Conformational effects on the magnetic ground state of diradicals coupled through extended conjugated chains. A theoretical investigation

Abstract

The magnetic properties of a series of stable diradicals based on imino nitroxide (IN) and nitronyl nitroxide (NN) are investigated. Both radical fragments are coupled through various diamagnetic conjugated organic spacers made of aromatic rings (4) alternating with either a triple (1_x, 3) or a double bond (2_x), where x indicates the length of the molecules with respect to the repeating unit. The optimised geometry and the corresponding electronic structure of the whole series (x=0,…,10) have been determined by means of semiempirical calculations based on the NDDO approximation within the AM1 parametrisation scheme. The singlet–triplet splitting has then been studied using configuration interaction within different active spaces. It turns out that the most important parameters are: (a) of geometrical nature (e.g. twist angles between the radical moieties and the planar conjugated spacer); and (b) of topological nature (e.g. the radical substitution at ortho, meta, and para positions of phenyl cycles). The results of the calculations enable us to predict some rules in relation to the experimental observations: (a) for a given value of x, the hierarchy of the exchange coupling within series of derivatives is such as J(R₁=R₂=NN)>J(R₁=IN, R₂=NN)>J(R₁=R₂=IN); (b) whatever the nature of the radical substituent, the singlet is the ground state and the exchange coupling decreases nearly exponentially with the length of the spacer, i.e. as x increases. The exchange coupling is still efficient up to x=8 for R₁=R₂=IN (experimentally it has been previously found efficient up to x=5 in the para position).

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):

• Both topologies represented by molecules 1 and 2 (noted family ‘para’) and 3 and 4 (family ‘meta’) are considered.

• Each radical is always connected to a planar phenyl group, and the geometry at this bond is characterised by the angle α₁. ¹

• The spacer is made of aromatic rings alternating with a conjugated coupler being either a triple bond (1_x, 4) or a double bond (2_x). 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].