Local information-distance thermodynamics of molecular fragments

2012

Information-theoretic description of the electron probabilities and currents in molecules is extended to cover the complex amplitudes (wave functions) of quantum mechanics. The classical information measures of Fisher and Shannon, due to the probability/density distributions themselves, are supplemented by the nonclassical terms generated by the wave-function phase or the associated probability current. The previous one-electron development in such an entropic perspective on the molecular electronic structure is extended to cover N -electron states by adopting the Harrimantype framework of equidensity orbitals. This analysis emphasizes the phase part of electronic states, which generates the probability-current density and the associated non-classical entropy contributions, which allow one to distinguish the information content of states generating the same electron density and differing in their current composition. A complementary character of the Fisher and Shannon information measures is explored in the associated vertical (density-constrained) information principles, for determining the equilibrium state corresponding to the fixed ground-state electron density. It is argued that the lowest "thermodynamic" state generally differs from the true ground state of the system, by exhibiting the space-dependent phase and hence also the non-vanishing probability current, linked to the system electron distribution.

Section: Resultssupporting

confidence: 87%

Use of Harriman’s construction in determining molecular equilibrium states

2012

“…This IT approach to the AIM partition of the molecular electron density has been shown to lead to the "stockholder" fragments of Hirshfeld [24]. Information theory also facilitates a deeper insight into the nature of bonded atoms [1][2][3][14][15][16][17][18][19][20][21][22][23], the electron fluctuations between AIM [25], and a thermodynamic-like description of molecules [25][26][27]. It also increases our understanding of the elementary reaction mechanisms [28].…”

Section: Introductionmentioning

confidence: 96%

Information-theoretic multiplicities of chemical bond in Shull’s model of H2

2012

Alternative information-theoretic (IT) measures of the chemical bond multiplicity and its covalent/ionic composition in the orbital communication theory (OCT) are examined using Shull's natural orbital (NO) model of the homopolar bond in H 2 . In OCT a molecule is treated as an information (probability-scattering) system, generated by the network of conditional probabilities (from the quantum mechanical superposition principle) linking elementary events of the adopted perspective. For the first time this atomic orbital (AO) invariant, two-NO description of Shull allows one to examine in several alternative representations the behavior of the previously adopted IT indices, of the channel average communication noise (OCT-covalency) and information flow (OCT-ionicity), with changing internuclear distance R, from the united atom (R = 0) to the separated atoms limit (SAL) (R → ∞). The adopted references include the two-electron atomic and ionic functions of the model, as well as the alternative one-electron functions, of the AO and NO sets, respectively. The numerical results for the Wang function description of H 2 are reported and a general agreement with the accepted chemical intuition is tested. Joint probabilities of Shull's reference states are linked to the energy partitioning. The incorrect SAL behavior of the OCTionicity index, giving rise to the constant (interaction independent) overall multiplicity measure, emphasizes a need for a revision of these IT bond descriptors. The modified set of indices is proposed, reflecting the complementary localization (determinicity) and delocalization (indeterminicity) aspects of the communication system in question.Here A, A, and A respectively denote the scalar quantity, row vector and a square/rectangular matrix. The logarithm of the information measure is taken to an arbitrary but fixed base: log = log 2 corresponds to information measured in bits (binary digits), while log = ln expresses the amount of information in nats (natural units): 1 nat = 1.44 bits. The novel IT-ionicity now reflects the diagonal (intra-orbital, additive) information propagation in the molecular channel, while the modified IT-covalency accordingly measures the effect of its off-diagonal (inter-orbital, nonadditive) probability scatterings. These components are shown to give rise to the interaction strength dependent overall IT bond-order, which adequately reflects the chemical intuition.

“…The former reveals the classical information term, while the latter determines its non-classical complement in the overall information measures [9,10,16,17]. The phenomenological IT description of equilibria in molecular subsystems has also been proposed [11,[19][20][21][22], which formally resembles the ordinary thermodynamics [23].…”

Section: Introductionmentioning

confidence: 99%

Quantum information descriptors and communications in molecules

2014

Several concepts of information theory (IT) are extended to cover the complex probability amplitudes (wave functions) of molecular quantum mechanics. The classical and non-classical aspects of the electronic structure are revealed by the electronic probability and phase distributions, respectively. The information terms due to the probability and current distributions are accounted for in the complementary Shannon and Fisher measures of the resultant information content of quantum states. Similar generalization of the information-distance descriptors is also established. The superposition principle (SP) of quantum mechanics, which introduces the conditional probabilities between quantum states, is used to generate a network of quantum communications in molecules, and to identify the non-additive contributions to physical and information quantities. The phase-relations in two-orbital model are explored. The orbital communication theory of the chemical bond introduces the entropic bond multiplicities and their partition into IT covalent/ionic components. The conditional probabilities between atomic orbitals, propagated via the network of the occupied molecular orbitals, which define the bond system and orbital communications in molecules, are generated from the bond-projected SP. In the one-determinantal representation of the molecular ground state the communication amplitudes are then related to elements of the charge and bond-order matrix. Molecular equilibria are reexamined and parallelism between the vertical (density-constrained) energy or entropy/information principles of IT and the corresponding thermodynamic criteria is emphasized.