Polyhedron 64 (2013) 172–180

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Polyhedron

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Manipulating the singlet–triplet energy gaps of arene-fused bis(1,2,3-dithiazoles):A computational study

Christos P. Constantinides, Theodosia A. Ioannou, Panayiotis A. Koutentis ⇑Department of Chemistry, University of Cyprus, P.O. Box 20537, 1678 Nicosia, Cyprus

a r t i c l e i n f o

Article history:Received 3 January 2013Accepted 26 March 2013Available online 4 April 2013

Dedicated to Prof. George Christou on theoccasion of his 60th birthday

0277-5387/$ - see front matter � 2013 Elsevier Ltd. Ahttp://dx.doi.org/10.1016/j.poly.2013.03.054

⇑ Corresponding author.E-mail address: koutenti@ucy.ac.cy (P.A. Koutentis

a b s t r a c t

Benzo- and azino-fused bis(1,2,3-dithiazoles) were investigated computationally using density functionaltheory (DFT) in an attempt to relate structure to ground state multiplicity preference. Structural changeson the central arene by substitution with electron donating (EDG) and electron withdrawing groups(EWG) or replacement of the central arene by pyridino or pyrazino rings, were studied by optimizingthe structures as singlet and triplet ground states. The aromaticity of each ring was probed using nucleusindependent chemical shift (NICS) calculations. Molecular orbital analysis identified the substituenteffects on the energy of the frontier orbitals. Calculations show that the ground state multiplicity canbe effectively controlled with strategic substitutions. EWG directly attached on the negative cyanine ofthe central arene stabilize zwitterionic singlet states whereas EDG attached at the same position favora triplet ground state. NICS calculations indicate that the central arenes sacrifice their aromaticity andbecome non-aromatic for molecules with zwitterionic ground states as an effective way to avoid theiroverall 4n p antiaromaticity.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Heteroatom radicals hold considerable potential in the design ofmaterials with electronic properties and, as such, have been the fo-cus of intense study [1]. A number of thiazyl radicals displayingmagnetic [2] and/or conductive [3] properties have been reported.In particular dithiazolyls (1,2,3- and 1,3,2-DTAs in Fig. 1) are a fer-tile ground for promising electronic materials owing to their re-duced inter-electron repulsion that leads to suppression of theirsolid-state dimerization [1b,e].

Historically, Mayer et al. made early progress on 1,2,3-DTAs inthe 80’s but this research was focused on their spectroscopic char-acterization [4] until the first stable crystalline derivatives weresynthesized by Oakley some 20 years later and interestingsolid-state properties were discovered [5]. The disproportionationenergy of the 1,2,3-DTAs was much lower than those reportedfor other thiazyl radicals indicating further enhancement of the pdelocalization and promising transport properties, however, these5-membered monocyclic radicals were more prone to dimeriza-tion. Nevertheless, 1D regular p stacks of 1,2,3-DTAs have been iso-lated but owing to the poor orbital overlap stemming fromslippage along the stacking direction, conductivity was of the orderof 10�6–10�7 S/cm [6]. Incorporation of selenium in place of the 2-sulfur resulted in bulk ferromagnetic ordering of bisthiaselenazolyl

ll rights reserved.

).

radicals with Tc of ca. 12–14 K denoting their potential as promis-ing materials for electronic devices [7].

The bis(1,2,3-dithiazoles) 1 was shown computationally to havea triplet ground state 5.1 kcal/mol more stable than the singletstate, however, Oakley and co-workers have synthesized the pyr-ido-fused bis(1,2,3-diathiazole) 2a (Fig. 2) that had a zwitterionicground state as supported by X-ray structure and calculations[8]. Similar zwitterionic singlets are also known with polyazaac-enes [9] and 1,2,4,5-tetrasubstituted benzenes [10]. These mole-cules avoid their ‘‘potential antiaromaticity’’ and hence a tripletground state, by partitioning their overall electronic system intotwo charge conjugated p subsystems (cyanines) which are struc-turally connected by r bonds but not electronically conjugated.Haas and Zilberg indicated that these molecules can be envisionedas the union of two odd electron radicals [11]. These zwitterionsare the result of an electron transfer from the donor to the acceptorradical subunit. This transfer will only take place if the donor andacceptor radicals have a low ionization potential and a high elec-tron affinity, respectively.

