Related Experiment Video
Updated: May 25, 2026

Isolating Free Carbenes, their Mixed Dimers and Organic Radicals
Published on: April 19, 2019
Strongly correlated barriers to rotation from parametric two-electron reduced-density-matrix methods in application
Andrew M Sand1, Christine A Schwerdtfeger, David A Mazziotti
1Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA.
Abstract:
Recently, parameterization of the two-electron reduced density matrix (2-RDM) has made possible the determination of electronic energies with greater accuracy and lower cost than traditional electron-pair theories including coupled cluster with single and double excitations [D. A. Mazziotti, Phys. Rev. Lett. 101, 253002 (2008)]. We examine the method's performance for strongly correlated barriers to rotation; in particular, we study two distinct pathways in the isomerization of diazene (N(2)H(2)) from cis to trans: (i) a strongly correlated rotational pathway and (ii) a moderately correlated inversion pathway. While single reference wavefunction methods predict that the rotational barrier is higher than the inversional barrier, the parametric 2-RDM method predicts that the rotational barrier is lower than the inversional barrier by 3.1 kcal/mol in the extrapolated basis set limit. The parametric 2-RDM results are in agreement with those from multireference methods including multireference perturbation theory and the solution to the anti-Hermitian contracted Schrödinger equation. We report energies, optimized structures, and natural orbital occupation numbers for three diazene minima and two transition states.
Related Concept Videos
π Molecular Orbitals of 1,3-Butadiene
The simplest conjugated diene is 1,3-butadiene: a four-carbon system where each carbon is sp2-hybridized and has an unhybridized p orbital that contains an unpaired electron. According to molecular orbital theory, atomic orbitals combine to form molecular orbitals such that the number...
Stability of Conjugated Dienes
A comparison of the enthalpies of hydrogenation of dienes reveals that conjugated dienes release less heat on hydrogenation, rendering them more stable than their nonconjugated analogs.
[4+2] Cycloaddition of Conjugated Dienes: Diels–Alder Reaction
[3,3] Sigmatropic Rearrangement of 1,5-Dienes: Cope Rearrangement
Thermal Electrocyclic Reactions: Stereochemistry
Selection Rules: Thermal Activation
Conjugated systems containing an even number of π-electron pairs undergo a conrotatory ring closure. For example, thermal electrocyclization of (2E,4E)-2,4-hexadiene, a conjugated diene containing two π-electron pairs, gives trans-3,4-dimethylcyclobutene.
Diels–Alder Reaction: Characteristics of Dienes
Characteristics of the diene
Conformation
The simplest example of a diene is 1,3-butadiene, an acyclic conjugated π system. At room temperature, the molecule exists as a mixture of s-cis and s-trans conformers by virtue of rotation around the carbon–carbon single bond. Although the s-trans isomer is more stable, the...

