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Solute cavity radii in solution and polarizabilities in excited electronic states from solvatochromic data
Journal of Molecular Liquids, 26 (1983) 109-115
Elsevier Science Publishers B.V., Amsterdam
109
- Printed in The Netherlands
SOLUTE CAVITY RADII IN SOLUTION AND POLARIZABILITiES IN EXCITED ELECTRONIC STATES FROM SOLVATOCHROMIC DATA
RAUL G.E. MORALES Department
of Chemistry,
and
GABRIEL
TRAVERSO
University of Chile, Casilla 653,
Santiago, C%ile
(Received 28 March 1983)
ABSTRACT An analysis of the polarizabilities in the ‘La excited electronic state of some aromatic hydrocarbons and 9,10-derivatives of anthracene is done in terms of three solvatochromic models: Suppan, Abe and a modified version of MC Rae’s model. Polarizabilities in excited electroni$tates obtained from electrochromic data were utilized in order to find out the best interaction radii of the solute molecule with their solvation shell. The theoretical expression derived by Abe gave the best polarizability value in excited state when van der Waals volume
was employed
for determining
of the molecular
cavity
of the solute
in
solution.
INTRODUCTION During the last twenty five years, theoreticians and experimentalists have worked on the determination of polarizabilities in excited electronic states [ 1 - 171. The theoretical studies have shown important progress but there is clearly a lack of systematic experimental data on this subject. There are two main experimental techniques to measure dipolar electric polarizabilities in excited states: solvatochromism and electrochromism [ 121. Electrochromic methods, based on the application of an external Stark effect to the molecular systems, seem to allow higher accuracy than solvatochromic methods [8 - 121. However, only few systematic studies have been published in this field due to the experimental difficulties of measurements [9, lo]. Therefore, the solvatochromic methods have been used more frequently. But the systems must be well chosen in order that the experimental data can be interpreted correctly with the interaction model used. Amos and Burrows [4,6] some time ago, have analysed two solvatochromic methods based on the common idea of the multipolar expansion theory, and they have emphasized the influence of the interaction radii between solute and solvent molecules. On
0167-7322/83/$03.00
0 1983
Elsevier
Science
Publishers
B.V.
110 the other hand, several authors [5,15] have adopted different criteria in order to select the most appropriate interaction radii of the spherical cavity in the solvent generated by the solute molecule. However, at present time, this complex matter, own of structural properties of liquid fluid, has not possible to understand well yet. Despite to the complexity involved in this systems, we have intented in the present work to gain insight about of the solute molecule radii in solution through an analysis of the experimental electronic polarizability in excited states of some nonpolar aromatic compounds. Three solvatochromic models are utilized and their results have been compared with electrochromic data reported on the literature. They are the model of Abe [14], basically based on the van der Waals forces developed by Margenau [18]; the model of Suppan [15] based on the dispersion forces of London, and a modified version of model of MC Rae [ 131 in the solvent Stark approximation.
Solvatochromic methods From the original work of Abe [14], the polarizability of the solute molecule the i-th excited electronic state ( Ui’) can be obtained from: B=[(I_LiU)’ where for nonpolar
A=[(p*,V)’ B=[((/_I;)~
-(~*ou)~
] + my
A
in
111
aromatic solute molecules, P p = P 0” = 0, and +1.5aV,(IV,ry/(I;+Iy)] +
1.5a;(I,VI,U/(I,V+L;)))
c ,
121
a,U--
N
hC ( Via-
Via ) ( ~ P’
c=[(~,v)2
/ 1.5 kT+uV,]-’
R-?,,v&’
1 C 9
131
1
,
141
and N = p: 1
R-6u,“(p)= [(P + rv )-4 + (P + 3 rv )” f (r” + 5 rv )” ] n/(rv)2
