Conformational effects on the magnetic ground state of diradicals coupled through extended conjugated chains. A theoretical investigation
Introduction
The set-up of intramolecular magnetic coupling in organic diradicals (or polyradicals) is the subtle combination of three mechanisms [1]: (a) the direct coupling resulting from wave functions overlap and dipolar coupling; (b) the indirect coupling or superexchange, well known in inorganic magnetic materials [2]; and (c) the spin polarisation, which strongly depends on the excited energy levels (empty levels) [1], [3]. The direct coupling is generally antiferromagnetic (AF) except for peculiar molecular conformations (leading to the orthogonality of the wave functions, for example [4]). Superexchange and spin polarisation mechanisms may yield either ferro (F) or AF magnetic exchange. It still remains a challenge to evaluate quantitatively the respective role of these contributions. Moreover, the wide use of some rules derived from the basic concepts [5], [6] has been recently debated much [7], [8]. An assessment of the various contributions and the important role of the temperature may be investigated through the theoretical and experimental study of a selected series of diradicals. The design of such families of diradicals will take into account the chemical nature of each radical and the different nature of the spacers. The nature of the radicals is mainly reflected in their spin distribution. The spacer involving double or triple bonds may be extended with different topologies. This extension of the spacers allows us to decrease the effect of the direct coupling; the spin distribution allows us to modify the spin polarisation contribution, and the superexchange should be sensitive to the spacer (double bonds versus triple bonds, topology,…).
The present study reports the results of semiempirical calculations performed on a series of diradicals, some molecules of which have been synthesised and experimentally studied [9], [10]. These are based on imino nitroxide (IN) and/or nitronyl nitroxide (NN) terminal radical fragments linked through a diamagnetic conjugated organic spacer with the following peculiarities (Fig. 1, Fig. 2):
- 1.
Both topologies represented by molecules 1 and 2 (noted family ‘para’) and 3 and 4 (family ‘meta’) are considered.
- 2.
Each radical is always connected to a planar phenyl group, and the geometry at this bond is characterised by the angle α1. 1
- 3.
The spacer is made of aromatic rings alternating with a conjugated coupler being either a triple bond (1x, 4) or a double bond (2x). The length of the molecules may be varied from x=0 up to x=10, which is actually a very large molecule. The possible through-bond magnetic exchange in such diradicals results from the combination of successive diamagnetic aromatic fragments (delocalised wave function) with conjugated couplers. The geometry of the spacer is then determined by the angles α2, α3,… between the neighbouring aromatic planar fragments.
In the two families, it is possible to vary the chemical nature of the radicals R1 and R2 (IN/NN), the conjugated couplers (double versus triple bonds), and the nature of the aromatic fragments. The radicals R1 and R2 allow us to vary the electronic (spin) density on the α-carbon linked to the phenyl group and the degeneracy of the SOMOs for the diradicals. The spacer allows us to vary the nature of the π-MOs (sp or sp2) for the conjugated coupler, and the conjugation pathways may be strongly perturbed by substitution of the aromatic bridges [9c]. The aim of this paper, restricted to semiempirical calculations in view of the size of most of the diradicals, is first to point out the role of the nature of the radicals and of the conjugated couplers in the ground state (T=0 K) and secondly to get some insight into the role of the temperature through the study of the molecular conformations. More precisely, we shall focus on the following three points: (a) What are the possible molecular conformations? (b) What is the effect of the temperature on the singlet–triplet splitting? (c) What knowledge of the various coupling mechanisms is brought about from these systematic studies?
The theoretical results are discussed and compared to the available experimental results [9], [10]. An extended discussion including the role of the direct through-space coupling in smaller molecules (in particular with respect to steric hindrance), the role of electron-donating or -accepting substituents on the aromatic fragments and the spin distribution will be reported elsewhere [9c].
Section snippets
Geometry optimisation and rotation barriers
Let us emphasise from the outset that, depending upon the relative positions of R1 and R2, the singlet–triplet splitting ΔEST may be significantly different even for large values of x. Therefore, for each diradical, we have fully optimised the geometry for all possible conformations of R1 and R2,1 using a semiempirical NDDO type approximation within the UHF AM1 scheme both for Nα−Nβ=0 or 2, where Nα and Nβ are the number of electrons with spin up and down, respectively [11], [12].
Configuration interaction (CI) calculations and singlet–triplet splitting
In view of the high spin contamination often encountered within UHF type calculations [13] it would be better to determine the geometries of the equilibrium state, the first excited state and the rotation barriers of the diradicals through geometry optimisation including some configuration interaction (CI). Unfortunately, in many of the diradicals we have studied, the minimum active space to be retained for CI, given the degeneracy or quasi-degeneracy, is [6,6] or [7,7].
Conclusions
Semiempirical calculations carried out at the same level of approximation enable us to determine the different equilibrium conformations for each diradical, which belongs to one of the two families we have investigated; the comparison to the experimental results available for some of these diradicals in the ground state [9b] shows that their essential characteristics are well reproduced: value of the twist angle α1, planarity of the spacer (α2≈0), non-planarity of the five-membered rings of the
Acknowledgements
We thank Mrs A. Helleboid for help in computer facilities and two of us (P.W. and L.C.) thank MENRT for financial support.
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