Zwitterionic biscyanines can be considered to combine the elec-tronic form of single carbenes and the structural motif of m-pheny-lene diradicals. Many theoretical and experimental studies oncarbenes and m-phenylene diradicals indicated that substituentscan influence their singlet–triplet energy gaps (DEST = SE � TE)and hence their ground state multiplicities [12]. To the best ofour knowledge, a broad computational study on fused 1,2,3-dithiazolyls has not been reported, but could identify structure–property-relationships (SPR) that can aid in the design of analogues

Fig. 1. 1,2,3- and 1,3,2-dithiazolyls.

Δ

Fig. 2. Bis(1,2,3-dithiazoles) 1 and the pyrido-fused bis(1,2,3-diathiazole) 2a.

Fig. 3. Selected fused bis(1,2,3-dithiazoles) for the DFT study. X and Y aresubstituents for compound 1 and are either electron donating (EDG) or electronwithdrawing (EWG) groups (see Table 1 for details).

C.P. Constantinides et al. / Polyhedron 64 (2013) 172–180 173

with desired electronic properties. Herein, we report how struc-tural changes, such as the direct introduction of substituents onthe cyanines and the modification of the central arene to hetero-azines, affects the ground state multiplicity of bis(1,2,3-dithiazoles)1 (Fig. 3).

2. Experimental

2.1. Computational procedure

The geometries of the triplet and open-shell singlet states ofmolecules 1–4 were fully optimized and analytical second deriva-tives were computed using vibrational analysis to confirm eachstationary point to be a minimum by yielding zero imaginary fre-quencies at the UB3LYP/6-31G(d) level of theory. Closed-shell sin-glet states were not calculated since previous studies have shownthat ground state zwitterionic singlets of polyazaacenes were con-taminated by low-lying higher multiplicity states [9]. Thereforeopen-shell singlet and triplet states were examined using spinpolarized density functional theory (UDFT). The reliable hybridB3LYP method [13] was employed for all the calculations using,however, a small basis set 6-31G(d) since the aim of this studywas to use qualitative results to draw conclusions on structure–property-relationships (SPR). Internal instabilities in the open-shell singlet wave functions of ground state zwitterions wereinvestigated using stability calculations. Where instabilities ap-peared the computations were repeated at the same level of theoryusing the broken symmetry (BS) approach. All the energies werecorrected after zero-point energies (ZPE) were scaled by 0.981[14]. All the above computations were performed using the GAUSS-

IAN 03 suite of programs [15].The lowest singlet and triplet states correspond to the energy

levels predicted by the Heisenberg spin-Hamiltonian H = �2JSaSb.The computationally determined spin-coupling constant J, de-scribes the effective exchange interaction between spin-carrier

sites. Positive values of J indicate a parallel alignment of spins ina triplet ground state and hence a ferromagnetic coupling mecha-nism while negative values of J designate antiparallel alignment ofspins in a singlet ground state and an antiferromagnetic exchangemechanism.

The broken symmetry (BS) approach [12e,f,16,17] is commonlyused for the calculation of singlet states of potential diradicalswhen they are spin-contaminated by higher multiplicity states.The BS approach provides lower energies for the singlet states. Incontrast triplet states show only a slight spin contamination[12e,f,16]. Spin-projected methods are employed to eliminateredundant spin contamination from the energy of the BS singletstates, however, these overestimate the stability of the pure singletstates. The true singlet energy lies between the spin-contaminatedand spin-projected singlet energies in a range of several kcal/mol[18]. Nevertheless, the BS approach is a powerful tool for the qual-itative description of the lowest singlet and triplet states of poten-tial diradicals. There are three spin-projected methods that differin their application ability, which depends on the degree of overlapbetween the magnetic orbitals. J(1) has been derived by Ginsberg[19], Noodleman [20] and Davidson [21] (GND) and is appliedwhen the overlap of the magnetic orbitals is sufficiently small.J(2) has been proposed by GND, Bencini [22] and Ruiz [23] and isused when the overlap is adequately large. Finally, J(3) has beendeveloped by Yamaguchi et al. [24], and reduces to the first andsecond spin-coupling constants J, in the weak and strong overlapregions, respectively (Scheme 1). When the spin-coupling con-stants J have small values close to zero but either positive or neg-ative then the singlet and triplet states are degenerate.Furthermore, when the overlap of the magnetic orbitals is weak(J(3) � J(1)) then there is no preference over the closed-shell singletand the triplet state and an open-shell singlet diradical might bethe ground state or alternatively there might be little coupling be-tween the unpaired electrons in a species regarded as two non-interacting doublets. The energy gap between the pure spin-pro-jected singlet and the UDFT triplets can be estimated as DEST = ThS2-

