17820
J. Phys. Chem. 1996, 100, 17820-17824
A New Optimization of Atom Polarizabilities in Halomethanes, Aldehydes, Ketones, and Amides by Way of the Atom Dipole Interaction Model Kimberly A. Bode and Jon Applequist* Department of Biochemistry and Biophysics, Iowa State UniVersity, Ames, Iowa 50011 ReceiVed: July 16, 1996X
A new optimization of atom polarizabilities is carried out by fitting observed mean molecular polarizabilities, polarizability anisotropies, and Kerr constants with values calculated by way of the atom dipole interaction (ADI) model which was used for similar purposes by this laboratory in 1972. New values are obtained for the polarizabilities of F, Cl, and Br in halomethanes, C′ and O in aldehydes, ketones, and amides, H in the aldehyde C′HO and the amide NH group, and N in amides. Most of the new values differ slightly from atom polarizabilities that were optimized to fit only observed mean polarizabilities in 1972, though differences up to 50% occur. The new values result in a considerably improved fit of calculated and observed anisotropies and Kerr constants, with a somewhat poorer fit to mean polarizabilities. The results are compared with those from studies by Birge, Thole, and Miller, who used modified versions of the ADI model. It is concluded that the unmodified model reproduces observed anistotropies about as well as any other model with the revised atom polarizabilities.
Introduction 1972,1
this laboratory reported the application of an atom In dipole interaction (ADI) model to the prediction of molecular polarizability tensors for a variety of organic and other polyatomic molecules. In that study a set of transferable isotropic atom polarizabilities was optimized to fit mean polarizabilities found from observed refractive indices of gases and liquids. While the model has since been applied with reasonable success to a variety of optical properties, a deficiency in the model noted in the 1972 study was its tendency to exaggerate the anisotropy of polarizability. The purpose of this paper is to address that deficiency and to present a new set of atom polarizabilities which reduce the discrepancies in anisotropies to the level of the most successful available theories in this regard. We first review some of the history of applications of the ADI model and the efforts by various workers to refine it, as we feel these matters justify continued use of the model as well as our present work on the reoptimization of parameters. A review2 of the ADI model in 1977 documented its success in predicting a number of properties. Those related directly to the polarizability tensor include the mean polarizability, light scattering depolarization, and molar Kerr constants. Higher order properties which depend in more subtle ways on the dipole interaction feature of the model were also predicted surprisingly well; these include optical rotations of chiral molecules, Raman scattering intensities of methane derivatives,3 and the uniformfield quadrupole polarizability of methane. The model was subsequently extended, in a series of studies,4-12 to the calculation of ultraviolet absorption and circular dichroic (CD) spectra of major polypeptide structures by incorporating a complex frequency-dependent polarizability of the peptide chromophore, along with the atom polarizabilities that had been determined in our 1972 study. The model proved superior to conventional exciton theory in such calculations in that it reproduced the highly nonconservative CD spectra observed in a variety of structures and showed fairly consistent agreement with experiment for both absorption and CD. In the meantime, other workers have proposed modifications of the ADI model that were designed to overcome the tendency of the model to exaggerate molecular anisotropies. Birge13 X
Abstract published in AdVance ACS Abstracts, October 15, 1996.
