Ground and excited states of benzil: A theoretical study

Journal of Molecular Structure (Theochem), 288 (1993) 55-61 0166-1280/93/%06.00 0 1993 - Elsevier Science Publishers B.V. All rights reserved

Ground and excited states of benzil: a theoretical

55

study

Kalyan Kumar Das*‘a, Devashis Majumdarb aDepartment of Chemistry, Physical Chemistry Section, Jadavpur University, Calcutta 700 032, India bDepartment of Physical Chemistry, Indian Association for the Cultivation of Science,Jadavpur, Calcutta 700 032, India

(Received 11 March 1993; accepted 18 April 1993) Abstract The ground and low-lying excited state potential energy curves of benzil have been studied. The ground state geometry is fully optimized by the AM1 method. The excited states are calculated by using the CNDO/S-CI method. The calculations confirm that benzil in the ground state has a skewed conformation whereas the first excited singlet and triplet states of this molecule are trans-planar. The geometry relaxation in the excited states of benzil agrees well with the experimental findings. The absorption and emission bands of benzil have been compared with the observed bands. The dipole moments of the ground and excited states at some conformations are also reported. The effect of solvents on the electronic states of benzil has been studied using the continuum dielectric model.

Introduction

The diaromatic a-dicarbonyl type of compounds are important for their photorotamerism [l-6]. Benzil is an excellent photoinitiator for several photochemical reactions. There are many photophysical and photochemical properties related to the excited state conformation and reactivity of the cY-dicarbonyl fragment. Crystallographic studies [7] on benzil indicate that the molecule exists as a skewed contbrmer in its ground state and that the dihedral angle between the two carbonyl groups is about 111”. The emission bands of benzil show a large Stokes shift and from the analysis of the absorption and emission bands, Bera et al. [1,2] have confirmed a change in the geometry of the excited states of this molecule. Electron nuclear double resonance (ENDOR) measurements [8,9] show that the near trans-planar conformation with the dihedral angle of about 157” corresponds *Corresponding

author.

to the lowest triplet (T,) state structure of benzil. Several other spectroscopic investigations [lo- 121 suggest that the strong localization of the electronic excitation on the -F-yfragment results in the 00 near trans-planar conformation of the T, state of benzil. Dipole moment measurements [ 121 also support the trans-planar structure of benzil in the Tt state. According to Morantz and Wright [3,4] the labile benzil molecule after excitation relaxes to a trans-planar conformation from which emission bands originate. Arnett and McGlynn [6] studied a series of this type of compounds in which emissions start from nearly coplanar relaxed excited states. Fluorescence from relaxed and unrelaxed excited states of benzil has been observed [1.3]. The dynamics involved in the geometry changes is very fast and occur in the picosecond time scale [14]. Roy et al. [15] have performed a time-resolved study of the emission bands of benzil and naphthyl in semi-solid glasses. They have also confirmed the geometrical relaxation occurring in the excited triplet

56

K.K.

Das and D. Majumdar/J.

Mol.

Struct.

(Theochem)

288 (1993)

55-61

states of benzil and naphthyl. Very recently the time-resolved resonance Raman analysis of the lowest triplet of benzil and its isotopomers has been reported by Locoge et al. [16]. These authors have confirmed the decrease in the CO bond order and increase in the CC bond order of the dicarbonyl fragment of benzil on going from the ground to the lowest excited triplet state. Bhattacharyya and Chowdhury [17] have studied the solvent shift for the absorption and emission bands of benzil. Methylcyclohexane (MCH) and ethanol solvents were used for the low temperature experiments. These authors observed that emissions from the relaxed transplanar geometry show no solvent effects whereas those from the unrelaxed skewed conformation show small blue shifts. In the present paper we have theoretically studied the ground state (So) and low-lying excited single (S,) and triplet (T,) states of benzil using semiempirical molecular orbital theories and limited CI calculations. The solvent effects on the electronic states of benzil have also been studied.

