J . Phys. Chem. 1989, 93, 43-48
43
M, and (d) 1 X M. It is shown that the dilution of compound I11 in ethanol solution destabilizes the twisted geometry of D,ADPH and decreases the a * fluorescence of the TICT state. This is presumably due to the fact that the intermolecular distance becomes longer and the intermolecular charge interaction becomes weaker when the concentration of D,A-DPH is reduced. IV. Conclusion
Wavelength (nrn) Figure 4. Emission spectra of 02N-Ph-(CH=CH)3-Ph-N02 at 77 K: (left) 1 X M in EPA excited at 313 nm (A), 334 nm (B), 365 M, (b) 1 X lod M, (c) nm (C), and 404 nm (D); (right) (a) 1 X 1 X lo-’ M, and (d) 1 X lo-* M in ethanol excited at 313 nm.
We have illustrated that p,p’-disubstituted 1,6-diphenyl1,3,5-hexatrienes with D and/or A = -N(CH3)2 and/or -NO2 display a dual fluorescence. The long wavelength a* fluorescence has been assigned to originate from a twisted intramolecular charge transfer (TICT) state. The observed nonplanarity of both electron-donating and -accepting groups from the conjugated r electron system of Ph-(CH=CH)3-Ph could cause the distortion of the *-electron distribution and thus enhance the optical nonlinearity in this class of molecules, D,A-DPH. The b* fluorescence originates from a planar conformation of D,A-DPH. The dynamic transformation process between a * and b* goes through an energy barrier that is shown to be sensitive to the polarity of solvents and the concentration of solutions. It is found that D,A-DPH exists in two different ground-state structures. The twisted conformation of D,A-DPH is stabilized by the intermolecular charge interaction.
in the dilute solutions. For concentration higher than 1 X lo4 M, compounds 11-V in all solvents give predominantly the a* fluorescence of TICT state. When the concentration is reduced, the intensity of T I C T fluorescence decreases while that of the locally excited state increases. The right-hand portion of Figure 4 shows the emission spectra of compound I11 in ethanol at various M, (b) 1 X lod M, (c) 1 X lo-’ concentrations: (a) 1 X
Acknowledgment. Financial support from the Research Corporation and the Northern Illinois University Graduate School and College of Liberal Arts and Sciences is acknowleged. C.T.L. thanks the Chemistry Department at UCLA for use of their fluorometer, Spex Fluorolog. Registry No. I, 31382-32-8; 11, 106545-80-6; 111, 34944-33-7; IV, 51079-93-7; V, 113687-28-8; Ph(CH=CH),Ph, 1720-32-7.
3M)
500
400
300
I
I
400
500
1
Calculation of Induced Moments In Large Molecules. 6. Scale of Polarlzatlon for Some Functional Groups. A Comparative Study J. Waite* and M. G. Papadopoulos National Hellenic Research Foundation, 48 Vas. Constantinou Avenue, GR-116 35,Athens, Greece (Received: December 30, 1987) An appropriate index has been used to study the effective polarizability and second hyperpolarizability of the functional groups C1, HC2, C2H3, C2H5, (CH3),CH, (CH3)3C,and C6H5. The established order for the average relative polarizability is F < H < NH2 < CH3 < C1 < N H 2 C 0 < C2H < (CH3)HN < CF3 < C2H5 < C2H3 < (CH3)2N < (CH3)HNC0 < (CH3)2CH< (CH3)2NC0< (CH3)3CC C6H5,while for the average relative hyperpolarizabilitythe order is F < H < CH3 < NH2 C (CH3)HN < C1 < NH2CO C2H5 < (CH3)ZN < (CH3)HNCO CF3 (CH3)ZCH C2H (CH3)2NCO < C2H3 < (CH3)3C< C6H5,where previously studied functional groups have been included for completeness. The average relative property values presented here result from the calculation of the polarizability and second hyperpolarizability of 129 molecules where the components of these properties have been computed with the CHF-PT-EB-CNDO method. The relative ordering is analyzed, and proposals for the scales’ use are given.
Introduction The polarizability, ar, and in particular the second hyperPolarizability, y, of molecules are subjects of intensive current interest.~-s our previous work on these properties we have (1) (a) The average polarizability and second hyperpolarizabilitylb are a=
%(axx
+ a y y + %A
given by
Y=
%(Yxxxx
+ Y y y y y + Y l Z Z Z + 27,
+ 2 Y x m + 2Y,L
where x , y , and z denote Cartesian components. (b) Buckingham, A. D.; Om, B. J. Q.Rev. Chem. Soc. 1961, 21, 195. (2) (a) Shelton, D. P. J . Chem. Phys. 1986,85, 4234. (b) Jamieson, C. J.; Fowler, P. W. J . Chem. Phys. 1986, 85, 3422.
considered several aspects of the structure-polarization relationship. The assumption on which this endeavour relies is that the structural changes in a molecule (or a fragment of it) may be correlated with the changes induced in its polarizability and second hyperpolarizability.6 Thus as a semiquantitative imple(3) Bishop, D. M.; Pipin, J.; SilverFan, J. N. Mol. Phys. 1986, 59, 165. (4) (a) Liu, S.-Y.; Dykstra, C. E.; Kolenbrander, K.;Lisy, J. M. J. Chem. Phys. 1986,85,2077. (b) Adamowicz, L.; Bartlett, R. J. J. Chem. Phys. 1986, 84, 4988. ( 5 ) Waite, J.; Papadopoulos, M. G. J . Chem. Phys. 1986, 85, 2831. ( 6 ) (a) Similar propositions also exist for other properties, e&, Hammett6b noted that “Yet systematic organic chemistry could hardly have existed were it not true that like changes in structure lead to like changes in reactivity. Linear free energy relationships constitute the quantitative specialization of this fundamental principle.” (b) Hammett, L. P. Advances in Linear Free Energy Relationships; Chapman, N. B., Shorter, J., Eds.; Plenum: London, 1972; Foreward, p vii.
