Equidensity orbitals in resultant-information description of electronic states

Abstract

The equidensity orbitals (EO) are used in the resultant entropic description of molecular states which combines the probability and current contributions in the overall information content. Continuities of the modulus and phase components of electronic wavefunctions are examined, and the Harriman-Zumbach-Maschke (HZM) construction of Slater determinants yielding the prescribed electron density is explored. The conditional probability interpretation of (complex) HZM wavefunctions is formulated, the entropy/information contributions due to the state phase component are summarized, and a nonclassical origin of quantum dynamics of the resultant gradient information, related to average kinetic energy of electrons, is emphasized. The phase equilibria maximizing the resultant-entropy measures are explored, and "thermodynamic" phase minimizing the overall gradient information is determined. It generates finite orbital currents giving rise to the vanishing resultant flow of electrons in the system as a whole. Potential use of atomic and molecular EO bases in electronic structure calculations and interpretations in chemistry is discussed, and illustrative example of Gaussian probability distribution is examined in some detail.

Information-Theoretic Descriptors of Molecular States and Electronic Communications between Reactants

“…( r ), common to all occupied EO reconstructing the given electron density ρ ( r ) = N p ( r ), is determined from the subsidiary minimum information principle [ 53 , 54 , 55 , 56 , 57 ]. It relates this phase contribution to the average wave vector in the configuration under consideration [ 78 , 79 ]: φ opt. ( r ) = φ [ p ; r ] = − 〈 q [ p ]〉 ⋅ f [ p ; r ], 〈 q [ p ]〉 = N −1 ∑ l q l [ p ], where the summation extends over all occupied EO.…”

“…Elsewhere, the application of DFT construction by Harriman, Zumbach, and Maschke (HZM) [ 76 , 77 ], of wavefunctions yielding the prescribed electron distribution, for a description of reactive systems has been examined [ 63 , 78 , 79 ]. In such density-constrained Slater determinants the defining equidensity orbitals (EO) of the Macke/Gilbert [ 80 , 81 ] type exhibit the same molecular probability density, with the orbital orthogonality being assured by the local phases alone.…”

Resultant Information Descriptors, Equilibrium States and Ensemble Entropy †

“…As complementary descriptors of electronic structure and reactivity phenomena, both the modulus and phase parts of molecular states contribute to the overall (resultant) content of their entropy (uncertainty) and information (determinicity) descriptors [2][3][4][5][6][7][8][9]. The need for such generalized information-theoretic (IT) measures of the entropy/information content in electronic states has been emphasized elsewhere [10][11][12][13][14].…”

“…Such descriptors combine the classical terms due to wavefunction modulus (or probability density), and the nonclassical contributions generated by the state phase (or its gradient determining the convection velocity). The overall gradient information, the quantum extension of Fisher's intrinsic accuracy functional for locality events, then represents the dimensionless measure of the state electronic kinetic energy [2][3][4][5][6][7][8][9][10][11][12][13][14][15]. This proportionality relation between the state resultant information content and the average kinetic energy of electrons ultimately allows applications of the molecular virial theorem [16][17][18][19][20][21][22][23][24][25][26][27][28][29] in an information interpretation of the chemical bond and reactivity phenomena [4,6,9,30].…”

Phase Equalization, Charge Transfer, Information Flows and Electron Communications in Donor–Acceptor Systems

“…Elsewhere [63,73,74], the potential use of the DFT construction by Harriman, Zumbach, and Maschke (HZM) [75,76], of wavefunctions yielding the prescribed electron distribution, in a description of reactive systems has been examined. In such density-constrained Slater determinants, the defining Equidensity Orbitals (EO), of the Macke/Gilbert [77,78] type, exhibit the same molecular probability density, with the orbital orthogonality being assured by the EO local phases alone.…”