the normal mode vibrational analysis. We have also carried out CNDO/S-CI calculations [19-211 for each fixed value of T to obtain the transition energies corresponding to the excitation of one electron from occupied to virtual orbitals. The total energies of the excited states are calculated by adding the transition energies to the ground state energy obtained from the AM1 calculations. The CI calculations are restricted to 100 contigurations. The linear configuration space is, therefore, spanned by exciting one electron from each of the 10 highest occupied molecular orbitals to the 10 lowest virtual orbitals of the CNDO/S calculations. The natural orbitals obtained from the CI wavefunctions generate one-electron density matrices which are used for the calculation of the dipole moment in the excited state of benzil. The effect of solvents on the total energies of the ground and excited states of benzil has been calculated by using Onsagar’s theory [22]. Assuming that the solute molecule having a dipole pi in the ith electronic state is fully solvated, the solvation energy is given by

Calculations

AEi

The ground state (So) geometry optimization and normal mode vibrational analysis of benzil have been carried out using the AM1 [18] method. The potential energy curve has been constructed by varying the total energy of the molecule around the C8-Cl0 bond (Scheme 1). The fully optimized geometry of benzil has been used for

where E is the dielectric constant of the solvent and a the cavity radius. In our calculation we have chosen a cavity radius of 5.8 A, which corresponds to the maximum molecular length. One may note that because of the large cavity radius the solvation energy will not be very large unless the dipole moment of the solute is very high.

sol

-2d

(&-‘1) a3 (2& + 1)

Results and discussion

Ground state conformation

09

Scheme 1.

of benzil

Table 1 shows the total energies of benzil in the ground state at different torsion angles r(9-810-l 1). For each fixed T all other geometrical parameters are fully optimized using the AM1 method. The ground state potential energy profiles are presented in Fig. 1. The angle r = 0” refers to the cis conformer and r = 180” corresponds to the trans

K.K. Das and D. Majumdar/J.

Mol.

Struct.

(Theochem)

288 (1993)

55-61 -2569.00

Table 1 Geometrical parameters, energies and dipole moments for different conformers of benzil in the ground state (So)

-2569

Parametera

7(9-8-10-l 102.8” (optimum)

Bond length

180” (trans)

0” (cis)

1.395 1.393 1.403 1.401 1.394 1.474 1.235 1.515

(6-7)

(S-8) (8-9) (8-10)

1.395 1.394 1.401 1.399 1.394 1.476 1.234 1.520

1.396 1.391 1.407 1.399 1.395 1.480 1.237 1.526

(deg)

(2-3-4) (3-4-5) (6-5-8) (5-8-9) (5-8-10) (8-10-11) (8-10-12) angle

(6-5-8-9) (6-5-8-10) (5-8-10-12)

E (W P@) aThe numbering

% ,E -2569.20 x $ 15 a -256930

(5-6)

Dihedral

10

1)

(A)

(2-3) (3-4) (4-5)

Bond angle

51

120.06 120.03 121.38 122.96 116.42 120.63 116.42

119.95 120.13 121.15 121.66 119.51 118.91 119.38

120.08 120.55 123.18 120.65 119.14 120.13 119.32

-162.48 18.23 101.40

-126.45 52.49 2.30

-154.37 28.25 175.16

-2569.35 3.89

-2569.02 5.26

-2569.16 0.07

(deg)

of the atoms is shown in Scheme 1.

coplanar conformation. The minimum of the potential energy curve has been found at the torsion angle T = 102.8”. The results further indicate that the trans-planar conformer is more stable than the cis-planar form by about 0.07eV. The potential energy curve of benzil is a symmetric double well, and the barrier top at 7 = 0” refers to the cis-planar conformation. The height of the barrier from the potential well (7 = 102.8”) is calculated to be 7.6 kcal mol-‘. The optimized geometrical parameters at three conformations (7 = 0, 180 and 102.8”) of benzil in the ground state are reported in Table 1. When the two carbonyl groups are in the trans

2 -2569.40

-256950 -180

-120 -60 Torsion angle

0 (g-6-10-11)

60

120 in deg

160

Fig. 1. Potential energy curves for the ground state of benzil: curve a, isolated molecule; curve b, in methylcyclohexane (MCH); curve c, in ethanol.