0022-3654/89/2093-0043$01.50/00 1989 American Chemical Society
44
Waite and Papadopoulos
The Journal of Physical Chemistry, Vol. 93, No. 1, 1989
mentation of this working hypothesis, scales of the average relative polarizability and second hyperpolarizability of some important functional groups have been determined (eight of which are studied here, while the properties of another eight functional groups have already been published.'J The study of a large number of substituents allows one to trace the effect of factors such as the aromatic character, the type of the involved bonds (single, double, etc.), the number of electrons and methylation on the magnitude of the functional group properties. An essential aspect of this work is the analysis of the effect of intramolecular interactions on the properties (a, y) of a functional group. For this purpose a large number of substrates (Y) have been associated with a substituent (X). Understanding of the above effect helps the appraisal of several approximate schemes (e.g., those that employ the additivity of bond properties), for the determination of molecular polarizabilities and hyperpolarizabilities. The reported scales (which embody the information resulting from extensive computational work) may provide insight into fundamental problems such as the connection between the reactivity of a molecule with the polarity of its substituents, as well as in more practical ones, for example, the design of materials with the desired properties. These are of essential importance for the construction of optical devices. The computations have been performed employing the CHFPT-EB-CNDO method.'-" This approach, with its shortcomings, has provided good results for a and y of an extensive set of medium and large sized molecules. The reported scale may be considered as an epitome of certain aspects of this computational work.
Method Description and Justification of the Theoretical Model. The calculation of the components of a and y has been performed by employing a computational model (CHF-PT-EB-CNDO) that relies on the following: (a) An extended basis (EB) C N D O wave function.I2 The employed set of orbitals is carefully optimized with respect to the property values (a and/or y) of some judiciously chosen model c o m p o u n d ~ . ~It* ~ is ~added ~ , ~ that only the electronic contribution to the polarizability and hyperpolarizability is treated; the vibrational contributions are not explicitly taken into account. (b) McWeeny et al.'sI3 coupled Hartree-Fock perturbation theory (CHF-PT). It is well documented that the quality of polarizability and especially hyperpolarizability values greatly depends on the basis Thus we have performed numerous tests employing up to f orbitals for C, N , 0, F, and C1 and up to d on H to establish certain rules (working experience) that facilitate the design of compact basis sets (that a r e computationally economic for the study of relatively large organic molecules). These sets of orbitals should also allow the physically correct description of the outer regions of the molecule on which the polarizabilities and hyperpolarizabilities mainly depend. These computations were performed on CH4,lIa C2H4,'lb NH3,9H20,1Sbetc. Analysis of the results has shown that high 1 AOs (e&, f orbitals for C, N, 0, (7) Waite, J.; Papadopoulos, M. G. J. Chem. Phys. 1985, 83, 4047. (8) Waite, J.; Papadopoulos,M. G. J. Chem. SOC.,Faraday Trans 2 1985, 81, 433. (9) Waite, J.; Papadopoulos, M. G. J. Chem. Phys. 1985, 82, 1427. (IO) (a) Waite, J.; Papadopoulos,M. G. J . Mol. Struct. (THEOCHEM.) 1984, 108, 247. (b) Papadopoulos, M. G.; Waite, J. J . Phys. Chem. 1986, 90, 549 1. (1 1) (a) Nicolaides, C. A.; Papadopoulos, M.; Waite, J. Theor. Chim. Acta 1982,61,427. (b) Papadopoulos, M. G.; Waite, J.; Nicolaides, C. A. J. Chem. Phys. 1982, 77, 2527. (c) Waite, J.; Papadopoulos,M. G.; Nicolaides, C. A. J. Chem. Phys. 1982, 77, 2536. (12) Pople, J. A.; Beveridge, D.L. Approximate Molecular Orbital Theory; McGraw-Hill: New York,1971. (13) (a) McWeeny, R. Phys. Reu. 1962, 126, 1028. (b) Diercksen, G.; McWeeny, R. J . Chem. Phys. 1966,44,3554. (c) Dodds, J. L.; McWeeny, R.; Raynes, W. T.; Riley, J. P. Mol. Phys. 1977, 33, 611. (14) Berns, R. M.; Wormer, P. E. S. Mol. Phys. 1981, 44, 1215.
TABLE I: Polarizability and Second Hyperpolarizability (in au)' of CH3CI, CH2C12,and C&&l a
Y
no. moleculeb~ccalcd
1 2
3
CH,CI CH2CI2 C6H5C1
exptl calcd exptl 6 220 7 100 [ref 28a] 28.8 30.5 [ref 28a] 39.6 44.8 [ref 28a] 11 700 11 300 [ref 28a] 82.5 79.9 [ref 28b,18] 38500 36500 [ref 28c]
1 au of polarizability N 0.148 176 X 1O-I' esu N 0.164867 X 10C2 m2 J-'. 1 au of hyperpolarizability N 0.503717 X lo-,' esu 5: 0.623 597 X C4 m4 J-,. *The geometry of the molecules is from the following: 1 [ref 291, 2 [ref 171, 3 [ref 171. cThe basis set for C1 (see text) was optimized with respect to a and y of CH3C1and CHI(21,; the values for chlorobenzene were predictive. and C1 and d for H ) are sufficient (they can lead to reasonable results) but not necessary, at the semiempirical level, especially if one takes advantage of the flexibility and freedom inherent in such methods?J1q$lsa It has also been established that moderately extended basis sets (e.g., Is, 2s, 2p STOs for H), the exponents of which have been carefully optimized, are adequate, in general, for the physically sound description of the various orders of polarization c o n ~ i d e r e d . ~ J * ~ - ~ It is known that the validity of semiempirical methods has often been questioned, perhaps more severely than their a b initio counterparts. However, it is considered that the ultimate test is the reliability of the results produced rather than a theoretical justification of the model.I6 The CHF-PT-EB-CNDO method satisfies this criterion since it has given good results for a and y of a large number of molecules belonging to several families of organic compounds (alkanes,Ila polyenes,Ilbaromatics,'Ic amines: amide^,^ etc.). The systematically observed agreement between experimental and theoretical results is due, to a great extent, to the carefully optimized (calibrated) basis sets and diminishes the possibility that the satisfactory results are due to cancellation of errors. Basis Sets. The basis set for chlorine (which has not been reported before) involves the STOs 3s(2.3), 3p(1.2) These have been optimized with respect to the experimental polarizabilityand hyperpolarizabilityvalues of CH3C1and CH2C12. The relevant computed and experimental values are given in Table I. It is noted that the above basis for C1 predicted reasonable values for a and y of C6H5Cl (Table I). Besides the above-defined basis set for chlorine, we have used a number of basis sets (defined in terms of STOs) that have been optimized with respect to experimental property ( a and/or y) values. These basis sets are given in footnote b of Table 11, together with the compounds with respect to which these orbitals have been optimized. These basis sets have been used to predict the properties reported in Tables 11-IX. It is noted that our published work has mainly concentrated on the prediction of the scalar average polarizability and second hyperpolarizability, since we have optimized our basis sets with respect to these properties. Thus properties like the first hyperpolarizability, for which our basis sets are not specifically optimized and which are very demanding, have not been considered in this study. Geometries. The coordinates of the molecules considered have been determined by employing the experimental geometries. In the absence of such information we have defined models using geometry data mainly from ref 17. Detailed references to the sources that have been used are given in the footnotes of Tables I-IX. The coordinates of all the molecules considered here are available on request. (a) Papadopoulos,M. G.; Waite, J. J . Chem. Phys. 1985,82, 1435. Waite, J.; Papadopoulos, M. G. Can. J . Chem. 1988, 66, 1440. (16) Murrell, J. N. Struct. Bonding 1977, 32, 93.