151
All the notations refer to Abe’s original work, where u and v(p) denote to the solute and solvent molecules respectively, p is the dipolar moment, a is the polarizability, I is the ionization potential where I P= 1: - h c vi: , r is the molecular radii and vi”, and Vi0 are the electronic transition frequency in vapor phase and solution respectively. The A and B parameters must be calculated for each solvent and from the linear plot of B against A, uy is obtained from the slope of the straight line. On the other hand, Baur and Nicol [16] showed that in the spectral solvent shift formulation of MC Rae [13], the term correspondent to the solvent Stark effect can be better estimated from considerations related to the nonvanishing mean square electric
111 field due to the solvent at a nonpolar solute molecules. Taking into account that other studies have shown that E’, effective dielectric constant, is a more adequate parameter for polar solvent [19] , the following MC Rae’s expression can be obtained finally : ‘io
‘Vi00
-C’(r?--l)/(2n2
+ 1)-D
(2e’+
l)(e’-1)/e’
161
where n is the solvent refractive index, C’ is taken to be a solute- and transitiondependent parameter which is assumed to be solvent independent, and D = 12 kT (hc)-‘(
UP-
a,“)[(
ln( R/P))‘]
/ R3
171
where R is interpreted at present as the interaction radii from a solute-bulk molecule to solvent shells. Therefore, C’ and D may be evaluated by least-square fitting if the spectral shifts, determined in a number of different polarity solvents, are available. An alternative theory of the solvent shift due to dispersion forces has been developed by Suppan [IS]. In his treatment the solvent shift is attributed to a change in polarizability on excitation according to Via(l) where
1 and
2 are two solvents, @(II’)=
RESULTS
- via(2) =
AND
(n2
r.(r”Y3.( a: - a,“).[ @(n’)(1)-$(n2)(2)1 I 8 I 7 is equal to 1.8 .lO-’ ’ c.g.s. units
-1)/(n’+2).
and 191
DISCUSSION
Electronic transition frequencies of anthracene, 9,10-dichloroanthracene, 9,10-dibromoanthracene, 9,10-dimethylanthracene, 9,10-diphenylanthracene, 1,2;5,6-dibenzanthracene, triphenylene and coronene in solution (10” M) as well as vapor phase were recently determined in our laboratory [20]. Therefore, the polarizabilities in the ‘L, excited state could be determined from this spectral data through equations / I/, / 7 / and / 8 / for the above mentioned compounds, in order to compare with polarizabilities values obtained for these same compounds from electrochromic data [8 - IO]. In general, the cavity radii of the solute molecule is an unknown value and frequently must be considered as an empirical parameter whose best value is obtained by comparison with other molecular systems. Figure 1 shows the radial dependence of the cavity volume of the solute molecule with the polarizability of anthracene in the ’ La excited state, according to Abe’s equations. The Abe model has received criticisms because it seems to yield too large polarizability values in excited states, however, this could be mainly due to a bad choice of the solute molecular volume in solution.
112
90
70
50 3 Fig. 1. in terms
4
5
Polarizability of anthracene in the ‘La excited state of the radial dependence with their cavity volume.
The values reported in Fig. 1 showed a great dependence between both parameters The slope of al: for anthracene in the range between 3.0 and 5.0 A ay and r”. was approximately 20 A2 and if it is considered that the cavity radius in solid or liquid state is approximately 3.9 8, the polarizability value in this excited state should be 12 A3 greater than the electrochromic value [9]. Evidently the molecular radius obtained from density value should be overestimated the since the density, a macroscopic parameter, includes the empty volume between the molecular species. Tirerefore , it can be observed from electrchromic data that interaction