orientation the calculated dipole moment is negligibly small (/L = 0.07 D) indicating a near planar geometry having a centre of symmetry. The cis conformer has a large dipole moment of 5.26D. The minimum skewed configuration of benzil has a dipole moment of 3.89 D. During the variation of the torsion angle 7 from the cis to the trans conformation the geometrical parameters of the two phenyl rings do not change much. All the C-C bond lengths of the phenyl ring are around 1.4A - similar to that of benzene. The C5-C8 bonds in the three conformers are somewhat shorter than normal C-C single bonds, indicating partial double bond character. The C8-Cl0 bond is of single bond character. However, at the optimum geometry (T = 102.8”) the C8-Cl0 bond is about 0.005 A shorter than the corresponding bond in the cis conformer and 0.011 A shorter than the corresponding bond in the trans conformer. The C5-C8 bond length is shortest in the optimum geometry, in which the r electron conjugation is enhanced to a small extent. Some of the bond angles and dihedral angles are also reported in Table 1. The results clearly show that these small variations in geometrical parameters do not contribute very much to the observed energy differences between the three main conformers of benzil. The

K.K.

58

higher conformational energies of the cis and tram forms might thus be attributed to the non-bonded interaction effect around the dicarbonyl region of the molecule. Vibrational frequencies of the ground state of benzil

The vibrational frequencies of benzil in the ground state calculated at the minimum of the potential energy curve are tabulated in Table 2. The frequencies obtained from AM1 calculations do not generally reproduce the experimental data. For a complex system like benzil the calculated values are on average lOOcm-’ different from the experimental results. Thus we have used the eigenvectors of the individual vibrational frequencies for the assignments. The calculated values are then uniformly scaled by a factor of 0.818 for comparison with the experimental values. The observed vibrational bands presented in Table 2 are obtained from the ground state IR spectra of benzil [16]. The symmetric C=O stretching band (1675 cm-‘) has been used for scaling with the calculated one. The results in Table 2 show that the calculated scaled frequencies are quite comparable to the experimental results. Table 2 Calculated and observed normal mode vibrational

Das and D. MajumdarlJ.

Mol.

Struct.

(Theochem)

288 (1993)

55-61

Our calculations predict the C=O asymmetric stretching vibrational band at around 1669 cm-‘, compared to the observed value of 1666 cm-‘. The dicarbonyl C-C stretching mode is found at 1036cm-’ and the IR band assigned to this vibrational mode has been observed at 1049 cm-i. The in-plane C-H stretching mode and the symmetric combination mode of the two ring carbonyl C-C stretching vibrational frequencies are calculated to be 1330 and 1284cm-‘, respectively. Experimental values of these two bands are tentatively assigned in the 1325 and 1292 cm-’ regions, respectively. The intense IR band observed around 1212 cm-’ due to the out-of-phase combination of the two ring carbonyl C-C stretchings corresponds to the calculated scaled frequency near 1199 cm-‘. The C-C=0 bending motion mode is observed at 335cm-i and the calculated value is tentatively assigned at around 325 cm-‘. The close proximity of the theoretical and experimental vibrational frequencies supports the existence of the skewed conformer of benzil in its ground state. Excited states of benzil

The calculations

of low-lying

excited states of

frequencies of benzil in its ground state

Calculated frequency (cn-l)a

Observed frequency (cm-‘)b

Assignmentb

1675 1669 1452 1442 1330 1284

1675 1666 1487 1450 1325 1292

1199

1210

1165 1036 699

1174 1049 615

325

335

CO stretch (sym) CO stretch (asym) (Ring CC + CH) of ring A (Ring CC + CH) of ring B In-plane C-H stretch Symmetric combination of two ring carbonyl C-C stretch Out of phase combination of two ring carbonyl C-C stretch Ring C-H stretch Dicarbonyl C-C stretch Phenyl in-plane C-C distortion C-C=0 bend

a Scaled uniformly b See Ref. 16.

by a factor of 0.8 18.

.

K.K. Das and D. Majumdar/J. -256600

Mol.

Struct.

(Theochem)

,

-2566

25

@ -2566 : w

50

288 (1993)

I

Table 3 Energies and dipole moments of S, and T, states of benzil at some selected conformations State

r(9-8-10-11) Wg)

E (total) (ev)

Dipole moment p (D)

Sl

0.0 48.0 94.0 102.8 180.0

-2566.11 -2566.43 -2566.03 -2566.13 -2566.80

8.41 3.36 4.83 3.29 0.0092

TI

0.0 47.0 70.0 102.8 180.0

-2566.12 -2566.44 -2566.26 -2566.31 -2566.80

8.42 3.36 5.21 4.10 0.0092

2, .F

75 B r -2566

-2567

75

00 7-O -180

-120 -60 Torsion angle

0 (9-8-10-l

120 60 1) in deg

Fig. 2. Potential energy curves of the excited S, and T, states of the isolated benzil molecule.