(15)
(b)
( 17) Tables of Interatomic Distances and Configurations in Molecules and Ions; Sutton, L. E., Ed.; Special Pulication No. 18; The Chemical Society: London, 1965.
Induced Moments in Large Molecules
The Journal of Physical Chemistry, Vol. 93, No. 1, 1989 45
TABLE 11: Relative Polarizability and Hyperpolarizability of the Substituent H m - as a Function of the Substrate
TABLE I V Relative Polarizability and Second Hyperpolarizability of the Substituent CHpCH2- as a Function of the Substrate
no. 1
2 3 4 5 6 7 8 9 10 11
12 13 14 15
moleculea~b HCZ-CH, HCz-NH2 HC&H HC2-C2H3 HC&HS HC2-NHCH3 HCZ-C~NH~ HC2-CZF HC2-C2CH, HC2-CONH2 HC&H(CH3)2 HC2-N(CH3)2 HC2-C(CH3)3 HCZ-CF, HC&H5
a’
7’
no.
1.20 1.13 1.01 0.86 0.80 1.58
5.80 2.28 2.20 3.07 3.14 3.55 3.31 -0.66 3.76 2.39 1.54 1.69 1.07 5.13 1.21
1
1.11
-0.06 0.92 0.84 0.54 0.65 0.43 1.10 0.40
“ The molecular geometries have been collected from the following sources: 1 [ref 171, 2 [ref 171, 3 [ref 171, 4 [ref 17, 291, 5 [ref 29, 301, 6 [ref 171, 7 [ref 17, 311, 8 [ref 17, 321, 9 [ref 291, 10 [ref 17, 331, 11 [ref 171, 12 [ref 171, 13 [ref 17, 291, 14 [ref 17, 341, 15 [ref 171. bFor the computation of the polarizability and hyperpolarizability components, the relative values of which are presented in Tables 11-IX, the following basis sets, defined in terms of STOs, have been used: (i) Alkyl group [ref lla]. H: 1s (l.O), 2s (0.5), 2p (0.5). C: 2s (1.625), 2p (1.625). These orbitals have been optimized with respect to a and y of CHI. (ii) Olefinic carbon and hydrogen [ref lob, llb]. H: 1s (0.8), 2s (0.4), 2p (0.4). C: 2s (1.325), 2p (1.325). These have been optimized with respect to a and y of C2H4 and y of C6Hs [ref llb]. (iii) Aromatic ring and corresponding hydrogens [ref 9, lob]. H: 1s (0.9), 2s (0.4223), 2p (0.4223). C: 2s (1.625), 2p (1.625). These orbitals have been optimized with respect to a and y of C6H6 [ref 91. (iv) Acetylenic carbon and hydrogen [ref 81. H: 1s (0.630), 2s (0.274), 2p (0.274). C: 2s (l.ll), 2p (1.11). These have been optimized with respect to a and y of C2H2. (v) Hydrogen and nitrogen belonging to amines and amides [ref 7, 91. H: ls (0.8), 2s (0.355), 2p (0.355). N: 2s (1.875), 2p (1.875). These have been optimized with respect to a and y of NH, [ref 91. (vi) Amide carbon, oxygen, and hydrogen bonded to CO [ref 7, lob]. H: 1s (0.9), 2s (0.45), 2p (0.45). C: 2s (1.625), 2p (1.625). 0: 2s (2.4), 2p (2.4). These have been optimized with respect to a of DMA, AC, NMA, FA, NMF, and DMF [ref 71. (vii) Fluorine [re 81. F 2s (2.6), 2p (2.6), 3s (0.6), 3p (0.8). These orbitals have been optimized with respect to a and y of CH3F, CH2F2,and CHF,. In the references next to the name of the functional group comparisons of results, derived by employing the above basis sets, with experimental data are given. TABLE 111: Relative Polarizability and Hyperpolarizability of the Substituent HX=CH- as a Function of the Substrate
no. 1
2 3 4 5 6 7 8 9 10 11
12 13
molecule” H3C2-CH3 H3C2-NH2 H,C&H HPC2-C2H3 H3C2-C2HS
HsCz-NHCHo H,C,-CONH2 H,CrCH(CH,)2 H3C2-N(CH3)2 H3C2-C4H5
HICZ-CF, H3C2-C(CH3)3 H3C2-C6HS
a’
7’
1.79 1.88 1.35 1.35 1.19 1.71 1.36 0.83 1.06 0.84 3.65 0.56 0.53
5.72 2.70 0.68 3.05 3.32 2.90 1.67 1.67 1.36 1.16 14.27 0.89 0.73
“The molecular geometries have been collected from the following sources: 1 [ref 351, 2 [ref 17, 361, 3 [ref 17, 291, 4 [ref 371, 5 [ref 17, 301, 6 [ref 17, 361, 7 [ref 17, 331, 8 [ref 171, 9 [ref 17, 361, 10 [ref 371, 11 [ref 17, 341, 12 [ref 171, 13 [ref 171. Results and Discussion
molecule” CzHS-CH, CZHS-NHz C2HS-CzH
2 3 4 5 6 7 8 9 10