iJ given by Ginsberg [19], where ThS2i is the total spin angularmomentum for the triplet state and DEST = SE � TE. A positive split-ting denotes a triplet ground state.

3. Results and discussion

3.1. Total energies, spin-coupling constants and singlet–triplet gaps

The energies of the singlet and triplet states, the spin-couplingconstants (J), and the corresponding energy splittings (DEST) forstructures 1–4 are presented in Table 1 for the full optimizationsat the UB3LYP/6-31G(d) level of theory. The benzo fused linear sys-tem 1a (X = Y = H) was compared to the pyrido- 2b, 3 and pyrazi-no- 4 fused analogues. Furthermore, the substitution ofhydrogens (X = H, Y = H) on the parent system 1a by electrondonating (EDGs) and electron withdrawing groups (EWGs) wasstudied in an effort to manipulate DEST (Scheme 2).

Our calculations for structures 1–4 indicate that the spin con-taminations of the triplet states are low and the deviation fromthe expected value of 2.0 is at most 0.046. All the singlet wavefunctions are unstable denoting that even where the ground stateis a zwitterionic singlet, there is a strong influence of a low-lyingtriplet state. A closed-shell singlet wavefunction would have beeninadequate to describe a zwitterionic singlet ground state since wefound considerable amount of spin contamination in the open-shell zwitterionic singlets. Spin contamination for the singlet statesof structures 1–4 has a broader range of values which span from0.0458 to 0.974. The results from the optimizations indicate thatmost of the studied structures have either open-shell triplet

Scheme 1. Spin-projected methods used to eliminate spin contamination.

Table 1BS<S2>, T<S2>, J coupling and DEST (kcal/mol) values for structures 1–4 calculated at the B3LYP/6-31G(d) level of theory.

NSS

N NS

S

N

SS

N NS

S

N

NSS

N NS

S

. .. . . .

2b 3 4

..

SS

N NS

S

1a-q

X

Y

Structure X Y BS<S2> T<S2> J1 DE1ST J2 DE2

ST J3 DE3ST

1a H H 0.8138 2.0427 0.16 0.33 0.08 0.17 0.14 0.281b H CN 0.6527 2.0423 �2.06 �1.04 �1.52 �4.20 �2.12 �3.111c H Br 0.7904 2.0422 �0.17 �0.08 �0.14 �0.34 �0.17 �0.281d H Cl 0.7933 2.0427 �0.10 �0.05 �0.08 �0.21 �0.10 �0.171e OMe H 0.8236 2.0424 0.28 0.14 0.24 0.58 0.29 0.491f Me H 0.8222 2.0433 0.33 0.17 0.28 0.68 0.34 0.571g CN H 0.8244 2.0463 0.41 0.21 0.35 0.85 0.43 0.711h OH H 0.8346 2.0420 0.43 0.88 0.22 0.44 0.37 0.751i F H 0.8361 2.0416 0.46 0.23 0.39 0.94 0.47 0.801j Br H 0.8323 2.0433 0.53 0.27 0.45 1.09 0.55 0.931k Cl H 0.8329 2.0435 0.55 0.28 0.47 1.13 0.57 0.961l NH2 H 0.8415 2.0431 0.55 0.28 0.47 1.13 0.57 0.961m H Me 0.8371 2.0433 0.64 0.32 0.54 1.30 0.65 1.111n H F 0.8716 2.0424 1.02 0.52 0.97 2.09 1.05 1.841o H OMe 0.8729 2.0414 1.88 0.95 1.65 3.84 1.93 3.381p H OH 0.9328 2.0402 2.18 1.09 2.02 4.44 2.23 4.111q H NH2 0.9745 2.0370 3.04 1.53 2.94 6.20 3.12 5.982b – – 0.5379 2.0330 �4.19 �8.52 �2.11 �4.28 �2.86 �5.823 – – 0.7933 2.0388 �0.04 �0.08 �0.02 �0.04 �0.03 �0.074 – – 0.4583 2.0329 �4.82 �9.79 �2.42 �4.92 �3.13 �6.35

