The correlation theory of the chemical bond

Abstract

The quantum mechanical description of the chemical bond is generally given in terms of delocalized bonding orbitals, or, alternatively, in terms of correlations of occupations of localised orbitals. However, in the latter case, multiorbital correlations were treated only in terms of two-orbital correlations, although the structure of multiorbital correlations is far richer; and, in the case of bonds established by more than two electrons, multiorbital correlations represent a more natural point of view. Here, for the first time, we introduce the true multiorbital correlation theory, consisting of a framework for handling the structure of multiorbital correlations, a toolbox of true multiorbital correlation measures, and the formulation of the multiorbital correlation clustering, together with an algorithm for obtaining that. These make it possible to characterise quantitatively, how well a bonding picture describes the chemical system. As proof of concept, we apply the theory for the investigation of the bond structures of several molecules. We show that the non-existence of well-defined multiorbital correlation clustering provides a reason for debated bonding picture.

k-stretchability of entanglement, and the duality of k-separability and k-producibility

“…Here we recall the structure of the classification and quantification of multipartite correlation and entanglement [14,40,41]. Our goal is to do this in the way sufficient to see how the permutation invariant properties can be formulated parallel to this in the next section.…”

“…If the system is described by quantum mechanics, then nonclassical forms of correlations arise, the most notable is entanglement [1][2][3][4]. It is the main resource of quantum information theory [5][6][7], and its nonclassical properties, playing important role also in many-body physics [8][9][10], make it influential in the behavior and characterization of strongly correlated systems [11][12][13][14].…”

“…Even for pure states, the nonexistence of a maximally entangled reference state [29,30] and the involved nature of state-transformations in general [31,32] seem to make the (S)LOCC-based classification practically unaccomplishable, and the standard (S)LOCC paradigm less enlightening so less expressive. Taking into account partial entanglement (partial separability) [33][34][35][36][37][38][39][40], or partial correlations [14,41,42] only, leads to a combinatoric [43][44][45], discrete classification (based on the lattice of set partitions [44]), endowed naturally with a well-behaving set of correlation and entanglement measures, characterizing the finite number of properties [14,40].…”

“…(In the case of entanglement, k-partitionability is called k-separability [35,37], while k-producibility [46][47][48][49] is also called entanglement depth [50][51][52]. Here we use both concepts for correlation and also for entanglement, this is why we use the naming "k-partitionability of correlation" and "k-producibility of correlation", "k-partitionability of entanglement" and "k-producibility of entanglement" [14,40,41].) These characterize the strength of two different (one-parameter-) aspects of multipartite correlation and entanglement: those which cannot be restricted inside at least k parts, and those which cannot be restricted inside parts of size at most k, respectively.…”

Quantification of electron correlation effects: Quantum Information Theory vs Method of Increments

“…The sum of all one‐orbital entropies gives a measure for the total correlation of the wave function …”