508
J. Phys. Chem. 1984, 88, 508-519
Vibrational Spectra of the Inositols R. M. Williams and R. H. Atalla* The Institute of Paper Chemistry, Appleton, Wisconsin 5491 2 (Received: July 6, 1983) The vibrational spectra of seven of the inositol isomers and of some of their hydroxyl deuterated counterparts were investigated and were interpreted on the basis of comprehensive normal-coordinateanalysis. The spectra of six molecules, scyllo-inositol, neo-inositol, rnyo-inositol, epi-inositol, deuterated scyllo-inositol, and deuterated neo-inositol, were used as the basis for developing a 33-parameter force field which was refined to give the best fit to the experimental spectra by using the Fletcher-Powell nonlinear least-squares algorithm. For these six inositols the overall average error was 10.4 cm-’ for 234 assigned frequencies. The generality of the force field was established by its successful use in predicting the vibrational frequencies for cis-inositol, L-chiro-inositol, and rnuco-inositol, which were not included in the force constant refinement; the average errors were only slightly higher than those obtained for the other inositols. The calculated potential energy distributions showed a majority of the vibrations to be composed of complex atomic motions with extensive coupling of the different motions typically occurring below 1500 cm-I. A group of temperature-sensitive bands observed in the region between 300 and 750 cm-I in the spectra of all the inositols was interpreted as modes involving the deformations of the hydrogen-bonded hydroxyl hydrogens. These bands were not assigned and could only be reproduced by inclusion of intermolecular potentials in the molecular models. Introduction The inositols, which are the cyclohexane hexols, are an important set of compounds because of both their chemistry and biological function, and because they represent a valuable set of models for investigating conformational effects that occur more generally among many more complex carbohydrates. In the present work, they were selected as the basis for exploring the effects of conformational differences on vibrational spectra among the carbohydrates. The Raman and infrared spectra of 7 of the 9 isomers were investigated. In order to properly assess the relationship between structure and spectra normal-coordinate analyses were carried out. These were in two parts. In the first, the spectra of four of the inositols were subjected to an analysis wherein a set of force constants was refined to give the best and most plausible fit to the experimental spectra. In the second part, the generality of the force field was demonstrated by its ability to predict the spectra of the compounds not included in refinement. Since the inositols each possess 66 degrees of internal freedom, and since a total of 7 molecules were investigated together with some hydroxyl deuterated analogues, a complete account is beyond the scope of the present report. Rather an overview of the general approach and methods is presented together with some representative results. A detailed record of the work is available elsewhere.’ Background The inositols, which are represented in Figure 1, have played an important role in studies of conformational effects among the carbohydrate^.*-^ They have been good models for clarifying the role of conformational factors in reactions common to many other carbohydrate^.^-^ They have also been used extensively in investigations of complexes with metal cationss-12and with borate a n i o n ~ . ~ ? ~Several J ~ - ‘ ~ inositols occur naturally, as do a variety ( I ) R. M. Williams, Doctoral Dissertation, The Institute of Paper Chemistry, Appleton, WI, 1977. (2) S. J. Angyal and D. J. McHugh, Chem. Ind., 1147-8 (1956). (3) S. J. Angyal and D. J. McHugh, J . Chem. SOC.,1423-31 (1957). (4) E. L. Eliel, N . L. Allinger, S. J. Angyal, and G. A. Morrison, “Conformational Analysis”, Interscience, New York, 1965, p 524. (5) L. Anderson, “The Carbohydrates”. W. Pigman, and D. Horton, Ed., Academic Press, New York, 1972, pp 519-79. (6) T. Posternak, ‘The Cyclitols”, Holden-Day, San Francisco, CA, 1965, p 431. (7) S. J. Angyal and L. Anderson, “Advances in Carbohydrate Chemistry”, Vol. 14, Academic Press, New York, 1959, pp 135-212. (8) R. A. Wood, V. J. James, and S. J. Angyal, Acta Crystallogr., Sect. E , 33, 2248-51 (1977). (9) S. J. Angyal and R. J. Hickman, Aust. J . Chem., 28, 1279-87 (1975). (10) S. J. Angyal, Pure Appl. Chem., 35, 131-46 (1973). (11) S. J. Angyal and K. P. Davies, Chew. Commun., 500-1 (1971). (12) J. A. Mills, Biochem. Biophys. Res. Commun., 6,418-21 (1961/62). (13) S . J. Angyal, J. E. Klavins, and J. A. Mills, Aust. J . Chem., 27, 1075-86 (1974).
