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Related Concept Videos

Extended Versions of Green’s Theorem01:27

Extended Versions of Green’s Theorem

Green’s Theorem connects the circulation of a vector field around a closed curve with the behavior of the field across the region enclosed by that curve. It provides a way to replace a line integral around a boundary with a double integral over the interior region, making it especially useful in plane geometry, fluid flow, and vector calculus.Although Green’s Theorem is often introduced using simple regions without gaps, it can also be applied to regions made from several simple parts. This...
Green’s Theorem01:27

Green’s Theorem

Green’s Theorem establishes a relationship between a line integral around a closed plane curve and a double integral over the region enclosed by that curve. It applies to a vector field F(x, y) = 〈P(x, y), Q(x, y)〉, where P and Q have continuous first partial derivatives on an open set containing the region.Let C be a positively oriented, simple, closed, piecewise smooth curve, and let R be the plane region bounded by C. Green’s Theorem states that\begin{equation*}\oint_C P\,dx+Q\,dy =\iint_R...
Vector Forms of Green’s Theorem01:26

Vector Forms of Green’s Theorem

The study of fluid motion often involves understanding how local rotational behavior relates to global circulation. In the context of a pond with pollutants, direct measurement of water movement along an irregular shoreline can be impractical. Green’s Theorem in vector form provides an alternative by relating the circulation around a closed boundary to properties of the flow within the enclosed region.Measurements of water velocity at different points define a continuous vector field that...
Debye–Huckel–Onsager Conductance Equation01:28

Debye–Huckel–Onsager Conductance Equation

The Debye-Hückel-Onsager equation is a cornerstone of physical chemistry, providing a method to determine the molar conductance (Λm) and molar conductance at infinite dilution (Λ°m) for uni-univalent electrolytes.Uni-univalent electrolytes are electrolytes that dissociate in solution to produce one cation with a +1 charge and one anion with a –1 charge per formula unit.This equation addresses two crucial phenomena: the asymmetry effect and the electrophoretic effect. According to this equation,...
Modeling and Similitude01:12

Modeling and Similitude

Scaled modeling is a fundamental technique in engineering, enabling the study of large and complex systems by creating smaller, manageable replicas that recreate critical characteristics of the original. In hydrology and civil infrastructure, for example, scaled models of dams help analyze water flow, turbulence, and pressure. This method allows for accurate predictions of real-world behavior within a controlled environment, significantly reducing the cost and time involved in full-scale...
Scaling01:26

Scaling

In designing and analyzing filters, resonant circuits, or circuit analysis at large, working with standard element values like 1 ohm, 1 henry, or 1 farad can be convenient before scaling these values to more realistic figures. This approach is widely utilized by not employing realistic element values in numerous examples and problems; it simplifies mastering circuit analysis through convenient component values. The complexity of calculations is thereby reduced, with the understanding that...

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Related Experiment Video

Updated: Jun 27, 2026

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics
10:52

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics

Published on: April 12, 2019

Low-Scaling Many-Body Green's Function Calculations for Molecular Systems via Interacting-Bath Dynamical Embedding

Christian Venturella1, Jiachen Li1, Tianyu Zhu1

  • 1Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States.

Journal of Chemical Theory and Computation
|June 25, 2026
PubMed
Summary

We introduce interacting-bath dynamical embedding theory (ibDET), an efficient method for calculating charged excitation energies in molecules. This approach accurately predicts spectral properties with significantly reduced computational cost.

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Last Updated: Jun 27, 2026

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics
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Area of Science:

  • Computational chemistry
  • Quantum chemistry
  • Materials science

Background:

  • Accurate computation of charged excitation energies is crucial for understanding molecular properties.
  • Existing methods often face high computational costs, limiting their applicability to large systems.

Purpose of the Study:

  • To present a molecular extension of the interacting-bath dynamical embedding theory (ibDET).
  • To develop an efficient and scalable framework for computing spectral properties of molecular systems.

Main Methods:

  • Developed a molecular extension of the Green's function embedding method, ibDET.
  • Constructed bath representations capturing impurity-environment entanglement using cluster-specific natural orbitals.
  • Assembled the self-energy from embedding problems using a GW or coupled-cluster Green's function solver.

Main Results:

  • ibDET accurately computes charged excitation energies at the GW and EOM-CCSD levels.
  • Achieved high accuracy for spectral properties of conjugated molecules and nanoclusters.
  • Errors in ionization potentials and electron affinities were ~0.1 eV compared to full-system calculations.

Conclusions:

  • ibDET offers an efficient and scalable framework for molecular spectral property calculations.
  • The method significantly reduces computational cost while maintaining high accuracy.
  • Provides a powerful tool for studying electronic properties of diverse molecular systems.