radius of solute molecule should be smaller than the radius obtained from density values. in agreement with Fig. 1. Bondi and Edward [21, 221 have introduced the concept of van der Waals volume This value is a good approximation to solute from increments of atomic volumes. molecular volume in liquid solution and we found it in good agreement with the electrochromic polarizability value in the ’ L, excited state of anthracene. Table 1 shows the different values of polarizabilities in the ’ La excited state obtained from eqns. (1) (7) and (8) for nonpolar aromatic compounds with the cavity radii obtained from incre ments of atomic volume. Polarizabilities in the ’ L il excited state obtained from Suppan’s equation were esti-
113 mated from the spectral solvent shifts observed between cyclohexane and n-pentane, The mean values are showed in Table I. On the and cyclohexane and benzene [20]. other hand, polarizabilities obtained from the modified version of MC Rae’s equations were estimated introducing an R value of twice the cavity radius ( 1.948 r u). This respect last value was obtained considering the minimum value of ([ ln(R/r”)]* .R3) In this way, the parameter R was applied in the same mode for the difto r” [23]. ferent molecular systems. TABLE 1 Polarizability ( A3) values of nonpolar aromatic compounds in the ground state (u,“) and excited states obtained from Abe’s model (a? (Abe)), Suppan’s model (a r(Suppan)), and determined from electrochromic a modified version of MC Rae’s model ( u?(NB)) data ( a y (elec.)) Compounds anthracene 9 ,I 0-dichloroanthracene 9,10-dibromoanthracene 9,10-dimethylanthracene 9,10-diphenylanthracene 1,2,5,6_dibenzanthracene coronene triphenylene
ua a0
a 9 (Abe)
ay(Suppan)
uy (NB)
Up
(elec.)d
25.9b
62.4
+ 0.8
27.1
f 0.2
26.1
+ 0.2
62 +3
29.2’
66.1
f 1.0
30.5 + 0.2
29.5
+ 0.2
65 f4
31.5c
69.6
f 0.9
32.8 f 0.2
32.0 f 0.2
66 f4
29.8
69.2
f 0.8
31.4 + 0.2
30.5 f 0.3
64 f4
41.2 40.8
103 99.4
f 1
49.9
f 0.4
48.1
f 0.4
82 f4
+ 1.1
42.8
+ 0.3
41.8
+ 0.3
81 +4
+ 0.2
43.2
f 0.3
42.5b
91.0
+ 0.9
44.0
30.6
19.4
f 1.2
32.5 + 0.3
31.2 + 0.2
16 f 4 63 f4
--_ a. Denbigh,
Trans.Faraday Sot., 36 (1940) 936. b. Schuyer, Blom and Van Krevelen, ibid., 49 (1953) 1391. c. Sanyal, Ahmad and Dixit, J. Phys. Chem., 77 (1973) 2552. d. Refs. 9 and 10.
In general, the polarizabilities obtained from Abe’s method were extremely great compared with the other two methods. However, they were in good agreement with electrchromic data [9, lo], although from Table 1 it can be observed that coronene, triphenylene, 1,2;5,6_dibenzanthracene and 9,lOdiphenylanthracene present upper slightly higher values. Two main conclusions could be obtained from this work. (i) The van der Waals radiis fitted the polarizability values of Abe’s method better than liquid density radii in relation to electrochromic data. (ii) The other two solvatochromic methods used in this work did not describe adequately the dispersion effect in terms of the respective molecular data and that can not be interpreted from errors in the choice of the interaction distances. Notwithstanding Suppan’s method and the modified MC Rae’s method have been extensively used with good results in the experimental frequency fitting data, we have shown that the molecular properties, like polarizabilities, are not adequately predicted.
114 TABLE 2 Van der Waals radii and ionization
potential
of nonpolar
aromatic compounds _
Compounds
r” (A) a
anthracene 9,10-dichloroanthracene 9,10-dibromoanthracene 9,10-dimethylanthracene 9,10-diphenylanthracene 1,2;5,6_dibenzanthracene coronene triphenylene
1:
(eV)
3.41
1.55
c
3.60
7.54 d
3.66
1.42
3.64
7.01
4.18
6.68
3.92
1.42 e
3.95
7.50 e
3.68
8.13 e
a. Refs. 21 and 22. b. R.G.E. Morales, Rev. Chil. Educ. Qur’m., 3 (1978) 5. V. Diveler, J. Chem. Phys., 31 (1959) 1557. d. A. Konovalov and V. Kiselev, 2 (1966) 142. e. R. Hedges and F. Matsen, J. Chem. Phys., 28 (1958) 950.