0022-3654/84/2088-0508$01.50/0
of their methyl ethers5S6 The role of myo-inositol and several of its derivatives have been studied quite e ~ t e n s i v e l y . ~Inositols -~ containing amino or substituted amino groups also occur in many natural and synthetic a n t i b i o t i c ~ . ~ J ~ J ~ Though the inositols are sufficiently interesting in themselves to justify exploration of their vibrational spectra, our interest in them derives from the opportunity they provide for exploration of factors of more general interest in the interpretation of the vibrational spectra of the carbohydrates. Two desirable attributes distinguish the inositols. First, in comparison with other carbohydrates, the inositols are chemically more simple in that they contain fewer distinct types of chemical bonds. Second, the inositols represent a departure from the norm for carbohydrates in that several possess a relatively high degree of symmetry, all but one of the isomers possessing at least one element of symmetry. These attributes provide an opportunity for a more rigorous test of the theoretical methodology and molecular models used in earlier studies of relatively more complex sets of carbohydrate compounds. The approach adopted in the present study was previously applied in our laboratory to a number of classes of sugars and related model compound^.^^^^ In every instance a force field was developed based on fitting the spectra of one subset and the generality of the force field was tested by predicting the spectra of a subset of structures not included in the refinement. The classes of compounds studied included the l,5-anhydropentitols,zothe alditols,21 the pentoses,22 and the hexoses.23 The broader motivation throughout our work has not been pursuit of an ultimate force field for the carbohydrates, but rather to develop a wellfounded perspective within which the spectra of cell wall oligoand polysaccharides could be examined. Experimental Section Professor L. Anderson of the University of Wisconsin at Madison kindly provided the following materials: epi-inositol, (14) P. A. J. Gorin and M. Mazurek, Carbohyd. Res., 27, 325-39 (1973). (15) P. J. Garegg and K. Lindstrom, Acta Chem. Scand., 25, 1559-66 (1971). (16) T. Posternak, E. A. C. Lucken, and A. Szente, Helu. Chim. Acta, 50, 326-30 (1967). (17) A. Weissbach, J . Org. Chem., 23, 329-30 (1958). (18) S. Umezawa, “Advances in Carbohydrate Chemistry and Biochemistry”, Vol. 30, Academic Press, New York, 1974, pp 11 1-82. (19) J. D. Dutcher, “Advances in Carbohydrate Chemistry”, Vol. 18, Academic Press, New York, 1963, pp 259-308. (20) L. J. Pitzner and R. H. Atalla, Spectrochim. Acta, Part A , 31,911-29 (1975). (21) G. M. Watson, Doctoral Dissertation, The Institute of Paper Chemistry, Appleton, WI, 1974. (22) S. L. Edwards, Doctoral Dissertation, The Institute of Paper Chemistry, Appleton, WI, 1976. (23) H. A. Wells, Doctoral Dissertation, The Institute of Paper Chemistry, Appleton, WI, 1976.
0 1984 American Chemical Society
The Journal of Physical Chemistry, Vol. 88, No. 3, 1984 509
Vibrational Spectra of the Inositols on
HO
doH no
OH
D -chirO- inosi to1
L -chiro-inositol
C.?
C?.
on
OH myo-~noritol
muco - inoritd
ep1-inosito1
cs
cs
CS
moH HO
HO
bH
OH
on
nm -inositol
cis-inositd
czfl
c3v
scy/lo-inositoI
b d
Figure 1. Structures and symmetries of the inositols
L-chiro-inositol, neo-inositol, and intermediates in the synthesis of muco-inositol and scyllo-inositol. The epi-inositol and L-chiro-inositol were used as received. The neo-inositol required further purification. The muco-inositol and scyllo-inositol were prepared from the intermediates and purified by procedures detailed elsewhere.' The cis-inositol was kindly provided by Professor F. Angyal of the University of New South Wales, Kensington, Australia; it also required further purification by procedures detailed elsewhere.' The myo-inositol was obtained commercially from Pfanstiehl Laboratory and was not purified further. The Raman spectra were measured with a spex 1401 Raman spectrometer using the 5145-A line from an argon ion laser for excitation. Spectrometer slits were set to give resolution of the order of 3 cm-'. Spectra were recorded at room temperature and at approximately -180 OC. The infrared spectra were recorded on a Perkin-Elmer Model 621 grating spectrometer. Both Fluorolube and Nujol mulls were used, with calcium fluoride and cesium iodide plates, respectively. Slits were set to provide 3-cm-I resolution. The infrared spectra also were recorded both at room temperature and at temperatures approaching those of liquid nitrogen. Infrared spectra were also recorded for KBr pellets. The hydroxyl protons of the inositols were exchanged to deuterium by repeated dissolution in 99.9% D 2 0 in a carefully controlled atmosphere. The procedures required a controlled environment to limit exchange with atmospheric moisture. Even so, in most instances complete exchange was not attained. The depolarization ratio measurements for the Raman spectra were carried out in water solution for all the inositols with the exception of neo-inositol, which was not sufficiently soluble to allow acquisition of useful spectra. Procedures for Normal-Coordinate Analysis The vibrational secular equations were set up by using the Wilson G F matrix method. The internal coordinates were defined
in accordance with the procedures described by Wilson et aLZ4 Seventy-eight internal coordinates were defined for each molecule. These included 24 bond stretching, 42 angle bending, and 12 torsion coordinates. The bond stretching and valence angle bending coordinates were identically defined for all the inositols. The torsion coordinates around the CC and C O bonds were defined for each inositol by the procedures described by HilderbrandLZ5 Since the molecules have only 66 internal degrees of freedom, there are 12 redundancies, 6 local at each carbon atom, and 6 cyclic. The structures used for the vibrational analyses were based on tetrahedral geometries and the most stable chair conformations. The ring dihedral angles were set equal to 60'. Common bond types were assigned the same bond lengths. These were as follows: CC, 1.545 A; CO, 1.425 A; CH, 1.10 A; and OH, 0.97 A. The hydroxyl groups were oriented so that the symmetry of the carbon-oxygen skeleton was preserved. In addition, calculations were carried out by using the crystal structures for the three molecules for which the structures have been determined.26-29 These structures were not, however, incorporated