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Many-Electron Integrals over Gaussian Basis Functions. I. Recurrence Relations for Three-Electron Integrals.

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Explicitly correlated F12 methods offer high accuracy in molecular orbital calculations. This study presents a new algorithm to directly compute three-electron integrals, avoiding approximations for enhanced computational accuracy.

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Area of Science:

  • Computational chemistry
  • Quantum chemistry
  • Theoretical chemistry

Background:

  • Explicitly correlated F12 methods are crucial for high-accuracy molecular orbital calculations.
  • Resolutions of the identity (RI) approximations are commonly used to handle electron integrals but require large auxiliary basis sets.
  • Large RI auxiliary basis sets can compromise the accuracy of F12 wave functions.

Purpose of the Study:

  • To develop an algorithm for the direct computation of three-electron integrals.
  • To avoid Resolution of the Identity (RI) approximations in F12 calculations.
  • To present a general methodology for deriving recurrence relations for integrals.

Main Methods:

  • Algorithm inspired by Head-Gordon-Pople and PRISM for two-electron integrals.
  • Direct computation of three-electron integrals over Gaussian basis functions.
  • Development of recurrence relations for vertical, transfer, and horizontal calculations.

Main Results:

  • A novel algorithm for direct computation of three-electron integrals is presented.
  • The method avoids RI approximations, preserving the intrinsic accuracy of F12 wave functions.
  • A general methodology for deriving recurrence relations is established.

Conclusions:

  • The developed algorithm enables accurate computation of three-electron integrals without RI approximations.
  • This approach enhances the reliability of explicitly correlated F12 methods.
  • The recurrence relation methodology offers a versatile tool for integral computations.