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Entropy of Two-Molecule Correlated Translational-Rotational Motions Using the kth Nearest Neighbor Method.

Federico Fogolari1,2, Gennaro Esposito2,3, Bruce Tidor4

  • 1Dipartimento di Scienze Matematiche, Informatiche e Fisiche (DMIF), University of Udine, Via delle Scienze 206, 33100 Udine, Italy.

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|April 15, 2021
PubMed
Summary
This summary is machine-generated.

The kth nearest neighbor method accurately estimates the entropy of correlated translation-rotations for two molecules. This approach works even in high-dimensional spaces with limited data samples.

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Area of Science:

  • Physical Chemistry
  • Computational Chemistry
  • Statistical Mechanics

Background:

  • Entropy is crucial for understanding physicochemical processes like association and solvation.
  • The kth nearest neighbor (kNN) method is effective for estimating entropy in high-dimensional spaces.
  • Previous applications of kNN focused on single molecule translational-rotational entropy.

Purpose of the Study:

  • To extend the kth nearest neighbor method for calculating the entropy of correlated translation-rotations of two molecules.
  • To investigate the applicability of kNN in the 12-dimensional product space of two translation-rotations.
  • To assess the relevance for systems involving correlated motions of multiple molecules.

Main Methods:

  • Utilizing the kth nearest neighbor (kNN) method.
  • Applying kNN to estimate entropy in a 12-dimensional product space.
  • Analyzing correlated translational-rotational motions of two molecules.

Main Results:

  • The kNN approach accurately estimates the entropy of two correlated translational-rotational motions.
  • Effective entropy estimation was achieved despite the high dimensionality (12D) of the space.
  • Accurate results were obtained even with a limited number of samples.

Conclusions:

  • The kth nearest neighbor method is a viable and accurate approach for computing the entropy of correlated translation-rotations of two molecules.
  • This extension of kNN is applicable to complex systems involving multiple interacting molecules.
  • The method demonstrates robustness in high-dimensional spaces and with sparse data.