problem, our results raise the possibility of quantitative quantum chemical modeling of transition metal clusters with spectroscopic accuracy.

physics.chem-ph↗

arXiv2022

Matrix product states with large sites

We explore various ways to group orbitals into clusters in a matrix product state (MPS). We explain how a generic cluster MPS can often lead to an increase in computational cost and instead propose a special cluster structure, involving only the first and last orbitals/sites, with a wider scope for computational advantage. This structure is a natural formalism to describe correlated multireference (MR) theories. We demonstrate the flexibility and usefulness of this approach by implementing various uncontracted MR configuration interaction, perturbation and linearized coupled cluster theories using an MPS with large cluster sites. Applications to the nitrogen dimer, the chromium dimer, and benzene, including up to triple excitations in the external space, demonstrate the utility of an MPS with up to two large sites. We use our results to analyze the quality of different multireference approximations.

physics.chem-ph↗

arXiv2021

Control of concerted back-to-back double ionization dynamics in helium

Double ionization (DI) is a fundamental process that despite its apparent simplicity provides rich opportunities for probing and controlling the electronic motion. Even for the simplest multielectron atom, helium, new DI mechanisms are still being found. To first order in the field strength, a strong external field doubly ionizes the electrons in helium such that they are ejected into the same direction (front-to-back motion). The ejection into opposite directions (back-to-back motion) cannot be described to first order, making it a challenging target for control. Here, we address this challenge and optimize the field with the objective of back-to-back double ionization using a (1 + 1)-dimensional model. The optimization is performed using four different control procedures: (1) short-time control, (2) derivative-free optimization of basis expansions of the field, (3) the Krotov method, and (4) control of the classical equations of motion. All four procedures lead to fields with dominant back-to-back motion. All the fields obtained exploit essentially the same two-step mechanism leading to back-to-back motion: first, the electrons are displaced by the field into the same direction. Second, after the field turns off, the nuclear attraction and the electron-electron repulsion combine to generate the final motion into opposite directions for each electron. By performing quasi-classical calculations, we confirm that this mechanism is essentially classical.

physics.atom-ph↗

arXiv2020

Minimal matrix product states and generalizations of mean-field and geminal wavefunctions

Simple wavefunctions of low computational cost but which can achieve qualitative accuracy across the whole potential energy surface (PES) are of relevance to many areas of electronic structure as well as to applications to dynamics. Here, we explore a class of simple wavefunctions, the minimal matrix product state (MMPS), that generalizes many simple wavefunctions in common use, such as projected mean-field wavefunctions, geminal wavefunctions, and generalized valence bond states. By examining the performance of MMPSs for PESs of some prototypical systems, we find that they yield good qualitative behavior across the whole PES, often significantly improving on the aforementioned ansätze.

physics.chem-ph↗

arXiv2019

Computing vibrational eigenstates with tree tensor network states (TTNS)

We present how to compute vibrational eigenstates with tree tensor network states (TTNSs), the underlying ansatz behind the multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method. The eigenstates are computed with an algorithm that is based on the density matrix renormalization group (DMRG). We apply this to compute the vibrational spectrum of acetonitrile (CH$_3$CN) to high accuracy and compare TTNSs with matrix product states (MPSs), the ansatz behind the DMRG. The presented optimization scheme converges much faster than ML-MCTDH-based optimization. For this particular system, we found no major advantage of the more general TTNS over MPS. We highlight that for both TTNS and MPS, the usage of an adaptive bond dimension significantly reduces the amount of required parameters. We furthermore propose a procedure to find good trees.

physics.chem-ph↗

arXiv2018

Resonance dynamics of DCO ($\widetilde{X}\,{}^2A'$) simulated with the dynamically pruned discrete variable representation (DP-DVR)

Selected resonance states of the deuterated formyl radical in the electronic ground state ($\widetilde{X}\,{}^2A'$) are computed using our recently introduced dynamically pruned discrete variable representation (DP-DVR) [H. R. Larsson, B. Hartke and D. J. Tannor, J. Chem. Phys., 145, 204108 (2016)]. Their decay and asymptotic distributions are analyzed and, for selected resonances, compared to experimental results obtained by a combination of stimulated emission pumping (SEP) and velocity-map imaging of the product D atoms. The theoretical results show good agreement with the experimental kinetic energy distributions. The intramolecular vibrational energy redistribution (IVR) is analyzed and compared with previous results from an effective polyad Hamiltonian. Specifically, we analyzed the part of the wavefunction that remains in the interaction region during the decay. The results from the polyad Hamiltonian could mainly be confirmed. The C=O stretch quantum number is typically conserved, while the D-C=O bend quantum number decreases. Differences are due to strong anharmonic coupling such that all resonances have major contributions from several zero-order states. For some of the resonances, the coupling is so strong that no further zero-order states appear during the dynamics in the interaction region, even after propagating for 300 ps.

physics.chem-ph↗

arXiv2017

Dynamical pruning of the multiconfiguration time-dependent Hartree method (DP-MCTDH): An efficient approach for multidimensional quantum dynamics

We present two strategies for combining dynamical pruning with the multiconfiguration time-dependent Hartree method (DP-MCTDH), where dynamical pruning means on-the-fly selection of relevant basis functions. The first strategy prunes the primitive basis that represents the single-particle functions (SPFs). This is useful for smaller systems that require many primitive basis functions per degree of freedom, as we will illustrate for NO$_2$. Furthermore, this allows for higher-dimensional mode combination and partially lifts the sum-of-product-form requirement onto the structure of the Hamiltonian, as we illustrate for nonadiabatic 24-dimensional pyrazine. The second strategy prunes the set of configurations of SPF at each time step. We show that this strategy yields significant speed-ups with factors between 5 and 50 in computing time, making it competitive with the multilayer MCTDH method.

physics.chem-ph↗