Theoretical Investigation of Stilbene as Photochromic Spin Coupler

Article pubs.acs.org/JPCA

Theoretical Investigation of Stilbene as Photochromic Spin Coupler Arun K. Pal, Shekhar Hansda, and Sambhu N. Datta* Department of Chemistry, Indian Institute of Technology, Bombay, Powai, Mumbai 400076, India

Francesc Illas Department de Químcia Física & Institut de Química Teòrica I Computacional (IQTCUB), Universitat de Barcelona, C/Martí i Franqués 1, 08028 Barcelona, Spain S Supporting Information *

ABSTRACT: Density functional theory (DFT) based calculations are used here to investigate the magnetic behavior, spectroscopic transitions, and possible photomagnetic properties of stilbene derivatives using photochromicity of cis- and trans-forms of the parent molecule. Nitronyl nitroxide (NN), iminonitroxide (IN), tetrathiafulvalene cation (TTF), and verdazyl (VER) are used as monoradical centers at the p, p′ positions. The B3LYP functional with the usual broken symmetry approach and a sufficiently large basis set is chosen to obtain reliable estimates of the intramolecular exchange coupling constants (J). It is found that, with stilbene as a spacer, the coupling of TTF with NN, IN, and VER is always antiferromagnetic with J being generally large and negative. Although J values obtained for cis- and transforms are both negative, the difference in J values is quite large. Spectroscopic transition energies and corresponding oscillator strengths of cis- and transstilbene diradicals are estimated by time-dependent (TD)-DFT calculations using the same functional. Interestingly, the spectral features of the diradicals are similar to those of cis- and trans-stilbene, which suggests that stilbene diradicals would have good photoswitching properties. Finally, we show that, when these diradicals are placed in a matrix, photochromicity would be accompanied by a significant change in paramagnetic susceptibility.

I. INTRODUCTION The reversible transformation of a chemical species to its isomer and vice versa, under the absorption of light of two different frequencies, is known as photochromism.1 By irradiating a photochromic material, molecular and crystal geometries as well as physical properties of the material can be changed. This is important for designing photoswitchable chemical species. If a photoswitchable molecule is used as a spin coupler between two magnetic units, then the magnetism of the resulting species can change upon irradiation.2 Stilbene is a photochromic molecule: Cis-stilbene converts to trans-stilbene when exposed to light.3 This is schematically illustrated in Figure 1 where the experimental wavelength for cis-stilbene correspond to a solution in n-heptane at room temperature4 and that for trans-stilbene has been observed by Suzuki.5 A major part of research on organic molecular magnetism has been on the synthesis and characterization of nitronyl nitroxide (NN),6 imino nitroxide (IN),7 and verdazyl (VER).8 This is because these radical centers are stable at a relatively high temperature, are easily synthesized and have the ability to generate co-operative magnetic properties.9−17 Relatively less work has been done on the magnetic properties of a potent candidate, namely, the tetrathiafulvalene cation (TTF) that can be used as a building block for mixed diradical systems. It is a © 2013 American Chemical Society

strong electron donor, and its electronic properties have drawn attention from various fields of chemistry.18 In TTF, two routes of conjugation exist from the point of contact with the coupler to the lone π electron in the central carbon−carbon bond. A structural change such as the modification of the dihedral angle between the coupler and TTF planes can favor a specific route over the other, thereby changing the nature of coupling. In fact, Latif et al.19 have theoretically predicted photoswtiching magnetic properties of NN coupled to TTF via polyene spacers. The monoradical centers are illustrated in Figure 2. The aim of this work is to investigate the photomagnetic nature of diradicals resulting from coupling of two radical centers such as NN-TTF, IN-TTF and VER-TTF via cis- and trans-stilbene fragments as spacer. First, from our theoretical calculations we show that with stilbene spacer the diradicals formed from the interaction of TTF with NN, IN, and VER are all antiferromagnetically coupled. This observation can be accounted for by spin alternation rule20 that is illustrated in Figure 3. Second, we estimate spectroscopic transition energies and oscillator strengths for both cis- and trans-isomers of these Received: July 6, 2012 Revised: January 31, 2013 Published: February 19, 2013 1773

dx.doi.org/10.1021/jp306715y | J. Phys. Chem. A 2013, 117, 1773−1783

The Journal of Physical Chemistry A

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Figure 1. Photoconversion of stilbene isomers. Experimental wavelengths are from refs 4 and 5, whereas the calculated ones belong to the present work.

diradicals would be strongly photochromic. Third, though we do not find any evidence for spin crossover, we predict interesting changes in the paramagnetic properties of the solids of these compounds upon irradiation.

II. COMPUTATIONAL DETAILS The computational procedure adopted here is the same as that in ref 21, where it has been discussed in detail. In short, we use density functional theory (DFT) based calculations with the hybrid B3LYP functional and sufficiently large basis sets. All calculations are done using Gaussian 09 suite of programs.22

Figure 2. Structures of nitronyl nitroxide (NN), imino nitroxide (IN), verdazyl (VER), and tetrathiafulvalene cation (TTF) with which the diradicals are constructed. The point of contact with stilbene is indicated by −Stil.

diradicals in the singlet state. These are generally comparable to the spectral features of cis- and trans-stilbenes, with differences that can be easily explained. Therefore, we predict that the

Figure 3. Diradical systems with spin alternation rule. The shorter path in TTF is favored, as discussed in the text. 1774



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Figure 4. Structures of optimized geometries calculated at UB3LYP/6-311G(d,p) level. Legend: S stands for singlet and T is for triplet.