174 C.P. Constantinides et al. / Polyhedron 64 (2013) 172–180

Scheme 2. Substitution pattern for the parent fused bis(1,2,3-dithiazoles) 1a(X = Y = H).

C.P. Constantinides et al. / Polyhedron 64 (2013) 172–180 175

ground states or degenerate singlet and triplet states. The equalityof DE1

ST and DE3ST (weak overlap of magnetic orbitals) along with a

marginally positive value of ca. 0.28 kcal/mol for the parent struc-ture 1a indicates a degenerate singlet–triplet ground state. How-ever, upon substitution at either the positive or negativecyanines the triplet open-shell state stabilizes to different degreesdepending on the electronic nature of the substituent and the placeof substitution at the central benzene. When electron deficientgroups are placed on the positive cyanine (X = EWG) the effecton the singlet–triplet gap was minimal with DE3

ST taking valuesbetween +0.80 (X = F, 1i) and +0.96 kcal/mol (X = Cl, 1k). Evenwhen CH was replaced by N at the center of the positive cyanine,structure 3 possessed a degenerate singlet–triplet ground state(DE1

ST � DE3ST) as did the parent 1a. Interestingly, substitution

with electron donating groups (X = EDG) at the same position pro-vided similar numbers with DE3

ST between +0.49 (X = OMe, 1e)and +0.96 kcal/mol (X = NH2, 1l). Modifications directly on the po-sitive cyanine did not lead to dramatic changes demonstrating itslimited significance to the ground state multiplicity.

A reverse behavior is observed with substituents directly at-tached to the negative cyanine. The higher spin contamination inthe BS singlet states of structures 1o–q (0.872–0.974) indicate thatEDG groups (Y = EDG) destabilized the singlet states as theypushed electron density in the already electron rich negative cya-nine. These structures cannot avoid anymore their overall antiaro-maticity through the formation of the bicyanines and therefore theground states are triplets with DE3

ST of +3.38, +4.11 and +5.98 kcal/mol for 1o–q, respectively. Electron withdrawing groups (Y = EWG)help to stabilize the singlet states by reducing the electron densityon the negative cyanine. The structures avoid their antiaromaticitybut the effect is less since the DE3

ST are marginally negative for 1d(Y = Cl) and 1c (Y = Br) with �0.17 and �0.28 kcal/mol, respec-tively. Stronger EWGs have a more profound effect on stabilizingthe zwitterionic singlet states (e.g., DE3

ST = �3.11 kcal/mol for 1bY = CN). The replacement of CH by N at the center of the negativecyanine in structure 2b has the greatest impact on the singlet–trip-

Fig. 4. NICS diagram [ppm =

let gap (DE3ST = �5.82 kcal/mol) indicating the importance of this

position in controlling the ground state multiplicity of bis(1,2,3-dithiazoles). Worthy of note, is the pyrazino-fused bis(1,2,3-dithiazole) 4 that has the most stable zwitterionic singlet statewith DE3

ST = �6.35 kcal/mol.