a CI with 100 configurations. The CNDOjS molecular orbitals are used for the CI calculations. Although an increase in the number of configurations in the CI space would improve the excited state results, the computational cost of such calculations would be enormously high. However, all dominant configurations are present in the lOO-configuration CI space. The potential energy curves for the singlet and triplet states of benzil are shown in Fig. 2. One may note that in both curves there is a local minimum around the skewed conformation. For the Si state the local minimum is found at Y-= 48” and for the Ti state it is at 47”, with a singlet-triplet gap of only 0.01 eV. The skewed minima are about 8.5 kcal mol-’ above the trans-planar geometry. The singlet and triplet states are nearly degenerate in the trans-planar conformation. This degeneracy may be due to the deficiency of the CNDOjS parameters. Both St and Tt states are most stable in the trans-planar geometry. The potential energy curve of the Si state shows a large barrier at r = 94” with a height of 17.8 kcal mol-’ from the trans-planar geometry. In the triplet state curve the corresponding barrier of height 12.5 kcalmol-’ has been found at r = 70”. The energy difference between the cis and trans conformers is about 0.70eV for both the Si and the Tt states. Hence during the benzil

59

55-61

involve

rotation from the trans to the cis conformation the S, state benzil molecule must cross a much larger barrier than the Tt state molecule. Table 3 reports energies and dipole moments of the St and T, states at five different conformations. The transition energy of the Franck-Condon singlet state is about 3.22eV at the ground state geometry and for the triplet state it is 3.04eV above the ground state. The absorption band, therefore, should originate around 385 nm, which corresponds to the vertical excitation from the Se state to the skewed unrelaxed S1 state. The effect of solvents on the absorption and emission bands has been studied by Bhattacharyya and Chowdhury [17]. Because of the n7r* nature of the excited states the absorption band undergoes a blue shift of 10 nm from ethanol to methylcyclohexane (MCH). These authors have reported the absorption band at 387nm in ethanol and at 397nm in MCH. In the continuum dielectric model the absorption should occur at 383 nm in ethanol (E = 24) and at 385 nm in MCH (E = 2) at room temperature. The potential energy curves of the ground state of benzil in MCH and ethanol are also shown in Fig. 1 curves b and c, respectively, along with that of the isolated molecule in curve a. In MCH the ground state minimum is found at the torsion angle of 100” and in ethanol it is near 91”.

60

K.K.

Experimentally an intense green phosphorescence with a X,,, of 53Onm at 77K in rigid alcohol glass and a weak broad shoulder around 570 nm have been observed [l]. The 570 nm shoulder has been interpreted as a vibronic band. At higher temperatures when the glass melts the green phosphorescence switches over to a sharp band at 570nm, which has been interpreted as being due to emission from the trans-planar excited triplet state. From our calculations it is evident that after the S,, + Si excitation there is an intersystem crossing and the molecule undergoes conformational relaxation from the skewed to the trans-planar geometry from which the phosphorescence would occur. In the present calculations the origin of this phosphorescence band is found to be around 530nm compared to the observed one at 570nm in the experimental situation, in which the molecule is able to relax its geometry through an orientation along the C-C bond of the dicarbonyl group. Because of the limitations of the CNDO/S parameters and restrictions in the number of configurations in the CI space the calculated value is expected to be larger than 530nm. The improved CI would stabilize the excited state further. The potential energy curves (Fig. 2) show that the excited molecule will not be able to relax its geometry to move into the optimum skewed conformations (T = 48” for the S, and 47” for the Ti states) because of the large barrier. The thermal energy at ordinary temperatures would not favour such barrier crossings. Therefore, the transitions from skewed local minima are not possible. Bhattacharyya et al. [13] observed that the fluorescence intensity (St + So) is very small compared to the phosphorescence intensity (Ti + So). In the solid glass the geometrical relaxation is prevented and the emission would originate from the unrelaxed state. However, at high temperatures the geometrical relaxation is favoured and all emissions would originate from the relaxed trans-planar conformation. The experimental fluorescence from the relaxed Si state in alcoholic medium has been obserted at 510nm. The present calculations predict this

Das and D. MajumdarlJ.