Both cis- and trans-stilbene have closed-shell singlet ground states that can be directly computed. The triplet−singlet gap is observed to be very large (≫ kT), and the species would be completely diamagnetic in their ground states. In the case of the open-shell singlet for the diradicals, the broken symmetry (BS) approach has been used.23−26 This is because the unrestricted Kohn−Sham formalism requires a single Slater determinant to describe the electron density of the “non-interacting” reference system, whereas the minimum acceptable wave function describing the open shell singlet involves a closed shell determinant (CS) and its doubly excited configuration (D) which are mixed either through configuration interaction (CI) or, preferably, through a complete active space self-consistent-field (CASSCF) calculation with two electrons and two orbitals defining the complete active space, usually denoted as CAS(2,2).25 The BS approach offers an avenue for calculating the magnetic coupling constant J from DFT based (and UHF) calculations as an energy difference and a suitable mapping between N-electron and spin states of the appropriate spin Hamiltonian.25

For a diradical, the spin Hamiltonian is usually written as

Hex = −2JS1·S2

(1)

when no magnetic field is present. The coupling constant thus defined can be calculated using the Yamaguchi expression26

J=

E BS − ET 2

⟨S ⟩T − ⟨S2⟩BS

(2)

where EBS is the total energy of the BS state and ET is the total energy of the triplet state. Expression 2 is equivalent to the mapping procedure described in detail by Moreira and Illas25 since, in most cases, the expectation values of the square of the total spin operator, ⟨S2⟩, are close to 2 and 1 for the triplet and broken symmetry states, respectively. However, in case of organic diradicals the expectation value for the BS state often deviates from 1 that corresponds to an exact 50% singlet and 50% triplet mixing, mainly because of the delocalization of the singly occupied orbitals. Then, the denominator in eq 2 allows one to take this effect into account. 1775



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Table 1. Total Energy and ⟨S2⟩ Values for Geometries Optimized at the B3LYP Level Using the 6-311G(d,p) Basis Set.a systems cis-stilbene trans-stilbene cis-NN-stilbene-TTF trans- NN-stilbene-TTF Cis-IN-stilbene-TTF trans-IN-stilbene-TTF cis-VER(C)-stilbene-TTF trans-VER(C)-stilbene-TTF

state

energy (a.u.)

⟨S2⟩

S T S T BS T BS T BS T BS T BS T BS T

− 540.825879 − 540.708335 − 540.841236 − 540.768335 −2896.663786 −2896.661388 −2896.672960 −2896.671160 −2821.466259 −2821.465931 −2821.475183 −2821.474979 −2738.975796 −2738.971870 −2738.985426 −2738.982831

0.000 2.052 0.000 2.052 0.758 2.070 0.748 2.077 0.914 2.025 0.904 2.028 0.583 2.033 0.604 2.037

All relevant molecular geometries are optimized using 6-311G(d,p) basis set. The singlet geometry optimization procedure led to a broken symmetry solution for every diradical. Because the exchange coupling constant ideally involves only spin degrees of freedom, the J value calculated from the optimized BS geometry would be compatible with the equilibrium geometry of the singlet and hence with Curie studies. Henceforth we will refer to this J as adiabatic or Curie-compatible coupling constant. In all present cases, the BS energy is more negative than the triplet energy, indicating intramolecular antiferromagnetic coupling. It is usual to evaluate the J value that is compatible with the one obtained from electron paramagnetic resonance (EPR) studies. To achieve this end, one normally considers a vertical transition and performs a single-point triplet calculation and a single-point BS calculation, both by employing the optimized geometry of triplet. This was also done here using the larger basis set 6-311++G(3df,3pd). This J will be called as vertical or EPR-compatible coupling constant. However, note that in the present case the adiabatic ground state is a singlet. Therefore, for the primary part of our discourse, we take the energy difference corresponding to the optimized geometries for each state at the B3LYP/6-311G(d,p) level as stated earlier. Relevant excitation energies and oscillator strengths are obtained from

J (cm−1)

−401 −297 −64.8 −40 −594 −397

a

The notations S, T, and BS stand for singlet, triplet, and broken symmetry, respectively, and J stands for the magnetic coupling constants calculated using energy differences at optimized geometries.

