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Role of π-Conjugation in Influencing the Magnetic Interactions in Dinitrenes: A Broken-Symmetry Approach Rikhia Ghosh, Prasenjit Seal, and Swapan Chakrabarti* Department of Chemistry, UniVersity of Calcutta, 92, A. P. C. Ray Road, Kolkata - 700 009, India, ReceiVed: May 30, 2009; ReVised Manuscript ReceiVed: NoVember 24, 2009
In the present study, we investigated the magnetic interactions of some dinitrenes by employing the broken symmetry-unrestricted density functional theoretical (BS-UDFT) approach along with the use of three basis sets. The magnetic coupling parameter (J) has been calculated, and thereby the magnetic character of the molecule and the strength of magnetic interaction are explored for these molecules. The exchange coupling parameters for the corresponding unconjugated systems are also calculated to see the role of π-conjugation. Our results suggest that a strong antiferromagnetic interaction exists in conjugated dinitrenes, and the strength of magnetic interaction decreases with increase in spacer length. For the unconjugated dinitrenes, the nature of magnetic interaction reduced appreciably and becomes weakly antiferromagnetic. The singlet-triplet energy gap for each system is also calculated. For the conjugated systems, it is observed that the singlet states are more stable than the triplet states, whereas for the unconjugated systems, the relative stability of the singlet state reduces to a considerable extent. This discrepancy of results for the conjugated and unconjugated dinitrenes can be attributed to the effect of π-conjugation, and the results can be well explained by this effect. Introduction Molecules with two weakly interacting unpaired electrons at two different atomic centers are known as diradicals.1 The role of diradicals in synthetic chemistry is of great importance because they serve as common intermediates in many chemical reactions. Apart from their role as reactive intermediates, these species also attract considerable attention over the years for their significant magnetic behavior. They form the basis of high-spin polyradicals, molecular magnets, and plastic materials.2,3 Diradicals also serve a major role in several biological processes, particularly as energy transfer intermediates in photosynthesis and in photochemistry. Among the various types of diradicals studied, conjugated systems are the ones widely investigated. Rajca in his review article4 focused on the spin coupling observed in various stable diradicals and polyradicals. In another work, Davidson and coworkers5 performed detailed analyses about the spin states of some small cyclic conjugated organic diradicals containing 4π electrons. Later on, Prasad et al.6 constructed a model that can predict the singlet triplet splitting using spin density and number of electrons participating in various conjugated diradicals. Very recently, Seal and Chakrabarti7 observed the nature of magnetic interactions in different unconjugated alkyl substituted cyclohexane diradical systems such as cyclohexane-1,3-diyls and cyclohexane-1,4-diyls. They also emphasized the effect of change of alkyl group on influencing the magnetic coupling constant (J) values under the light of the broken symmetry approach. Among several types of conjugated diradicals, dinitrenes play a significant role.8-12 In an elegant attempt, Wasserman and coworkers8 reported for the first time the synthesis of these interesting as well as important classes of compounds. In general, diazides are found to be the precursors of several dinitrenes. Iwamura and coworkers9 prepared isomeric vinylidenebis(phenylnitrenes) along with some other diradical systems and estimated effective magnetic moments over a wide * Corresponding author. E-mail:
[email protected].