into the force constant refinement procedures. The potential function used was based on a simplification of a quadratic force field. It was assumed that all interactions between stretching coordinates which do not have one atom In common were negligible and that all interactions between bending coordinates which do not have two common atoms were negligible. In addition, it was assumed that all internal coordinates of a common type, such as the six C C stretching coordinates, could be assigned a single force constant. The 33 force constants defined in the final force field are included in Table I. Development of the force field and the final force constant values will be discussed in a later section. The isolated molecule approximation is clearly implicit in the approach adopted. The computational procedures were those of Schacht~chneider,~~ as adapted to include the nonlinear least-squares refinement method of Fletcher and Powell,31by Pit~ner;~' the Fletcher-Powell algorithm from IBM33was incorporated into the refinement program written by Scha~htschneider.~~ Symmetry coordinates were constructed by taking suitable linear combinations of the internal coordinates using the projection operator t e c h n i q ~ e . ~ ~These - ~ ' were then normalized and used to factor the G and F matrices. Result and Discussion The normal-coordinate analyses of the inositols were carried out to aid assignment and interpretation of the observed spectra. The key to success was development of a satisfactory force field; the calculated frequencies and potential energy distributions are dependent on the force constants. Since the complexity of the systems precluded definition of a unique or absolute set of force constants, the constants developed in this work are viewed as ~
(24) E. B. Wilson, J. C. Decius, and P. C. Cross, "Molecular Vibrations", McGraw-Hill, New York, 1955, p 388. (25) R. Hilderbrandt, J . Mol. Spectrosc., 44, 599-601 (1972). (26) I. N. Rabinowitz and J. Kraut, Acta Crystallogr., 17, 159-68 (1964). (27) G. A. Jeffrey and H. S. Kim, Acta Crystallogr., Sect. B, 27, 1812-7 (1971). (28) G. A. Jeffrey and H. S. Kim, Carbohyd. Res., 15, 310-4 (1970). (29) H. C. Freeman, D. A. Langs, C. E. Nockolds, and Y . L. Oh, personal communication. (30) J. H. Schachtschneider, Technical Report No. 231-64, Shell Development Co., Emeryville, CA, 1964. (31) R. Fletcher and M. J. D. Powell, Comput. J . , 6 , 163-8 (1963). (32) L. G. Pitzner, Doctoral Dissertation, The Institute of Paper Chemistry, Appleton, WI, 1973. (33) IBM System/360 Scientific Subroutine Package Version 111, 5th ed, International Business Machine Corporation, August, 1970, p 221. (34) J. H. Schachtschneider, Technical Report No. 57-65, Shell Development Co., Emeryville, CA, 1965. (35) D. Steele, "Theory of Vibrational Spectroscopy", Saunders, Philadelphia, 1971, p 226. (36) F. A. Cotton, "Chemical Applications of Group Theory", Wiley-Interscience, New York, 1971, p 386. (37) D. S. Schonland, "Molecular Symmetry", Van Nostrand-Reinhold, London, 1965, p 298.
510 The Journal of Physical Chemistry, Vol. 88, No. 3, 1984
Williams and Atalla
TABLE I: SVQFF Force Constant Parameters for the Inositol Models force c ons t ant number
group
coordinates involved
final value
c o m m o n atoms
Wells (hexoses)
STRETCHING CONSTANTS
Edwards (pentoses)
Pitzner (1,5-AHP's)
Snyder and Zerbi
(mdyn. /A)
1
C-OH
c-0
--
5.144
5.120
5.122
5.103
2
c-c
c-c
--
4.193
4.215
4.183
4.247
4.261
---
4.690
4.650
4.694
4.589
4.688
6.283
5.500
6.283
6.283
--
3
H-C-OH
C-H
4
0-H
0-H
BENDING CONSTANTS
5
C-C(H)-OH
HCC
6
H-C-OH
HCO
7
C-0-H
CO H
8
C-C-OH
cco
9
c-c-c
ccc
------
[ m d y n . A/ ( r a d .
5.n90
)21
0.728
0.671
0.698
0.725
0.718
0.969
0.861
0.980
0.963
0.961
0.923
0.950
0.871
0.734
--
1.205
1.332
1.137
1.180
1.182
1.044
1.028
1.112
1.056
1.071
STRETCH-STRETCH INTERACTION CONSTANTS ___-
(mdyn. /A)
10
C-C-OH
c-c
,c-0
C
0.302
0.351
0.127
0.107
0.101
11
c-c-c
c-c, c-c
C
0.043
0.112
0.117
0.107
0.101
12
H-C-OH
C-0,HCO
13
C-0-H
C-0, COH
14
C-C-OH
15
C-C(H)-OH
STRETCH-BEND co
INTERACTION CONSTANTS
(mdyn. / r a d . )
0.360
0.502
0.452
0.388
0.387
co
0.425
0.430
0.342
0.357
--
c-0 ,cco
co
0.707
0.522
0.657
0.664
0.618
C-C ,HCC
cc
0.329
0.330
0.518
0.481
0.478
16
C-C-OH
c-c ,cco
cc
0.495
0.443
0.408
0.381
0.403
17
c-c-c
c-c ,ccc
cc
0.482
0.467
0.271
0.485
0.417
--
BEND-BEND INTERACTION CONSTANTS
[ m d y n . A/ ( r a d . )2]
18
C-C(H)-OH
HC0,HCC
CH
0.140
0.035
0.157
0.135
0.115
19
C-c( H ) -OH C-C(H)-C C-C(H) -OH
HCC ,CCO HCC, CCC HCO, CCO
cc
-0.076
-0.076
-0.067 -0.012 -0.067
-0.094
-0.031
20
C-C(OH)-C C-C(OH)-C
cco,cco cco, ccc
co cc
0.017
0.090
0.074 0.133
0.052
-0.041
21
C-C-C-OH HD-C-C-OH
(C)C-C(o) (O)C-C(O) (C)C-c(C)
gauche
0.008
0.017
0.018 0.074 0.031
-0.024
0.011
c-c-c-c
ccc, cco cco,cco ccc, ccc
C-C-C-OH HC-C-C-OH
ccc,cco cco,cco
(C)C-C(O) (O)C-C(O)
trans
-0.007
-0.002
-0.014
-0.011
23
H-C-C-OH
CCO, HCC
(H)C-C(O)
gauche
-0.230
-0.198
-0.238
-0.113
24
H-C-C-OH
CC0,HCC
(H)C-C(O)
trans
-0.084
0.126
-0.008
0.037
0.028
25
H-C-C-C
CCC,HCC
(C)C-C(H)
gauche
-0.111
0.017
-0.179
-0,106
-0,052
26
H-C-C-C
CCC ,HCC
(C)C-C(H)
trans
0.087
0.126
-0.155
-0.047
0.049
27
H-C-C-H
HCC ,HCC
(Ha)C-C(Hb)
0.018
-0.032
-0.004
-0.002
0.004
0.121
22
cc co
gauche
gauche
0.048
0.004
trans
gauche
-0.164
28
H-C-C-H
HCC,HCC
(Ha)C-C(Hb)
0.095
0.147
0.057
0.049
29
H-C-OH H-C-OH
COH, H CO COH, H CO
(H)c-c(H) (H)o-c(H)
gauche trans
0.059
0.043
0.117 0.132
0.0 0.016
30
C-C-OH C-C-OH
CCO, COH CC0,COH
(C)C-O(H) (C)C-O(H)
gauche
0.115
-0.068 -0.165
0.151
0.010
0.100 0.025
0.023 0.059
0.027 0.028
trans
trans
--
T O R S I O N CONSTANTS
31 32 33
c-c
c-c
-_
c-0 -All f o r c e c o n s t a n t s a s s i g n e d a z e r o v a l u e . C-OH
0.100 0.015
0.024 0.026
The Journal of Physical Chemistry, Vol. 88, No. 3, 1984 511
Vibrational Spectra of the Inositols TABLE 11: Point Groups, Symmetry Species, and Raman and Infrared Vibrational Activities of the Inositols
point group sycllo-inositol
DPd
syinmctry spccics
Ra- infrainan rcd no. of activ- activ- normal ity ity modes
++ -
cis-ino sitol
t
-
rzeo-inositol
rnyo-inositol
CS
CS CS
L-chiro-inositol
C,
D-ChirO-in Osi to1
C,
allo-inositol
c,
+ + +
8 3 22 4
I 22
15
t
44
t
-
19
t
-
-
+
t
t
+ t
ii7uco-inositol
-
t
t
epi-inositol
-
+ +
t
+ + + +
I 14
15 18 37 29 31 29
37
t
29
+
t t
34 32
t f
+
t
t
34 32
+
t
66
