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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...
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Photoelectron Imaging of Anions Illustrated by 310 Nm Detachment of F−
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Frozen Natural Orbital-Based Extended Second-Order Algebraic Diagrammatic Construction for Core Ionization: Theory,

Kamal Majee1, Tamoghna Mukhopadhyay1, Amrita Manna1

  • 1Department of Chemistry, Indian Institute of Technology Bombay, Mumbai 400076, India.

The Journal of Physical Chemistry. A
|June 2, 2026
PubMed
Summary

A new, cost-effective computational method, core-ionization potential algebraic diagrammatic construction (IP-ADC(2)-x), efficiently calculates ionization potentials. It uses frozen natural orbitals and natural auxiliary functions for speed and accuracy in complex molecular systems.

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Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Theoretical Chemistry

Background:

  • Accurate calculation of core-ionization potentials is crucial for understanding molecular electronic structure and chemical processes.
  • Traditional methods often face challenges with computational cost and scalability for larger molecules.

Purpose of the Study:

  • To develop a computationally efficient and accurate low-cost method for calculating core-ionization potentials.
  • To enhance the existing algebraic diagrammatic construction method for practical applications.

Main Methods:

  • Extended second-order algebraic diagrammatic construction (IP-ADC(2)-x) method.
  • Incorporation of frozen natural orbitals (FNOs), natural auxiliary functions (NAFs), core-valence separation (CVS), and density fitting (DF) approximations.
  • Application of spin-free exact two-component Hamiltonian (SFX2C1e) and projector-based embedding theory.

Main Results:

  • The developed FNO-IP-ADC(2)-x method offers a significant speed-up compared to standard approaches while maintaining controlled accuracy.
  • A simple correction was introduced to mitigate errors from virtual orbital space truncation.
  • The spin-free exact two-component Hamiltonian improved agreement with experimental data.
  • Successful computation of core-ionization energies for large molecules like azafullerene and chlorophyll-a using embedded methods.

Conclusions:

  • The FNO-IP-ADC(2)-x method provides a balanced and efficient approach for core-ionization potential calculations.
  • The integration of FNOs, NAFs, and other approximations leads to substantial computational gains.
  • The method demonstrates scalability and accuracy for complex molecular systems, paving the way for advanced chemical studies.