# Analysis of complexity measures and information planes of selected molecules in position and momentum spaces.

@article{Esquivel2010AnalysisOC, title={Analysis of complexity measures and information planes of selected molecules in position and momentum spaces.}, author={Rodolfo O. Esquivel and Juan Carlos Angulo and Juan Antol{\'i}n and Jes{\'u}s S. Dehesa and Sheila L{\'o}pez-Rosa and Nelson Flores-Gallegos}, journal={Physical chemistry chemical physics : PCCP}, year={2010}, volume={12 26}, pages={ 7108-16 } }

The Fisher-Shannon and LMC shape complexities and the Shannon-disequilibrium, Fisher-Shannon and Fisher-disequilibrium information planes, which consist of two localization-delocalization factors, are computed in both position and momentum spaces for the one-particle densities of 90 selected molecules of various chemical types, at the CISD/6-311++G(3df,2p) level of theory. We found that while the two measures of complexity show general trends only, the localization-delocalization planes clearly…

## 61 Citations

### Atomic and Molecular Complexities: Their Physical and Chemical Interpretations

- Chemistry
- 2011

Within the present work on the meaning, interpretation and applications of the complexity measures, different order-uncertainty planes embodying relevant information-theoretical magnitudes are…

### Information-theoretic space from simple atomic and molecular systems to biological and pharmacological molecules

- ChemistryTheoretical Chemistry Accounts
- 2016

In this letter, we present an Information-Theoretic Space generated from the Shannon entropy, the Fisher information, and the disequilibrium measures along with their corresponding Fisher–Shannon and…

### Information entropy and complexity measure in generalized Kratzer potential

- Computer ScienceChemical Physics Letters
- 2019

### Information and complexity measures in molecular reactivity studies.

- ChemistryPhysical chemistry chemical physics : PCCP
- 2014

Analysis of the results displayed on planes between the three information-theoretical (IT) based measures has shown that the S-I plane provides "richer" information about the pattern, organization, similarity of used molecules than the I-D and D-S planes.

### Entropy and complexity analysis of the $$D$$D-dimensional rigid rotator and hyperspherical harmonics

- Computer Science
- 2015

An information-theoretic analysis of the $$D$$D-dimensional rigid rotator by studying the entropy and complexity measures of its wavefunctions, which are controlled by the hyperspherical harmonics.

### Predicting Atomic Decay Rates Using an Informational-Entropic Approach

- Physics
- 2017

We show that a newly proposed Shannon-like entropic measure of shape complexity applicable to spatially-localized or periodic mathematical functions known as configurational entropy (CE) can be used…

### Generalized Shannon’s entropies in position and momentum spaces

- Physics
- 2017

In this report, we present three generalized expressions of Shannon’s entropy using the electron densities of position and momentum spaces. Such expressions were obtained using the definition of…

### Uncertainty inequalities among frequency moments and radial expectation values: Applications to atomic systems

- Physics
- 2012

Rigorous and universal bounds on frequency moments of one-particle densities in terms of radial expectation values in the conjugate space are obtained. The results, valid for any d-dimensional…

## References

SHOWING 1-10 OF 78 REFERENCES

### Atomic complexity measures in position and momentum spaces.

- PhysicsThe Journal of chemical physics
- 2008

It is shown that Fisher-Shannon and LMC complexities are qualitatively and numerically equivalent for these systems and new complexity candidates are defined, computed, and compared by using the following information-theoretic magnitudes.

### Complexity analysis of ionization processes and isoelectronic series

- Computer Science
- 2009

It is concluded that the studied complexity measures detect not only randomness or localization, but also pattern and organization, and their study is not only sufficient in the usual position space but also in the complementary momentum space, to have a complete description of the information–theoretic behavior of these systems.

### Fisher-Shannon analysis of ionization processes and isoelectronic series

- Physics
- 2007

The Fisher-Shannon plane which embodies the Fisher information measure in conjunction with the Shannon entropy is tested in its ability to quantify and compare the informational behavior of the…

### Net Fisher information measure versus ionization potential and dipole polarizability in atoms

- Physics
- 2007

### Information entropy, information distances, and complexity in atoms.

- Computer ScienceThe Journal of chemical physics
- 2005

The complexity measure shows local minima at the closed-shell atoms indicating that for the above atoms complexity decreases with respect to neighboring atoms, and it is seen that complexity fluctuates around an average value, indicating that the atom cannot grow in complexity as Z increases.

### The Fisher-Shannon information plane, an electron correlation tool.

- Physics, Computer ScienceThe Journal of chemical physics
- 2004

A new correlation measure, the product of the Shannon entropy power and the Fisher information of the electron density, is introduced by analyzing the Fisher-Shannon information plane of some…