S0022-3654(96)02119-3 CCC: $12.00
adopted an ADI model in which each atom was characterized by an anisotropic polarizability and found that discrepancies in components of the molecular polarizability tensor were reduced. Thole14 developed a model which replaced the point dipole of the atom with an extended charge distribution and replaced the dipole field tensor with a tensor whose distance dependence is damped at short interatomic distances. He optimized atom polarizabilities to fit molecular polarizability components as well as mean polarizabilities and found that this model also reduced the discrepancies in the molecular components. Birge and coworkers15 subsequently adopted Thole’s approach using Slatertype orbitals to represent atom charge distributions. These workers optimized atom polarizabilities to fit molecular tensor components and obtained a fit comparable to that of Birge13 and Thole.14 Miller16 adopted a related modification of the ADI model in which a damped, or attenuated, dipole interaction tensor was applied, anisotropic atoms were introduced, and interactions between bonded atoms were neglected. Results for molecular polarizability components were as close to experimental values as the best of the various ADI methods for most molecules. One might gain the impression from the studies of Birge, Thole, and Miller that the isotropic point-atom model of our 1972 study should be discarded in favor of one of the models that have better reproduced molecular anisotropies. We believe such a conclusion would be premature for the following reasons: (i) One major reason the studies of these workers have yielded a better fit is that the parameters were optimized to fit the molecular polarizability components, while our 1972 study sought to optimize only the mean polarizabilities. The present study achieves a fit comparable to those of other workers without abandoning the isotropic point-atom model by including measures of the molecular anisotropy in the optimizations. (ii) Our point-atom model is a well-defined system whose behavior can be calculated to a high degree of accuracy on the basis of known physical laws. The methods which use damped, or attenuated, dipole field tensors do not correspond exactly to any known physical model and thus give less insight into the underlying causes of observed molecular behavior. (iii) The isotropic pointatom model has a demonstrated capacity to predict higher order polarization properties, including particularly optical rotation and circular dichroism, which are highly sensitive to the manner © 1996 American Chemical Society
A New Optimization of Atom Polarizabilities of interaction among the parts of the molecule. The Birge model has been shown to predict Raman intensities,17 but as far as we are aware, no calculation of the chiroptical properties from the models of Birge, Thole, or Miller has been reported. A fact that prompted the present work is the finding by Ladanyi and Keyes18 and later by Applequist19 that the polarizabilities of C and H atoms optimized for alkanes by a fit to molecular anisotropy data led to improved calculations of molecular anisotropies for alkanes, even though the changes in the C and H polarizabilities required for this improvement were rather small. We thus expected that small variations in other atom polarizabilities would give a better fit to molecular anisotropies of a variety of polyatomic molecules without abandoning the isotropic point-atom model. It is worth noting some recent progress in quantum mechanical calculations, which go beyond the dipole interaction models in providing a detailed picture of the distortions of the charge distribution experienced by a molecule in an electric field. In particular, the studies of Stone20 and of Bader and coworkers21,22 are relevant to the present work in that they give details of the changes in charge distribution in regions of a molecule that can reasonably be identified as atoms. These authors find that the polarization of typical polyatomic molecules can be described by transfer of charge among atoms as well as dipole and quadrupole polarization of the atoms. The difficulties in drawing a correspondence among the quantum mechanical models and the ADI models have been discussed elsewhere.19 Suffice it to say here that a modification of the ADI model that includes charge transfer among atoms (the atom monopoledipole interaction, or AMDI, model) did