semiempirical parameters which retain a close numerical similarity to force constants calculated directly for small molecules, and which can be used to interpret the potential energies in a semiquantitative manner. For the purposes of this work a satisfactory force field was defined as one which met the following conditions: (1) provide the best fit between the refined calculated frequencies and the assigned experimentally observed frequencies, (2) permit adequate prediction of frequencies for inositols not included in the refinements, (3) result in reasonable potential energy distribution, and (4) provide reasonable values of the force constants. The degree to which these conditions were met in the final inositol force field and the calculated results will be examined in this section. First, the assignments of the observed bands will be discussed because a correct assignment is crucial to the development of a satisfactory force field. The development of the final force field will then be described. Following this the fit of the calculated frequencies to the assigned observed frequencies will be considered both for the inositols involved in the refinement of the force constants and for the inositols used to test predictive power. The potential energy distributions will then be described, and finally the validty of some of the assumptions made in the analysis will be discussed. Assignment ofthe Spectra. The infrared and Raman spectra of the inositols used in the force constant refinement are shown in Figure 2. In addition to these the spectra of the hydroxyl deuterated molecules were also recorded. In Figure 3 the spectra of the three molecules used to test predictive capabilities of the force field are shown. Other spectra used in the study are reported elsewhere.' The primary bases of the assignments were the symmetry of the molecules and the normal-coordinate calculations carried out within the framework of the refinement. The symmetry, symmetry species analysis, and the spectral activity of the different modes are summarized in Table I1 for all the inositols. The two molecules with highest symmetry, scyllo-inositol and neo-inositol, possess a center of inversion as an element of their symmetry. Thus it is anticipated that Raman and infrared spectra would obey mutual exclusion. This expectation is predicated, however, on the validity of the isolated molecule approximation. Inspection of the experimental spectra showed that for a large
majority of the bands mutual exclusion was clearly obeyed. In some cases, bands were observed at very nearly the same frequency in both the Raman and infrared spectra, but it was found that both a Raman-active and an infrared-active mode were calculated for the corresponding observed bands. Thus the apparent breakdown of mutual exclusion was in fact the consequence of accidental degeneracy. In summary the observed and calculated spectra for scyllo- and neo-inositol and their deuterated analogues support the validity of mutual exclusion. In addition the symmetry species of point group D3dto which scyllo-inositol belongs include two species with modes that are neither Raman nor infrared active. The bands calculated in these symmetry species were not observed experimentally. Thus, the selection rules based on the isolated molecule approximation were in general obeyed. Another important source of information in the frequency assignments were the measured depolarization ratios. As noted earlier these were measured for solutions of all the inositols except neo-inositol. They permitted assignment of corresponding bands in the spectra of the solids. Two additional sources of information were used to aid the assignments. The first was the characteristic gaps which occur in the experimental spectra below 1500 cm-l. In general, three gaps were used to categorize the frequencies. The first occurs between 1200 and 1150 cm-I, the second between 975 and 930 cm-', and the third between 870 and 800 cm-I. The other set of aids in the assignments were the low-temperature Raman and infrared spectra. There were several instances where individual bands could not be resolved in the room temperature spectra but where the individual bands were clearly identified at low temperatures. An interesting observation, not unrelated to the assignments, concerns the effect of exchanging the hydroxyl protons with deuterium on the vibrational selection rules. If the hydroxyl groups play a significant role in determining the symmetry of the molecules, then partial deuteration of the hydroxyl groups which should destroy the centrosymmetric symmetry of neo- and scyllo-inositol should result in a breakdown of the selection rules and mutual exclusion. This was not observed to be the case with the deuterated scyllo- or deuterated neo-inositol. The degree of deuteration in both cases was approximately 70%. A comparison of the Raman active and infrared active observed frequencies for the two deuterated molecules showed that a majority of the frequencies had no apparent counterparts. The calculations confirmed cases of accidental degeneracy where the Raman and infrared frequencies were nearly the same. These observations strongly suggest that the mutual exclusion has not broken down as a result of the partial deuteration, and, further, that the selection rules are governed primarily by the symmetry of the carbon and oxygen skeleton and perhaps the methine hydrogens, but are not significantly affected by the hydroxyl hydrogen. Thus, hydrogen-bonding patterns in the crystal that depart from the symmetry of the isolated molecule are expected to have only minor effects, if any at all. For almost all the inositols, there were a small number of observed bands which remained unassigned. A specific group of these bands, which were observed in the region between 750 and 300 cm-', will be discussed in a later part of this section. For the inositols involved in the refinements, where the assignments are particularly critical, the frequency assignments were examined after almost every refinement to determine whether improvements could be made. Several times the refinements led to conclusions that assignments needed to be changed. By the final refinement, it was felt that a large majority of the assignments were sound and the best that could be attained for molecules of the complexity of the inositols on the basis of the information available. Development of the Final Force Field. The force field was developed over a series of approximately 45 refinement computations based initially on the spectra of neo-inositol, myo-inositol, and epi-inositol and later including the spectra of scyllo-inositol, deuterated neo-inositol, and deuterated scyllo-inositol.