TABLE 3 Solvent parameters Solvent ______ n-pentane n-hexane n-heptane isoctane cyclohexane benzene dioxane chloroform diethylether dichloromethane ethanol isopropanol methanol acetone N,N-dimethylformamide acetonitrile
utilized in the solvatochromic r
&)a
3.575 3.131 3.881 3.991 3.506 3.285 3.239 3.178 3.463 2.948 2.855 3.119 2.579 3.085 3.131 2.757
PCDP __. 0 0 0 0 0 0 0 1.05 1.14 1.57 1.67 1.68 1.69 2.85 3.80 3.94
c d d d e
f f f f
c. M. Wacks and Zh. Organ. Khim.,
study
I (eV)g a(‘43)b Y.95 11.78 13.61 14.88 10.87 10.32 9.44 8.23 5.16 6.48 5.13 6.98 3.46 6.33 7.88 4.42
b
10.55 10.43 10.35 10.28 9.88 9.38 9.52 11.42 9.53 11.35 10.50 10.15 10.85 9.69 9.11 12.39
h h h r ’ h
k
1
1
n (25Oc)
E (25 ‘C)
1.3579 2ooC 1.3723 1.385 1 1.4006 1.4235 1.4979 1.4203 1.4429 1.3495 1.4211 1.3594 1.3772 2ooc 1.3265 1.3560 1.3560 1.4282
1.84 1.89 1.93 1.96 2.02 2.28 2.21 4.81 4.34 8.93 ;;.“9;
2o”c
32.70 20.70 36.71 37.50
/a/. r r (3M/4r1 dN)l13, M: molecular weight, d: density ; /b/ Landolt-Bornstein,“PhysikaJischeChimishe Tabellen”, 6th Ed., Springer, Ber1.(1951); /cl T. Ree et al., J. Am. Chem. Sot, 73 (1951 ) 2263; /d/ S. Soundarajan and S. Krishnamurthy, J. Phys. Chem., 73 (1969) 4083; /e/ R. Meighan and R.H. Cole, ibid., 68 (1964) 503; /f/ Calculated from Lorenz-Lorents’ equation; /g/ K. Watanabe J. Chem. Phys., 26 (1957) 542; /h/ R. Honing,ibid., 16 (1948) 105; /i/ R.G.E. Morales, Tesis de Licenciatura, University of Chile (1976); /j/ M. Wacks and V. Diveler, J. Chem. Phys., 31 (1959) 1557; /k/ J. Morrison and A. Nicholson, ibid., 20 (1952) 1021; /l/ R. L. Schenider, Eastman Organic Chemical Bulletin, 47 (1975) 1.
115
Therefore, it is recommendable to do more quantitative work with these method relation with molecular properties in order to get a deeper picture of the models.
in
APPENDIX In order to estimate the polarizability values in the ’ La excited state of these nonpolar aromatic compounds, Tables 2 and 3 show the different parameters involved in the equations (1) to (8). ACKNOWLEDGEMENTS This work has been supported by the Departamento de Desarrollo de la Investigato the Centro cion de la Universidad de Chile. We extended our acknowledgements de Computation de la Universidad de Chile for generous amounts of free computer time. REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
R.G.E. Morales, J. Phys. Chem., 86 (1982) 2550. J.E. Sanhueza, Theor. Chem. Acta, (Berl.), 60 (1981) 143. G. Barnett, Int. J. Quant. Chem., 12 (1977) 427. A. Amos and B. Burrows, Theor. Chim. Acta, 24 (1973) 139. A. Amos and B. Burrows, Adv. Quant. Chem., 7 (1973) 289. A. Amos and B. Burrows, Theor. Chim. Acta, 23 (1972) 327. M. Trsic. B. Uzhinov and P. Matzke, Mol. Phys., 18 (1970) 851. J. Hall and G. Barnett, Chem. Phys. Letters, 23 (1973) 311. G. Barnett, M.A. Kurzmack and MM. Malley, ibid., 23 (1973) 237. M.A. Kurzmack and M.M. Malley, ibid., 21 (1973) 385. R. Mathies and A. Albrecht, J. Chem. Phys., 60 (1974) 2500. W. Liptay, Angew. Chem. Internat. Edit., 8 (1969) 177. E. G. MC Rae, J. Phys. Chem., 61 (1957) 562. T. Abe, Bull. Chem. Sot. Jpn., 38 (1965) 1314. P. Suppan, J. Chem. Sot. (A), (1968) 3125. M. Baur nad M. Nicol, J. Chem. Phys., 44 (1966) 3337. M. Nicol, J. Swain, Y. Shim, R. Merin and R.H. Chen, ibid., 48 (1968) 3587. H. Margenau, Rev. Mod. Phys., 11 (1939) 1. G.A. Gerhold and E. Miller, J. Phys. Chem., 72 (1968) 2737. R. G. E. Morales and G. Traverso, Spectroscopy Letters, 15 (1982) 623. A. Bondi, J. Phys. Chem., 68 (1964) 441. J. Edward, J. Chem. Educ., 47 (1970) 261. R.G.E. Morales, V. Vargas and G. Traverso, Acta sud Am. Quim., 2 (1982) 9.