Table 2. Optimized Bond Lengths, Bond Angles, and Dihedral Angles for the Stilbene Isomers and Comparison with Other Calculated and Observed Data cis-stilbene B3LYP 6-311G(d, p) (our results) C1−C2 C2−C3 C3−C4 C4−C5 C5−C6 C6−C7 C7−C8 C3−C8 C4−H9 C5−H10 C6−H11 C7−H12 C8−H13 C2−H14 C1−C2−C3 C2−C3−C4 C3−C4−C5 C4−C5−C6 C5−C6−C7 C6−C7−C8 C3−C8−C7 C4−C3−C8 C3−C4−H9 C4−C5−H10 C5−C6−H11 C6−C7−H12 C7−C8−H13 C3−C2−H14 H15−C1−C2−H14 C16−C1−C2−C3

1.3345 1.4907 1.3999 1.3930 1.3931 1.3932 1.3930 1.3999 1.0844 1.0845 1.0842 1.0845 1.0844 1.0892 126.3 120.7 120.7 120.2 119.6 120.2 120.7 118.6 119.3 119.7 120.2 120.1 119.9 115.8 0.0 0.2

B3LYP/cc-pVDZ (ref 31)

trans-stilbene X-ray (ref 29)

Bond Length (in Å) 1.3511 1.334 1.4786 1.389 1.4088 1.398 1.3954 1.398 1.3993 1.398 1.3977 1.398 1.3962 1.398 1.4085 1.398 1.0906 1.0927 1.0924 1.0926 1.0933 1.0964 Bond Angles, deg 131.3 129.5 123.3 120.8 120.5 119.4 120.1 121.2 118.0 119.5 119.5 120.3 120.1 119.7 115.3 Dihedral Angles, deg 0.0 0.0 1776

B3LYP 6-311G(d, p) (our results) 1.3449 1.4653 1.4069 1.3882 1.3959 1.3923 1.3911 1.4051 1.0835 1.0845 1.0840 1.0844 1.0853 1.0869

B3LYP/cc-pVDZ (ref 31) 1.3508 1.4677 1.4096 1.3957 1.3970 1.4007 1.3930 1.4114 1.0934 1.0925 1.0922 1.0926 1.0915 1.0949

127.2 123.6 121.0 120.5 119.4 120.1 121.4 117.7 120.0 119.6 120.3 120.1 119.6 114.1

127.2 118.7 121.4 120.1 119.4 120.5 120.9 117.7 119.0 119.8 120.4 119.9 119.1 118.7

180.0 180.0

180.0 180.0

X-ray (ref 30) 1.326 1.471 1.392 1.384 1.381 1.383 1.381 1.397

126.4 119.0

117.8



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Table 3. Selected Important Dihedral angles of cis- and trans-Forms of the Diradicals

Table 5. Calculated TDDFT (B3LYP/6-311++G(d,p)) Vertical Excitation Energies (in eV) and Oscillator Strengths (f) of cis-Stilbenea

(stilbene)C−C−(TTF)C−S dihedral angle (deg)

CASPT236

this work

experimental4

systems

BS

triplet

eV

f

eV

f

eV

cis-NN-stilbene-TTF trans-NN-stilbene-TTF cis-IN-stilbene-TTF trans-IN-stilbene-TTF cis-VER(C)-stilbene-TTF trans-VER(C)-stilbene-TTF

33.7 33.4 31.5 30.5 33.7 33.0

28.7 27.1 29.7 27.8 22.8 25.9

5.23 5.61 5.73 5.88 5.94 6.04 6.22 6.31 6.58 6.68 6.75 6.93 7.00

0.000 0.034 0.011 0.012 0.015 0.012 0.131 0.159 0.027 0.216 0.534 0.122 0.313

4.11 4.45 4.61 5.46 5.56 5.61 5.78 5.96 6.00 6.00 6.03 6.09 6.18

0.007 0.004 0.334 0.406 0.007 0.118 0.013 0.029 0.057 0.266 0.005 0.001 0.002

4.48 5.54

Table 4. Broken Symmetry Energies and Coupling Constants of Diradicals from Single-Point UB3LYP Calculations Using 6-311++G(3df,3pd) Basis Set and Optimized Triplet Geometry system cis-NN-stilbene-TTF trans-NN-stilbene-TTF cis-IN-stilbene-TTF trans-IN-stilbene-TTF cis-VER-stilbene-TTF trans-VER-stilbene-TTF

ET in a.u. (⟨S2⟩)

EBS in a.u. (⟨S2⟩)

−2896.814092 (2.068) −2896.823734 (2.075) −2821.611328 (2.027) −2821.620383 (2.029) −2739.113037 (2.035) −2739.124227 (2.039)

−2896.815399 (0.852) −2896.824408 (0.818) −2821.611315 (0.974) −2821.620229 (0.964) −2739.114129 (0.773) −2739.124370 (0.778)

JY (cm−1) −236

6.14

a

CASPT2/VDZP estimates and experimental data are included for comparison.

−118

Table 6. Calculated TDDFT (B3LYP/6-311++G(d,p)) Vertical Excitation Energies (in eV) and Oscillator Strengths ( f) of trans-Stilbenea

2.66 31.7

CASPT237

this work

−191 −24.9

experimental

eV

f

eV

f

eV

f

3.85 4.47 4.50 5.03 5.62 6.22 6.30 6.50 6.64 6.92 7.00 7.27

0.900 0.031 0.000 0.216 0.006 0.052 0.377 0.031 0.064 0.303 0.040 0.272

3.77 4.07 4.13 4.95 5.30 5.42 5.42 5.46 5.95

0.038 0.723 0.000 0.000 0.000 0.117 0.371 0.019 0.524

4.22b, 4.00c

0.740c

5.43b, 5.4c

0.29c

6.15b

0.14c

a

CASPT2/VZP estimates and experimental data are included for comparison. bReference 5. cReference 34.

