Captodative Substitution Enhances the Diradical Character of

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Captodative Substitution Enhances the Diradical Character of Compounds, Reduces Aromaticity and Controls Single Molecule Conductivity Patterns: A Valence Bond Study Thijs Stuyver, David Danovich, and Sason Shaik J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.9b06096 • Publication Date (Web): 18 Jul 2019 Downloaded from pubs.acs.org on July 23, 2019

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The Journal of Physical Chemistry

Captodative Substitution Enhances the Diradical Character of Compounds, Reduces Aromaticity and Controls Single Molecule Conductivity Patterns: A Valence Bond Study

Thijs Stuyver,*a,b David Danovich,a and Sason Shaik*a

a.

Department of Organic Chemistry and the Lise Meitner-Minerva Centre for Computational Quantum Chemistry, The Hebrew University, Jerusalem 91904, Israel

b.

Algemene Chemie, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussels, Belgium

Abstract The present contribution uses a VB perspective to consider the captodative substitution strategy, a method to enhance the diradical character of (potentially aromatic) compounds. We confirm the qualitative reasoning which has generally been used to rationalize the diradical-characterenhancing effect of captodative substitution: this type of substitution scheme disproportionally stabilizes specific Dewar/diradical(oid) VB structures, thus increasing their weight in the full ground state wave function. Furthermore, we assess the effect of captodative substitution on the aromaticity of the considered compound. We observe a clear trade-off between diradical character and aromaticity for our model systems: as one of them increases, the other decreases. This finding is especially significant within the field of single-molecule electronics, since it enables the unification of the previously observed inverse proportionality between the aromaticity of a compound and the magnitude of conductance through that molecule, with the observed proportionality between diradical character and the magnitude of conductance

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associated to a compound. To some extent, both properties, i.e. aromaticity and diradical character, appear to be the flip-sides of the same coin.

Introduction Captodative substitution, originally devised over forty years ago as a strategy to stabilize organic radicals,1,2 has witnessed a revival in its interest in recent years. This renewed attention stems from the attributed capability of this substitution scheme to selectively stabilize specific diradical resonance structures, leading to an increasing weight of these structures in the overall resonance hybrid, and thus to an enhancement of the diradical character of the compound under consideration (Fig. 1).3,4,5


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Figure 1. (a) Frontier orbital interaction scheme for captodative stabilization in the NH2CHBH2 radical. Overall, the orbital interactions stabilize the BCN system. The doubly occupied MO in the dashed box is significantly lower in energy than the N lone pair orbital, more than compensating for the slight destabilization of the singly occupied MO in the box compared to the SOMO on C.6 (b) An illustration of a captodative substitution strategy applied to benzene. The stabilizing interaction exerted on the C-centers by the B-, and N-substituents are generally assumed to lead to an increase in the weight of the shown diradical resonance structure in the resulting azaborine compound.

Diradical character has been associated with a variety of desirable properties in recent years, and diradicaloids, i.e. compounds with a significant diradical character, have been considered for a wide range of applications, among others within the fields of singlet fission,3,4,7 non-linear optics8,9,10,5 and molecular electronics.11,12,13,14 As demonstrated by Nakano and co-workers, the "diradical character" of a compound, though not an observable, is nevertheless experimentally measurable.15 Up to this point, attempts to quantify "diradical character" have been primarily based on MO-based wave function methods (e.g. PUHF, CASSCF), which enable the attribution of a single global (method-dependent) value to this property.8,16,17,18 However, as outlined concisely in the first paragraph, the conventional interpretation of the mechanism through which the captodative substitution scheme imparts diradical character to a compound is inherently embedded in a resonance/valence bond (VB) framework: it focuses on the weights of specific contributing diradical(oid) structures in the resonance hybrid/ground-state wave function. As such, it would be interesting to verify whether the qualitative reasoning invoked to rationalize the effects caused by this substitution scheme holds up against a quantitative VB treatment, i.e. do actual VB calculations support the prediction that a captodative substitution scheme increases mainly