3.2. Aromaticity considerations

The aromaticity of the central arene has a detrimental role onthe ground state multiplicities of structures 1–4. It has been previ-ously shown, that for polyazaacenes the aromaticity of the centralarene is sacrificed in favor of the formation of the two ‘‘double-bar-rel’’ zwitterionic bicyanines as an effective way for these moleculesto avoid their overall 4n p antiaromaticity [9]. Furthermore, Houkand co-workers, demonstrated with computational studies that byincreasing the size of the central arene to tetracene, it was possibleto create structures with nearly degenerate singlet and tripletstates [25]. The latter cannot sacrifice the aromaticity of four cen-tral benzene rings to create the biscyanines. Therefore the groundstate multiplicities and the DEST values was expected to followtrends based on aromaticity indices such as the nucleus indepen-dent chemical shifts (NICS).

NICS calculations are commonly used to probe aromaticityqualitatively by estimating the ring currents arising from the delo-calization of electrons. NICS can be diatropic (indication for aro-matic character), paratropic (antiaromatic) or estimate no ringcurrent (non-aromatic). Negative NICS indicate diatropic ring cur-rents and positive values paratropic ring currents. NICS values (inppm) are measured in the plane [NICS(0)], and above the planeat the center of each ring to estimate the local currents for eachindividual ring. While NICS(0) are often affected by the r electronsof neighboring bonds, the most accurate NICS values [NICS(1)] arethe ones measured 1 Å above plane where p electron density ismainly situated [26]. The NICS(1) value for antiaromatic cyclobut-adiene is +16.6 ppm and for aromatic benzene �4.1 ppm [27].

NICS calculations for structures 1–4 were performed at theB3LYP/6-31G(d) level of theory. To assess the aromaticity of eachof the three rings of the bis(1,2,3-dithiazoles) 1–4, diagrams corre-lating the NICS values (in ppm) versus the distance above each ringcenter f(r) (in Å) were constructed (Figs. 4 and 5). In these diagramsnegative minimums denote diatropic ring currents, while positivemaximums stand for paratropic and when negative NICS values ap-proach zero in an asymptomatic manner with increasing distance,then no ring current is present [28].

The outer 1,2,3-dithiazoles (rings A and C) for all studied struc-tures, have negative NICS values which become asymptomatic tozero on going from 0 to 10 Å above the ring center (Figs. 4 and

f(r)] for structures 1a–4.

Fig. 5. NICS diagram [ppm = f(r)] for structures 1a–q.

Fig. 6. NICS diagram [ppm = f(r)] for the monocyclic and benzo-fused 1,2,3-dithiazolyls.

Table 2Ground state C1–C2 and C4–C5 bond lenghts (A) and dipole moments (D).

C1

C2N

C4

C5C6S

SN N

S

S

. .

2b

..

C1

C2C3

C4

C5C6S

SN N

S

S

1a-q

X

Y

Structure X Y C1

la H H 1.4lb H CN 1.4lc H Br 1.4Id H CI 1.4le OMe H 1.4If Me H 1.4lg CN H 1.4lh OH H 1.4li F H 1.4lj Br H 1.4lk CI H 1.411 NH2 H 1.4lm H Me 1.4In H F 1.4lo H OMe 1.4lp H OH 1.4iq H NH2 1.42b – – 1.43 – – 1.44 – – 1.4

176 C.P. Constantinides et al. / Polyhedron 64 (2013) 172–180

5). These values are compared to the ones of the monocyclic 1,2,3-dithiazolyl and benzo-fused 1,2,3-dithiazolyl calculated at thesame level of theory (Fig. 6). The 1,2,3-dithiazole rings are non-aro-matic, in line with their 7p electron system. The fused benzene ringhas a NICS(1) value of �8.77 ppm and is formally more aromaticthan benzene (�4.1 ppm).

Structures 1a and 3, as already discussed in Section 3.1, havedegenerate singlet–triplet ground states. Their central arene rings(ring B) have negative NICS(1) values at ca. �6 ppm and a mini-mum in the [ppm = f(r)] diagram indicative of diatropic ring cur-rents and therefore aromatic character. In contrast, the centralrings of structures 2b (pyrido) and 4 (pyrazino), which have singletground states with DE3

ST of �5.82 and �6.35 kcal/mol, respec-tively, have weakly positive NICS(0) values, very weakly negativeNICS(1) values and an asymptomatic zero at higher distances,

C1

C2C3

C4

C5NS

S

N N

SS C1

C2N

C4

C5NS

SN N

S

S

. . . .

