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Protons and neutrons, collectively called nucleons, are packed together tightly in a nucleus. With a radius of about 10−15 meters, a nucleus is quite small compared to the radius of the entire atom, which is about 10−10 meters. Nuclei are extremely dense compared to bulk matter, averaging 1.8 × 1014 grams per cubic centimeter. If the earth’s density were equal to the average nuclear density, the earth’s radius would be only about 200 meters.
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Nuclear-electronic all-particle density matrix renormalization group.

Andrea Muolo1, Alberto Baiardi1, Robin Feldmann1

  • 1ETH Zürich, Laboratory of Physical Chemistry, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland.

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|June 4, 2020
PubMed
Summary
This summary is machine-generated.

We developed the Nuclear-Electronic All-Particle Density Matrix Renormalization Group (NEAP-DMRG) method for quantum systems. This approach accurately calculates energies for molecules with over 12 particles, overcoming limitations of other methods.

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Area of Science:

  • Quantum chemistry
  • Computational physics
  • Theoretical chemistry

Background:

  • Accurate quantum mechanical calculations are crucial for understanding molecular behavior.
  • Existing multicomponent methods face challenges with larger, complex systems.
  • The Schrödinger equation describes quantum systems but is difficult to solve exactly.

Purpose of the Study:

  • Introduce a novel method, Nuclear-Electronic All-Particle Density Matrix Renormalization Group (NEAP-DMRG), for solving the time-independent Schrödinger equation.
  • Develop a robust approach for simultaneous treatment of electrons and other quantum particles.
  • Overcome limitations of current multicomponent quantum chemistry methods.

Main Methods:

  • Construct a multi-reference trial wave function using stochastically optimized non-orthogonal Gaussian orbitals.
  • Iteratively refine Gaussian orbital positions and widths for a compact wave function expansion.
  • Extend the Density Matrix Renormalization Group (DMRG) algorithm to handle multicomponent wave functions and correlations.

Main Results:

  • NEAP-DMRG accurately approximates full configuration interaction energies for systems with >3 nuclei and >12 particles.
  • Demonstrated the method's capability on small systems (H2, H3+) and a larger system (BH3).
  • Successfully incorporated inter- and intra-species correlation effects.

Conclusions:

  • NEAP-DMRG offers a powerful new tool for high-accuracy quantum mechanical calculations.
  • The method is particularly effective for systems previously intractable for other multicomponent approaches.
  • NEAP-DMRG advances the field of computational quantum chemistry.