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the weight of specific diradical resonance structures? Some pioneering studies on the VB interpretation of diradical character have already been performed in recent years,19,20,21,22 but an in-depth investigation of substitution effects – as far as we can tell – hasn't been undertaken so far. Expressing diradical character in terms of the weights of individual VB structures brings additional advantages as well: within the field of molecular electronics, the exact locations of the radical centers in the stabilized resonance structure(s) has been suggested to play an outsized role, i.e. a global value for the diradical character of a compound does not necessarily reveal much about the transport properties of the considered compound.11,23 As such, expressing the diradical character of a compound in terms of the weights of individual VB structures enables a direct validation of the established rules connecting diradical character to the magnitude of conductance through a molecular junction.11,12,13,22 Below, we present a careful quantitative VB analysis of the wave function of some prototypical captodatively substituted compounds which have previously been considered both as singlet fission chromophores, and as building blocks for highly conducting nanowires (Fig. 2).4,12 We will focus specifically on the weights of the individual VB structures and how they interact to give rise to the full ground state wave function. Additionally, we will devote some attention to probe the impact of captodative substitution patterns on the aromaticity of the considered compounds.24 To this end, we will focus mainly – though not exclusively – on the Nucleus Independent Chemical Shift (NICS) aromaticity indices (vide infra); one of the most versatile and conceptually straightforward descriptors available to probe the multi-faceted property of aromaticity.25,26,27,28 We will end by illustrating how the considered substitution patterns affect the conductivity of the molecules.


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Figure 2. The structures of the compounds considered in the present study.

Methods Geometry optimization of the species under consideration was carried out using B3LYP/6-311++G** as implemented in Gaussian 09 program.29,30,31,32 Note that all of the captodatively substituted compounds considered here retained a planar geometry, in line with the geometrical data previously reported in Refs. 4 and 12. The validity of the single-reference (KS-DFT) description of these structures was confirmed by checking the stability of the wave function upon symmetry breaking. For compound 2, the unrestricted solution collapsed into the restricted one, for compound 3, the unrestricted solution ended up a negligible 0.01 kcal/mol lower in energy than the restricted one (no significant deviations in the geometry or accumulation of spin density were observed either). As such, it should be clear that even though some electron correlation is present in these molecules, the functional and basis set employed generate a reasonable description of the electronic structure of the captodatively substituted compounds. All the VB calculations were carried out at the VBSCF/VDZ level of theory33,34,35 with the XMVB code, which is an ab initio valence bond program.36,37,38 The GIAO/B3LYP/6311++G** method was applied for the NICS (nucleus-independent chemical shift) calculations. NICS values were computed at 1 Å above the ring center [NICS(1)], together with its out-ofplane tensor component [NICSzz(1)].25,27 The electron transport calculations were performed using the Non-Equilibrium Green’s Function (NEGF) method combined with DFT as implemented in the Artaios code,39,40 a


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postprocessing tool for output from electronic structure calculations with various quantum chemistry codes, among which is Gaussian 09.30 Au (111) surfaces were chosen as the electrodes and thiolethynyl linkers (-C ≡C-SH) were added to the molecule to facilitate the connection to the contacts. In the first step, the examined structures were optimized at the B3LYP/6-31G(d) level of theory. After this optimization, the thiol’s hydrogen atoms were removed and Au9 clusters, approximating the electrode surface, were attached in accordance with the methodology presented in a recent study.41 The adsorption site is the fcc-hollow site. The Au-S distance was set to 2.48 Å.42 For the resulting structures, single-point calculations were performed at the B3LYP/LanL2DZ level of theory. In the final step, the Hamiltonian and overlap matrices were extracted to carry out the NEGF calculation within the wide-band-limit (WBL) approximation.43 In the WBL approximation, we used a constant value of 0.036 eV−1 for the local density of states (LDOS) of the electrode surface. This value was taken from the literature.43 The VBSCF Method The VBSCF method uses a wave function which is a linear combination of VB structures K with coefficient CK as shown in eq. 1,44

   CK  K , K

(1)

where each VB structure is a multi-determinantal wave function corresponding to a specific chemical structure, and each VB determinant is constructed from occupied atomic orbitals (here, the 2p orbitals; the generators of the  system). The coefficients CK are determined by solving the secular equation in eq. 2, in the usual variational procedure:

HC  EMC .

(2)

Here H, M, C are respectively, the Hamiltonian, Overlap, and Coefficient matrices, while E is the total energy of the system (including the  frame). The variational procedure involves a


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double optimization of the coefficients CK, together with the orbitals of the VB structures, in a given atomic basis set. The -frame is treated as a set of doubly occupied MOs (taken from the corresponding Hartree-Fock wave function) that are optimized during the VBSCF procedure. Thus, the VBSCF method is analogous to CASSCF in the sense that both methods optimize structure coefficients (cf. the CK’s in Eq. 1) as well as the orbitals within the used atomic basis set.21,22 The VB structures K are the Rumer structures assembled from VB determinants.45 Rumer structures are the canonical structures, and for the hexagonal -electronic system of benzene (as well as for its isoelectronic captodatively substituted analogues), they correspond to the well-known Kekulé and Dewar structures (Fig. 3; for an elaborate introduction into the construction of Rumer sets we refer to ref. 45).