C2HS-C2H3b C2HS-C2H5
12 13 14
CzHS-NHCH, C2HS-CONH2 C2HS-CH(CH3)2 C~HS-N(CH& C2HS-CONHCH, C2HS-NHCOCH, C2H5-C(CH3)3 CZHs-CF, CzHS-CON(CH,)2
15
C2H5-C6H5
11
a’
7’
1.76 0.39 1.31 1.22 1.18 1.68 1.39 0.83 0.82 1.02 0.99 0.59 2.27 0.69 0.69
3.10 1.37 0.05 1.64 1.71 1.81 0.72 1.04 0.71 0.78 0.55 0.58 8.29 0.49 0.57
” The molecular geometries have been collected from the following sources: 1 [ref 381, 2 [ref 30, 361, 3 [ref 30, 291, 4 [ref 17, 301, 5 [ref 301, 6 [ref 30, 361, 7 [ref 30, 331, 8 [ref 17, 301, 9 [ref 30, 361, 10 [ref 30, 331, 11 [ref 17, 331, 12 [ref 17, 301, 13 [ref 17, 341, 14 [ref 30, 391, 15 [ref 17, 301. bFully staggered. TABLE V Relative Polarizability and Hyperpolarizability of the Substituent CI- as a Function of the Substrate
no.
molecule” CI-CHI Cl-NHZ Cl-C2H CI-C2H, CI-CZHS CI-NHCH, CI-CH(CH3)2 CI-N(CH,)Z CI-CH2CI Cl-CH2CONH2 C1-C (CH,) 3 Cl-CF, CI-CSHg CI-CH,CONHCH, CI-C~HS C1-C6H,lb Cl-C6H, l e 1,2-C1-C6H4CI 1,3-C1-C&C1 1,4-CI-CsH4CI 1,2-CI-C6H4CO”2d 1,2-Cl-C6H4CONH2‘ 1,3-Cl-C6H&O”2 1,4-Cl-C6H4CONH2 1-CI-CloH7 2-CI-CloH7 1,3,5-Cl-C6H,C12
1
2 3 4 5 6 7 8 9 10 11
12 13 14 15
16 17 18 19 20 21
22 23 24 25 26 27
a’
7’
0.67 1.73 -0.10 0.54 0.70 2.00 0.55 1.63 0.38 0.34 0.44 1.10 0.31 0.26 0.21 0.16 0.18 0.29 0.17 0.13 0.22 0.22 0.17 0.14 0.15 0.14 0.25
0.55 3.03 -0.06 2.14 2.03 4.48 1.62 2.32 0.88 1.17 1.03 5.29 0.59 0.98 0.73 0.34 0.39 1.47 0.28 0.27 0.94 0.96 0.74 0.66 0.44 0.39 0.35
The molecular geometries have been collected from the following sources: 1 [ref 291, 2 [ref 17, 361, 3 [ref 171, 4 [ref 171, 5 [ref 171, 6 [ref 17, 361, 7 [ref 171, 8 [ref 17, 361, 9 [ref 171, 10 [ref 401, 11 [ref 171, 12 [ref 17, 341, 13 [ref 171, 14 [ref 401, 15 [ref 171, 16 [ref 171, 17 [ref 171, 18 [ref 171, 19 [ref 171, 20 [ref 171, 21 [ref 411, 22 [ref 411, 23 [ref 421, 24 [ref 421, 25 [ref 171, 26 [ref 171, 27 [ref 171. bAxial ‘Equatorial. d p form [ref 411. ‘a form [ref 411. the scale to zero for hydrogen ( X = H). The parameter P’gives a measure of the effective polarizing ability with respect to H, of the considered functional group X. It is noted that eq 1 cannot be used to define P‘ for properties that are zero for centrosymmetric molecules (e.g., the dipole moment or the first hyperpolarizability). The variation of P’, for a given substituent, indicates the effect of the substrate Y. Thus we define
The relative property measure
where P is either a or 7 , has been defined for the study of functional The factor 1 in the definition of P’ shifts
where P’is the average P’for the n considered pairs (XU and HY), E is the variation of P’and measures the effect of Y on the property value of X
7
9
*
46
The Journal of Physical Chemistry, Vol. 93, No. 1, 1989
TABLE VI: Relative Polarizability and Hyperpolarizability of the Substituent F E - as a Function of the Substrate
no. 1 2 3 4 5 6 7 8 9 10 11
molecule” FpC-CHB F3C-CzH F,C-C2H, F3C-CzHS F$-CH(CH,)2 F$-C(CHI), F3C-CF3 F,C-C,H 5 F$-C2CFs F,C-C(CF,)CHz F,C-CH(CH3)CFB
a’ 0.75 0.49 1.62 0.81 0.71 0.50 4.59 0.73 0.67 0.39 0.50
7’ 0.52 -0.47 2.20 2.18 1.66 0.60 9.43 3.92 -0.51 2.44 1.51
“ The molecular gametries have been collected from the following sources: 1 [ref 17, 341, 2 [ref 17, 341, 3 [ref 17, 341, 4 [ref 17, 341, 5 [ref 17, 341, 6 [ref 17, 341, 7 [ref 441, 8 [ref 17, 341, 9 [ref 17, 341, 10 [ref 17, 341, 11 [ref 30, 341. TABLE VI1 Relative Polarizability and Hyperpolarizability of the Substituent (CHa)&H- as a Function of the Substrate
no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