Figure 5. Schematic representation of E(BS) and E(T) as function of molecular geometry (x-axis): (a) trans-IN-stilbene-TTF, (b) cis-VERstilbene-TTF. Case (a) shows BS is higher in energy for vertical transition from the optimized triplet while the BS (or the singlet) equilibrium appears at a lower energy. Energy differences are in unit cm−1. Case (b) shows the general trend for NN-TTF and VER(C)TTF diradicals.

III. RESULTS AND DISCUSSION Equilibrium Optimized Geometries. Singlet and triplet geometries are optimized for the unsubstituted stilbene isomers. For the diradicals, triplet geometries are optimized, while the singlet geometry optimization leads to optimized BS geometries. The optimized structures are shown in Figure 4. All geometry optimization are carried out using 6-311G(d,p) basis set. The optimized structure of cis-stilbene is approximately planar with C2 point group whereas trans-stilbene turns out to be completely planar with C2h symmetry. Computed total energies and ⟨S2⟩ values are given in Table 1. The closed shell determinant singlet state defines the electronic ground state for both stilbene isomers. From the optimized geometries of cis- and trans-isomers, we find all bond lengths, bond angles, and dihedral angles (reported in Table 2) to be more or less comparable to the X-ray crystallographic data29,30 and also to previously reported B3LYP/cc-PVDZ calculations.31

the time-dependent (TD)-DFT calculation on the singlet species by using RB3LYP/6-311++G(d,p) computational setup. Before closing this section it is worth mentioning that the magnitude of the exchange coupling constant is known to depend significantly on the choice of the exchange-correlation functional.27,28 A comparison of the calculated values predicted by different functionals has also been carried out, and the results are included in Supporting Information as Tables S1, S2, and S3. We stress that the hybrid B3LYP functional with a large basis set has been known to yield qualitatively good magnitudes for the exchange coupling constant as compared to the experiment. Besides, the conclusions reached in this work rely on the sign of J and the differences in the values of J between isomers, and these are less likely to be affected by the exchangecorrelation potential. 1777



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Figure 6. UV−visible plots of cis- and trans-stilbene isomers from TDDFT calculations using RB3LYP method with 6-311++G(d,p) basis set.

would leave mark on the change in paramagnetic property of an ensemble of these diradicals on photoconversion at room temperature. Of course, the fractional change would be less prominent between the IN-TTF diradicals. Spin Alternation. The intramolecular antiferromagnetic coupling predicted by the B3LYP/6-311G(d,p) calculations can be justified by spin alternation rule20 (Figure 3) where for spin propagation to the unpaired electron in TTF we select the shorter path (through S) and not the longer path (through −C−S−). The reason for this has been explained in ref 19: a dihedral angle equal to about 35° makes one of the nonbonding orbitals of each sulfur atom in TTF almost parallel to the π framework of stilbene, but the carbon pz orbital deviates from the parallel position. This makes the shorter route more favorable for spin wave propagation. The longer path is favored by a zero dihedral angle, but it causes a mismatch in conjugation through the next sulfur. Since all of the dihedral angles are considerably large and in fact close to 35° in the BS state (Table 3), the shorter path is active in spin propagation. This is the reason for the antiferromagnetic coupling within each diradical. In fact, as noticed in ref 19, the sign and magnitude of J is sensitive to the dihedral angle subtended by TTF to the coupler. This indicates a very strong competition between the spin flows along the two possible paths in TTF. Table 3 shows that the dihedral angles in the BS state of the IN-TTF diradical are relatively small. This leads to a reduced coupling constant for these species as indicated in Table 1. The vertical J values reported in Table 4 are significantly reduced to the extent that for cis-IN-stilbene-TTF and trans-INstilbene-TTF the coupling constant becomes almost zero and small positive, respectively. Table 3 shows that the dihedral angle considerably deviates from 35° in the triplet state. This explains the reduced intramolecular antiferromagnetic nature in Table 4 for all diradicals, as the triplet geometry is used in both triplet and BS calculations. Spectroscopic Transitions. The absorption spectrum for cis-stilbene in n-heptane at room temperature was studied by Beale and Roe4 and that for trans-stilbene was examined by Suzuki.5 In 3-methylpentane, one-electron absorption spectrum of trans-stilbene was investigated by Hohlneicher and Dick34 and Gudipati et al.35 Molina et al.36,37 made an extensive computational study on cis- and trans-stilbene and compared their results with the experimental measurements of Beale et al.4 for cis-stilbene and those of Hohlneicher et al.34 for trans-stilbene.