range of temperature. Of the several classes of dinitrenes studied, the quinonoidal dinitrenes are systems of considerable interest. These compounds have two localized unpaired electrons in σ-type orbitals with conjugated π-electrons allowing the possibility of π-delocalization. Through the conjugated π-electrons operative in these systems, interaction between the isolated unpaired electrons takes place. Ling et al.10 experimentally observed the dependence of the aforementioned indirect exchange interaction on conjugation length in the quinoid dinitrenes of the type :NPh-X-PhN:. They observed the zero-field splitting parameters from ESR spectra of quinonoidal dinitrenes with excited triplet states at 77 K.10 The data obtained by them are inconsistent with simple dipole-dipole analysis of the ESR spectra in localized biradicals but can be explained with a spinpolarized model involving the π-electron cloud, but no such theoretical verification of this phenomenon has been observed until date. Later on, in a similar study, Minato et al.11 described the exchange interactions in isomeric biphenyl dinitrenes of the type :NPh-PhN:, where the X unit is a carbon-carbon single bond. Lahti and coworkers11,12 also prepared another class of dinitrenes, known as quinonoidal dinitrenes, by reducing dinitroarenes to corresponding diamines by standard methods, followed by transforming them to diazides. By photolyzing the corresponding diazides, the dinitrenes are then prepared. In recent years, we have also witnessed the importance of quintet dinitrenes.13-16 Lahti and his groups13 performed DFT and post Hartree-Fock calculations on lowest singlet, triplet, and quintet states of some conjugated dinitrenes. In his work, Chapyshev15 reported the structures and properties of quintet pyridyl-2,6-dinitrenes by ESR techniques and using DFT. Very recently, Chapyshev16 for the first time calculated fine structure levels in an external magnetic field for axially symmetrical quintet dinitrenes. Although there have been many theoretical investigations performed on dinitrenes, most of them are concerned only with the zero-field splittings and ground-state stability. In the present study, emphasis has been given in determining the nature of
10.1021/jp905077s 2010 American Chemical Society Published on Web 12/18/2009
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magnetic interactions in some conjugated dinitrenes of quinonoidal type. The corresponding exchange coupling constant, J, has been calculated to predict whether ferromagnetic (FM) interaction or antiferromagnetic (AFM) interaction exists between the unpaired electrons at the two radical centers in each of the dinitrenes studied. The effect of basis sets on the J values has also been explored with the use of two basis sets. The influence of π-conjugation on the magnetic interaction is also highlighted by calculating the exchange coupling parameter for the corresponding unconjugated systems. To evaluate the strength of magnetic interaction, broken symmetry unrestricted density functional theory (BS-UDFT)17 has been taken as the main investigating tool. 2. Computational Details The geometries of all dinitrene systems, that is, conjugated and unconjugated, are optimized using the hybrid-type exchangecorrelation functional of Becke and Lee-Yang-Parr (B3LYP)18 and Pople’s 6-311G(d,p) basis within the Gaussian 0319 suite of programs. In the present work, we have performed the magnetic calculations by employing the BS-UDFT technique. This BS-UDFT method is one of the most efficient and popular approaches for calculating the strength of magnetic interaction in a system containing unpaired electrons. In this broken symmetry formalism, our objective is to generate a wave function for such systems that breaks spatial and spin symmetry, thereby introducing a multideterminantal character within a single determinant framework.17,20 The BS wave function is expressed as -
|φBS〉 ) |φaφb |
(1)
where φa and φb are BS magnetic orbitals.20 To predict the nature of magnetic interactions between the electronic spins in quinonoidal dinitrenes, we have calculated the exchange coupling parameter (J) for such systems. The evaluation of magnetic coupling constant, J, is one of the convenient ways to measure FM and AFM interaction in a system with unpaired electrons at different sites. A positive J value implies FM interaction, whereas a negative value indicates the presence of an AFM interaction in the system concerned. In general, J can be evaluated from the Heisenberg-Dirac-van Vleck Hamiltonian to be
ˆ HDvV ) -2JSˆaSˆb H
(2)
where Sa and Sb are the local spin operators for the two interacting sites a and b, respectively.21,22 There are two very well-known formalisms for calculating the J value; one is developed by Noodleman and coworkers,23 whereas the other one was from the group of Yamaguchi.24 In the BS formalism, after obtaining the spin-unrestricted solutions for the determinants of maximum spin Ms ) Sa + Sb and broken spin symmetry Ms ) |Sa - Sb|, the formula for coupling constant, given by the group of Noodleman23 can be expressed as
J)-
EHS - EBS 2 Sˆmax
(3)
where EHS and EBS represent energies of high-spin (HS) and BS determinants, respectively; however, the constraint of the above-mentioned formula is that it is valid only in the weak coupling region. Yamaguchi and coworkers24 give a more generalized and modified version of the above expression, where
Figure 1. Schematic representations of the conjugated dinitrenes (A-E) under investigation. (A) 1,4-phenylenedinitrene, (B) 4,4′biphenylnitrene, (C) 4,4′-stilbenedinitrene, (D) 1,4-bis(p-nitrenophenyl)1,3-butadiene, and (E) 1,6-bis(p-nitrenophenyl)-1,3,5-hexatriene. The dots in each are the radical centers.
