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Random or indeterminate errors originate from various uncontrollable variables, such as variations in environmental conditions, instrument imperfections, or the inherent variability of the phenomena being measured. Usually, these errors cannot be predicted, estimated, or characterized because their direction and magnitude often vary in magnitude and direction even during consecutive measurements. As a result, they are difficult to eliminate. However, the aggregate effect of these errors can be...
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Scientists always try their best to record measurements with the utmost accuracy and precision. However, sometimes errors do occur. These errors can be random or systematic. Random errors are observed due to the inconsistency or fluctuation in the measurement process, or variations in the quantity itself that is being measured. Such errors fluctuate from being greater than or less than the true value in repeated measurements. Consider a scientist measuring the length of an earthworm using a...
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An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
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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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Beyond Walkers in Stochastic Quantum Chemistry: Reducing Error Using Fast Randomized Iteration.

Samuel M Greene1, Robert J Webber2, Jonathan Weare2

  • 1Department of Chemistry and James Franck Institute , University of Chicago , Chicago , Illinois 60637 , United States.

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|August 8, 2019
PubMed
Summary
This summary is machine-generated.

We developed new computational methods for quantum chemistry, called FCI-FRI, which improve the efficiency of solving the full configuration interaction problem. A systematic approach within FCI-FRI shows significant statistical gains over existing methods like FCIQMC.

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Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Theoretical Chemistry

Background:

  • The full configuration interaction (FCI) problem is crucial for accurate quantum chemistry calculations.
  • Existing methods like FCIQMC face challenges in computational efficiency and scalability.
  • Stochastic methods offer a promising avenue for tackling the FCI problem.

Purpose of the Study:

  • Introduce a novel family of methods, FCI-FRI, based on the fast randomized iteration (FRI) framework.
  • Generalize FCIQMC by stochastically imposing sparsity during power method iterations.
  • Develop and compare different sampling schemes for excitations within the FCI-FRI framework.

Main Methods:

  • Implement FCI-FRI methods utilizing the fast randomized iteration (FRI) framework.
  • Adapt the power method with stochastic sparsity imposition.
  • Compare a systematic excitation sampling scheme against the standard multinomial scheme used in FCIQMC.

Main Results:

  • FCI-FRI methods offer a walker-less generalization of FCIQMC.
  • The systematic FCI-FRI scheme demonstrates superior statistical efficiency compared to the multinomial FCI-FRI scheme.
  • Both FCI-FRI schemes show significant efficiency improvements over the original FCIQMC algorithm for ground-state calculations.

Conclusions:

  • The developed FCI-FRI methods provide a more efficient approach to solving the full configuration interaction problem.
  • The systematic sampling scheme within FCI-FRI offers substantial statistical advantages.
  • These findings pave the way for more accurate and feasible quantum chemical simulations.