not provide a better fit to experimental polarizabilities of saturated hydrocarbons than the ADI model.19 The AMDI model did prove superior to the ADI model in fitting polarizabilities of aromatic hydrocarbons.19 For the present work we assume that the ADI model, without charge transfer, is adequate to treat the molecules studied, as these are primarily saturated aside from the carbonyl groups in the aldehydes, ketones, and amides. Our immediate objective is to obtain a self-consistent set of atom polarizabilities for simple molecules that may be used in more complex molecules to predict a variety of polarization properties. The experimental data used in the 1972 study are supplemented here by more recent data where possible, including data on a larger number of compounds. Newer computational methods have made it much easier now to optimize several parameters simultaneously to fit a complex model. For present purposes we have felt it desirable to include as target data as many experimental measurements as possible in order to ensure the best possible optimum parameters. As a consequence, there remain few experimental data on homologous compounds that would serve to test independently the predictions of polarizability tensors based on the new parameters. One test of the validity of the model and its parameters is contained in the standard deviations of the parameters from the error function and in the deviations between theoretical and experimental polarizabilities. Several tests of the predictive value of the model are presented in the accompanying study of spectral properties of polypeptides.23 Theory The theory of the atom dipole interaction model has been described previously.1,2 In short, the model allows one to predict the optical properties of a molecule from isotropic atom polarizabilities and molecular structure. In this model atoms interact only through their mutally induced fields when in the presence of an external electric field. The model is applied here to the calculation of anisotropy δ, mean polarizability R j , and
J. Phys. Chem., Vol. 100, No. 45, 1996 17821 molar Kerr constant [K]. Equations relating the molecular polarizability components and these optical properties are24,25
δ2 ) 3/2(r:r - 3R j 2)
(1)
R j ) 1/3(R1 + R2 + R3)
(2)
[K] ) 2/9πNA(b1 + b2)
(3)
jR j 0)/15kT b1 ) (r:r0 - 3R
(4)
j µ2)/15k2T2 b2 ) (r:µµ - R
(5)
where Ri is the ith principal component of polarizability, r is the optical polarizability tensor, r0 is the static polarizability tensor, µ is the permanent dipole moment, NA is Avogadro’s number, k is the Boltzmann constant, and T is the absolute temperature. Static polarizabilities are approximated as 1.1 times the optical polarizabilities. Methods The variables to be optimized are the isotropic polarizabilites of all atoms in the molecules considered except for those of alkane C and H, whose values are taken from a previous optimization.19 A given atom species is assumed to have the same polarizability in all molecules of a homologous series. Optimization was carried out by the Levenberg-Marquardt method as described previously.19 The χ2 quantity which is minimized in this method is
χ2 ) ∑[Yi(expt) - Yi(theo)]2/σi2
(6)
i
j , |δ|, or [K], and σi is a weighting factor where Yi is a value of R which is proportional to the standard deviation of the experimental quantity. In our treatment of halomethane, aldehyde, and ketone optical data, this deviation is taken to be the experimental uncertainty given in the literature except for the cases in which more than one experimental value is available; in such cases an average value is calculated, and the standard deviation of the set of values is used as σi. For the amide data, an arbitrary weighting scheme was chosen in which mean polarizabilities were assigned a 1% experimental error and the anisotropies and Kerr constants given 3% error. The results from this scheme appeared more reasonable than those found with weighting factors based on the few available estimates of experimental uncertainty. Molecular structures were taken from ref 26 and the sources in ref 1, with the following exceptions: the structure of CH2F2 was taken from ref 27, and the coordinates of (CH3)3CCHO (pivaldehyde), the haloaldehydes, and the haloamides were created from those of acetaldehyde and acetamide by substitution of tetrahedral methyl and halomethyl groups from the corresponding CHX3 structures of ref 