Figure 3. The Rumer set associated to the benzene and its isoelectronic captodatively substituted analogues. Multiple approaches exist to quantify the weights of the individual VB structures in the full ground state wave function, e.g. Chirgwin-Coulson weights, Lowdin weights, inverse weights and renormalized weights.45 Throughout our analysis, we will focus on the inverse weights, but, as can be straightforwardly confirmed by inspection of Section S1 in the Supporting Information, each of the methods mentioned above lead to very similar weights. As such, our results are essentially independent of the method used for calculating the weights.

Types of Atomic Orbitals in VBSCF


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In describing the VB structures, one can use atomic orbitals (AOs), such that the Rumer structures will be purely covalent (Fig. 1a). This level of calculations is referred to as VBSCF(AO-C), where C means that we used only covalent Rumer structures. In a previous study we have shown that using this type of orbitals does not lead to correct trends when considering series of compounds.22 What the VBSCF(AO-C) method misses are ionic structures. However, as argued before in Ref. 21, adding explicitly the ionic structures for example, in benzene, C6H6, generates a complete set of 176 VB structures. Thus, considering all the ionic structures becomes quickly impractical. To avoid this multitude of ionic structures, there are ways to account for these structures effectively, while conserving the original number of Rumer structures. This is achieved by allowing the AOs to have small delocalization tails on atoms other than the one the AO “belongs” to. In this manner, the formally covalent Rumer structures, which, so-to-speak, are impregnated with ionic structures (see pp. 40-42 in Ref. 45). One such set of orbitals is called BDO,46,47 where BDO stands for a bond-distorted-orbital in which each AO on a given carbon atom is allowed to have a tail only on the atom to which it is bonded. Let us focus for a moment on a simple example molecule: butadiene. For this molecule, there are eight BDOs, which participate in all the possible bonding interactions in butadiene. The pair of BDOs describing the C1−C2 terminal π-bond of butadiene is shown in Fig. 4b. One can see that each orbital is centered on one of the C atoms of the terminal bond but having a tail on the other atom; the tail is quite substantial, which indicates the importance of ionic structures in this π-bond. The same description will apply to the other terminal bond, C3−C4, as well as to the long bond structure connecting C1-C4 (cf. the Dewar structures in benzene).


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Figure 4. Atomic orbital types used in VBSCF: (a) pure AO for C4H6. (b) The two BDOs for the terminal C1−C2 bond of C4H6. (c) The two BDOs for the long C1−C4 bond. Reprinted with permission from Reference 21, copyright 2017 American Chemical Society. When in a given Rumer structure, the pairing involves non-connected carbon atoms, such as 1-4 in butadiene, or even more distant pairing, we refer to these as long-bonds, and the corresponding structures are generally called “diradicaloid structures”.21 In the case of benzene and its isoelectronic analogues, these diradicaloid VB structures translate themselves in the Dewar structures shown in Fig. 3. As such, these VB structures can be connected directly to the diradical resonance structures alluded to in the introduction. Furthermore, their respective weights can be interpreted as a probe of the diradical character of the molecule under consideration.

Results and Discussion

Valence bond analysis of the electronic structure First, let us start by considering the electronic structure of the unsubstituted benzene molecule, i.e. compound 1 in Fig. 2. In accordance with common chemical knowledge, the main


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contributors to the wave function of benzene are the two Kekulé structures, both with a weight of ±29%. The three Dewar/diradical(oid) structures are required to have equivalent weights as well since they are symmetry related; their weights amount to ±14% each (Fig. 5a). Focusing on the energetics of the individual structures and how they interact to give rise to the full ground state, one can observe that the individual Dewar structures lie approximately 48 kcal/mol above the individual Kekulé structures. The individual Kekulé structures in their turn lie approximately 59 kcal/mol above the full ground state, pointing to the presence of a very strong resonance/aromaticity within the system. This resonance is mainly driven by the two Kekulé structures; taking a linear combination of these structures leads to a stabilization of the wave function by almost 39 kcal/mol. Note that this observation is perfectly in line with the traditional notion that aromatic stabilization is the result of the interaction of two or more equivalent, fully-paired resonance structures.48 Introduction of the three Dewar structures leads to an aggregate additional energy gain of a mere 20 kcal/mol (Fig. 5b). Note also that the magnitude of the resonance energy calculated within the context of the present study is in line with previously reported values found in the literature.49,50


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Figure 5 (a) The weights of the individual Rumer structures of benzene in the ground state wave function. (b) A scheme depicting the energetic location of the individual Rumer structures (and the (positive) linear combination of the Kekulé structure), and the full ground state.