molecule” (CHj)2HC-CH3 (CH,)2HC-NH2 (CH,)2HC-C2H (CH,)ZHC-C2H, (CH,)2HC-C2HS (CHJ2HC-NHCH3 (CH,)2HC-NHCOH (CH3)2HC-CONH2 (CH3)2HC-CH(CHj)2 (CH,)ZHC-N(CH,)2 (CH,)2HC-CONHCH, (CH,),HC-NHCOCH, (CH,)2HC-N(CH,)COH (CH,)2HC-C(CH,), (CH,)2HC-CF, (CH~)~HC-C~HS
a’ 2.89 3.13 2.13 1.95 1.89 2.17 2.42 2.22 1.18 1.36 1.33 1.63 1.58 0.85 3.89 0.98
Y’ 5.36 2.12 0.27 2.24 3.05 2.58 1.58 1.42 1.29 1.31 1.10 1.18 1.30 0.75 14.39 0.71
” The molecular geometries have been collected from the following sources: 1 [ref 171, 2 [ref 17, 361, 3 [ref 171, 4 [ref 171, 5 [ref 17, 301, 6 [ref 17, 361, 7 [ref 17, 431, 8 [ref 17, 331, 9 [ref 171, 10 [ref 17, 361, 11 [ref 17, 331, 12 [ref 17, 331, 13 [ref 17, 331, 14 [ref 171, 15 [ref 17, 341, 16 [ref 17, 301. TABLE VI11 Relative Polarizability and Hyperpolarizability of the substituent (CH&C- as a Function of the Substrate
no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
molecule”
(cH;);c-cF, (CH&IC-N(CH,)COCH, (CH,)$-CON(CHj);! (CH,),C-C6H5
a’
Y’
4.36 4.55 3.09 2.53 2.53 3.00 2.99 1.61 1.77 1.77 1.14
9.89 3.06 0.60 2.54 3.86 3.37 1.82 1.71 1.61 1.64 0.94 13.37 1.38 1.11 0.94
5.05 1.36 1.34 1.32
” The molecular geometries have bebn collected from the following sources: 1 [ref 171, 2 [ref 17, 361, 3 [ref 17, 291, 4 [ref 171, 5 [ref 17, 30],6 [ref 17, 361, 7 [ref 17, 331, 8 [ref 171, 9 [ref 17, 361, 10 [ref 17, 331, 11 [ref 171, 12 [ref 17, 341, 13 [ref 17, 331, 14 [ref 17, 391, 15 [ref 17, 301. In Tables 11-IX we present the relative polarizability and hyperpolarizability of compounds containing the functional group under consideration, and in Table X we give the average relative properties of the eight functional groups that are analyzed in this work. The revised values of the functional groups that have previously been discussed are also reported in Table X. These
Waite and Papadopoulos TABLE I X Relative Polarizability and Hyperpolarizability of the Substituent CJ-ISI~as a Function of the Substrate
no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
molecule“ C~HS-CH~ C6Hs-NH2 C6H&H C6H5-C2H3 C6H5-C2HS
C~HS-NHCH, C~HS-NHCOH C~HS-CONH~ C6H5-CH(CH3) 2 C~HS-N(CH~)~ C~HS-CONHCH, C~HS-NHCOCH~ C~HS-C(CHS)~ C~HS-CF, C~HS-CON(CH~)~ C&-C&’ C6H5-C2H2C6H5
fff
Y’
4.37 4.55 3.06 2.53 2.83 4.43 12.3 1 3.01 1.83 2.07 2.20 10.27 1.35 6.08 1.41 1.14 1.14
10.68 4.58 1.46 3.67 5.90 6.46 11.36 3.09 2.80 3.29 2.91 10.54 1.79 62.24 1.89 2.40 1.43
” The molecular geometries have been collected from the following sources: 1 [ref 171, 2 [ref 451, 3 [ref 171, 4 [ref 171, 5 [ref 17, 301, 6 [ref 36, 451, 7 [ref 17, 431, 8 [ref 421, 9 [ref 17, 301, 10 [ref 36, 451, 11 [ref 17, 331, 12 [ref 17, 331, 13 [ref 17, 301, 14 [ref 17, 341, 15 [ref 17, 391, 16 [ref 171, 17 [ref 17, 461. ’The angle between the planes defined by each phenyl group is 45O [ref 1IC]. TABLE X Average Relative Properties of Some Functional Groups functional group a’ f e functional group 7’f e
FHH2NH3CCINH20CHC2(CH3)HNF,CHJ2H3C2(CH3)2N(CH,)HNOC(CHAHC(CH3)zNOC(CH,),CC6HS-
-0.07 f 0.07” 0.0 0.35 f 0.52” 0.39 f 0.16” 0.48 f 0.37 0.63 f 0.24’ 0.83 f 0.30 0.89 f 0.38’ 1.07 f 0.74 1.12 f 0.40 1.39 f 0.53 1.42 f 0.53’ 1.46 f 0.45’ 1.97 f 0.63 2.17 f 0.78’ 2.56 f 1.02 3.80 f 2.26
FHH,CC H2NC (CH,)HNC1-
NH20CHSCZ(CH3)zN(CH3)HNOCF3C(CH,),HCHC2(CH3)2NOCH3C2(CHj),CCsH5-
-0.50 f 0.24”
0.0 0.34 0.52 1.10 1.30 1.30 1.56 1.68 1.94 2.13 2.54 2.63 2.87 3.09 3.19 8.03
f 0.30“ f 0.35” f 0.60* f 0.91 f 0.82’ f 1.17 f 1.03’ & 0.83’ f 1.73 f 1.90 f 1.25 f 1.50’ f 2.16 f 2.36 f 7.37
’
“ Reference 8. Reference 7. In ref 7 the values for 9’ f e of NH2 and CH, are misprinted. The correct values are NH2(56 f 39) and CH3(44 f 50).