1. Permanent dipole moments required for calculation of Kerr constants were obtained mostly from McClellan’s tables.28 The direction and magnitude of the moment in formamide were taken from Kurland and Wilson,29 and the same direction was assumed for N-methylformamide and N,N-dimethylformamide. For the acetamide derivatives the dipole moment angles were calculated from the dipole moment magnitudes of pairs of acetamides in a manner similar to that described by Khanarian et al.30 The method is simplified as follows. Let µA and µAX be the dipole moments of acetamide and a trihaloacetamide, respectively. Let the dipole moment of the CX3 group be µCX3, where X ) H, F, Cl, or Br. This dipole
17822 J. Phys. Chem., Vol. 100, No. 45, 1996
Bode and Applequist TABLE 3: Optimized Atom Polarizabilities (Å3)
Figure 1. Amide structure and permanent dipole moment angle.
TABLE 1: Gas Phase Dipole Moments28 (debye) at 293 and 289 K high low
CH3CF3
CH3F
CH3CCl3
CH3Cl
CH3Br
2.35 2.27
1.906 1.729
2.03 1.79
2.02 1.66
1.83 1.76
TABLE 2: Permanent Dipole Moments and Dipole Moment Angles of Amides compound
µ (D)
βi (deg)
formamide N-methylformamide N,N-dimethylformamide acetamide N-methylacetamide N,N-dimethylacetamide trifluoroacetamide trichloroacetamide tribromoacetamide N-methyltrifluoroacetamide N-methyltrichloroacetamide N-methyltribromoacetamide
3.8542 3.8442 3.9542 3.8730 3.9730 3.8144 4.2630 3.9030 3.9930 4.4130 4.0830 3.8430
219.929 219.9 219.9 211.6 ( 5.6 211.6 ( 5.6 211.6 ( 5.6 177.8 ( 0.4 188.1 ( 1.1 186.2 ( 0.1 177.5 ( 0.3 186.8 ( 0.9 194.5 ( 0.4
atom
this work
refs 1, 2
C (alkane) H (alkane) F Cl Br C′ (aldehyde/ketone) O (aldehyde/ketone) H (aldehyde) C′ (amide) O (amide) N (amide) H (amide)
0.777 ( 0.00519 0.172 ( 0.00419 0.352 ( 0.007 1.761 ( 0.009 2.819 ( 0.084 0.763 ( 0.071 0.284 ( 0.086 0.134 ( 0.018 0.563 ( 0.114 0.423 ( 0.098 0.559 ( 0.066 0.149 ( 0.021
0.878 ( 0.01419 0.135 ( 0.006 0.32 ( 0.01 1.91 ( 0.02 2.88 ( 0.05 0.616 ( 0.008 0.434 ( 0.010 0.167 ( 0.001 0.616 ( 0.008 0.434 ( 0.010 0.530 ( 0.006 0.161 ( 0.005
TABLE 4: Anisotropies (Å3) and Polarizabilities (Å3) of Halomethanes expt31
CF4 a
CHF3
CH2F2b,c CH3Fa CCl4 CHCl3a CH2Cl2c,d CH3Cla CHBr3a
moment is taken to be along the C-C′ bond in acetamides. The additivity relation for dipole moments may be expressed as
µAX ) µA + µCX3 - µCH3
(7)
∆µ ) µCX3 - µCH3
(8)
|δ|
compd
CH2Br2c,e CH3Bra
calc expt32-35 calc expt33-35 calc expt33,35 calc expt36 calc expt34,36,37 calc expt34-37 calc expt34,35,37 calc expt36 calc expt36 calc expt35 calc
0.26 0.10 0.39 0.59 0.31 0.37 2.67 2.76 2.73 2.52 1.54 1.53 4.64 5.17 2.02 2.35
R j
R1
R2
R3
2.91 2.89 2.88 2.79 2.73 2.83 2.61 2.62 10.45 9.19 8.51 7.59 6.57 6.00 4.53 4.23 11.79 11.18 8.65 8.37 5.60 5.33
2.91 2.89 2.79 2.76
2.91 2.89 2.79 2.76
2.91 2.89 3.05 2.86
3.22 2.71 2.74 10.45 9.19 9.40 8.51
2.58 2.71 2.74 10.45 9.19 9.40 8.51
2.69 2.40 2.38 10.45 9.19 6.73 5.75
4.88 4.02 3.72
7.64 4.02 3.72
5.47 5.56 5.25
12.73
12.73
8.09
6.03 4.93 4.55
11.73 4.93 4.55
7.35 6.95 6.90
a R || 3-fold axis. b R ⊥ FCF plane. c R || 2-fold axis. d R ⊥ ClCCl 3 1 3 1 plane. e R3 ⊥ BrCBr plane.
Let
∆µ is a dipole moment increment which is also directed along the C-C′ bond. Taking the dot product of eq 7 with itself gives
µAX ) µA + (∆µ) + 2µA(∆µ) cos θ 2
2
2
(9)
where θ is the angle between ∆µ and µA. From Figure 1 it is seen that βA ) θ + ω, where βA is the dipole moment angle for acetamide or N-methylacetamide. Once the quantity ∆µ is known, then θ and βA are known. By the additivity of group moments, ∆µ is simply the dipole moment of CH3CX3. Since the dipole moment of a compound CX4 is zero, we have, again by the additivity hypothesis, µCX ) µCX3, and hence ∆µ may be taken as the dipole moment of a trihalomethane. The highest and lowest available gas phase dipole moment measurements of the appropriate trihalomethane and trihaloethane compounds at 293 or 298 K,28 shown in Table 1, were used to calculate βA, which was found to be the same within the range of uncertainty for both acetamide and N-methylacetamide. Once each permanent dipole moment angle was determined for a nonhalogenated amide, the dipole moment component of the haloamide was calculated from eq 7. The polar angle βi for a given species is determined from the components of µAX. The values shown in Table 2 are the average angles with standard deviations among 2-4 calculations based on various halomethane and haloethane dipole moments.
