Maxima of : A connection between quantum mechanics and Lewis structures

Abstract

The maxima of squared electronic wave functions |Ψ|2 are analyzed for a number of small molecules. They are in principle observables and show considerable chemical insight from first principles. The maxima contain substantial information about the relative electron positions in a molecule, such as the pairing of opposite spin electrons and the Pauli repulsion which are lost in the electron density. Single bond and double bond as well as polar bond pairs and lone pairs are obtained from the maximum analysis. In many cases, we find a correspondence to the electron arrangements in molecules as assumed by Lewis in 1916.

Pleading for a Dual Molecular‐Orbital/Valence‐Bond Culture

“…Searching for the maxima of the square of the wave function, as originally proposed by Artmann, is another method that allows one to retrieve meaningful sets of electron arrangements into real space. [49] From these electron configurations,s ingle electron densities can also be obtained, making chemical motifs appears,such as core electrons,lone pairs,a nd bonds.T he dynamic Voronoi Metropolis sampling (DVMS) is another very recent method that also enables one to extract chemical motifs from accurate wave functions. [44] Both methods reveal two equivalent rabbit ears as the lone pairs of water as well as two bent bonds for ethylene.T he DVMS method also reveals atriple bent-bonded structure for the N 2 molecule and when applied to C 2 arrives at an interpretation of its bonding in terms of an ear triple bond (actually three bent bonds) with singlet-coupled outer electrons,q uite equivalent to the MPD picture and to the VB and unitary-transformed CASSCF ones.…”

Chemical Bonding: The Orthogonal Valence-Bond View

“…Such calculations were made by Scemama et al . [ 69 ] and Lüchow [ 70 ]; the combination of OVB and QMC methods seems to be very promising for investigating the processes of chemical bonding. With such combined investigations, it should be possible to clarify the reality (or otherwise) of fragment states in a molecule.…”

Decoding the Chemical Bond—On the Connection between Probability Density Analysis, QTAIM, and VB Theory

“…Instead, a partition can then be mapped to a group of resonance structures, that have the same formal charges. In probability density analysis [24][25][26] -pioneered by Scemama et al 21 -, attractors of the probability density P(R) partition the all-electron position space R 3N into their basins of attraction Ω Ω Ω. The surfaces S(Ω Ω Ω) of these basins are of zero flux in the gradient vector field of P(R):…”

“…23 However, they discarded the approach in favor of the maximum probability domains. Lüchow and coworkers reintroduced the topological analysis of |Ψ| 2 , 24 added the definition of a basin as the 3Ndimensional analogue to the quantum atom, 25 and used this partitioning to investigate the anomeric effect. 26 This topological analysis of |Ψ| 2 is now relabelled as probability density analysis (PDA).…”