Mol.

Struct.

(Theochem)

288 (1993)

55-61

band to originate at 530 nm for the isolated molecule. In the presence of the more polar solvent ethanol there will be a blue shift in the calculated value of about 10 nm. Since in the relaxed geometry (T = 180”) the dipole moments of the ground and excited states are nearly zero, the electronic states in the trans-planar conformation do not have any solvent effect. Hence the fluorescence and phosphorescence bands have no shift due to a change of the polarity of the solvent. Conclusion Isolated benzil in the ground state has been found in the skewed conformation with a torsion angle ~(9-8-10-11) of 102.8” when full optimization has been carried out at the AM1 level. In the presence of a solvent treated as a continuum dielectric based on Onsagar’s theory, the ground state minimum is shifted towards the smaller r values. The first excited singlet (S,) and triplet (T,) states of nrr* type are most stable in the trans-planar conformation. The potential energy curves of S, and Ti show local minima around T = 47”. Because of the large barrier the molecule cannot attain these conformations at normal temperatures. The absorption band of the isolated molecule is calculated to originate around 385nm, compared to the experimental value of 397 nm in MCH at room temperature. Our calculations predict the fluorescence and phosphorescence bands to originate around 53Onm, owing to emission from the relaxed trans-planar conformation and that no solvent shifts occur in the emission bands. Acknowledgement The authors would like to thank Professor S.P. Bhattacharyya of IACS, Calcutta for providing computational facilities and for helpful discussions. References 1 SC. Bera, R.K. Mukherjee Chem. Phys., 51 (1969) 754.

and M. Chowdhury,

J.

K.K. Das and D. Majumdar/J.

Mol.

Struct.

(Theochem)

288 (1993)

2 S.C. Bera, R.K. Mukherjee and M. Chowdhury, Indian J. Pure Appl. Phys., 7 (1969) 345. 3 D.J. Morantz and A.J.C. Wright, J. Chem. Phys., 53 (1970) 1622. 4 D.J. Morantz and A.J.C. Wright, J. Chem. Phys., 54 (1971) 692. 5 SC. Bera, R.K. Mukherjee, D. Mukherjee and M. Chowdhury, J. Chem. Phys., 55 (1971) 5026. 6 J.F. Arnett and S.P. McGlynn, J. Phys. Chem., 79 (1975) 626. 7 C.J. Brown and R. Sadanaga, Acta Crystallogr., 18 (1965) 158. 8 Y. Teki, T. Takni, M. Hirai, K. Itoh and H. Iwamura, Chem. Phys. Lett., 89 (1982) 263. 9 Y. Chan and B.A. Heath, J. Chem. Phys., 71 (1979) 1070. 10 S. Yamauchi and N. Hirota, J. Phys. Chem., 88 (1984) 4631. 11 AI. Grant and K.A. McLauchlan, Chem. Phys. Lett., 101 (1983) 120.

55-61

61

12 R.W. Fessenden, R.M. Carton, H. Shimamori and J.C. Scaiano, J. Phys. Chem., 86 (1982) 3803. 13 K. Bhattacharyya, D.S. Roy and M. Chowdhury, J. Lumin., 22 (1980) 95. 14 K.B. Eisenthal, Annu. Rev. Phys. Chem., 28 (1977) 225. 15 D.S. Roy, K. Bhattacharyya, S.C. Bera and M. Chowdhury, Chem. Phys. L&t., 69 (1980) 134. 16 N. Locoge, G. Buntinx, N. Ratovelomanana and 0. Poizat, J. Phys. Chem., 96 (1992) 1106. 17 K. Bhattacharyya and M. Chowdhury, J. Photochem., 33 (1986) 61. 18 M.J.S. Dewar, E.G. Zoebisch, E.F. Healy and J.J.P. Stewart, J. Am. Chem. Sot., 107 (1985) 3902. 19 J. Hinze and H.H. Jaffe, J. Am. Chem. Sot., 84 (1962) 540. 20 J. Del Bene and H.H. Jaffe, J. Chem. Phys., 48 (1968) 1807. 21 J. Hinze and H.H. Jaffe, J. Phys. Chem., 67 (1963) 1501. 22 C.J.F. Bottcher, in Theory of Electric Polarization, Vol. I, Elsevier, Amsterdam, 1983.