Computations were carried out on a DEC 3000/300L workstation using double-precision Fortran programs. Results The optimized atom polarizabilities are shown in Table 3. The values for alkane C and H atoms from previous optimizations1,19 are included for completeness. The 1993 values19 for C and H were used without further adjustment in the halomethanes and methyl groups in the molecules studied here. Tables 4-7 show the calculated optical properties with the experimental data used for optimizations. Tables 8 and 9 show the root-mean-square (rms) deviations between experiment and theory for the mean polarizabilities and anisotropies, respectively, for each series of compounds. Corresponding deviations found in previous studies of ADI models are shown for comparison. For this purpose values of |δ| were calculated from the polarizability components listed by previous workers. The rms deviations in |δ| are generally much larger than those of the components themselves, since |δ| is of the order of differences between components. We choose |δ| for comparison of experiment and theory as it is more directly related to experimental observations than the components. The sets of molecules considered in each study are not always the same, though there is much overlap in the choice of molecules and sources of experimental data. Where more than one experimental value was cited in a paper, the value closest to the theoretical result in the same paper was used for calculation
A New Optimization of Atom Polarizabilities
J. Phys. Chem., Vol. 100, No. 45, 1996 17823
TABLE 5: Anisotropies (Å3) and Polarizabilities (Å3) of Aldehydes and Ketones compd (CH3)2COa Cl2COb HCHOc CH3
CHOd
CCl3CHOe CBr3CHOf (CH3)3CCHOg
expt38-40 calc expt1 calc expt1,40 calc expt39-41 calc expt39,41 calc expt39,41 calc expt41 calc
|δ|
R j
3.20 2.33
6.41 6.73 6.78 6.15 2.45 2.25 4.58 4.58 10.52 10.19 14.05 14.04 9.96 9.16
4.00 1.32 2.01 2.95 2.53 6.20 9.69 1.47
R1
R2
R3
8.16
6.53
5.50
7.82
7.10
3.52
2.95
2.89
0.92
6.18
4.26
3.31
13.78
6.63
10.18
17.43
8.99
15.71
10.06
9.06
8.37
R3 ⊥ CC′O plane, R2 || C′-O bond. b R3 ⊥ ClC′Cl plane, R2 || C′-O bond. c R3 ⊥ HC′H plane, R2 || C′-O bond. d R3 ⊥ CC′O plane, ∠(R2,C′-O) ) 44.1° toward C′-C. e R3 ⊥ CC′O plane, ∠(R2,C′-O) ) 39.0° toward C′-C. f R3 ⊥ CC′O plane, ∠(R2,C′-O) ) 39.2° toward C′-C. g R3 ⊥ CC′O plane, ∠(R2,C′-O) ) 53.1° toward C′-C. a
TABLE 6: Anisotropies (Å3), Molar Kerr Constants (1012 esu), and Polarizabilities (Å3) of Amides |δ|
compda FAb ACb NMFb NMAb DMFb DMAb TFAc TCAc TBAc mTFAc mTCAc mTBAc
expt42-44 calc expt30,42,44 calc expt42 calc expt30,42,43,45 calc expt42-44 calc expt43-45 calc expt30 calc expt30 calc expt30 calc expt30 calc expt30 calc expt30 calc
4.04 2.53 2.79 1.98 2.63 2.88 2.14 2.79 2.84 2.01 2.28 2.91 2.32 2.34
[K]
R j
290 566 242 253 210 248 175 114 415 427 354 270 291 148 275 217 279 269 417 397 366 346 310 320
4.08 3.62 5.91 5.28 5.91 5.52 7.97 7.60 7.81 7.59 9.24 9.50 6.03 5.38 12.20 10.21 17.40 13.89 8.49 7.70 14.20 12.54 16.51 16.21
R1
R2
R3
ψ (deg)
5.95
3.64
1.28
30.6
6.59
5.55
3.70
64.3
6.70
6.19
3.69
3.7
9.04
7.74
6.02 149.5
9.26
7.58
5.93
48.3
10.61 10.25
7.66
32.8
6.82
5.74
3.60
67.8
11.47
9.98
9.18
39.0
15.36 12.83 13.47
32.3
9.27
7.91
5.93 147.1
14.01 12.22 11.39 165.9 17.76 15.28 15.59 174.8
a
FA, formamide; AC, acetamide; NMF, N-methylformamide; NMA, N-methylacetamide; DMF, N,N-dimethylformamide; DMA, N,N-dimethylacetamide; TFA, trifluoroacetamide; TCA, trichloroacetamide; TBA, tribromoacetamide; mTFA, N-methyltrifluoroacetamide; mTCA, N-methyltrichloroacetamide; mTBA, N-methyltribromoacetamide. b R1 and R2 lie within the NC′O plane; R3 ⊥ NC′O plane. c R1 and R2 lie near the NC′O plane; ψ is the polar angle of the projection of the R1 axis onto the NC′O plane.