the use of expectation values for the spin-squared operator for the HS and BS determinants is being made of. The expression is given in eq 4
J)-
EHS - EBS 〈S 〉HS - 〈Sˆ2〉BS ˆ2
(4)
This formula is valid for the whole range of coupling strength and reduces to the Noodleman eq 3 in the weak coupling region. In eq 4, it is the difference of the spin-squared operator in the denominator that plays a crucial role. The ideal value for the difference is 1.0 if the HS state is triplet in nature, and DFT methods are used when the BS state has got a spin expectation value of 1.0. However, this difference varies for systems, and hence a quasi-linear relationship between J and EBS - EHS exists. Here the BS-UDFT technique used is implemented in the ORCA21 computational package. All calculations of magnetic interaction are done in three basis sets, viz., IGLO-III, IGLOII, and TZV, using the B3LYP-type hybrid functional. The reason for choosing IGLO-III and IGLO-II is that these basis sets are specially designed for performing NMR/EPR calculations.25 3. Results and Discussions Schematic representations of all five dinitrene systems, A-E, under consideration are given in Figure 1. The optimized structures of the conjugated dinitrenes are planar in nature. For the corresponding unconjugated systems, the structures are found to be nonplanar. The radical centers in each system are the two terminal N atoms. In the present analysis, we use both the Noodleman and Yamaguchi formalisms via the BS-UDFT method for the calculation of magnetic coupling parameter of the class of
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TABLE 1: Values of Magnetic Coupling Constant, J (in inverse centimeters), Singlet-Triplet Splitting, ES-T (in electronvolts), and the Overlap Integral, SVar, Calculated for Conjugated Dinitrene Systems A-E under Investigationa
basis sets IGLO-III
IGLO-II
TZV
a
conjugated dinitrenes
N-N distance (present work) (Å)
N-N distance (obtained by Lahti et al.) (Å)b
A B C D E A B C D E A B C D E
5.44 9.73 12.00 14.37 16.77 5.44 9.73 12.00 14.37 16.77 5.44 9.73 12.00 14.37 16.77
5.50 9.70 12.10 14.40
singlet-triplet gap, ES-T ) EBS - EHS (eV)
JY (cm-1)
JN (cm-1)
Svar.c
-0.0207 -0.0571 -0.0443 -0.0392 -0.0429 -0.0225 -0.0657 -0.0507 -0.0482 -0.0403 -0.0311 -0.0846 -0.0683 -0.0590 -0.0586
-172.77 -594.62 -460.98 -410.27 -453.44 -188.20 -707.02 -548.98 -529.17 -521.72 -262.42 -961.28 -784.84 -686.52 -685.35
-167.17 -460.53 -356.93 -316.50 -346.38 -181.69 -529.58 -409.26 -388.51 -387.71 -251.11 -682.63 -550.85 -475.81 -472.54
0.03247 0.01411 0.00004 0.00026 0.00000 0.03261 0.01405 0.00007 0.00026 0.00000 0.04604 0.01478 0.00027 0.00029 0.00000
5.50 9.70 12.10 14.40 5.50 9.70 12.10 14.40
Level of theory used is B3LYP. b Ref 26. c SVar ) 〈φA|φB〉.
TABLE 2: Values of Magnetic Coupling Constant, J (in inverse centimeters), Singlet-Triplet Splitting, ES-T (in electronvolts), and the Overlap Integral, SVar, Calculated for the Unconjugated Dinitrene Systems B′-E′ of Corresponding Conjugated Systems B-Ea basis set IGLO-III
IGLO-II
TZV
a
unconjugated dinitrenes
N-N distance (Å)
singlet-triplet gap, ES-T ) EBS - EHS (eV)
JY (cm-1)
JN (cm-1)
SVarb
B′ C′ D′ E′ B′ C′ D′ E′ B′ C′ D′ E′
9.358 11.689 14.056 16.517 9.358 11.689 14.056 16.517 9.358 11.689 14.056 16.517
-0.0021 -0.0014 -0.0016 -0.0014 -0.0011 -0.0003 -0.0004 -0.0004 -0.0027 -0.0002 -0.0008 -0.0011
-17.11 -11.45 -12.55 -11.29 -8.93 -2.36 -2.96 -3.35 -21.92 -1.70 -6.12 -8.68
-17.09 -11.45 -12.55 -11.29 -8.92 -2.36 -2.96 -3.35 -21.89 -1.70 -6.12 -8.68
0.00931 0.00030 0.00020 0.00000 0.00326 0.01405 0.00020 0.00000 0.00990 0.00045 0.00020 0.00000
Level of theory used is B3LYP. b SVar ) 〈φA|φB〉.