3 4

–C2 (Å) C4–C5 (Å) Dipole moment (D)

41 1.441 1.8139 1.439 5.9041 1.441 2.6641 1.441 2.9239 1.439 2.5439 1.439 2.4038 1.438 2.0341 1.436 2.2140 1.440 0.6541 1.441 1.0341 1.441 0.6837 1.437 3.0341 1.439 1.3539 1.439 2.9142 1.436 1.2930 1.440 2.1034 1.434 0.6577 1.477 5.4942 1.442 0.2072 1.472 4.04

C.P. Constantinides et al. / Polyhedron 64 (2013) 172–180 177

characteristic of non-aromatic rings. This result was in agreementwith their zwitterionic bis-cyanine ground states and the loss ofaromaticity in the central arene rings.

NICS calculations verify the importance of the pyridyl nitrogenposition on the ground state multiplicity of structures 2b and 3.Placing the nitrogen at the center of the positive cyanine did notalter the aromatic character of the central ring (c.f., 3), however,when nitrogen was at the center of the negative cyanine (c.f., 2)the central arene becomes non-aromatic. Substitution at the cen-tral fused benzene of structure 1 did not affect the non-aromaticityof the peripheral dithiazoles and interestingly, it did not cause sig-nificant changes to the aromatic character of the central ring(Fig. 5). Structure 1b (Y = CN) with a zwitterionic singlet groundstate (DE3

ST = �3.11 kcal/mol) has a central ring (�6.33 ppm) morearomatic than the corresponding ring (�5.02 ppm) of 1q (Y = NH2)which has a triplet ground state DE3

ST = +5.98 kcal/mol. This con-tradictory result is in line with previous observations by Fleisch-hauer et al., that there was no obvious relationship between theNICS and the DEST values [9e] and that NICS calculations provideonly qualitative results.

It was previously shown that the lateral C–C bond lengths,which connect the two cyanine units, gave a good indicationwhether the central ring is aromatic or non-aromatic [9–11]. Inthe charge separated zwitterionic ground states of polyazaacenesthe lateral C–C bong lengths were longer and had significant rcharacter reflecting the conversion of the arene to an anti-quinoidstructure in which resonance stabilization was mainly within thetwo separate cyanine units [9]. In contrast, for structures with trip-let ground states these C–C bonds were shorter and had bondlengths typical of aromatic benzene C–C bonds. For structures 1–4 the lateral C–C bond lengths of the ground states along withthe dipole moments are presented in Table 2. Structures 2b and4 with the zwitterionic single ground states have lateral C–C bondlength of ca. 1.47 Å and dipole moments of 4–5 D indicating thecharge redistribution and the formation of the cyanines. In con-trast, structure 1b, which had the largest dipole moment (5.9 D)

N N

Fig. 7. Qualitative correlation diagram of the benzo-fused bis(1,2,3-dithiazole)

and a singlet ground state, had shorter lateral C–C bonds (1.44 Å)compared to structures 2b and 4. This was in agreement with itsNICS(1) value of �6.33 ppm, that indicated a more aromatic char-acter for the central arene. For structure 1q, which has the tripletstate with the largest DE3

ST (+5.98 kcal/mol), the lateral C–C bondlengths were the shortest (1.43 Å) and closer to the expected 1.4 Åof aromatic benzene. The dipole moment of 1q is 0.65 D demon-strating that this structure did not possess a charge separatedground state.

3.3. Molecular orbital analysis

Other factors which influence the singlet–triplet energy gapsand hence the ground state multiplicities of these structures arethe SOMO–SOMO energy splitting (DESS) and their topological dis-tributions. Haas and Zilberg rationalized the origins of the zwitter-ionic ground states of 1,2,4,5-tetra-substituted benzenes in termsof the molecular orbitals of the 1,2,4,5-tetramethylenebenzene(TMB), a diradical for which no classical Kekulé structure can bewritten [11].

