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General exponential basis set parametrization: Application to time-dependent bivariational wave functions.

Mads Greisen Højlund1, Alberto Zoccante2, Ove Christiansen1

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Summary
This summary is machine-generated.

We developed new equations of motion for adaptive basis sets in quantum chemistry. Exponentially parameterized basis sets offer a constraint-free, easily implemented approach for nuclear dynamics and electronic structure calculations.

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Area of Science:

  • Quantum Chemistry
  • Computational Physics

Background:

  • Adaptive basis sets are crucial for accurate quantum dynamics simulations.
  • Existing methods for time-dependent bivariational wave functions often involve constraints.
  • Efficient handling of basis set evolution is computationally demanding.

Purpose of the Study:

  • To present a novel, constraint-free formulation for adaptive basis sets.
  • To develop equations of motion (EOMs) for exponentially parameterized biorthogonal basis sets.
  • To simplify and implement these EOMs for practical applications in quantum dynamics.

Main Methods:

  • Derivation of general EOMs for time-dependent wave functions.
  • Application of the time-dependent bivariational principle.
  • Utilizing Lie algebraic techniques to simplify non-linear basis set equations.
  • Implementation within the time-dependent modals vibrational coupled cluster (TDMVCC) method.

Main Results:

  • The derived EOMs are fully bivariational and constraint-free.
  • Computational costs are comparable to linearly parameterized basis sets.
  • A scheme for identifying and removing singularities in basis set equations was developed.
  • Exponentially parameterized basis sets showed slightly larger integrator step sizes in TDMVCC calculations.

Conclusions:

  • The proposed method provides an efficient and flexible alternative for adaptive basis sets.
  • This approach simplifies implementation and broadens applicability in nuclear dynamics and electronic structure.
  • Exponentially parameterized basis sets demonstrate good propagation properties, enabling potentially larger time steps.