Elsevier Science Publishers B.V., Amsterdam
109
- Printed in The Netherlands
SOLUTE CAVITY RADII IN SOLUTION AND POLARIZABILITiES IN EXCITED ELECTRONIC STATES FROM SOLVATOCHROMIC DATA
RAUL G.E. MORALES Department
of Chemistry,
and
GABRIEL
TRAVERSO
University of Chile, Casilla 653,
Santiago, C%ile
(Received 28 March 1983)
ABSTRACT An analysis of the polarizabilities in the ‘La excited electronic state of some aromatic hydrocarbons and 9,10-derivatives of anthracene is done in terms of three solvatochromic models: Suppan, Abe and a modified version of MC Rae’s model. Polarizabilities in excited electroni$tates obtained from electrochromic data were utilized in order to find out the best interaction radii of the solute molecule with their solvation shell. The theoretical expression derived by Abe gave the best polarizability value in excited state when van der Waals volume
was employed
for determining
of the molecular
cavity
of the solute
in
solution.
INTRODUCTION During the last twenty five years, theoreticians and experimentalists have worked on the determination of polarizabilities in excited electronic states [ 1 - 171. The theoretical studies have shown important progress but there is clearly a lack of systematic experimental data on this subject. There are two main experimental techniques to measure dipolar electric polarizabilities in excited states: solvatochromism and electrochromism [ 121. Electrochromic methods, based on the application of an external Stark effect to the molecular systems, seem to allow higher accuracy than solvatochromic methods [8 - 121. However, only few systematic studies have been published in this field due to the experimental difficulties of measurements [9, lo]. Therefore, the solvatochromic methods have been used more frequently. But the systems must be well chosen in order that the experimental data can be interpreted correctly with the interaction model used. Amos and Burrows [4,6] some time ago, have analysed two solvatochromic methods based on the common idea of the multipolar expansion theory, and they have emphasized the influence of the interaction radii between solute and solvent molecules. On
0167-7322/83/$03.00
0 1983
Elsevier
Science
Publishers
B.V.
110 the other hand, several authors [5,15] have adopted different criteria in order to select the most appropriate interaction radii of the spherical cavity in the solvent generated by the solute molecule. However, at present time, this complex matter, own of structural properties of liquid fluid, has not possible to understand well yet. Despite to the complexity involved in this systems, we have intented in the present work to gain insight about of the solute molecule radii in solution through an analysis of the experimental electronic polarizability in excited states of some nonpolar aromatic compounds. Three solvatochromic models are utilized and their results have been compared with electrochromic data reported on the literature. They are the model of Abe [14], basically based on the van der Waals forces developed by Margenau [18]; the model of Suppan [15] based on the dispersion forces of London, and a modified version of model of MC Rae [ 131 in the solvent Stark approximation.
Solvatochromic methods From the original work of Abe [14], the polarizability of the solute molecule the i-th excited electronic state ( Ui’) can be obtained from: B=[(I_LiU)’ where for nonpolar
A=[(p*,V)’ B=[((/_I;)~
-(~*ou)~
] + my
A
in
111
aromatic solute molecules, P p = P 0” = 0, and +1.5aV,(IV,ry/(I;+Iy)] +
1.5a;(I,VI,U/(I,V+L;)))
c ,
121
a,U--
N
hC ( Via-
Via ) ( ~ P’
c=[(~,v)2
/ 1.5 kT+uV,]-’
R-?,,v&’
1 C 9
131
1
,
141
and N = p: 1
R-6u,“(p)= [(P + rv )-4 + (P + 3 rv )” f (r” + 5 rv )” ] n/(rv)2
151