Williams and Atalla
512 The Journal of Physical Chemistry, Vol. 88, No. 3, 1984
4
/-
I
E
p
: i T
i 4
d
2
-4
< I
I
4
--E
-8
4
H
Vibrational Spectra of the Inositols
a
The Journal of Physical Chemistry, Vol. 88, No. 3, 1984 513
U-INOSITOL
1
L-CHIRQ-INOSITOL
b
h
m-INOSITOL
1-=-INOSITOL
Figure 3. The vibrational spectra of cis-inositol, muco-inositol, and L-chiro-inositol: (a) Raman spectra; relative intensity ordinates; (b) infrared spectra; percent transmittance ordinates.
514
The Journal of Physical Chemistry, Vol. 88, No. 3, 1984
RSSIGNEE
Williams and Atalla
RAM4rJ ACTIVE FPECUENC:ES
:43c.
4JO.
CR,CL;LATEO FREQUENCIES
I 11-
140C
---
33c.
40c.
A S C I I G W O INFRRREO
i 4DC
2c3.
- RG 440 BG REPRESENTPTISNS
J I 15oc
320.
130:
1200
1153
>: 1boo
CQLCULRTEb
900.
FREDbENCIES -
7
ZOO.
RC-lVE FREQUEACIES
6GO.
700
600.
5CO
40C.
3CO.
20s
RU AN0 3U REPRESEY-WIONS
Figure 4. Bar graph representation of the assigned experimentally observed frequencies and calculated frequencies for neo-inositol.
The two criteria which guided selection of the molecules to be included in the refinement set were their symmetry and availability of structural data. cis-Inositol was not included, in spite of its high symmetry, because the 1:3:5 triaxial arrangement of its hydroxyl groups causes substantial distortion from the tetrahedral structure. The initial force field defined for the inositols included 46 constants taken from the force fields of P i t ~ n e and r ~ ~of Edwards?* The average errors for the initial assignments were as follows: neo-inositol, 25.5 cm-' with 41 bands assigned; myo-inositol, 20.7 cm-' with 43 bands assigned; and epi-inositol, 35.0 cm-' with 42 bands assigned. Only bands observed below 1500 cm-I were assigned for the refinements. During the sequence of refinements, modifications were continually made to ascertain correct assignment of the frequencies and to provide optimum adjustment of the force constants. The resulting force field is that defined in Table I. Upon close examination of the frequency assignments, the force constant values, the calculated potential energy distributions, and the predictive capabilities of the force field, it was concluded that the criteria listed earlier in this section had been met as well as can be expected in light of the complexity of the systems. The final force constants are those listed in Table I. In the final refinement, 234 frequencies assigned for scylloinositol, neo-inositol, myo-inositol, epi-inositol, and the deuterated scyllo-inositol and neo-inositol were used to adjust 28 of the force constants. Force constants numbered 1, 2, 31, 32, and 33 in Table I were not incorporated in the refinements. In Table I, the final inositol force constants are compared with the constants developed by Wells for the hexoses,23Edwards for the pentoses,22Pitzner for the 1,5-anhydropentitol~,~~ and Schneider and Zerbi for the ethers.38 Comparison of the Calculated and Assigned Observed Frequencies in the Refinement Set. The first criterion for a satisfactory force field was that the assigned observed frequencies be reproduced within reasonable error limits. In this section the fit of the calculated frequencies to the assigned bands will be reviewed. Though such comparisons have been carried out for all the (38) (1967)
R.G. Snyder and G. Zerbi, Spectrochim. Acta, Part A , 23, 391-437
molecules in the refinement set, space limitations have led to the selection of one representative for detailed comparison in this report. In Figure 4 the assigned experimental frequencies and the calculated frequencies for neo-inositol are compared. To illustrate more clearly the reproducibility of the assigned observed frequencies the comparisons are presented separately for the Raman and infrared active bands. The top bar graph shows the assigned observed Raman active frequencies while the second bar graph shows the frequencies calculated in the Raman active A, and B, symmetry species. The third bar graph shows the assigned infrared-active frequencies and the bottom bar graph the frequencies calculated in the infrared-active A, and B, symmetry species. It is clear that the calculated frequencies reproduce the observed ones fairly well. Even in the regions where only a few bands were observed, for example between 500 and 800 cm-I, the calculated modes closely reproduce the observed bands. The frequency assignments are not explicitly indicated in Figure 4, but in most cases the assignments are readily apparent from the one to one correspondence. For neo-inositol, 42 frequencies were assigned with an average error of 8.8 crn-'. The dotted lines in Figure 4 indicate two cases of accidental degeneracy, where two calculated frequencies were assigned to a single experimental band. For the other inositols included in the refinements, the calculated frequencies reproduced the assigned observed frequencies with the following average errors: scyllo-inositol, 13.3 cm-' with 35 frequencies assigned; myo-inositol, 9.7 cm-' with 42 bands assigned; epi-inositol, 8.5 cm-' with 44 bands assigned; deuterated scyllo-inositol, 12.1 cm-' with 30 bands assigned; and deuterated neo-inositol, 10.9 cm-' with 41 bands assigned. In all these cases, the calculated frequencies clearly reproduced the distribution of observed bands as well as the gaps in the observed spectra which were discussed earlier. Overall, 234 experimentally observed frequencies assigned for the six inositols included in the refinements were reproduced with an average error of 10.4 cm-I. Considering the constraints of the relatively small number of force constants, the execution of the refinements in symmetrized form, and the inclusion of the deuterated compounds in the refinement, the quality of agreement between calculated frequencies and assigned frequencies was judged to be quite good.