The correlation diagram of TMB is constructed by the molecularorbitals of two pentadienyl radicals containing 5p electrons each[29]. The p orbitals are connected via r bonds to form the TMBelectronic system. The two non-bonding molecular orbitals maybechosen so that they are disjoint i.e., do not have atoms in commonand the unpaired electrons can be confined to different sets ofatoms so that the coulombic repulsion energy from the electronsof opposite spins is minimized. These two orbitals have the sameenergy as there is no p electron density on the atoms that connectthe two 5p electron radical fragments. TMB a formally 10p aro-matic molecule decomposes into two separated 5p electron radicalunits with relatively long lateral C–C bonds connecting the twofragments.

When the two bonded fragments are nonequivalent the energyof the frontier orbitals change. The molecular orbitals of the benzo-fused bis(1,2,3-dithiazoles) can be constructed based on the TMB

SS S

S

1 constructed by the two non-equivalent 11p and 5p radical fragments.

Fig. 8. Frontier orbitals of ground state structures 1a–4 calculated at the B3LYP/6-31G(d) level of theory.

Table 3Energy levels (1ES and 2ES) and the energy gaps (DESS) of the SOMOs for the triplet states of molecules 1–4 at the B3LYP/6-31G(d) level of theory.

NSS

N NS

S

N

SS

N NS

S

N

NSS

N NS

S

. .. . . .

2b 3 4

..

SS

N NS

S

1a-q

X

Y

Structure X Y 1ES (au) 2ES (au) DESS (eV) DE3ST (kcal/mol)

1a H H �0.20906 17591 0.90 0.281b H CN �0.22492 18924 0.97 �3.111c H Br �0.21168 17959 0.87 �0.281d H CI �0.21277 18035 0.88 �0.171e OMe H �0.20785 17524 0.89 0.491f Me H �0.20641 17356 0.89 0.571g CN H �0.22268 19011 0.89 0.711h OH H �0.20924 17705 0.88 0.751i F H �0.21366 18185 0.87 0.801j Br H �0.21321 18098 0.88 0.931k CI H �0.21412 18196 0.88 0.961l NH2 H �0.20539 17379 0.86 0.961m H Me �0.20420 17273 0.86 1.111n H F �0.21062 18080 0.81 1.841o H OMe �0.19302 17048 0.61 3.381p H OH �0.19982 17601 0.65 4.111q H NH2 �0.18348 16858 0.41 5.982b – – �0.22102 18166 1.07 �5.823 – – �0.21645 18278 0.92 �0.074 – – �0.23085 18935 1.13 �6.35

178 C.P. Constantinides et al. / Polyhedron 64 (2013) 172–180

approach using two nonequivalent fragments; one 11p sulfur-substituted radical fragment (S) and one 5p imino-substitutedradical (N). The two non-bonding molecular orbitals and the anti-bonding molecular orbital are depicted in Fig. 7.

The S1�N1 molecular orbital has mostly N1 character withlarge atomic coefficients on the imino 5p radical fragment. Theantibonding orbital S2 + N2 is close in energy to the out-of-phasenon-bonding orbital S1�N1 and has more S2 character with largercoefficients on the sulfur 11p radical fragment. The neardegeneracy of these two orbitals can lead to a triplet ground state.A transfer of an electron from the donor 11p sulfur-substitutedradical fragment (S) to the acceptor 5p imino-substituted radical(N) subunit results in a 10p positive and 6p negative cyanines.

From the calculated frontier orbitals of the ground state struc-tures 1–4 at the B3LYP/6-31G(d) level of theory (Fig. 8) the SOMO1/HOMO is the S1�N1 non-bonding molecular orbital and theSOMO 2/LUMO is the antibonding S2 + N2 molecular orbital. It

should be noted that the SOMO 1/HOMO has a large atomic coef-ficient at the center of the negative 6p cyanine, as such, substit-uents directly attached to this position can significantly alter theenergy of this orbital. For example, the introduction of the elec-tronegative pyrido nitrogen on this position (structure 2b), stabi-lizes this orbital and opens up the energy gap of the frontierorbitals leading to pairing of electrons and therefore singletground state. In contrast, SOMO 2/LUMO has a node at the centerof the positive 10p cyanine and therefore any substituent at thisposition does not affect significantly its energy. For structureswith zwitterionic ground states such as 1b the two electronsare paired in a doubly occupied S1�N1 orbital which has nodesover the lateral C–C bonds. However, promotion of an electronfrom the S1�N1 orbital (HOMO) to the S2 + N2 orbital (LUMO)supplies the lateral C–C bonds with some p-bonding character(smaller bond lengths) as is evident from the atomic coefficientsover these bonds (Figs. 7 and 8).