Two main observations from Table 1 are as follows. First, the trans-form is lower in energy than the cisform for all the species in each spin statesinglet, triplet, and BS. Second, the singlet is always more stable than the triplet in bare stilbenes, and the BS states are more stable for the diradicals. It transpires that the actual ground states of the diradicals are in fact open shell singlets. These can be described by linear combinations of the CS and D determinants as discussed in the previous section. The methyl groups in NN have almost free rotation. The local symmetries of the cis- and trans- diradicals are C2 and C2h respectively. The important dihedral angles of cis- and trans-forms of NNstilbene-TTF, IN-stilbene-TTF, and VER-stilbene-TTF are given in Table 3. The calculated magnetic coupling constants (J) are reported in Table 1. All coupling constants are negative, in agreement with spin alternation rule as illustrated in Figure 3. The Yamaguchi eq 2 is applied to evaluate the magnetic coupling. It takes care of the error in energy difference due to spin contamination. However, the spin contamination is not taken into account while the geometry is optimized. This casts some doubt on the validity of the optimized BS geometry, particularly for the NN-TTF and VER(C)-TTF diradicals where the BS solutions show significant spin contamination. Kitagawa et al. have addressed this issue and presented a geometry optimization method based on Yamaguchi’s approximate spin projection procedure.32 In this context, we show in Table 4 the energy values obtained from single point calculations using the much larger basis set 6-311++G(3df,3pd) and the optimized triplet geometry. The calculated J values in Tables 1 and 4 are generally of the same order. They also retain the same sign except for the cisand trans-isomers of IN-stilbene-TTF. The sign difference of the calculated J for the IN-stilbene-TTF isomers in these two tables is schematically illustrated in Figure 5 where the BS−T energy difference is shown to be small and of different signs at the two (T and BS) optimized geometries. It is also of interest to note that Malrieu and Trinquier have recently suggested a method to obtain the singlet geometry from calculated BS geometry33 and have explained the situation by using a similar illustration for the energy curves. Although both cis- and trans-forms of all diradicals have negative values of adiabatic J and hence intramolecular antiferromagnetic coupling, the difference between the J values for the cis and trans isomers are 104 cm−1 for NN-TTF, 25 cm−1 for IN-TTF, and 197 cm−1 for VER(C)-TTF diradicals, respectively. This 1778



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In this work, we first use TD-DFT to calculate the transition energies for the cis- and trans-stilbene isomers which have closed shell ground states, and then explore the possibility of using this methodology to estimate the transition energies of the geometrical isomers of the diradicals with stilbene as coupler. However, most of the diradicals exhibit an open-shell singlet ground state which implies some caution as discussed later. The experimentally observed n−π*, π−π*, and σ−σ* transition energies are 4.48, 5.54, and 6.14 eV for cis-stilbene, respectively,4 and 4.22, 5.43, and 6.15 eV for trans-stilbene.5 Somewhat smaller values were found by the CASPT2 calculations of Molina et al.36,37 Tables 5 and 6 show the transition energies and oscillator strengths calculated for the stilbene isomers by the RB3LYP methodology. It is easy to notice that the average error of TDDFT excitation energy is always less than the error calculated from the CASPT2 calculations, except in the case of the n−π* transitions of cisstilbene. In addition, the transitions of cis-isomer are of low intensity and that of trans-isomer are highly intense, which is in agreement with experiment. The TDDFT calculations show the n−π* transition of cis-stilbene at somewhat higher energy (5.2 eV) and that for trans-stilbene at lower energy (3.85 eV) compared to the experimental data.4,5,34 The calculated π−π* transitions are found in the range 5.6−5.9 eV (for cis-) and 5.0−5.6 eV (for trans-) and are moderately intense in both cases. The σ−σ* transitions are found at ≥6.0 eV for the cisform and ≥6.2 eV for the trans-isomer. The simulated spectra of cis- and trans-stilbene are given in Figure 6. Stilbene is a stable system as there is delocalization of π-electrons between two phenyl rings. By addition of two monoradicals at the positions (p,p′), the π-electron delocalization becomes more extensive which leads to an increased number of π and π* states with a concomitant broader band for transitions involving these orbitals. This leads to a red shift accompanied by a large increase in intensity. To check these trends, we have used TDDFT to estimate the excited states of the corresponding diradicals. However, TDDFT is based on a closed shell reference state (which is the ground state for a closed shell species) while Table 1 shows that the electronic ground state of each diradical is an open shell singlet. Therefore, TDDFT calculations on the diradicals must correspond to transitions from a closed shell excited state. Hence these transitions are expected to show not only increased band widths and oscillator strengths but also an extra large red shift. The additional largeness of TDDFT red shift owes its origin to the energy difference between the TDDFTmodified CS state and the ground state. Table 7 gives the TDDFT excitation energies for all diradical isomers. The simulated spectra are reproduced in Figure 7. Clearly, the calculated n−π* and π−π* band gaps are smaller than those of the parent molecule by several electron volts (Table 7 versus Tables 5 and 6; Figure 7 compared to Figure 6). The absorption coefficients also show an interesting trend. The mixing of the charge transfer transitions involving the two resonating N−O groups with the n−π* and π−π* transitions increases the total intensity of these transitions by several fold for NN-TTF diradicals, while the IN-TTF and VER(C)-TTF diradicals exhibit only a moderate amount of increase in the overall absorption intensity. This is easily found from a comparison of Figure 6 with Figure 7. Thus each diradical derivative shows similar but red-shifted transitions with greater bandwidth and moderate to large increase in intensities. In spite of the calculated extra large red shift, the

Table 7. TDDFT Excitation Energies (eV) and Oscillator Strength ( f) of Diradical Derivatives of cis- and trans-Stilbenea eV