Vibrational Spectra of the Inositols
The Journal of Physical Chemistry, Vol. 88, No. 3, 1984 515
RSSIGNEO EXPERIMENTRL FREQUENCIES - fll REPRESENTRTION
CRLCULflTEO FREQUENCIES -
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RSSIGNEO EXPERIMENTRL FREQUENCIES
REPRESENTRTIBN
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Figure 5. Bar graph representation of the assigned experimentally observed frequencies and calculated frequencies for mum-inositol.
Comparison of the Predicted and Assigned Observed Frequenciesfor cis-Inositol, L-chiro-Inositol, and muco-Inositol. The measure of the value of a force field is its ability to predict the vibrational frequencies for molecules not included in the force constant refinements. The predictive abilities reflect the generality and transferability of the force constant to molecules of similar structure. The final inositol force field was used to predict the vibrational spectra of cis-inositol, L-chiro-inositol, and muco-inositol. cisInositol and muco-inositol were not included in any of the refinements. Early in the work L-chiro-inositol was included in some refinements during the development of the force field, but it was not incorporated in the final refinement. Bar graph representations of the assigned frequencies and the calculated frequencies for muco-inositol are presented in Figure 5. For clarity the frequencies have again been divided into two groups, corresponding respectively to the A' and A'' symmetry species. For muco-inositol 42 frequencies were assigned with an average error of 10.4 cm-I. Figure 5 demonstrates graphically that the frequencies predicted for muco-inositol reproduce the observed distribution of bands quite well. The results for L-chiro-inositol were similar to those for muco-inositol. Forty-three bands were assigned, with an average error of 10.5 cm-'. The comparison is reported in detail elsewhere.' For cis-inositol, 42 bands were assigned with an average error of 13.4 cm-I. This average error is somewhat higher than the average errors for the other inositols and reflects two unusual features in the structure of cis-inositol. The structure shown in Figure 1 shows that cis-inositol has three axial hydroxyl groups in 1:3:5 relative positions on the ring. The resulting 1:3 diaxial interactions are expected to distort the molecule from the tetrahedral structure to a greater extent than in any of the other structures. The crystal structure data obtained from Freeman et al.29bore this expectation out. In the crystal the 1:3 diaxial 0-0distances averaged 3.0 A, whereas in the assumed tetrahedral model these distances are 2.5 A. Distortions from the tetrahedral structure were also present in the ring angles. The other unusual feature of the structure of crystalline cisinositol is that it has two nonequivalent molecules in the unit cell.
This results in departures from the selection rules for the C3" symmetry possessed by the tetrahedral model. A majority of the frequencies calculated in the A, symmetry species, which should be inactive in both Raman and infrared spectra, were assigned to observed bands. Also, in all cases two observed bands were assigned to the frequencies calculated in the doubly degenerate E symmetry species, indicating that the degeneracies have been split into nondegenerate bands; the splitting was, on average, about 10 cm-'. A comparison of the frequencies calculated on the basis of the tetrahedral model with frequencies calculated on the basis of the X-ray crystal structure revealed noticeable differences in the frequencies of some of the bands, with the frequencies calculated from the crystal structure providing a better approximation of the observed bands assigned to the E species. In the case of cis-inositol then, it was felt that the degree of distortion from the assumed tetrahedral structure contributed to the poorer average error. If we take into account the special situation for cis-inositol, the predicted frequencies calculated on the basis of the inositol force field gave fairly good fits to the assigned observed frequencies. Thus, the force field can be regarded as providing a sound basis for the interpretation of the vibrational spectra. For the nine inositols for which frequency assignments were made, including deuterated scyllo-inositil and neo-inositol, the inositol force field reproduced 361 frequencies with an overall average error of 10.8 crn-'. Vibrational Modes and Potential Energy Distributions. Since the vibrational modes of the inositols involve a great deal of coupling between similar internal coordinates, their interpretation is based on an analysis of the potential energy distributions among the different internal coordinates. One of the criteria for a successful analysis was that the potential energy distributions among the internal coordinates be consistent with the contributions of such coordinates in the modes of smaller molecules. In spite of extensive coupling and the complexity of a majority of the vibrational modes, the spectra of the inositols are conveniently divided into five regions for purposes of discussion. The first region, between 3450 and 2350 cm-', contains the bands arising from the OH stretching, OD stretching, and CH stretching
516 The Journal of Physical Chemistry, Vol. 88, No. 3, 1984
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ENERGY LEVEL I C M - 1 1 Figure 7. Bar graph representation of the internal coordinate potential energy distribution for oxygen-deuteratedneo-inositol. modes. These modes were not included in any of the analyses and refinements. The OH and OD stretching modes were observed in the regions between 3450 and 3100 and 2600 and 2350 cm-', respectively. Most of the OH stretching bands were observed to shift in frequency by as much as 50 cm-' in the low-temperature spectra. The methine CH stretching modes occurred in the region between 2880 and 2970 cm-I. The second region is between 1460 and 1160 cm-'. The potential energy distributions show this region to be dominated by
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motions of the methine hydrogens, both in-plane (HCO) and out-of-plane (HCC), and the COH in-plane bending deformations. Only the motions of the methine hydrogens are present in this region of the spectra of the deuterated compounds. These distributions are illustrated in Figure 6 for neo-inositol and in Figure 7 for the deuterated neo-inositol. The different types of internal coordinates have been divided into four groups which are shown in bar graphs in the figures. The vertical lines represent the calculated frequencies. The contribution of each group to the