dinitrene systems concerned. The variation of J value with increase in conjugation in the dinitrenes is illustrated in a tabular form in Table 1 using IGLO-III, IGLO-II, and TZV basis sets. All conjugated dinitrenes exhibit AFM interaction (negative J value) irrespective of the basis sets used. In other words, we can say that the dinitrenes possess ground-state singlet characters that are well in accordance with the results obtained by Lahti and coworkers.26 The Ovchinnikov theorem27 for the groundstate determination of alternant hydrocarbons also predicts a spin quantum number of zero for each conjugated dinitrene. This, in turn, indicates that the systems are ground-state singlets. It has been observed that the conjugated systems have J values much higher than the dinitrene monomer. A close inspection of Table 1 reveals the fact that the AFM interaction, in general, decreases as we approach higher conjugated systems (increases the distance between the two radical centers) using IGLO-III, IGLO-II, and TZV basis sets with the only exception observed in the case of the largest system (E) using the IGLO-III basis set. In this context, it is to be noted that we have also compared the distance between two radical centers in each conjugated dinitrene (except that of E) obtained from the optimization with that of the work of Minato and Lahti.26 In both the cases, the N-N distances are almost equal for a particular dinitrene. The singlet-triplet splitting, that is, EBS - EHS, has also been determined, and it follows a similar trend as that of the J values. It is worth mentioning that the
difference in the numerical values of JY and JN are significant for each individual basis set. The reason behind this discrepancy is mainly attributed to the fact that the Noodleman formula is valid only for weak coupling limit, whereas Yamaguchi formalism adequately describes both strong as well as weak coupling. Moreover, the magnetic coupling constant values differ considerably with a change in the basis set, which reveals that the results are highly basis-set sensitive. An interesting observation is that the overlap integral values for the system E are unanimously zero for all of these basis sets, representing it as a diamagnetic species. Similar to the conjugated systems, the calculation of J values and other parameters, such as Svar. and singlet-triplet gap (EBS - EHS) for the corresponding unconjugated systems, is also carried out, except for the monomer for the same three basis sets (IGLO-III, IGLO-II, and TZV), as was done for the conjugated analog. The relevant data are presented in Table 2. The nature of magnetic interactions is found to be weakly AFM for all systems (B′-E′). For the IGLO-III basis set, an even-odd effect is observed in the JY and JN values, whereas for the other two basis sets, that is, IGLO-II and TZV, an almost monotonic decrease is observed, except for going from B′ to C′. Another interesting observation is the JY and JN values. Using all basis sets, the two J values for a particular unconjugated dinitrene remain almost unchanged, unlike those for the corresponding conjugated systems where a major difference between the J
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values is noticed. It is to be noted that in unconjugated systems, only the spacer part has been changed to saturated ones, keeping the two quinonoidal rings unaltered and thereby removing the conjugation. The “prime” notation for the unconjugated dinitrenes is used to differentiate them from their conjugated analogs. The singlet-triplet energy splitting has also been computed, and it has been observed that the relative stability of the singlet state to that of the triplet reduces to a considerable extent, which is also reflected in the J values. All of the above observations made in the present investigation highlight a radical change in the strength and nature of magnetic interaction between the electronic spins residing on the two N centers while going from conjugated to unconjugated systems. This in turn emphasizes the explicit role of π-conjugation. Remarkably, this π-conjugation plays a pivotal role in tuning the magnetic interactions in these conjugated dinitrenes. The spin density mappings for both the triplet and unrestricted singlet states in each dinitrenes given in the Supporting Information (Figures F1 and F2) also justify our prediction. A complete delocalization is observed in conjugated systems, whereas the densities are centered only on the two quinonoidal rings in the case of unconjugated systems. 4. Conclusions In summary, the BS-UDFT approach has been employed in some conjugated and unconjugated dinitrene systems to calculate the nature of magnetic interaction present in them. A strong AFM interaction exists in the conjugated systems, which significantly decreases in the case of unconjugated systems, and they become weakly AFM in nature. Interestingly, the strength of the magnetic interactions reduces appreciably as one increases the N-N distance or the spacer length. The results are highly basis-set-sensitive for the conjugated systems. The nature of magnetic interaction is very much influenced by the π-conjugation operating in such systems. This becomes quite evident when the magnetic interaction in the corresponding unconjugated systems is studied where a radical change of the same is observed. Acknowledgment. S.C. gratefully acknowledges the financial support from DST, Govt. of India (Under FIST Program) to purchase the Gaussian 03 program. P.S. thanks UGC, Govt. of India for the financial assistance. S.C. acknowledges the financial support (UPE Project) for providing us eight CPU cluster machines. We thank Department of Chemistry, University of Calcutta for the computational facility. Supporting Information Available: Spin density mapping for triplet and unrestricted singlet states of the dinitrenes. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Salem, L.; Rowland, C. Angew. Chem., Int. Ed. Engl. 1972, 11, 92.
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