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Symbolic Algebra Development for Higher-Order Electron Propagator Formulation and Implementation.

Teresa Tamayo-Mendoza1, Roberto Flores-Moreno1

  • 1Departmento de Química, Universidad de Guadalajara , Blvd. Marcelino García Barragán 1421, Guadalajara Jal., C.P. 44430, México.

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Summary
This summary is machine-generated.

This study developed a symbolic algebra program to automatically calculate electron propagator self-energy matrices. The program successfully computed ionization energies, demonstrating a robust method for higher-order electron propagator calculations.

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Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Theoretical Physics

Background:

  • Calculating electron propagator self-energy matrices is crucial for understanding electronic properties.
  • Higher-order approximations are computationally intensive and complex to derive manually.
  • Existing software packages may lack automated methods for generating these expressions.

Purpose of the Study:

  • To develop a symbolic algebra program for automatic derivation of electron propagator self-energy matrix elements.
  • To generate modules for the Lowdin software package.
  • To validate the program's accuracy by calculating second- and third-order electron propagator results.

Main Methods:

  • Utilized symbolic algebra implemented in a computer program.
  • Developed an algorithm for automatic generation of Fortran 90 modules.
  • Applied the diagonal approximation for second- and third-order calculations.
  • Tested the program by computing ionization energies.

Main Results:

  • Successfully obtained algebraic expressions for self-energy matrix elements.
  • Automatically generated a functional module for the Lowdin software.
  • Achieved accurate ionization energy calculations using second- and third-order electron propagators.
  • Demonstrated the program's capability in the diagonal approximation.

Conclusions:

  • The developed symbolic algebra program provides an efficient and automated approach for electron propagator calculations.
  • The generated Fortran 90 modules are effective for determining ionization energies.
  • This work establishes a foundation for implementing more advanced, higher-order electron propagator methods.