All the notations refer to Abe’s original work, where u and v(p) denote to the solute and solvent molecules respectively, p is the dipolar moment, a is the polarizability, I is the ionization potential where I P= 1: - h c vi: , r is the molecular radii and vi”, and Vi0 are the electronic transition frequency in vapor phase and solution respectively. The A and B parameters must be calculated for each solvent and from the linear plot of B against A, uy is obtained from the slope of the straight line. On the other hand, Baur and Nicol [16] showed that in the spectral solvent shift formulation of MC Rae [13], the term correspondent to the solvent Stark effect can be better estimated from considerations related to the nonvanishing mean square electric
111 field due to the solvent at a nonpolar solute molecules. Taking into account that other studies have shown that E’, effective dielectric constant, is a more adequate parameter for polar solvent [19] , the following MC Rae’s expression can be obtained finally : ‘io
‘Vi00
-C’(r?--l)/(2n2
+ 1)-D
(2e’+
l)(e’-1)/e’
161
where n is the solvent refractive index, C’ is taken to be a solute- and transitiondependent parameter which is assumed to be solvent independent, and D = 12 kT (hc)-‘(
UP-
a,“)[(
ln( R/P))‘]
/ R3
171
where R is interpreted at present as the interaction radii from a solute-bulk molecule to solvent shells. Therefore, C’ and D may be evaluated by least-square fitting if the spectral shifts, determined in a number of different polarity solvents, are available. An alternative theory of the solvent shift due to dispersion forces has been developed by Suppan [IS]. In his treatment the solvent shift is attributed to a change in polarizability on excitation according to Via(l) where
1 and
2 are two solvents, @(II’)=
RESULTS
- via(2) =
AND
(n2
r.(r”Y3.( a: - a,“).[ @(n’)(1)-$(n2)(2)1 I 8 I 7 is equal to 1.8 .lO-’ ’ c.g.s. units
-1)/(n’+2).
and 191
DISCUSSION
Electronic transition frequencies of anthracene, 9,10-dichloroanthracene, 9,10-dibromoanthracene, 9,10-dimethylanthracene, 9,10-diphenylanthracene, 1,2;5,6-dibenzanthracene, triphenylene and coronene in solution (10” M) as well as vapor phase were recently determined in our laboratory [20]. Therefore, the polarizabilities in the ‘L, excited state could be determined from this spectral data through equations / I/, / 7 / and / 8 / for the above mentioned compounds, in order to compare with polarizabilities values obtained for these same compounds from electrochromic data [8 - IO]. In general, the cavity radii of the solute molecule is an unknown value and frequently must be considered as an empirical parameter whose best value is obtained by comparison with other molecular systems. Figure 1 shows the radial dependence of the cavity volume of the solute molecule with the polarizability of anthracene in the ’ La excited state, according to Abe’s equations. The Abe model has received criticisms because it seems to yield too large polarizability values in excited states, however, this could be mainly due to a bad choice of the solute molecular volume in solution.
112
90
70
50 3 Fig. 1. in terms
4
5
Polarizability of anthracene in the ‘La excited state of the radial dependence with their cavity volume.
The values reported in Fig. 1 showed a great dependence between both parameters The slope of al: for anthracene in the range between 3.0 and 5.0 A ay and r”. was approximately 20 A2 and if it is considered that the cavity radius in solid or liquid state is approximately 3.9 8, the polarizability value in this excited state should be 12 A3 greater than the electrochromic value [9]. Evidently the molecular radius obtained from density value should be overestimated the since the density, a macroscopic parameter, includes the empty volume between the molecular species. Tirerefore , it can be observed from electrchromic data that interaction radius of solute molecule should be smaller than the radius obtained