Upon introduction of a simple captodative substitution (cf. compound 2), the weight of the Kekulé structures increases slightly compared to unsubstituted benzene; both of these structures now contribute approximately 34% to the full ground state wave function. In this case, the three Dewar structures are no longer equivalent; in accordance with the qualitative reasoning outlined in the introduction, one Dewar structure, the one with the "long bond" between the two carbon centers, has a significantly augmented weight in the wave function,


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amounting to 30%. As such, the weight of this stabilized Dewar structure has become very similar to the weights of the individual Kekulé structures, and thus the traditional notion concerning the emergence of aromaticity in benzenoids, outlined in the previous paragraph, starts to break down. The combined weight of two remaining Dewar structures does not exceed 5% so that these structures are more or less negligible (Fig. 6a). Turning again to the energetics, we observe that the preferential Dewar structure has now approached the Kekulé structures up to less than 4 kcal/mol. The Kekulé structures themselves lie approximately 55 kcal/mol higher in energy than the full ground state wave function. This energy gap is lower than the earlier mentioned energy gap for unsubstituted benzene. This finding is in line with the calculated increase in weight of these Kekulé structures in the ground state, i.e. from 29% to 34%. Upon combining the two Kekulé structures, one ends up with a wave function stabilized by only 25 kcal/mol compared to the individual structures. The Dewar structures are responsible for the additional 30 kcal/mol of delocalization energy present in the full ground state wave function (Fig. 6b).


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Figure 6. (a) The weights of the individual Rumer structures in the ground state wave function of compound 2. (b) A scheme depicting the energetic location of the individual Rumer structures (and the (positive) linear combination of the Kekulé structure), and the full ground state.

Finally, let us turn to compound 3. Compared to compound 2, the weights of the Kekulé structures have now decreased somewhat; they amount to 31% each. Notably, the stabilized Dewar structure has become the main contributor to the ground state of the molecule: its weight


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amounts to over 35%. The dominance of one of the Dewar structures and the secondary role of the Kekulé structures is a complete reversal compared to the traditional notion of aromaticity. The remaining two Rumer structures now have an even lower weight than in the wave function associated to compound 2; their combined contribution to the ground state amounts to less than 3% (Fig. 7a). Once more, the energetic location of the different structures is perfectly in line with their respective weights. The stabilized Dewar structure has now become over 2 kcal/mol more stable than the Kekulé structures, and lies approximately 56 kcal/mol above the full ground state of the system. The other Dewar structures are situated almost a 100 kcal/mol higher in energy, underscoring the negligible role they play in shaping the electronic structure of this compound. The delocalization stabilization imparted by the Kekulé structures has decreased even further compared to compound 2; a linear combination of these two structures now leads to a stabilization of barely 22 kcal/mol. As such, the Dewar structures are responsible for the bulk of the delocalization stabilization (33 kcal/mol; Fig. 7b).


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Figure 7. (a) The weights of the individual Rumer structures in the ground state wave function of compound 2. (b) A scheme depicting the energetic location of the individual Rumer structures (and the (positive) linear combination of the Kekulé structure), and the full ground state.

In summary, the results presented above constitute an unequivocal confirmation of the qualitative resonance-theory-based reasoning about captodative substitution outlined in the introduction. Captodative substitution indeed enhances the diradical character of a molecule significantly by stabilizing specific Dewar/diradical(oid) structures. Notably however, the total


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weight of the Kekulé structures is barely affected: the growth in the weight of the stabilized Dewar structures is mainly at the expense of the remaining Dewar structures. Furthermore, we have established that the traditional notion about the emergence of aromaticity in benzene starts breaking down upon substitution: in the captodatively substituted compounds, the viewpoint that the wave function is dominated by two equivalent fully-paired structures which impart the bulk of the energetic stabilization within the system becomes increasingly unjustified. The resonance stabilization provided by mixing the two Kekulé structures goes down significantly, from 39 kcal/mol for compound 1 to 22 kcal/mol for compound 3. Also the total resonance energy, i.e. the energy difference between the most stable individual VB structure and the full ground state, decreases upon captodative substitution, but this decrease is less steep (from 59 to 55 kcal/mol). These are clear indications that the aromaticity of benzene decreases upon captodative substitution, i.e. upon increasing the diradical character of the compound. To confirm this assertion, we will investigate the detailed evolution of the aromaticity throughout the systems considered in the following subsection.

