Abstract
This work studies the partitioning of the electron density into two contributions which are interpreted as the paired and the effectively unpaired electron densities. The topological features of each density field as well as of the total density are described localizing the corresponding critical points in simple selected molecules (local formalism). The results show that unpaired electron-density concentrations occur out of the topological bonding regions whereas the paired electron densities present accumulations inside those regions. A comparison of these results with those arising from population analysis techniques (nonlocal or integrated formalisms) is reported.
Highlights
The theory of atoms in moleculesAIM, introduced long time ago,[1] describes the topology of electron density in molecular systems providing important information which is essentially twofold
For all of the other atoms except the C and Na ones in C2H4 and NaCl molecules, the nuclear position is located between the ͑uand cp’s. This means that the cp’s of ͑pand are placed in the internuclear region, while that of ͑udoes not. All these results indicate the accumulation of paired density over the bonding region with the corresponding decrement of the unpaired one
The fact that the unpaired density is not involved in bonding phenomena does not mean that it vanishes in the internuclear or bonding region
Summary
The pth-order reduced density matrixp-RDMcorresponding to an N-electron system is derived as an average of the N-electron-density matrixnonreduced density matrix.[3,4] The procedure to obtain a lower-order RDM from a higher one is called contraction mapping. The electron density, expressed as the diagonal part of the first-order reduced density matrix1-RDM, can be derived from the contraction mapping from the second-order reduced density matrix2RDM ͑pair densityto the first-order density matrix1RDM ͑particle density This algorithm allows one to perform a decomposition of the electron density into two parts, the paired density matrix and the effectively unpaired density matrix.[5,6,7,8,9] This result provides the appropriate method for studying the topology of each component in an independent way and to draw out all the features of the electron density. Partitioning of the electron density within the pth-RDM framework into two terms so that the properties of both of them can topologically be analyzed For this purpose, a matrix formulation of RDM is briefly introduced and the coordinate representation is used to describe the electron density and their components.
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