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The energy stored by a structure and location of matter in space is called potential energy. For instance, raising a kettlebell changes its spatial location and increases its potential energy. Similarly, a stretched rubber band contains potential energy which, under certain conditions, can be converted into other forms of energy, such as kinetic energy.
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A conservative force, such as a gravitational or elastic force, gives the body the capacity to do work. This capacity, measured as the potential energy, depends on the body's location or “position” relative to a fixed reference position or datum. The gravitational potential energy is considered zero at the reference point. Suppose a body is located at some vertical distance above a fixed horizontal reference or datum. In that case, the weight of the body has positive gravitational potential...
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Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
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MCTDH on-the-fly: Efficient grid-based quantum dynamics without pre-computed potential energy surfaces.

Gareth W Richings1, Scott Habershon1

  • 1Department of Chemistry and Centre for Scientific Computing, University of Warwick, Coventry CV4 7AL, United Kingdom.

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Summary

We developed faster quantum dynamics simulations using Gaussian functions and singular value decomposition to represent potential energy surfaces. This accelerates calculations for chemical reactions like proton transfer without sacrificing accuracy.

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Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Chemical Dynamics

Background:

  • Direct quantum dynamics methods are crucial for simulating molecular behavior.
  • Representing potential energy surfaces (PES) accurately is computationally intensive.
  • Existing grid-based methods face challenges in computational efficiency.

Purpose of the Study:

  • To enhance algorithmic efficiency in direct quantum dynamics.
  • To accelerate simulations by improving potential energy surface representation.
  • To maintain accuracy in quantum dynamics calculations.

Main Methods:

  • Developed a novel approach using weighted sums of Gaussian functions for PES representation.
  • Implemented singular value decomposition for secondary PES fitting.
  • Utilized on-the-fly simulations with standard grid-based methods and multi-configuration time-dependent Hartree (MCTDH).

Main Results:

  • Demonstrated significant acceleration of standard grid-based quantum dynamics methods.
  • Achieved this acceleration without compromising the accuracy of simulations.
  • Successfully applied the method to simulate proton transfer in salicylaldimine and non-adiabatic dynamics in pyrazine.

Conclusions:

  • The proposed method offers a computationally efficient alternative for quantum dynamics simulations.
  • Gaussian function expansions and SVD fitting are effective for PES representation.
  • This advancement facilitates more complex and accurate simulations of chemical dynamics.