TABLE 7: Calculated Polarizability Components (Å3) of Haloamides compd
R11
R21
R31
R22
R32
R33
TFA TCA TBA mTFA mTCA mTBA
5.89 10.86 14.67 8.87 13.91 17.74
0.38 0.74 1.09 -0.62 -0.42 -0.18
-0.01 -0.04 -0.06 -0.01 -0.06 -0.09
6.66 10.56 13.61 8.31 12.32 15.41
-0.01 0.11 0.23 -0.01 0.07 0.16
3.60 9.20 13.37 5.93 11.39 15.48
of rms deviations. The vanishing anisotropies of tetrahedrally symmetric molecules were not included in the calculations for Table 9. Halomethanes. Polarizabilities of F, Cl, and Br atoms were obtained by fitting data for 3-4 halomethanes containing each halogen (Table 4). The new halogen atom polarizabilities do not differ greatly from the 1972 values (Table 3). From Table 8 it is seen that the fit to R j is somewhat poorer than our 1972
TABLE 8: Root-Mean-Square Deviations (percent) between Theoretical and Experimental Mean Polarizabilities r j from Various Studiesa,b series alkanes halomethanes aldehydes/ketones amides all of the above
App721 Bir8013 Tho8114 Bir8315 Mil9016 2.0 (6) 1.7 (4) 2.8 (13) 0.6 (4) 4.1 (2) 1.0 (5) 2.1 (28) 2.7 (6)
1.4 (5) 2.7 (2) 5.1 (2) 2.9 (9)
this work
3.0 (4) 1.3 (6) 6.6 (7)c 9.3 (13) 6.5 (11) 6.1 (2) 4.0 (7) 6.0 (7) 3.3 (4) 11.8 (12) 4.3 (6) 6.6 (30) 8.5 (37)
a Column headings indicate previous studies by acronym for author and date. b Numbers of molecules in each sample are given in parentheses. c From ref 19 using same C and H polarizabilities as this work.
TABLE 9: Root-Mean-Square Deviations (percent) between Theoretical and Experimental Anisotropies |δ| from Various Studiesa,b series
App721 Bir8013 Tho8114 Bir8315 Mil9016
this work
alkanes 75.7 (4) 54.2 (4) 16.3 (4) 22.9 (4) 25.6 (4) 11.3 (5)c halomethanes 149.1 (10) 75.6 (10) 31.9 (7) aldehydes/ketones 110.0 (2) 51.7 (2) 16.3 (2) 35.6 (2) 13.3 (6) 35.0 (3) amides 73.0 (4)d 31.6 (2) all of the above 124.3 (16) 54.3 (6) 16.3 (6) 27.8 (6) 56.4 (24) 28.1 (17) a Column headings indicate previous studies by acronym for author and date. b Numbers of molecules in each sample are given in parentheses. c From ref 19 using same C and H polarizabilities as this work. d Experimental polarizability components were interpreted by the author such that one polarizability component is equal to zero, resulting in excessively large anisotropy values.
results, but somewhat better than Miller’s modified ADI model. Table 9 shows that the fit to |δ| is a considerable improvement over both our 1972 results and those of Miller. Aldehydes and Ketones. The carbonyl C′, carbonyl O, and aldehyde H atom polarizabilities were simultaneously optimized from anisotropy and mean polarizability of the aldehydes and ketones shown in Table 5. This single optimization incorporated fixed 1993 alkane carbon and hydrogen polarizabilities and fixed chlorine and bromine atom polarizabilities from the halomethane optimizations. The most notable difference of the atom polarizabilities from the 1972 values is the shift of about 0.15 Å3 from the O atom to C′ in the carbonyl group. Table 8 indicates that the fit to R j is substantially poorer than our 1972 results but comparable to the other ADI model studies that have sought a simultaneous fit to both mean polarizability and components. The fit to |δ| in Table 9 shows considerable improvement over our 1972 results, comparable to those of Birge but somewhat poorer than those of Thole and Miller. Amides. The amide N, C′, O, and H atom polarizabilities were simultaneously optimized to fit anisotropy, mean polarizability, and Kerr constant of the amides listed in Table 6. Polarizabilities of halogen, aldehyde H, and methyl C and H atoms from the preceding optimizations were kept fixed. The aldehyde H atom polarizability was required for the H in the formamide C′HO group. The new atom polarizabilities do not differ greatly from the 1972 values (Table 3). Principal polarizability components are defined such that R1 > R2 and R3 is perpendicular (or nearly so) to the NC′O plane. The angle ψ in Table 6 is the counterclockwise rotation from the x axis to the projection of the R1 axis in the xy plane. The conformation of the CX3 group in acetamides was chosen so that one dihedral angle θ(O,C′,C,X) is equal to 90°. The xy plane is not a plane of molecular symmetry in this conformation; hence, the R1 and R2 axes do not necessarily lie in that plane. However, their deviation from the plane is significant only in the haloacetamides. For these cases the full molecular polarizability tensors in the coordinate system of Figure 1 are given in Table 7. The fit to R j in Table 8 is seen to be the poorest of the various