from density values. in agreement with Fig. 1. Bondi and Edward [21, 221 have introduced the concept of van der Waals volume This value is a good approximation to solute from increments of atomic volumes. molecular volume in liquid solution and we found it in good agreement with the electrochromic polarizability value in the ’ L, excited state of anthracene. Table 1 shows the different values of polarizabilities in the ’ La excited state obtained from eqns. (1) (7) and (8) for nonpolar aromatic compounds with the cavity radii obtained from incre ments of atomic volume. Polarizabilities in the ’ L il excited state obtained from Suppan’s equation were esti-
113 mated from the spectral solvent shifts observed between cyclohexane and n-pentane, The mean values are showed in Table I. On the and cyclohexane and benzene [20]. other hand, polarizabilities obtained from the modified version of MC Rae’s equations were estimated introducing an R value of twice the cavity radius ( 1.948 r u). This respect last value was obtained considering the minimum value of ([ ln(R/r”)]* .R3) In this way, the parameter R was applied in the same mode for the difto r” [23]. ferent molecular systems. TABLE 1 Polarizability ( A3) values of nonpolar aromatic compounds in the ground state (u,“) and excited states obtained from Abe’s model (a? (Abe)), Suppan’s model (a r(Suppan)), and determined from electrochromic a modified version of MC Rae’s model ( u?(NB)) data ( a y (elec.)) Compounds anthracene 9 ,I 0-dichloroanthracene 9,10-dibromoanthracene 9,10-dimethylanthracene 9,10-diphenylanthracene 1,2,5,6_dibenzanthracene coronene triphenylene
ua a0
a 9 (Abe)
ay(Suppan)
uy (NB)
Up
(elec.)d
25.9b
62.4
+ 0.8
27.1
f 0.2
26.1
+ 0.2
62 +3
29.2’
66.1
f 1.0
30.5 + 0.2
29.5
+ 0.2
65 f4
31.5c
69.6
f 0.9
32.8 f 0.2
32.0 f 0.2
66 f4
29.8
69.2
f 0.8
31.4 + 0.2
30.5 f 0.3
64 f4
41.2 40.8
103 99.4
f 1
49.9
f 0.4
48.1
f 0.4
82 f4
+ 1.1
42.8
+ 0.3
41.8
+ 0.3
81 +4
+ 0.2
43.2
f 0.3
42.5b
91.0
+ 0.9
44.0
30.6
19.4
f 1.2
32.5 + 0.3
31.2 + 0.2
16 f 4 63 f4
--_ a. Denbigh,
Trans.Faraday Sot., 36 (1940) 936. b. Schuyer, Blom and Van Krevelen, ibid., 49 (1953) 1391. c. Sanyal, Ahmad and Dixit, J. Phys. Chem., 77 (1973) 2552. d. Refs. 9 and 10.
In general, the polarizabilities obtained from Abe’s method were extremely great compared with the other two methods. However, they were in good agreement with electrchromic data [9, lo], although from Table 1 it can be observed that coronene, triphenylene, 1,2;5,6_dibenzanthracene and 9,lOdiphenylanthracene present upper slightly higher values. Two main conclusions could be obtained from this work. (i) The van der Waals radiis fitted the polarizability values of Abe’s method better than liquid density radii in relation to electrochromic data. (ii) The other two solvatochromic methods used in this work did not describe adequately the dispersion effect in terms of the respective molecular data and that can not be interpreted from errors in the choice of the interaction distances. Notwithstanding Suppan’s method and the modified MC Rae’s method have been extensively used with good results in the experimental frequency fitting data, we have shown that the molecular properties, like polarizabilities, are not adequately predicted.
114 TABLE 2 Van der Waals radii and ionization
potential
of nonpolar
aromatic compounds _
Compounds
r” (A) a
anthracene 9,10-dichloroanthracene 9,10-dibromoanthracene 9,10-dimethylanthracene 9,10-diphenylanthracene 1,2;5,6_dibenzanthracene coronene triphenylene
1:
(eV)
3.41
1.55
c
3.60
7.54 d
3.66
1.42
3.64
7.01
4.18
6.68
3.92
1.42 e
3.95
7.50 e
3.68
8.13 e
a. Refs. 21 and 22. b. R.G.E. Morales, Rev. Chil. Educ. Qur’m., 3 (1978) 5. V. Diveler, J. Chem. Phys., 31 (1959) 1557. d. A. Konovalov and V. Kiselev, 2 (1966) 142. e. R. Hedges and F. Matsen, J. Chem. Phys., 28 (1958) 950.