have been calculated by considering the extra property values that recently became available, and further the molecules for which the substrate ( Y ) is a single atom have been excluded, because they tend to lead to abnormally high effective property values. It is added that the af and =yf for CH3,reported in Table X, have been derived by considering 92 molecules. If a compound has P’> 0 this means that its functional group, in the particular intramolecular environment, is characterized by a polarizing ability, while if P’ C 0, the functional group shows a depolarizing capacity with respect to hydrogen. The functional groups H3CZ-, H5C2-, (CH3)*HC-, (CH3)3C-, and C6HS- are included in compounds that have P’> 0 (Tables 111, IV, and VII-IX), while the functional groups HC2-, C1-, and F3C- are involved in molecules that have either positive or negative P’(Tab1es 11, V, and VI). These observations refer specifically to the compounds analyzed in the present work. Comparison of 7’ for H5Cz- and H3Cz- clearly demonstrates the large effect of the double bond, with respect to the single bond, on the second hyperpolarizability (Tables 111, IV, and X). This phenomenon is also shown by a’ but less strongly. It is observed that the vinyl and acetylenic groups (Tables 11, 111, and X) have relatively large 7’ (taking into account their number of electrons). This considerable ability for polarization is due to their double and triple bonds, respectively.
Induced Moments in Large Molecules
The Journal of Physical Chemistry, Vol. 93, No. 1, 1989 41
The effect of the aromatic character on the hyperpolarizability is clearly demonstrated in a number of cases, for example, by comparing the 7‘ of (CH,),NOC- and C6H5-, which have similar numbers of electrons (the atoms involved in the first functional group have 39 electrons and in the second 41 electrons). It is observed that 4’ of C6H5- is larger than that of (CH3)2NOC- by a factor of 2.8 (Tables IX and X). The a’ results show that the aromatic character affects the polarizability as well but in a less pronounced way (in comparison to that of the hyperpolarizability). Further the large interaction between C6H5and its substrates, for both a and y, is shown by large 6 values for this group. We have considered methylation of three different functional groups: NH2-, NH20C-, and CH3- (Tables IV, VII, VIII, and X). It has been observed that both d and 7’ of these groups (Table X) increase by this process (C- or N-methylation). The change in 7’ as we go from NH2- to (CHJHN- and then to (CH3)2N- is constant. This is approximately true for the changes in a’ as well. As we go from NH20C- to (CH3)HNOCand then to (CH,),NOC-, we observe (Table X) that the two resulting changes in 7’ are not equal and the second difference is larger than the first (the opposite trend is observed for the variations of a’). Several of the functional groups are isoelectronic (e.g., F-, H$-, H2N-i (CH,)HN-, C1-, H5C2-i (CH3)2N-, (CH3)2HC-, etc.). This allows one to see how the variation of the structure differentiates the behavior of the functional group as this is probed by the polarizability and the hyperpolarizability. We observe that F3C- is characterized by relatively high, positive a’ and 7’ despite the fact that fluorine alone has negative a’ and 7’ (Tables VI and X). In general, the more electrons the functional group has, the higher its properties (a’ and 7’) are, but there are several exceptions (e.g., those that are due to fluorine and functional groups containing double or triple bonds). The results (a’ or 7’) for H3C-, H5C2-, (CH,),HC-, and (CH3)3C- clearly show that methylation of H3C- leads to changes of a’ and 7’ that are not equal. Therefore this process cannot be described correctly by an additivity scheme that neglects interactions of intramolecular fragments. On the other hand, although the properties of C6H5- (like any other functional group) vary greatly as a function of the intramolecular environment (-Y), the average relative properties of C6H5- can be derived, approximately, by adding the properties of three vinyl groups. Examples have already been mentioned that verify both trends (additive changes or otherwise). These observations indicate that the properties of functional groups that have some similarities in their structure are likely to be reasonably predicted by bond additivity schemes. However the overall pattern that emerges from the present computations (Tables 11-IX) emphasizes, in general, the role of the intramolecular interactions and thus simple additivity schemes, which neglect them, “hide” a significant aspect of linear and nonlinear polarization. For completeness it is added that carefully designed simple additivity schemes have provided in several cases reasonable results, in particular for aI8(various explanations have been proposed for this success, e.g., cancellation of conflicting factor^.'^^^^ For example, both Denbigh’s2I and our method gave for eight functional groups (NH2-, CH3-, HC2-, C2H5-, (CH3)2HC-, (CH3)3C-, and C6H5-), for which parameters were given by Denbigh, the same ordering for their polarizabilities, except for C2H3- and C2H5-, for which Denbigh’s method predicts that a(CZH5-) > a(C2H3-), while in Table X the reverse trend is reported. Furthermore it is noted that more elaborate and realistic approaches (in comparison to the bond additivity approximation where interactions between bonds are neglected) have been proposed and successfully applied. For example, one may note the interacting
segment model, in which electrostatic interactions between adjacent segments within the molecule are taken into a c c o ~ n t . ’ ~ . ~ ~ It has long been recognized that one of the factors that influence reactivity is the polarity of the s~bstituent.2~Taft’s equation for evaluating the polar effect of a substituent R in the ester R C 0 2 R is w e l l - k n o ~ n . ~The ~ * ~present ~ results show that there is good correlation for a’ and 4’ of CH3-, C2H5-, (CH3)2HC-, and ~~ (CH3)3C- with A M * , (total steric energy of a ~ t i v a t i o n ) .The correlation-like coefficient^^^ are 0.93 and 0.90 for the pair of properties a r / A A E * sand T’/AAE*,, respectively. Most works in the literature related to the induced moments of molecular fragments refer specifically to the polarizabilities. However it has been reported that large fields may be found in the vicinity (a few angstroms) of an ion or polar molecule.26 In this situation the term due to the hyperpolarizability contribution may have a considerable contribution to various inter- and intramolecular phenomena. Finally the reported scales complement other existing orderings (e.g., the “inductive order” of relative electron release2’ and allow a more comprehensive understanding to be reached concerning the properties of functional groups.