Assessment of the trends in the aromaticity In this subsection, we aim to probe the trends in the aromaticity of benzene upon captodative substitution. Since aromaticity is not a well-defined magnitude, its quantification can only be done indirectly.24,51 Over the years, a multitude of aromaticity indices have been proposed,

respectively

based

on

structural-,

energetic-,

magnetic-,

or

electronic-criteria.27,26,52,53,54,55,56,57 Below, we will briefly explore some of these. Let us first take a look at the geometries of the two captodatively substituted compounds considered in the present study, i.e. compound 2 and 3.53,58 Focusing specifically on the C-N bond, we find that the bond length shortens slightly when going from compound 3 (1.360 Å) to


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compound 2 (1.357 Å). According to the literature, the reference bond length for a perfectly aromatic C-N bond amounts to 1.339 Å (single bond lenghts typically amount to 1.474 Å; double bond lengths to 1.271 Å).59 This is already a first indication that the captodatively substituted compounds considered here are still reasonably aromatic, but that compound 3 is (ever so slightly) less aromatic than compound 2, i.e. a decreasing diradical character indeed appears to correspond to an increasing aromaticity. Turning to the HOMO-LUMO gap (or chemical hardness)60,61 of the compounds, another regularly employed aromaticity index, one observes that this gap goes down as the diradical character increases; for compound 1, the HOMO-LUMO gap amounts to 6.6 eV, for compound 2, it amounts to 3.6 eV, and for compound 3 it reaches 2.8 eV.62 Since a big HUMOLUMO gap generally indicates a high degree of aromaticity,52,63 this is another indication that as the diradical character increases, the aromaticity of the compound goes down. Finally, let us consider some indices connected to the magnetic criterion of aromaticity.25,27,28 Significant magnetic shielding, caused by induced diatropic ring currents upon exposure of the compound to a magnetic field, is one of the key features of aromaticity. As such, a variety of indices quantifying the resulting chemical shift have been proposed: the so-called NICS indices. For all of these indices, negative values (shielding) correspond to aromatic behavior, whereas positive values (deshielding) denote anti-aromatic behavior.25 Here, we decided to focus specifically on the out-of-plane isotoropic chemical shift evaluated 1 Å above the plane, i.e. NICS(1), as well as the zz-component of the shielding tensor evaluated at the same point, i.e. NICS(1)zz, since we are mainly interested in the -effects.25,64 For the NICS(1)-index, one observes a steep decrease in the shielding as one goes form compound 1 to compound 2 (from -10.2 ppm to -6.8 ppm). For compound 3, the NICS(1)-index reaches a value slightly lower than for compound 2 (-6.5 ppm). A similar trend can be observed for the NICS(1)zz-index: a steep decrease from compound 1 (-29.2 ppm) to compound 2 (-22.0),


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followed by a much more moderate decrease up to compound 3 (-19.0 ppm). Since the three compounds we have considered all have the same ring-size, the different values obtained can be compared directly without the need of any size correction.65 As such, both NICS-indices point unequivocally to a decreasing aromaticity as one proceeds through the series of compounds considered. Note that a similar decrease in the chemical shielding has also been reported by Merino and co-workers for the structurally related borazine (B3N3H6).66 An overview of the different aromaticity indices/criteria discussed can be found in Table 1. In summary, we can conclude that all of the aromaticity indices discussed here, as well as the VB resonance criteria discussed in the previous subsection, point in the same direction: an increasing diradical character corresponds to a decreasing aromaticity.

Table 1. The deviation of the C-N bond length compared to the aromatic limit (R(C-N) – R(CN)aromatic), the HOMO-LUMO gap (HL-gap), and NICS(1) and NICS(1)zz indices. Compound R(C-N) – R(C-N)aromatica

HL-gapb

NICS(1)c

NICS(1)zzc

1

/

6.593

-10.2

-29.2

2

0.018

3.614

-6.8

-22.0

3

0.021

2.759

-6.5

-19.0

a

in Å in eV c in ppm b

The trade-off between diradical character and aromaticity and its relevance within the field in single-molecule electronics In the previous subsection, we confirmed that for the considered compounds, there is a clear trade-off between aromaticity and diradical character, i.e. as the diradical