F

Cis-NN-stilbene-TTF 1.40 0.232 2.12 0.228 2.90 0.471 3.37 0.039 3.63 0.220 3.95 0.118 4.01 0.103 4.32 0.086 4.40 0.245 4.73 0.060 4.92 0.023 5.08 0.005 5.16 0.103 Cis-IN-stilbene-TTF 0.94 0.057 1.93 0.037 2.29 0.061 2.51 0.018 3.31 0.859 3.88 0.145 3.91 0.084 4.05 0.034 4.43 0.206 4.65 0.096 4.75 0.093 4.88 0.059 4.96 0.011 Cis-VER(C)-stilbene-TTF 1.13 0.182 1.96 0.197 2.47 0.056 3.14 0.654 3.78 0.014 3.88 0.093 4.07 0.140 4.37 0.017 4.49 0.038 4.59 0.209 4.61 0.146 4.84 0.030 4.99 0.054 5.12 0.039 a

eV

f

Trans-NN-stilbene-TTF 1.03 0.131 1.81 0.132 2.09 0.076 2.66 0.015 3.04 1.889 3.31 0.016 3.64 0.038 3.84 0.083 3.97 0.171 4.21 0.060 4.61 0.059 4.87 0.047 4.97 0.034 Trans-IN-stilbene-TTF 0.86 0.109 1.95 0.001 2.13 0.139 2.61 0.020 3.20 1.769 3.32 0.090 3.93 0.069 4.02 0.028 4.38 0.029 4.61 0.088 4.75 0.016 4.86 0.003 4.96 0.000 Trans-VER(C)-stilbene-TTF 1.86 0.002 2.10 0.217 2.38 0.028 3.09 0.167 3.13 1.763 3.55 0.019 3.79 0.019 3.90 0.006 3.99 0.156 4.26 0.029 4.60 0.035 4.68 0.082 4.84 0.025 4.98 0.000

The basis set used is 6-311++G (d,p).

n−π* and π−π* transitions are still energetic enough to cross the activation barrier that is known to be about 0.15 eV only,38 and the diradicals are certainly photochromic. Paramagnetic Effects. The cis⇌trans interconversion is accompanied by a change in molecular geometry. For pure Stilbene, the change is not considerably large. For the diradicals, however, the change is rather drastic owing to the requirement of repositioning the radical centers. A pure solid of any of the diradicals may not be photochromic because of lattice rigidity. Thus, the diradical interconversion that can easily occur in gas phase and in solvent medium, can also happen in a gel matrix or a somewhat disordered solid but not so easily in an ordered crystal without causing a phase change. In any case, the intermolecular magnetic interaction is expected to be weak. 1779



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Figure 7. UV−visible plots of cis- and trans-forms of diradicals from TDDFT calculations.

where μS is the spin magnetic moment, μS = ℏ−1geβS, ge is the EPR g factor, β is the Bohr magneton, and B is the applied magnetic field. For a canonical ensemble of N molecules per unit volume (cm3) in thermal equilibrium, the magnetic susceptibility is given by the celebrated Bleaney−Bowers equation,40

Each diradical has a thermal ground state that represents an equilibrium between the diamagnetic and paramagnetic forms. The triplet-singlet energy gap is quite small, especially for the IN-stilbene-TTF isomers. It is well-known that in such cases a temperature-dependent paramagnetism can be observed.39−41 Therefore, the substances in condensed phase, whether photoswitchable or not, are expected to be paramagnetic at ordinary temperatures, in contrast with substances having diamagnetic ground states and a large T-S energy gap. For the diradical system, the spin Hamiltonian in a magnetic f ield can be written as Hspin = Hex − μS ·B

χ=

2Nμ12 /kT 3 + e−2J / kT

(4)

This gives the molar susceptibility χM =

(3) 1780

3.00067 (3 + e−2.8773J / T )T

(5)



Article

Figure 8. Variation of paramagnetic susceptibility with temperature for J equal to (a) 594, (b) 401, (c) 397, (d) 297, (e) 65, and (f) 40 cm−1, (g) zero J, and (h) infinitely large J. Plots of χM versus T and 1/χM versus T are familiar in the study of single-center paramagnetism, especially in solid state physics. Plots of χMT versus T and χM versus 1/T are useful to study the Bleany−Bowers equation, for spin crossover complexes of inorganic chemistry and organic diradicals.