17824 J. Phys. Chem., Vol. 100, No. 45, 1996 studies for amides, though not unacceptable (11.8%) for many purposes. The fit to |δ| in Table 9 is of the same order as for the other compound series and apparently better than that of Miller, though the experimental anisotropies from Miller’s components were evidently in error (see footnote in Table 9). It should be noted also that the rms deviation in [K] for the amides in this study is 34.4% while the corresponding figure for our 1972 study was 78.1%. These figures also indicate a substantial improvement in the polarizability tensors of amides in the present study. Discussion This study has produced a new set of isotropic polarizabilities of atoms in halomethanes, aldehydes, ketones, and amides from the atom dipole interaction model, retaining the isotropic atom and point dipole field features of our 1972 study. Optimizations yielding these atom polarizabilities incorporated a larger set of compounds than the 1972 study, and the range of experimental target data has been expanded to include optical properties which depend on the anisotropy of the molecular polarizability. For the most part the new atom polarizabilities do not differ greatly from the 1972 values (Table 3), evidently due to the high sensitivity of the anisotropy to these parameters. This finding shows that the optimum atom polarizabilities are fairly stable with respect to the choice of target data. The more important inference is that the new atom polarizabilities should be more valid in predicting properties related to molecular anisotropy. The compounds for which the predictions should be valid are those which are chemically related to those used in the optimization, i.e., primarily saturated alkane derivatives and carbonyl compounds. The comparison of fit between theory and experiment in this and related studies in Tables 8 and 9 gives an indication of the relative success of each treatment. The data must be viewed with some caution since the choice of compounds and experimental data varied among the studies. The 8.5% overall rms deviation in R j in this study indicates a somewhat poorer fit than found in previous studies. On the other hand, the 28.1% overall rms deviation in |δ| compares favorably with all previous studies. This finding shows that the tendency of the ADI model to exaggerate anisotropies in our 1972 study is not an inherent property of the isotropic point-atom model, but rather, for the molecules considered here, is simply a consequence of the fact that the atom polarizabilities had been optimized to fit only observed mean polarizabilities; it has little to do with the choice of isotropic atom symmetry or the strict point-dipole interaction tensor. The advantages found in the theories of other workers using additional atom parameters or modified interaction tensors appear to be small at best. A stronger case for the use of such models for polyatomic molecules might be found in their ability to predict a wider variety of optical properties, but such a case has not yet been forthcoming. On the other hand, the diatomic molecules present a special problem that is not easily accommodated by the isotropic pointatom model. It has been noted1 that, for homonuclear diatomic molecules, the model becomes less realistic as the fraction of valence shell electrons involved in the covalent bond increases; e.g., the model is fairly good for Cl2 but poor for H2. All of the models of Birge, Thole, and Miller have proven capable of reproducing observed anisotropies of such molecules. In closing it is worth reflecting on the significance of the fact that the simple physical model which we have adopted here behaves in so many ways like real molecules. The behavior of a molecule of many atoms in a light wave depends in sensitive ways on the distribution of polarization throughout the molecule. It is remarkable, then, that there is so much evidence that a