Vibrational Spectra of the Inositols calculated frequencies is represented on the coordinate axes. Only contributions greater than 10% were considered. These graphs provide a visual representation of the bands to which the different groups of motion make their major contributions in the spectral region between 1500 and 200 cm-'. neo-Inositol and deuterated neo-inositol were chosen as having representative potential energy distributions for the inositols and deuterated inositols, respectively, but minor variations in the energy distribution were observed for each of the inositols. Figure 6 shows that the methine hydrogen bending and C O H bending deformations contribute extensively throughout the region between 1460 and 1160 cm-'. The highest contributions of COH bending are centered around and above 1400 cm-', whereas the methine hydrogen bending deformations make their largest contributions starting just below 1400 cm-'. The methine in-plane and out-of-plane bending deformations are highly mixed, but there was a noticeable trend for the in-plane deformations to contribute below approximately 1270 cm-' and the out-of-plane deformations above 1270 cm-I. Deuteration of the inositols shifted the C O H bending deformations to lower frequencies, leaving only the methine bending deformations in this region. This is illustrated in Figure 7. The methine in-plane and out-of-plane modes are still highly mixed, with the in-plane deformations again tending to concentrate in the lower regions below approximately 1350 cm-I, and the out-of-plane deformations above 1350 cm-I. The third region in the spectrum is from 1160 to 850 cm-'. Figure 6 shows that the CO and CC stretching deformations are predominant in this region, but significant methine hydrogen bending and heavy atom bending (CCO and CCC bending) contributions are also present. The contribution of several types of deformations in this region is indicative of the complexity of the vibrational modes of the inositols. The high degree of coupling of these stretching modes is also reflected in the interaction constants in the force field. These stretching modes couple extensively with each other and also with the bending deformations, both the methine hydrogen bending and heavy atom bending deformations. Figure 7 shows that the 1160-850-cm-' region of the deuterated inositols contains contributions from all of the types of motion just described, but in addition, the coupling is further complicated by contributions from the COD in-plane bending deformations. The C O and C C stretches are still predominant in the region, but the COD bending deformations contribute heavily to several of the modes. The fourth region is between 850 and 250 cm-', which in Figure 6 is shown to be dominated by the CCO and CCC bending deformations, but with some significant contributions from the C O and CC stretches and the methine out-of-plane deformations. The potential energy distributions indicate a very high degree of coupling between all of these deformations in this region. Figure 7 shows that much the same situation prevails in the spectrum of the deuterated compound. Figure 2 shows that this region includes Raman bands which are among the most intense in the spectra. In most instances these are highly polarized bands which are associated with ring breathing vibrations. This region of the spectrum also contains bands which were not assigned to any of the fundamental modes; these will be discussed in the next subsection. The fifth region of the spectrum is that below 250 cm-I. The two types of deformations which dominate this region are the CO torsions (OH out-of-plane bending) and the C C torsions (ring torsions). Significant contributions from the CCO and CCC heavy atom bending and the methine out-of-plane bending deformation are also present in some of the bands. Because observation of the spectra in this region was incomplete, these were not included in the refinement. Rather, their contributions were assessed on the basis of the force constants derived from studies of other smaller molecules. Additional experimental and theoretical analyses need to be undertaken for a more complete interpretation of the bands observed in this region. An examination of the potential energy distribution, as well as visual inspection of several vibrational mode drawings, indicates that most of the vibrational modes of the inositols are quite
The Journal of Physical Chemistry, Vol. 88, No. 3, 1984 517
I
1
'
1
'
1
600
WAVENUMBER ( C h ' )
'
1
I
800
/
I
400
WAVENUMBER (CM")
Figure 8. The 800-400-cm-' region of the room-temperature, liquid-
nitrogen-temperature, and room-temperature oxygen-deuterated Raman and infrared spectra of neo-inositol: (A) Raman spectrum room temperature; (B) Raman spectrum liquid nitrogen temperature; (C) oxygen-deuterated Raman spectrum room temperature; (D) infrared spectrum room temperature; (E) infrared spectrum liquid nitrogen temperature; (F) oxygen-deuterated infrared spectrum room temperature. complex, involving motion of many atoms in the molecules. This is to be expected for molecules of the size of the inositols incorporating many bonds of approximately the same energy, and many atoms of approximately the same mass. The high degree of coupling is particularly obvious for all the different modes which occur below 1500 cm-'. Examination of the variation of coupling patterns with the symmetry of the particular inositols reveals some interesting changes, discussed in detail elsewhere.] The most interesting one, reflecting a trend, is an increase in the degree of delocalization of the atomic motions around the ring as the symmetry of the molecule increases. This is perhaps a consequence of the greater constraint imposed by symmetry on the patterns of coupling permitted between the different vibrational motions. The Temperature-Sensitive Bands in the 300-750-cm-' Region. The spectra of all the inositols included bands in the region between 300 and 750 cm-I for which no calculated frequencies within reasonable proximity could be assigned. Comparison of the room-temperature and low-temperature spectra revealed that these bands characteristically shifted, almost always upward, in frequency in the low-temperature spectra. The behavior is illustrated in segments of the spectra of neo-inositol and deuterated neoinositol in the 400-800-cm-] region shown in Figure 8. For neo-inositol the room-temperature Raman spectra has very weak and broad bands at 758 and 584 cm-l. In the low-temperature spectrum, these bands shift up to 776 and 597 cm-I, respectively, and become relatively more intense. The Raman bands at 665 and 688 cm-' were assigned as fundamentals; their shift is relatively small. In the room-temperature infrared spectrum, bands which are 758 and 604 cm-l shift up to 777 and 622 cm-', re-
518
The Journal of Physical Chemistry, Vol. 88, No. 3, 1984