(18) (19) (20) (21)
Le FBvre, R. J. W. Adu. Phys. Org. Chem. 1965, 3, 1. Miller, C. K.; Orr, B. J.; Ward, J. F. J . Chem. Phys. 1977, 67, 2109. Pitzer, K. S.Adu. Chem. Phys. 1959, 2, 59. Denbigh, K. G. Trans. Faraday SOC.1940, 36, 936.
Concluding Remarks The average relative polarizability and hyperpolarizability of several important functional groups have been studied. The reported orderings of polarization complement those that have been given previously. Thus overall 16 functional groups have been studied and analyzed, employing the properties ( a and y) of a very large number of molecules. An essential finding of this work is the scale of polarization reported in Table X. This scale contributes to the better understanding of the structure-polarization relationship, by classifying several important functional groups that represent a wide variety of structural features according to their polarizing abilities
(22) Miller, C. K.; Orr, B. J.; Ward, J. F. J . Chem. Phys. 1981, 74, 4858. (23) Shorter, J. Advances in Linear Free Energy Relationships; Chapman, N. B., Shorter, J., Eds.; Plenum: London, 1972; p 71. (24) Ingold, C. K. Structure and Mechanism in Organic Chemistry, 2nd ed.; G. Bell and Sons: London, 1969. (25) Lindgen, B. W. Statistical Theory, 3rd ed.; Collier and MacMillan: London, 1976; p 478. (26) . , (a) . , Buckinnham. A. D. 0.Reu. Chem. SOC.1959. 13. 183. (b) ., Braunman, J. I.; Bkir, L. K. J . A&. Chem. SOC.1970, 92, 5986. (27) Broxton, T. J.; Deady, L. W.; Katritzky, A. R.; Liu, A,; Topsom, R. D. J . Am. Chem. SOC.1970, 92, 6845. (28) (a) Bogaard, M. P.; Orr, B. J.; Buckingham, A. D.; Ritchie, G. L. D. J . Chem. Soc., Far. Trans. 2 1978, 74, 1573. (b) Le FBvre, R. J. W.; Rao, B. P. J . Chem. SOC.1958, 1465. (c) Oudar, J. L.; Chemla, D. S.; Batifol, E. J . Chem. Phys. 1977, 67, 1626. (29) Costain, C. C. J . Chem. Phys. 1958, 29, 864. (30) Allen, H. C., Jr.; Plyler, E. K. J . Chem. Phys. 1969, 31, 1062. (31) The H,N-C is MNDO optimized (QCPE353). The NH, bond lengths and angles are from: Strametz, C. C.; Schmidtke, H. H. Theor. Chim. Acta 1976, 42, 13. (32) Strausz, 0. P.; Norstrom, R. J.; Hopkinson, A. C.; Schoenborn, M.; Csizmadia. I. G. Theor. Chim. Acta 1973. 29, 183. (33) Del Bene. J. E. J . Am. Chem. Soc. 1978. 100. 1387. (34j Arrighini, G. P.; Guidotti, C.; Maestro, M.;Moccia, R.; Salvetti, 0. J . Chem. Phys. 1969, 51, 480. (35) Lide, D. R., Jr.; Mann, D. E. J . Chem. Phys. 1957, 27, 868. (36) Dewar. M. J. S.: Thiel. W. J . Am. Chem. SOC.1977. 99. 4907. (37) Nascimento, M. A. C.; Goddard 111, W. A. Chem. Phys. 1979, 36, 147. ( 3 8 ) Snyder, L. C.; Basch, H. Molecular Wave Functions and Properties; Wiley: New York, 1972. (39) Sabatino, A.; LaManna, G.; Paolini, L. J . Phys. Chem. 1980, 84, 2641. (40) Dejace, J. Acta Crystallogr. 1955, 8 , 851. (41) Kato, Y.; Takaki, Y.; Sakurai, K. Acta Crystallogr., Sect. E 1974, 30, 2683. (42) Penfold, B. R.; White, J. C. B. Acta Crystallogr. 1959, 12, 130. (43) Hirota, E.; Sugisaki, R.; Nielsen, C. J.; Sarensen, G. 0. J . Mol. Spectrosc. 1914, 49, 25 1. (44) Gallaher, K. L.; Yokozeki, A.; Bauer, S. H. J. Phys. Chem. 1974, 78, 2389. (45) Lister, D. G.; Tyler, J. K. Chem. Commun. 1966, 152. (46) Hoekstra, A,; Meertens, P.; Vos, A. Acta Crystallogr., Sect. E 1975, 31, 2813.
The Journal of Physical Chemistry, Vol. 93, No. I , 1989
Waite and Papadopoulos
as these are expressed by two scalar properties ( a , y). These relationships are of use in the design of materials for specific applications in nonlinear optics. In particular we note that this work documents, with numerous examples, the considerable effect of intramolecular interactions on the polarizability and even more on the hyperpolarizability. This is a factor that has to be taken into account by any approximate scheme, which relies on physically correct assumptions, for the prediction of these properties. More specifically Tables 11-IX illustrate the variation in a' and y' of a substituent as a function of the properties of the substrate (-Y) and thus of the intramolecular interactions. The reliability of the observations is strengthened by the numerous studied cases, whereas Table X presents the averages (a', 7') which allow the correlation of these properties for the functional groups with factors such as the number of its electrons, the type of the involved bonds (single, double, etc.), its overall properties (e.g., the aromatic character), and the number of methyl groups. The computations of the polarizability and hyperpolarizability components have been performed by employing the CHF-PTEB-CNDO method, which relies on optimized and carefully tested basis sets. These basis sets have given results (for a and y) in satisfactory agreement with the available experimental data.7-9*Iob*11a,b The advantages of the employed method are that it constitutes a well-defined and tested theoretical framework and it makes use of the existing experimental information to determine the requisite properties. The drawback of our approach is that, being a simple semiempirical model, limitations are imposed on the accuracy of several of the reported results for the second hyperpolarizability (which is a very sensitive property to the quality of the wave function). Thus although the reported scales represent an improvement in comparison to the values produced by an additivity scheme, they certainly need further refinement before they lead to accurate, quantitative answers.
