Thinking in Complexity

Mainzer, Klaus

doi:10.1007/978-3-662-13214-2

Cited by 69 publications

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“…To complement the about present studies, two additional complexes with d 10 -s 2 interactions were analyzed by our group. These were [Pt (PH 3 ) 3 Tl] + and [AuCl(PH 3 ) 2 ]Tl + complexes, [128,129] which were modeled by methods HF, MPn (n = 2-4), CCSD and CCSD(T) (see Figure 5B,C). We found that the changes in the geometry in both models are sensitive to the electron correlation energies.…”

Section: Metallophilic Interactionsmentioning

confidence: 99%

Noncovalent interactions in inorganic supramolecular chemistry based in heavy metals. Quantum chemistry point of view

Barrientos

Miranda-Rojas

Mendizábal

2018

Int J of Quantum Chemistry

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Complexity is a concept that is being considered in chemistry as it has shown potential to reveal interesting phenomena. Thus, it is possible to study chemical phenomena in a new approach called systems chemistry. The systems chemistry has an organization and function, which are regulated by the interactions among its components. At the simplest level, noncovalent interactions between molecules can lead to the emergence of large structures. Consequently, it is possible to go from the molecular to the supramolecular systems chemistry, which aims to develop chemical systems highly complex through intra-and intermolecular forces. Proper use of the interactions previously mentioned allow a glimpse of supramolecular system chemistry in many tasks such as structural properties reflecting certain behaviors in the chemistry of materials, for example, electrical and optical, processes of molecular recognition and among others. In the last time, within this area, inorganic supramolecular systems chemistry has been developed. Those systems have a structural orientation which is defined by certain forces that predominate in the associations among molecules. It is possible to recognize these forces as hydrogen bonding, π-π stacking, halogen bonding, electrostatic, hydrophobic, charge transfer, metal coordination, and metallophilic interactions. The presence of these forces in supramolecular system yields certain properties such as light absorption and luminescence. The quantum theoretical modeling plays an important role in the designing of the supramolecular system. The goal is to apply supramolecular principles in order to understand the associated forces in many inorganic molecules that include heavy metals for instance gold, platinum, and mercury. Relevant systems will be studied in detail, considering functional aspects such as enhanced coordination of functionalized molecular self-assembly, electronic and optoelectronic properties. K E Y W O R D Sdensity functional theory, dispersion term, Post-Hartree-Fock, van der Waals forces Grimme´s dispersion (D3)

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Section: Metallophilic Interactionsmentioning

confidence: 99%

Noncovalent interactions in inorganic supramolecular chemistry based in heavy metals. Quantum chemistry point of view

Barrientos

Miranda-Rojas

Mendizábal

2018

Int J of Quantum Chemistry

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“…"Complexity" is a word rich with ambiguity comprising as many as lo2 anharmonically and highly dependent on context (1). Chem-oscillating bonds) and several times this numistry has its own understandings of this word.…”

Section: Complexity In Chemistrymentioning

confidence: 99%

Complexity in Chemistry

Whitesides

Ismagilov

1999

Science

362

253

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“…As known, the non-extensive statistical mechanics is based on the following definitions for logarithmic and exponential functions [12], it is easy to verify that they satisfy the usual properties ln q (x ⊗ q x) = ln q x + ln q y, ln q (x q x) = ln q x − ln q y; exp q (x) ⊗ q exp q (y) = exp q (x + y), exp q (x) q exp q (y) = exp q (x − y) (A. 3) of the logarithmic and exponential functions.…”

Section: Discussionmentioning

confidence: 95%

“…i n−1 of the upper level n − 1. Then, the summation over nodes of the level n belonging to all remaining clusters is carried out and the same procedure is repeated for each subsequent hierarchical level l < n. 3 Expression (24) is a basis for the numerical definition of the complexity of arbitrary hierarchical ensemble (for example, in case of the complex defect structure of solids subject to intensive external influence type of strong plastic deformation or rigid radiation treatment). Unlike the amorphous systems, the number of structure levels of a real crystal is rather not large.…”

Section: Discussionmentioning

confidence: 99%

“…Despite a daily appearance of hierarchy in society and comprehension of its role in physical, biological, economical and other complex systems [1][2][3][4][5] theory of hierarchically constrained statistical ensembles has been developed only at the description of dynamics of spin glasses [6,7]. The formal basis of this theory is that states of hierarchically constrained objects are related to an ultrametric space whose geometrical image is the Cayley tree with nodes corresponding to statistical (sub)ensembles [8].…”

Section: Introductionmentioning

confidence: 99%

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Complexity of hierarchical ensembles

Olemskoĭ

Острик

Kokhan

2009

Physica A: Statistical Mechanics and its Applications

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a b s t r a c tWithin the framework of generalized combinatorial approaches, complexity is determined as a disorder measure for hierarchical statistical ensembles related to Cayley trees possessing arbitrary branching and number of levels. With strengthening hierarchical coupling, the complexity is shown to increase monotonically to the limit value that grows with tree branching. In contrast to the temperature dependence of thermodynamic entropy, the complexity is reduced by the variance of hierarchical statistical ensemble if the branching exponent does not exceed the gold mean. Time dependencies are found for both the probability distribution over ensemble states and the related complexity. The latter is found explicitly for self-similar ensemble and generalized for arbitrary hierarchical trees.

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Thinking in Complexity

Cited by 69 publications

References 0 publications

Noncovalent interactions in inorganic supramolecular chemistry based in heavy metals. Quantum chemistry point of view

Noncovalent interactions in inorganic supramolecular chemistry based in heavy metals. Quantum chemistry point of view

Complexity in Chemistry

Complexity of hierarchical ensembles

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