where J is in cm−1 and T is in Kelvin. Note, however, that even if J corresponds to magnetic coupling within the diradical as in Tables 1 and 4, the magnetic susceptibility arises from the contribution of the total magnetic moment of the isolated diradicals in the triplet state neglecting intermolecular coupling which will be very weak due to the distance between the diradicals in such ensemble. The dimensions of the molar susceptibility in eq 5 are cm3 mol−1 and is in the 0.75/T ≤ χM ≤ 1/T when J ≥ 0 and 0 ≤ χM ≤ 0.75/T when J ≤ 0. The temperature dependence of susceptibility for these diradical solids is illustrated in four different ways in Figure 8. The χM versus T and 1/χM versus T plots are familiar in singlecenter paramagnetism of solid state physics.42 For diradicals, χMT versus T and χM versus 1/T plots are quite common.42 The χM versus 1/T plot for J = 0 is a straight line passing through the origin (line g in Figure 8) and with slope about 0.75. For a negative J (intramolecular antiferromagnetic coupling), χM initially increases with 1/T along the straight line (g), but the slope decreases with increasing 1/T so that the curve reaches a maximum and finally approaches the 1/T axis in an asymptotic manner. The decrease of χM as T decreases is due to a reduced population of the triplet state at lower temperatures. For a positive J (intramolecular ferromagnetic interaction), molar susceptibility initially increases with 1/T along the straight line (g). Nevertheless, the slope increases as 1/T increases, and finally the slope approaches about 1.0 and the plot becomes parallel to line (h); (this is not shown in Figure 8). The calculated room temperature susceptibilities are given in Table 8. These are quite large, of the order of 10−4 to 10−3 cm3 mol−1. Normally inorganic complexes of rare earths have χM of the order of 10−5 cm3 mol−1. In contrast, Rajca found χM about 3.3 × 10−3 emu mol−1 for mixed diamagnetic-paramagnetic organic diradicals at room temperature. Thus, the calculated susceptibilities

Table 8. Molar Susceptibility for Paramagnetic Solids at Room Temperature as Obtained from Eq 5 Using the J Values Reported in Table 1 systems

χM (10−3 cc mol−1)

ΔχM (10−4 cc mol−1)

cis-stilbene(TTF-NN) trans-stilbene(TTF-NN) cis-stilbene(TTF-IN) trans-stilbene(TTF-IN) cis-stilbene(TTF-VER) trans-stilbene(TTF-VER)

0.20 0.49 2.17 2.25 0.03 0.21

2.9 0.8 1.8

are somewhat smaller than those for organic diradicals with triplet ground states. The calculated susceptibilities, however, show a substantially large change on photoconversion (of the order of 10−4 cm3 mol−1). The implication is that these species would exhibit a pronounced photomagnetic behavior.

IV. CONCLUSIONS We have used DFT based calculations with the hybrid B3LYP exchange correlation functional and large basis sets to examine the electronic structure of cis- and trans-stilbene and of three pairs of diradicals that are cis- and trans- forms of NN-stilbeneTTF, IN-stilbene-TTF, and VER(C)-stilbene-TTF. For the diradicals, the exchange coupling constants J have been obtained through the well-known broken symmetry approach. At the B3LYP/6-311G(d,p) level, all diradicals are found to have intramolecular antiferromagnetic coupling but with noticeably large differences in the magnitude of J between the cis- and trans- isomers, especially for the first and third pairs of diradicals. The spin wave propagation takes the shorter route in TTF which is responsible for the intramolecular antiferromagnetic coupling. The J values would be valid for Curie studies which involve a thermal equilibrium between singlet and triplet states. 1781