Computation of the Properties. For the calculation of the polarizability and hyperpolarizabilitycomponents the CNDO wave function is perturbed by employing the theory of McWeeny et a1.I3 The required first- and second-order density matrices are stored in single precision. All sums and inner products are computed in double precision. Convergence Criteria. For the computations of the density matrices the following criteria have been used:
48
Acknowledgment. W e thank A. Vasiliou for running the correlation tests presented in this work. Appendix We give a synopsis of the main features of the computational procedure that is used to calculate the components required to determine the average polarizability and second hyperpolarizability.' Unperturbed Wave Function. Atomic Coordinates. The computation of the coordinates has been performed by employing a polar-to-Cartesian conversion subroutine similar to that available in Dewar's M I N D 0 and MNDO programs (QCPE 309 and 353). SCF. This is an extended and upgraded version of the C N D O / 2 program (QCPE 141). Basis sets including up to f oritals can be used, and molecules involving transition metal elements can be studied. This is wholly in double precision.
I&')
- k-IRLm)I
< 10-"N
where k is the iteration number, m is the order of the density matrix R, and N is the number of orbitals. We have for every ij form=O n=4 form=1.2 n = 6 Registry No. HC2CH3,74-99-7; HC2NH2,52324-04-6; HC2C2H, 460-12-8; HC2C2H3, 689-97-4; HC2C2H5, 107-00-6; HCZNHCHS, 40908-74-5; HCzC2NH2,75074-98-5;HC2C2F, 74706-98-2;HC2CtCH3, 491 1-55-1;HC2CONH2, 7341-96-0; HC2CH(CH3)2, 598-23-2; HC2N(CH,),, 24869-88-3; HC,C(CH,),, 917-92-0;HC2CF3, 661-54-1; HC2C6H5, 536-74-3;H3CzCH3, 11 5-07-1; HgC2NH2, 593-67-9;H3CzC2H3, 106-99-0;H3C2C2H5, 106-98-9;H,C2NHCH3,2308-42-1; H3C2CONH2, 79-06-1; HIC,CH(CH&, 563-45-1; HjC2N(CH3)2, 5763-87-1; H3C2CF3, 677-21-4; H,C,C(CH,),, 558-37-2; H ~ C ~ C ~100-42-5; H S , CzHSCH3, 74-98-6; CzHSNHZ, 75-04-7; C2HSC2H5, 106-97-8; C2HSNHCH3, 62478-2; C2HsCONH2, 79-05-0;C2HSCH(CH,)z, 78-78-4; CzHsN(CH3)2, 598-56-1; C,H&ONHCHI, 1187-58-2; C2HSNHCOCH3, 625-50-3; C2HSC(CHp),, 75-83-2; C2HSCF3, 421-07-8; C2HSCON(CH3)2, 75896-3; C ~ H S C ~100-41-4; H ~ , CICH3,74-87-3; ClNH2, 10599-90-3;ClCzH, 593-63-5; CICZH3, 75-01-4; CIC2H5, 75-00-3; CINHCHI, 6154-14-9; CICH(CHI)2,75-29-6;ClN(CHj)z, 1585-74-6;ClCH,C1,75-09-2; CICH2CONH2, 79-07-2; CIC(CH,)I, 507-20-0; CICFj, 75-72-9; ClCH2CONHCH3,96-30-0;CIC6H5, 108-90-7;C~C,&II,542-18-7; 1,2-Cl-C6H&l, 95-50-1; 1,3-C1-C6H&I, 541-73-1; 1,4-Cl-C6H4CI, 106-46-7; 1,2-c1C6HdCONH2, 609-66-5; 1,3-CI-C,H4CONH2, 6 18-48-4; 1,4-ClC6HdCONH2, 619-56-7; l-CI-CloH,, 90-13-1; 2-CI-CloH7, 91-58-7; 1,3,5-C1-C6H,C1,, 108-70-3; FICCHI, 420-46-2; FPCCH(CHP),, 155049-8; F-,CC(CH,)I, 55757-33-0; FICCF3, 76-16-4; F ~ C C ~ H98-08-8; S, FBCCZCFI, 692-50-2; FICC(CF3)CH2, 382-10-5; F,CCH(CH,)CFj, 382-09-2; (CH&2HCCHj, 75-28-5; (CH&HCNH2,75-3 1-0; (CHJ2HCNHCH3,4747-21-1;(CH3)2HCNHCOH, 16741-46-1; (CH3)zHCCO"2, 563-83-7; (CHI)2HCCH(CH3)2, 79-29-8; (CHS)2HCN(CH3)2, 996-35-0; (CH3)zHCCONHCHI. 2675-88-9; (CH3)2HCNHCOCH3, 1118-69-0; (CHI)ZHCN(CH,)COH, 34855-40-8; (CH>)2HCC(CH,),, 464-06-2; (CH&+HCC,H5,98-82-8; (CH,)jCCH3,463-82-1; (CH3)3C"2, 75-64-9; (CHI)&NHCH3, 14610-37-8; (CHI)jCCONH2, 75410-9; (CH,),CN(CH&, 918-02-5; (CH&$CONHCH,, 6830-83-7; (CH,)pCC(CH3)3, 594-82-1; (CHj)3CN(CHI)COCH,, 24331-69-9; (CHJ$CON(CHJ2, 24331-71-3; (CH3)3CC6HsI98-06-6; C ~ H S C H ~ , 108-88-3; C,HsNH2,62-53-3; C~HSNHCH~, 100-61-8; C6H5NHCOH, 103-70-8; C6HsCONH2, 55-21-0; C6HsN(CH3)2, 121-69-7; C6H5CONHCH,, 613-93-4; C6H5NHCOCH3, 103-84-4;C~HSCON(CH~),, 61 174-5; C ~ H ~ C ~92-52-4; H S , C ~ H ~ C ~ H ~588-59-0; C ~ H S ,cl, 22537-15-1.