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character of the compound increases, the aromaticity decreases. Whether this is a general relationship will be further investigated in the near future, but we do want to remark that if such a relationship were to hold, it would unify two important empirical (qualitative) rules put forward within the field of single-molecule electronics to predict the magnitude of conductance through a single-molecule assembled in a molecular junction: on one hand, the magnitude of conductance has been proposed to be inversely proportional to the aromaticity of the compound,67,68,69,70,71,72 on the other hand, the magnitude of conductance is said to be proportional to the diradical character of the compound.11,12,13,22 Our current results indicate that – to some extent – these two observations are flip-sides of the same coin. However, since aromaticity is a global property of a ring system, whereas the transport properties of a compound are highly dependent on the exact connection points of the contacts to the molecule, caution should be taken when generalizing the former empirical rule.73,74,75 Diradical character expressed in terms of the weights of the individual resonance/VB structures on the other hand enables a straightforward discrimination between different contact positions on the molecule, as discussed in detail in Refs. 11, 22 and 23. As an illustration, we included some transmission spectra calculated for compound 2, for three different configurations of contacts (cf. Fig. 8). According to the established rule connecting diradical resonance structures to the magnitude of conductance, placing the contacts on those positions on the ring on which the radical centers are located in the dominant Dewar/diradical(oid) structure, should lead to the highest conductance. This is exactly what is found. The C-C connection (cf. Fig. 8a) leads to a much higher transmission probability at (and around) the Fermi level (E=0) than either of the other configurations of contacts (cf. Fig. 8b; the difference amounts to almost an order of magnitude). Since the conductance of a molecular junction under small bias is – in a first approximation – proportional to the integral of the transmission probability around the Fermi level, this is a clear indication that the conductance


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will also be much higher than for the configurations of contacts in which the contact positions correspond to radical centers in the minor Dewar structures.

Figure 8. (a) The structure of the molecular junctions associated to the individual Dewar structures of compound 2. (b) The transmission spectra calculated for the junctions shown in Fig. 8a.


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Conclusions In the present contribution, we have confirmed the qualitative reasoning which has generally been used to rationalize the diradical-enhancing-effect of captodative substitution: this type of substitution scheme disproportionally stabilizes specific Dewar/diradical(oid) VB structures, thus increasing their weight in the full ground state wave function. Notably however, the total weight of the individual Kekulé structures is barely affected by such a substitution: the growth in the weight of the stabilized Dewar structures is mainly at the expense of the remaining Dewar structures. As such, the diradical character of these compounds does not seem to be caused simply by an overall increase in the weight of the diradical(oid) structures, but instead by one diradical(oid) structure becoming disproportionally important compared with the others. This finding illustrates that more scrutiny of the exact mechanism of emergence of diradical character from individual VB structures is needed. Additionally, with the help of a number of aromaticity indices, we confirmed that for the considered compounds, there is a clear trade-off between aromaticity and diradical character, i.e. as the diradical character of the compound increases, the aromaticity decreases. If such a relationship were to hold in general, it would unify two important empirical (qualitative) rules put forward within the field of single-molecule electronics to predict the magnitude of conductance through a single-molecule assembled in a molecular junction: on one hand, there is a reported inverse proportionality between the magnitude of conductance and the aromaticity of a compound,67,68,69,70,71,72 on the other hand, a direct proportionality between the magnitude of conductance and the diradical character has been established as well.11,12,13,22 Our current results indicate that – to some extent – these two observations are flip-sides of the same coin. However, since aromaticity is a global property of a ring system, whereas the transport


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properties of a compound are highly dependent on the exact connection points of the contacts to the molecule, caution should be taken when generalizing the former empirical rule. Diradical character expressed in terms of the weights of the individual resonance/VB structures on the other hand enables a straightforward discrimination between different contact positions on the molecule. From this perspective, estimating the magnitude of conductance based on the latter empirical rule is more versatile than when it is based on the former.

Supporting Information The Supporting Information is available free of charge on the ACS Publications website at http://pubs.acs.org The different VB structure weight measures and the geometries for all the calculated systems.

Author Information *[email protected] *[email protected] ORCID Thijs Stuyver: 0000-0002-8322-0572 David Danovich: 0000-0002-8730-5119 Sason Shaik: 0000-0001-7643-9421 Notes The authors declare no competing financial interest.

Acknowledgements


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T.S. acknowledges the Research Foundation-Flanders (FWO) for a position as postdoctoral research fellow (1203419N). S.S. is supported by the Israel Science Foundation (ISF 520/18). Table of Contents


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