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A driven similarity renormalization group approach to quantum many-body problems.

Francesco A Evangelista1

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The similarity renormalization group (SRG) method and its novel driven version (DSRG) offer efficient many-body theories for electron correlation. A modified commutator approximation resolves convergence issues for specific molecular applications.

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Area of Science:

  • Computational physics
  • Quantum chemistry
  • Many-body theory

Background:

  • The similarity renormalization group (SRG) is a powerful tool for simplifying quantum Hamiltonians.
  • Developing accurate and efficient many-body theories for electron correlation remains a significant challenge in computational chemistry.

Purpose of the Study:

  • To explore the application of the SRG approach for electron correlation problems.
  • To introduce and investigate a novel integral version of the SRG, termed the driven SRG (DSRG).
  • To compare the computational efficiency and accuracy of SRG and DSRG with established methods.

Main Methods:

  • Implementation of a production-level SRG using a single-reference formalism.
  • Development of the integral-based driven SRG (DSRG) where Hamiltonian flow is controlled by a source operator.
  • Calculation of molecular properties (equilibrium distances, vibrational frequencies, anharmonicities) using SRG and DSRG approximations.

Main Results:

  • Both SRG and DSRG show good agreement with benchmark coupled cluster results for diatomic molecules.
  • DSRG offers computational advantages over SRG due to its polynomial equation structure.
  • SRG and DSRG encounter convergence issues for C2 and yield an unbound potential for F2.
  • A modified commutator approximation successfully corrects these DSRG issues.

Conclusions:

  • The DSRG presents a computationally advantageous alternative to the SRG for many-body electron correlation.
  • The modified commutator approximation is crucial for extending DSRG's applicability to challenging molecular systems.
  • Further development of SRG-based methods holds promise for accurate quantum chemical calculations.