Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Hybridization of Atomic Orbitals II03:35

Hybridization of Atomic Orbitals II

33.7K
sp3d and sp3d 2 Hybridization
33.7K
Hybridization of Atomic Orbitals I03:24

Hybridization of Atomic Orbitals I

48.9K
The mathematical expression known as the wave function, ψ, contains information about each orbital and the wavelike properties of electrons in an isolated atom. When atoms are bound together in a molecule, the wave functions combine to produce new mathematical descriptions that have different shapes. This process of combining the wave functions for atomic orbitals is called hybridization and is mathematically accomplished by the linear combination of atomic orbitals. The new orbitals that...
48.9K
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

100
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
100
Reduction of Alkenes: Asymmetric Catalytic Hydrogenation02:17

Reduction of Alkenes: Asymmetric Catalytic Hydrogenation

3.4K
Catalytic hydrogenation of alkenes is a transition-metal catalyzed reduction of the double bond using molecular hydrogen to give alkanes. The mode of hydrogen addition follows syn stereochemistry.
The metal catalyst used can be either heterogeneous or homogeneous. When hydrogenation of an alkene generates a chiral center, a pair of enantiomeric products is expected to form. However, an enantiomeric excess of one of the products can be facilitated using an enantioselective reaction or an...
3.4K
2D NMR: Overview of Homonuclear Correlation Techniques01:16

2D NMR: Overview of Homonuclear Correlation Techniques

287
Homonuclear correlation spectroscopy (COSY) is a powerful technique used in Nuclear Magnetic Resonance (NMR) spectroscopy to study the correlations between nuclei of the same type within a molecule. It provides information about scalar couplings between adjacent nuclei, which helps determine connectivity and structural information. There are several COSY variants, each with its unique strengths and experimental parameters.
COSY90 is the standard two-dimensional (2D) COSY experiment that...
287
Reduction of Alkynes to cis-Alkenes: Catalytic Hydrogenation02:24

Reduction of Alkynes to cis-Alkenes: Catalytic Hydrogenation

8.1K
Introduction
Like alkenes, alkynes can be reduced to alkanes in the presence of transition metal catalysts such as Pt, Pd, or Ni. The reaction involves two sequential syn additions of hydrogen via a cis-alkene intermediate.
8.1K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Large-scale stochastic simulation of open quantum systems.

Nature communications·2025
Same author

Wavefunction Optimization at the Complete Basis Set Limit with Multiwavelets and DMRG.

The journal of physical chemistry. A·2025
Same author

Evaluating Ground State Energies of Chemical Systems with Low-Depth Quantum Circuits and High Accuracy.

The journal of physical chemistry. A·2025
Same author

Ternary Unitary Quantum Lattice Models and Circuits in 2+1 Dimensions.

Physical review letters·2023
Same author

Numerical observation of emergent spacetime supersymmetry at quantum criticality.

Science advances·2018
Same author

Numerical evidence of fluctuating stripes in the normal state of high-<i>T</i><sub>c</sub> cuprate superconductors.

Science (New York, N.Y.)·2017

Related Experiment Video

Updated: Sep 8, 2025

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
08:04

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

8.5K

Enhanced Krylov Methods for Molecular Hamiltonians: Reduced Memory Cost and Complexity Scaling via Tensor

Yu Wang1, Maxine Luo2,3, Matthias Reumann1

  • 1Department of Computer Science, Technical University of Munich, CIT, Boltzmannstraße 3, 85748 Garching, Germany.

Journal of Chemical Theory and Computation
|July 2, 2025
PubMed
Summary

We developed a memory-efficient algorithm for quantum chemistry simulations using matrix-product states (MPS) and tensor-hypercontraction (THC). This method reduces computational cost and improves accuracy for large-scale high-performance computing (HPC) applications.

More Related Videos

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
12:11

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

8.3K
Spatial Separation of Molecular Conformers and Clusters
10:37

Spatial Separation of Molecular Conformers and Clusters

Published on: January 9, 2014

9.1K

Related Experiment Videos

Last Updated: Sep 8, 2025

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
08:04

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

8.5K
Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
12:11

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

8.3K
Spatial Separation of Molecular Conformers and Clusters
10:37

Spatial Separation of Molecular Conformers and Clusters

Published on: January 9, 2014

9.1K

Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Materials Science

Background:

  • Accurate simulation of molecular Hamiltonians is crucial for understanding chemical reactions and material properties.
  • Matrix-product states (MPS) offer a powerful framework for representing quantum states, but their application can be computationally demanding.
  • Existing methods for applying Hamiltonians to MPS often face challenges with memory and computational scaling.

Purpose of the Study:

  • To introduce a novel, memory-efficient, and low-scaling algorithm for applying ab initio molecular Hamiltonians to MPS.
  • To leverage the tensor-hypercontraction (THC) format for computational gains.
  • To enhance the performance of Krylov subspace methods for quantum simulations.

Main Methods:

  • Developed an algorithm representing the molecular Hamiltonian as a sum of products of four MPOs (matrix-product operators), each with a bond dimension of 2.
  • Applied the MPOs iteratively to MPS, followed by summation and recompression.
  • Integrated this approach with Krylov subspace methods for finding eigenstates and simulating time evolution.

Main Results:

  • Achieved memory cost equivalent to the bare MPS.
  • Demonstrated reduced computational cost scaling compared to conventional MPO constructions.
  • Validated theoretical findings with numerical experiments, showcasing significant advantages.
  • Confirmed high parallelizability for large-scale HPC simulations.

Conclusions:

  • The proposed algorithm offers a significant improvement in efficiency and scalability for quantum chemistry simulations.
  • This method enables accurate simulations of quantum time evolution and finding low-lying eigenstates.
  • The approach is well-suited for tackling complex problems on modern high-performance computing architectures.