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VAMPyR-A high-level Python library for mathematical operations in a multiwavelet representation.

Magnar Bjørgve1, Christian Tantardini1,2, Stig Rune Jensen1

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Wavelets and multiwavelets offer numerical advantages in quantum chemistry. The VAMPyR Python library leverages these for solving fundamental equations with high precision.

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Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Numerical Analysis

Background:

  • Traditional basis sets (Gaussian orbitals, plane waves) present challenges in quantum chemistry.
  • Wavelets and multiwavelets offer numerical advantages like precision, locality, and linear scaling.
  • A need exists to bridge theoretical formalism with practical computational implementation.

Purpose of the Study:

  • Introduce the VAMPyR (Very Accurate Multiresolution Python Routines) library.
  • Demonstrate the application of multiwavelets in quantum chemistry.
  • Showcase the library's capability in solving fundamental quantum mechanical equations.

Main Methods:

  • Development of the VAMPyR Python library, interfacing with a C++ backend for multiwavelet computations.
  • Implementation of multiresolution analysis using multiwavelets.
  • Application of the library to solve equations such as Hartree-Fock, Poisson, Dirac, and time-dependent Schrödinger equations.

Main Results:

  • VAMPyR provides a framework for high-precision numerical solutions to quantum chemistry problems.
  • The library demonstrates efficient operator application and linear scaling with system size.
  • Illustrative examples showcase the code's capabilities and interoperability.

Conclusions:

  • Multiwavelet-based methods, as implemented in VAMPyR, offer a powerful alternative for quantum chemistry calculations.
  • VAMPyR facilitates the practical implementation of advanced theoretical methods.
  • The library enables solving complex quantum equations with high accuracy and efficiency.