C.P. Constantinides et al. / Polyhedron 64 (2013) 172–180 179

According to Hund’s rule the DEST should be inverse correlatedto the energy gap of the two SOMOs (DESS) [30]. The energy levels(1ES and 2ES) and energy gaps (DESS) of the two SOMOs for the trip-let states of structures 1–4 are presented in Table 3.

Hoffmann provided a rough empirical criterion based on ex-tended Hückel calculations on benzynes and diradicals which sug-gests that if DESS < 1.5 eV [31], the two non-bonding electrons willprefer to occupy different degenerate orbitals with a parallel-spinconfiguration to minimize their electrostatic repulsion leading totriplet states. We previously showed that triplet states for poly-azaacenes require DESS < 1.3 eV [9c] while Schreiner suggestedDESS < 0.9 eV for the ground state triplets for related compounds[9f]. Structure 1a with a DESS = 0.9 eV and degenerate singlet andtriplet states (DE3

ST = + 0.28 kcal/mol) was in agreement withSchreiner’s observation. A SOMO–SOMO splitting of 0.9 eV is thelimit where the singlet and triplet states are isoenergetic. DESS ofless than 0.9 eV would favor a triplet state as for example in struc-ture 1d (DESS = 0.41 eV and DE3

ST = + 5.98 kcal/mol) and DESS ofmore than 0.9 eV would lead to singlet ground states as in struc-ture 2 (DESS = 1.07 eV and DE3

ST = �5.82 kcal/mol).

4. Conclusions

The singlet and triplet states of the substituted benzo- 1a(X = Y = CH), pyrido- 2b, 3 and pyrazino- 4 fused bis(1,2,3-dithiaz-oles) have been studied using DFT calculations in combinationwith the BS approach and spin-projected methods. The calcula-tions show that the multiplicity of these molecules is determinedby their ability to form zwitterionic independent cyanines by sac-rificing the central arene aromaticity. NICS calculations show thatthe pyrido and pyrazino rings in molecules 2b and 4 readily sacri-fice their aromaticity to access the ‘‘double-barreled’’ biscyanineavoiding in this way their overall 4n p antiaromaticity and a tripletground state. The spatial distributions of the disjoint SOMO orbi-tals are another important factor for the determination of theground state multiplicity. The large atomic coefficient on the cen-tral atom of the negative cyanine possesses a high impact role onthe singlet–triplet gap contrary to the central atom of the positivecyanine which has a node. EWG attached to the center of the neg-ative cyanine of the parent system 1a stabilize the singlet states byremoving electron density from the electron rich cyanine, leadingto a drop in the energy of the SOMO 1 and therefore to the openingof the SOMO–SOMO energy splitting. EDG, attached at the sameposition, push electron density to the negative cyanine and raisethe energy of the SOMO 1 resulting in the degeneration of thetwo SOMOs and therefore to a triplet ground state. Strategic substi-tution on organic molecules with ‘‘double-barreled’’ zwitterionicbiscyanines offers an effective way to alter their ground state mul-tiplicity and therefore their electronic properties.

Acknowledgments

The authors thank the University of Cyprus (Medium SizedGrants), the Cyprus Research Promotion Foundation (Grant No.DPARH: TEXNO/0104/04) and the following organizations in Cy-prus for generous donations of chemicals and glassware: the StateGeneral Laboratory, the Agricultural Research Institute, the Minis-try of Agriculture and Biotronics Ltd. Furthermore, we thank theA.G. Leventis Foundation for helping to establish the NMR facilityin the University of Cyprus.

Appendix A. Supplementary data

Supplementary data associated with this article can be found, inthe online version, at http://dx.doi.org/10.1016/j.poly.2013.03.054.

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