TABLE 3 Solvent parameters Solvent ______ n-pentane n-hexane n-heptane isoctane cyclohexane benzene dioxane chloroform diethylether dichloromethane ethanol isopropanol methanol acetone N,N-dimethylformamide acetonitrile
utilized in the solvatochromic r
&)a
3.575 3.131 3.881 3.991 3.506 3.285 3.239 3.178 3.463 2.948 2.855 3.119 2.579 3.085 3.131 2.757
PCDP __. 0 0 0 0 0 0 0 1.05 1.14 1.57 1.67 1.68 1.69 2.85 3.80 3.94
c d d d e
f f f f
c. M. Wacks and Zh. Organ. Khim.,
study
I (eV)g a(‘43)b Y.95 11.78 13.61 14.88 10.87 10.32 9.44 8.23 5.16 6.48 5.13 6.98 3.46 6.33 7.88 4.42
b
10.55 10.43 10.35 10.28 9.88 9.38 9.52 11.42 9.53 11.35 10.50 10.15 10.85 9.69 9.11 12.39
h h h r ’ h
k
1
1
n (25Oc)
E (25 ‘C)
1.3579 2ooC 1.3723 1.385 1 1.4006 1.4235 1.4979 1.4203 1.4429 1.3495 1.4211 1.3594 1.3772 2ooc 1.3265 1.3560 1.3560 1.4282
1.84 1.89 1.93 1.96 2.02 2.28 2.21 4.81 4.34 8.93 ;;.“9;
2o”c
32.70 20.70 36.71 37.50
/a/. r r (3M/4r1 dN)l13, M: molecular weight, d: density ; /b/ Landolt-Bornstein,“PhysikaJischeChimishe Tabellen”, 6th Ed., Springer, Ber1.(1951); /cl T. Ree et al., J. Am. Chem. Sot, 73 (1951 ) 2263; /d/ S. Soundarajan and S. Krishnamurthy, J. Phys. Chem., 73 (1969) 4083; /e/ R. Meighan and R.H. Cole, ibid., 68 (1964) 503; /f/ Calculated from Lorenz-Lorents’ equation; /g/ K. Watanabe J. Chem. Phys., 26 (1957) 542; /h/ R. Honing,ibid., 16 (1948) 105; /i/ R.G.E. Morales, Tesis de Licenciatura, University of Chile (1976); /j/ M. Wacks and V. Diveler, J. Chem. Phys., 31 (1959) 1557; /k/ J. Morrison and A. Nicholson, ibid., 20 (1952) 1021; /l/ R. L. Schenider, Eastman Organic Chemical Bulletin, 47 (1975) 1.
115
Therefore, it is recommendable to do more quantitative work with these method relation with molecular properties in order to get a deeper picture of the models.
in
APPENDIX In order to estimate the polarizability values in the ’ La excited state of these nonpolar aromatic compounds, Tables 2 and 3 show the different parameters involved in the equations (1) to (8). ACKNOWLEDGEMENTS This work has been supported by the Departamento de Desarrollo de la Investigato the Centro cion de la Universidad de Chile. We extended our acknowledgements de Computation de la Universidad de Chile for generous amounts of free computer time. REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
R.G.E. Morales, J. Phys. Chem., 86 (1982) 2550. J.E. Sanhueza, Theor. Chem. Acta, (Berl.), 60 (1981) 143. G. Barnett, Int. J. Quant. Chem., 12 (1977) 427. A. Amos and B. Burrows, Theor. Chim. Acta, 24 (1973) 139. A. Amos and B. Burrows, Adv. Quant. Chem., 7 (1973) 289. A. Amos and B. Burrows, Theor. Chim. Acta, 23 (1972) 327. M. Trsic. B. Uzhinov and P. Matzke, Mol. Phys., 18 (1970) 851. J. Hall and G. Barnett, Chem. Phys. Letters, 23 (1973) 311. G. Barnett, M.A. Kurzmack and MM. Malley, ibid., 23 (1973) 237. M.A. Kurzmack and M.M. Malley, ibid., 21 (1973) 385. R. Mathies and A. Albrecht, J. Chem. Phys., 60 (1974) 2500. W. Liptay, Angew. Chem. Internat. Edit., 8 (1969) 177. E. G. MC Rae, J. Phys. Chem., 61 (1957) 562. T. Abe, Bull. Chem. Sot. Jpn., 38 (1965) 1314. P. Suppan, J. Chem. Sot. (A), (1968) 3125. M. Baur nad M. Nicol, J. Chem. Phys., 44 (1966) 3337. M. Nicol, J. Swain, Y. Shim, R. Merin and R.H. Chen, ibid., 48 (1968) 3587. H. Margenau, Rev. Mod. Phys., 11 (1939) 1. G.A. Gerhold and E. Miller, J. Phys. Chem., 72 (1968) 2737. R. G. E. Morales and G. Traverso, Spectroscopy Letters, 15 (1982) 623. A. Bondi, J. Phys. Chem., 68 (1964) 441. J. Edward, J. Chem. Educ., 47 (1970) 261. R.G.E. Morales, V. Vargas and G. Traverso, Acta sud Am. Quim., 2 (1982) 9.