Bode and Applequist collection of isotropic point particles, interacting only by way of the fields of their induced dipoles, behaves very much like the continuous electron distribution in a real molecule. This implies that the underlying forces in the behavior of the real molecule are not very different from the dipole interaction forces of the model. This insight is useful both for an understanding of the molecule and for providing a simple means of calculating its behavior. Acknowledgment. This investigation was supported by a research grant from the National Institute of General Medical Sciences (GM-13684). References and Notes (1) Applequist, J.; Carl, J. R.; Fung, K.-K. J. Am. Chem. Soc. 1972, 94, 2952. (2) Applequist, J. Acc. Chem. Res. 1977, 10, 79. (3) Applequist, J.; Quicksall, C. O. J. Chem. Phys. 1977, 66, 3455. (4) Applequist, J. J. Chem. Phys. 1979, 71, 4332. Erratum: J. Chem. Phys. 1980, 73, 3521. (5) Applequist, J. Biopolymers 1981, 20, 387. (6) Applequist, J. Biopolymers 1981, 20, 2311. (7) Applequist, J. Biopolymers 1982, 21, 703. (8) Applequist, J. Biopolymers 1982, 21, 779. (9) Caldwell, J. W.; Applequist, J. Biopolymers 1984, 23, 1891. (10) Sathyanarayana, B. K.; Applequist, J. Int. J. Peptide Protein Res. 1985, 26, 518. (11) Sathyanarayana, B. K.; Applequist, J. Int. J. Peptide Protein Res. 1986, 27, 86. (12) Thomasson, K. A.; Applequist, J. Biopolymers 1991, 31, 529. (13) Birge, R. R. J. Chem. Phys. 1980, 72, 5312. (14) Thole, B. T. Chem. Phys. 1981, 59, 341. (15) Birge, R. R.; Schick, G. A.; Bocian, D. F. J. Chem. Phys. 1983, 79, 2256. (16) Miller, K. J. J. Am. Chem. Soc. 1990, 112, 8543. (17) Bocian, D. F.; Schick, G. A.; Hurd, J. K.; Birge, R. R. J. Chem. Phys. 1982, 76, 4828. (18) Ladanyi, B.; Keyes, T. Mol. Phys. 1979, 37, 1809. (19) Applequist, J. J. Phys. Chem. 1993, 97, 6016. (20) Stone, A. J. Mol. Phys. 1985, 56, 1065. (21) Laidig, K. E.; Bader, R. F. W. J. Chem. Phys. 1990, 93, 7213. (22) Bader, R. F. W.; Keith, T. A.; Gough, K. M.; Laidig, K. E. Mol. Phys. 1992, 75, 1167. (23) Bode, K. A.; Applequist, J. J. Phys. Chem., 1996, 100, 17825. (24) Born, M. Optik; Springer: Berlin, 1933; p 380. Born’s Ω is equal to δ2/15. (25) Bo¨ttcher, C. J. F.; Bordewijk, P. Theory of Electric Polarization, 2nd ed.; Elsevier: Amsterdam, 1978; Vol. II, p 320. (26) Interatomic Distances 1960-65; organic and organometallic crystal structures. Utrecht, Crystallographic Data Centre: Cambridge, UK, 1972. (27) Landolt-Bo¨ rnstein. Structure Data of Free Polyatomic Molecules; Springer-Verlag: New York, 1987; Vol. 15. (28) McClellan, A. L. Tables of Experimental Dipole Moments; W. H. Freeman: San Francisco, CA, 1963, 1974, and 1989; Vols. I, II, and III. (29) Kurland, R. J.; Wilson, Jr., E. B. J. Chem. Phys. 1957, 27, 585. (30) Khanarian, G.; Mack, P.; Moore, W. J. Biopolymers 1981, 20, 1191. (31) Watson, H. E.; Ramaswamy, K. L. Proc. R. Soc. London, Ser. A 1936, 156, 144. (32) LeFe`vre, C. G.; LeFe`vre, R. ReV. Pure Appl. Chem. 1955, 5, 261. (33) Buckingham, A. D.; Orr, B. J. Trans. Faraday Soc. 1969, 65, 673. (34) Bridge, N. J.; Buckingham, A. D. Proc. R. Soc. London, Ser. A 1966, 295, 334. (35) Bogaard, M. P.; Buckingham, A. D.; Pierens, R. K.; White, A. H. J. Chem. Soc., Faraday Trans. 1 1978, 74, 3008. (36) Vogel, A. I. J. Chem. Soc. 1948, 1833. (37) Bogaard, M. P.; Orr, B. J.; Buckingham, A. D.; Ritchie, G. L. J. Chem. Soc., Faraday Trans. 2 1978, 74, 1573. (38) LeFe`vre, C. G.; LeFe`vre, R. J. Chem. Soc. 1953, 4041. (39) Partington, J. P. An AdVanced Treatise on Physical Chemistry; Longmans, Green and Co.: London, 1953. (40) Parathasarathy, S. Indian J. Phys. 1932, 7, 139. (41) Weast, R. C., Ed. Handbook of Chemistry and Physics, 71st ed.; CRC Press: Boca Raton, FL, 1989-1990. (42) Aroney, M. J.; LeFe`vre, R. J. W.; Singh, A. N. J. Chem. Soc. B 1965, 3179. (43) Aroney, M. J.; Dowling, K. M.; Parsalides, E.; Pierens, R. K.; Filipczuk, S. W. J. Chem. Soc., Faraday Trans. 1 1988, 84, 4169. (44) Beevers, M. S. J. Chem. Soc., Faraday Trans. 1 1979, 75, 679. (45) Ingwall, R. T.; Flory, P. J. Biopolymers 1972, 11, 1527.
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