Article

M. Photoswitching of Intramolecular Magnetic Interaction Using Diarylethene with Oligothiophene π-Conjugated Chain. J. Org. Chem. 2001, 66, 8799−8803. (3) Dou, Y.; Allen, R. E. Detailed Dynamics of a Complex Photochemical Reaction: Cis−trans photoisomerization of stilbene. J. Chem. Phys. 2005, 119, 10658−10666. (4) Beale, R. N.; Roe, E. M. F. Ultra-violet Absorption Spectra of Trans- and Cis-Stilbenes and their Derivatives. Part I. Trans- and CisStilbenes. J. Chem. Soc. 1953, 116, 2755−2763. (5) Suzuki, H. Relations between Electronic Absorption Spectra and Spatial Configurations of Conjugated Systems. V. Stilbene. Bull. Chem. Soc. Jpn. 1960, 33, 379−388. (6) (a) Romero, F. M.; Ziessel, R.; Bonnet, M.; Pontillon, Y.; Ressouche, E.; Schweizer, J.; Delley, B.; Grand, A.; Paulsen, C. Evidence for Transmission of Ferromagnetic Interactions through Hydrogen Bonds in Alkyne-Substituted Nitroxide Radicals: Magnetostructural Correlations and Polarized Neutron Diffraction Studies. J. Am. Chem. Soc. 2000, 122, 1298−1309. (b) Caneschi, A.; Ferraro, F.; Gatteschi, D.; Lirzin, A. L.; Rentschler, E. Ferromagnetic Intermolecular Coupling in the Nitronyl Nitroxide Radical 2-(4-thiomethylphenyl)-4,4,5,5-tetramethylimidazoline-1-oxyl-3-oxide, NIT(Sme)Ph. Inorg. Chim. Acta 1995, 235, 159−164. (7) (a) Lescope, C.; Luneau, D.; Rey, P.; Bussiere, G.; Reber, C. Synthesis, Structures, and Magnetic and Optical Properties of a Series of Europium(III) and Gadolinium(III) Complexes with Chelating Nitronyl and Imino Nitroxide Free Radicals. Inorg. Chem. 2002, 41, 5566−5574. (b) Oshio, H.; Watanabe, T.; Ohto, A.; Ito, T. A OneDimensional Helical Copper(II) Imino Nitroxide. Inorg. Chem. 1997, 36, 1608−1610. (8) (a) Gilroy, J. B.; McKinnon, S. D. J.; Kennepohl, P.; Zsombor, M. S.; Ferguson, M. J.; Thompson, L. K.; Hicks, R. G. Probing Electronic Communication in Stable Benzene-Bridged Verdazyl Diradicals. J. Org. Chem. 2007, 72, 8062−8069. (b) Lemaire, M. T.; Barclay, T. M.; Thompson, L. K.; Hicks, R. G. Synthesis, Structure, and Magnetism of a Binuclear Cobalt(II) Complex of a Potentially Bis-tridentate Verdazyl Radical Ligand. Inorg. Chim. Acta 2006, 359, 2616−2621. (9) (a) Ullman, E. F.; Boocock, D. G. B. “Conjugated” NitronylNitroxide and Imino-Nitroxide Biradicals. J. Chem. Soc., Chem. Commun. 1969, 20, 1161−1162. (b) Ullman, E. F.; Osiecki, J. H.; Boocock, D. G. B.; Darcy, R. Stable Free Radicals. X. Nitronyl Nitroxide Monoradicals and Biradicals as Possible Small Molecule Spin Labels. J. Am. Chem. Soc. 1972, 94, 7049−7059. (10) Castell, O.; Caballol, R.; Subra, R.; Grand, A. Ab Initio Study of Ullman’s Nitroxide Biradicals. Exchange Coupling versus Structural Characteristics Analysis. J. Phys. Chem. 1995, 99, 154−157. (11) Barone, V.; Bencini, A.; Matteo, A. Intrinsic and Environmental Effects in the Structure and Magnetic Properties of Organic Molecular Magnets: Bis(imino)nitroxide. J. Am. Chem. Soc. 1997, 119, 10831− 10837. (12) Vyas, S.; Ali, Md. E.; Hossain, E.; Patwardhan, S.; Datta, S. N. Theoretical Investigation of Intramolecular Magnetic Interaction through an Ethylenic Coupler. J. Phys. Chem. A 2005, 109, 4213−4217. (13) Fischer, P. H. H. LCAO-MO Calculations on Verdazyls. Tetrahedron 1967, 23, 1939−1952. (14) Markovsky, L. N.; Polumbrik, O. M.; Nesterenko, A. M. Quantum-Chemical Investigation of Spatial and Electronic Structure of Verdazyl and its Derivatives. Int. J. Quantum Chem. 1979, 16, 891− 899. (15) Green, M. T.; McCormick, T. A. Controlling the Singlet− Triplet Splitting in Bisverdazyl Diradicals: Steps toward Magnetic Polymers. Inorg. Chem. 1999, 38, 3061−10. (16) Ciofini, I.; Daul, C. A. DFT Calculations of Molecular Magnetic Properties of Coordination Compounds. Coord. Chem. Rev. 2003, 238, 187−209. (17) (a) Takui, T.; Sato, K.; Shiomi, D.; Ito, K.; Nishizawa, M.; Itoh, K. Magnetic Coupling of Nitronyl Nitroxide-based Biradical Salts. Synth. Met. 1999, 103, 2271−2272. (b) Romero, F. M.; Ziessel, R.; Bonnet, M.; Pontillon, Y.; Ressouche, E.; Schweizer, J.; Delley, B.; Grand, A.; Paulsen, C. Evidence for Transmission of Ferromagnetic

The excitation characteristics of the diradicals have been studied using TD-DFT at the B3LYP/6-311++G(d,p) level. These calculations agree with the expected trends of red shift, increased bandwidth, and increased absorption intensity and predict that the diradical isomers are strongly photochromic. From examination of paramagnetism for a canonical ensemble of the diradicals, we conclude that photochromicity would accompany a considerable change of magnetization in the condensed phase. Finally, as shown by Table 4, the B3LYP/6-311++G(3df,3pd) single point calculations using optimized triplet geometries give smaller values for coupling constants. These values would be relevant to vertical transitions in EPR. This EPR can be obtained only for the IN-TTF diradicals for which there would be a significant population in the triplet state at higher temperatures. In thermal equilibrium, the cis-isomer has an estimated 33% triplet with ΔST about −130 cm−1 while the trans-isomer has 40% triplet with ΔST about −80 cm−1 (Table 1). The cis→trans interconversion would involve a transition from a rather EPR silence (Jvertical ∼ 0) to EPR activity with Jvertical ∼ 30 cm−1.

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ASSOCIATED CONTENT

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AUTHOR INFORMATION

* Supporting Information S

Log files of all calculations and ref 22. This material is available free of charge via the Internet at http://pubs.acs.org.

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS S.N.D. and A.K.P. are grateful to DST Grant SR-S1-PC-192010 for financial support of this work. S.N.D. and F.I. thank Indo-Spain Collaborative Program in ScienceNanotechnology (DST Grant INT-Spain-P42-2012 and Spanish Grant PRIPIBIN-2011-1028) for financial support. S.H. thanks UGC for a research fellowship, and F.I. acknowledges additional financial support from Spanish MICINN through research grants FIS2008-02238 and CTQ2012-30751 and partial support from Generalitat de Catalunya through grants 2009SGR1041, XRQTC, and the 2009 ICREA Academia award for excellence in research. We acknowledge IIT Bombay computer center for making their facilities available to us.

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REFERENCES

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Theoretical Investigation of Stilbene as Photochromic Spin Coupler

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