Molecular electron density distributions in position and momentum space

Rawlings, Diane C.; Davidson, Ernest R.

doi:10.1021/j100252a016

Cited by 45 publications

(20 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Standard procedures for the Fourier transformation of position space orbitals generated by ab-initio methods have been described [72]. The orbitals employed in ab-initio methods are linear combinations of atomic basis functions and since analytic expressions are known for the Fourier transforms of such basis functions [73], the transformation of the total molecular electronic wavefunction from position to momentum space is computationally straightforward [74].…”

Section: Information-theoretic Measures and Complexitiesmentioning

confidence: 99%

Information-theoretical complexity for the hydrogenic identity S N 2 exchange reaction

et al. 2012

View full text Add to dashboard Cite

We investigate the complexity of the hydrogenic identity S N 2 exchange reaction by means of information-theoretic functionals such as disequilibrium (D), exponential entropy (L), Fisher information (I), power entropy (J) and joint information-theoretic measures, i.e., the I-D, D-L and I-J planes and the Fisher-Shannon (FS) and López-Mancini-Calbet (LMC) shape complexities. The several information-theoretic measures of the one-particle density were computed in position (r) and momentum (p) spaces. The analysis revealed that the chemically significant regions of this reaction can be identified through most of the information-theoretic functionals or planes, not only the ones which are commonly revealed by the energy, such as the reactant/product (R/P) and the transition state (TS), but also those that are not present in the energy profile such as the bond cleavage energy region (BCER), the bond breaking/forming regions (B-B/F) and the charge transfer process (CT). The analysis of the complexities shows that the energy profile of the identity S N 2 exchange reaction bears no simple behavior with respect to the LMC and FS measures. Most of the chemical features of interest (BCER, B-B/F and CT) are only revealed when particular information-theoretic aspects of localizability (L or J), uniformity (D) and disorder (I) are considered.

show abstract

Section: Information-theoretic Measures and Complexitiesmentioning

confidence: 99%

Information-theoretical complexity for the hydrogenic identity S N 2 exchange reaction

et al. 2012

View full text Add to dashboard Cite

show abstract

“…Standard procedures for the Fourier transformation of position space orbitals generated by ab-initio methods have been described [77]. The orbitals employed in ab-initio methods are linear combinations of atomic basis functions and since analytic expressions are known for the Fourier transforms of such basis functions [78], the transformation of the total molecular electronic wave function from position to momentum space is computationally straightforward [79].…”

Section: Information-theoretical Measures and Complexitiesmentioning

confidence: 99%

“…The product of the power entropy J-explicitly defined in terms of the Shannon entropy-(see below) and the Fisher information measure, I, combine both the global character (considering the distribution as a whole) and the local one (in terms of the gradient of the distribution), to preserve the general complexity properties. As compared to the LMC complexity, aside of the explicit dependence on the Shannon entropy which serves to measure the uncertainty (localizability) of the distribution, the Fisher-Shannon complexity replaces the disequilibrium global factor D by the Fisher local one to quantify the departure of the probability density from disorder [77,78] of a given system through the gradient of the distribution.…”

Section: Introductionmentioning

confidence: 99%

Concurrent Phenomena at the Reaction Path of the SN2 Reaction CH3Cl + F−. Information Planes and Statistical Complexity Analysis

Molina-Espíritu

Esquivel

Angulo

et al. 2013

Entropy

View full text Add to dashboard Cite

An information-theoretical complexity analysis of the S N 2 exchange reaction for CH 3 Cl + F − is performed in both position and momentum spaces by means of the following composite functionals of the one-particle density: D-L and I-J planes and Fisher-Shannon's (FS) and López-Ruiz-Mancini-Calbet (LMC) shape complexities. It was found that all the chemical concepts traditionally assigned to elementary reactions such as the breaking/forming regions (B-B/F), the charge transfer/reorganization and the charge repulsion can be unraveled from the phenomenological analysis performed in this study through aspects of localizability, uniformity and disorder associated with the information-theoretical functionals. In contrast, no energy-based functionals can reveal the above mentioned chemical concepts. In addition, it is found that the TS critical point for this reaction does not show any chemical meaning (other than the barrier height) as compared with the concurrent processes revealed by the information-theoretical analysis. Instead, it is apparent from this study that a maximum delocalized state could be identified in the transition region which is associated to the charge transfer process as a new concurrent phenomenon associated with the charge transfer region (CT) for the ion-complex is identified. OPEN ACCESS Entropy 2013, 15 4085Finally it is discussed why most of the chemical features of interest (e.g., CT, B-B/F) are only revealed when some information-theoretic properties are taken into account, such as localizability, uniformity and disorder.

show abstract

“…(1) and this will be the choice throughout the article. Standard procedures for the Fourier transformation of position space orbitals generated by ab‐initio methods have been described 45. The orbitals used in ab‐initio methods are linear combinations of atomic basis functions and since analytic expressions are known for the Fourier transforms of such basis functions,46 the transformation of the total molecular electronic wavefunction from position to momentum space is computationally straightforward 47…”

Section: Information‐theoretic Measures and Complexities: Basicsmentioning

confidence: 99%

Concurrent phenomena at the transition region of selected elementary chemical reactions: An information‐theoretical complexity analysis

Esquivel¹,

Molina-Espíritu²,

Dehesa³

et al. 2012

Int J of Quantum Chemistry

View full text Add to dashboard Cite

In this work, we have investigated in position (r) and momentum (p) spaces the concurrent phenomena occurring at the vicinity of the transition state (TS) (the so-called transition region) of selected chemical reactions (such as the hydrogenic abstraction and the exchange hydrogenic reactions) by means of a broad set of single informationtheoretic functionals of the one-particle density (such as the disequilibrium (D), exponential entropy (L), Fisher information (I) and the power entropy (J)) and composite informationtheoretic measures which includes various information planes (such as the I-D, D-L, and I-J planes) and complexities of the Fisher-Shannon and L opez-Mancini-Calbet (LMC) types. The analysis of the single functionals and the information planes revealed that these information-theoretical elements can identify all the chemically significant regions, not only the reactant/product regions (R/P) and the TS but also those that are not present in the energy profile, such as the bond cleavage energy region (BCER), the bond breaking/forming regions (B-B/F) and the charge transfer complex. Moreover, the analysis of the complexities shows that in position as well as in the joint (r-p) spaces, the energy profile of the abstraction reaction bears the same information-theoretical features of the LMC and FS measures. Finally, it is shown why most of the chemical features of interest (such as e.g., BCER and B-B/F) are lost in the energy profile, being only revealed when particular information-theoretical aspects of localizability (L or J), uniformity (D) and disorder (I) are considered.

show abstract

Molecular electron density distributions in position and momentum space

Cited by 45 publications

References 1 publication

Information-theoretical complexity for the hydrogenic identity S N 2 exchange reaction

Information-theoretical complexity for the hydrogenic identity S N 2 exchange reaction

Concurrent Phenomena at the Reaction Path of the SN2 Reaction CH3Cl + F−. Information Planes and Statistical Complexity Analysis

Concurrent phenomena at the transition region of selected elementary chemical reactions: An information‐theoretical complexity analysis

Contact Info

Product

Resources

About