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

NMR Spectrometers: Resolution and Error Correction01:14

NMR Spectrometers: Resolution and Error Correction

914
When magnetic nuclei in a sample achieve resonance and undergo relaxation, the signal detected in NMR is an approximately exponential free induction decay. Fourier transform of an exponential decay yields a Lorentzian peak in the frequency domain. Lorentzian peaks in an NMR spectrum are defined by their amplitude, full width at half maximum, and position, where the peak width is governed by the spin-spin relaxation time alone. In real experiments, however, the applied magnetic field is rendered...
914
Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule01:10

Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule

2.1K
In the AX proton spin system, proton A can sense the two spin states of a coupled proton X, resulting in a doublet NMR signal with two peaks of equal (1:1) intensity. When proton A is coupled to two equivalent protons (AX2 spin system), the spin states of each X can be aligned with or against the external field, creating three possible scenarios. This results in a 1:2:1  triplet signal, where the central peak corresponds to the chemical shift of A and is twice as large or intense as the...
2.1K
2D NMR: Overview of Heteronuclear Correlation Techniques01:18

2D NMR: Overview of Heteronuclear Correlation Techniques

497
Heteronuclear correlation spectroscopy is an analytical technique that investigates the coupling between different types of nuclei, often a proton and an X-nucleus, such as carbon-13 or nitrogen-15. This method is commonly used in nuclear magnetic resonance (NMR) spectroscopy to gain insights into complex chemical compounds' structural and compositional aspects. A typical heteronuclear correlation spectrum displays X-nucleus chemical shifts on one axis and a proton spectrum on the other...
497
2D NMR: Overview of Homonuclear Correlation Techniques01:16

2D NMR: Overview of Homonuclear Correlation Techniques

434
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...
434
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

199
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
199
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

241
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
241

You might also read

Related Articles

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

Sort by
Same author

Analytic gradients for spin multiplets in natural orbital functional theory.

The Journal of chemical physics·2020
Same author

NWChem: Past, present, and future.

The Journal of chemical physics·2020
Same author

An efficient method for strongly correlated electrons in two-dimensions.

The Journal of chemical physics·2020
See all related articles

Related Experiment Video

Updated: Nov 17, 2025

Author Spotlight: Non-Invasive Imaging of Complex Bio-Structures Using Polarization-Sensitive Two-Photon Microscopy
05:54

Author Spotlight: Non-Invasive Imaging of Complex Bio-Structures Using Polarization-Sensitive Two-Photon Microscopy

Published on: September 8, 2023

1.5K

Resolution of the identity approximation applied to PNOF correlation calculations.

Juan Felipe Huan Lew-Yee1, Mario Piris2, Jorge M Del Campo1

  • 1Departamento de Física y Química Teórica, Facultad de Química, Universidad Nacional Autónoma de México, Mexico City C.P. 04510, Mexico.

The Journal of Chemical Physics
|February 16, 2021
PubMed
Summary

This study introduces DoNOF-RI, an efficient computational method for Piris Natural Orbital Functional (PNOF) calculations. It significantly reduces computational time and memory requirements for electronic structure calculations.

More Related Videos

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
07:56

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Published on: September 5, 2019

8.8K
Using Three-color Single-molecule FRET to Study the Correlation of Protein Interactions
11:22

Using Three-color Single-molecule FRET to Study the Correlation of Protein Interactions

Published on: January 30, 2018

10.4K

Related Experiment Videos

Last Updated: Nov 17, 2025

Author Spotlight: Non-Invasive Imaging of Complex Bio-Structures Using Polarization-Sensitive Two-Photon Microscopy
05:54

Author Spotlight: Non-Invasive Imaging of Complex Bio-Structures Using Polarization-Sensitive Two-Photon Microscopy

Published on: September 8, 2023

1.5K
A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
07:56

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Published on: September 5, 2019

8.8K
Using Three-color Single-molecule FRET to Study the Correlation of Protein Interactions
11:22

Using Three-color Single-molecule FRET to Study the Correlation of Protein Interactions

Published on: January 30, 2018

10.4K

Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Theoretical Chemistry

Background:

  • Piris Natural Orbital Functional (PNOF) methods offer a way to approximate electron correlation.
  • High computational cost limits the application of PNOF methods to larger systems.
  • Resolution of the Identity (RI) approximations can reduce computational scaling.

Purpose of the Study:

  • To develop and implement an efficient RI approximation for PNOF methods.
  • To reduce the computational scaling of PNOF calculations.
  • To enable accurate electronic structure calculations for larger molecular systems.

Main Methods:

  • Developed the algebraic framework for Resolution of the Identity (RI) within Piris Natural Orbital Functional (PNOF).
  • Implemented the new approach as DoNOF-RI.
  • Tested DoNOF-RI on cycloalkanes and other molecules.

Main Results:

  • Achieved a reduction in arithmetic scaling from fifth-order to fourth-order.
  • Reduced memory scaling from fourth-order to third-order.
  • Demonstrated significant computational time savings compared to PNOF7.

Conclusions:

  • DoNOF-RI provides a computationally efficient and accurate method for PNOF calculations.
  • The approach allows for a quick convergence to the exact result by removing auxiliary basis set incompleteness.
  • This method enables the study of larger and more complex molecular systems using PNOF theory.