spectively, in the low-temperature spectrum and are substantially increased in relative intensity. The room-temperature infrared band at 538 appears to shift to 552 cm-I leaving another band at 527 cm-'. Again the room temperature infrared bands assigned as fundamentals at 738 and 726 cm-I do not shift appreciably. In the comparison with the spectra of the deuterated neo-inositol, the temperature-sensitive Raman bands at 758 and 584 cm-I do not appear in the spectrum of the deuterated neo-inositol, but two new bands appear at 542 and 490 cm-'. The temperature-sensitive infrared bands at 758,604, and 538 cm-I also do not occur in the spectrum of the deuterated compound. Rather new bands appear at 577, 438, and 393 cm-l. Bands exhibiting characteristics similar to those observed in the spectra of neo-inositol occurred in the spectra of all the other inositols. The bands characteristically shifted to higher frequencies by an average of approximately 16 cm-I at the low temperature. Bands exhibiting these same characteristics have been reported in the spectra of other carbohydrates.3843 Kogan et al,42examined the room-temperature, low-temperature, and hydroxyl-deuterated infrared spectra of several methyl pyranosides. They observed in the region between 400 and 750 cm-' bands which shifted up to 25 cm-I upon cooling, and which disappeared and were replaced by new bands in the spectra of the deuterated compounds. These findings are very similar to the phenomena observed in the spectra of the inositols. The characteristics of these bands led Kogan et al. and other authors to interpret them as OH out-of-plane bending vibrations. In pursuit of this interpretation the analysis by Dempster and Zerbi,44who investigated hydrogen bonding in crystalline methanol, was adapted for an investigation of the effect of hydrogen bonding in neo-inositol. A very simple model was developed wherein a rigid carbon-oxygen bond was defined in conjunction with each hydroxyl group, and the hydroxyl groups were assumed involved in a single hydrogen bond each. The model was not meant to simulate the complete hydrogen bonding scheme of neo-inositol, but represented a very simple approximation to the crystalline enrivonment. The geometry of the hydrogen bonds was assumed to be the same as used by Dempster and Zerbi in their model of methanol. The four additional types of internal coordinates and their corresponding force constants were also adapted from Dempster and Zerbi. The calculations based on this simple model of hydrogen bonding in neo-inositol did indeed predict the deformations of the hydrogen-bonded hydroxyl groups, including the OH0 out-ofplane bending deformations, in the 300-750-cm-' region. These modes were in addition to the previously calculated fundamentals assigned in this region. When deuterium masses were substituted for the hydroxyl hydrogens in the model, the calculated frequencies shifted to lower values below 560 cm-l. Thus, the calculated results closely paralleled the behavior of the observed temperature-sensitive bands. This reinforces the interpretation of the temperature-sensitive bands in the inositol spectra as vibrations involving deformations of the hydrogen bonds, including the O H 0 outof-plane deformations. The results of the calculations also suggest that the manner in which the OH out-of-plane deformations (the CO torsions) were originally defined is not adequate in the case of hydrogen-bonded systems. Originally the CO torsions were defined as if the hydroxyl groups were free and not hydrogen bonded. The model calculations demonstrate that this is not an adequate description of the potential involved in the OH out-of-plane deformations. However, in order to calculate the OH out-of-plane modes in the 600-cm-' region, using the original simple definitions of the torsional coordinates, the CO torsion force constant would have to be un(39) J. E. Katon, J. J. Miller, and F. F. Bently, Curbohyd. Res., 10, 505-16 (1969). (40) A. J. Michell, Aust. J . Chem., 21, 1257-66 (1968). (41) A. J. Michell, Aust. J . Chem., 23, 833-8 (1970). (42) G. A. Kogan, V. M. Tul'Chinskii, M. L. Schulman, S.E. Zurabyan, and A. Ya. Khorlin, Carbohyd. Res., 26, 191-200 (1973). (43) A. J. Michell, Aust. J . Chem., 28, 335-41 (1975). (44) A. B. Dempster and G. Zerbi, J. Chem. Phys., 54, 3600-9 (1971).
Williams and Atalla reasonably large to a point that it would have a pronounced effect on the frequencies of a large number of the other calculated frequencies. An Assessment of the Procedures and Assumptions in the Normal-Coordinate Analysis. One of the primary motivations for the present study was that it afforded an opportunity for assessing the applicability of the methods used to molecules as large and diverse in conformation as the inositols. Since the number of force constants needed is smaller than that used for the other carbohydrate systems while the number of internal degrees of freedom of the molecules is comparable, the quality of the fit with the inositols is expected to be more sensitive to second-order effects, such as hydrogen bonding or anharmonicities in the potentials governing the vibrations. This section is concerned both with the assumptions incorporated in the analysis and an appraisal of the possible contributions of second-order effects. A number of assumptions are implicit in the nature of the force field used: that the potential function is harmonic, that the isolated molecule approximation is valid, and that the force constants are transferable among all internal coordinates of a common type within each molecule and between the molecules. Furthermore no distinction is made between diagonal force constants corresponding to the axial and equatorial orientations of hydroxyl groups. The assumptions are in essence equivalent to the assertion that the differences between the observed spectra of the inositols can be adequately accounted for by the difference between the G matrices of the isolated molecules. An additional assumption, made in generating the G matrices for the inositols, was the tetrahedral geometry adopted for the molecular structures for the force constants refinement. The assumptions outlined can contribute to varying degrees to the residual error in the fit to the observed frequencies. To assess the effect of assuming tetrahedral geometry in generation of the G matrices, those of myo-inositol and epi-inositol were also calculated on the basis of the crystal structures determined by X-ray diffractometry. The only departures from the published crystal structures were adjustment of the OH and CH bond lengths to 0.97 and 1.1 A, respectively, because the positions of the hydrogens are not accurately determined in the X-ray analyses. The differences between the frequencies calculated on the basis of the crystal structure and on the basis of the tetrahedral structure were relatively minor. For myo-inositol, the average error of the assigned frequencies was 10.2 cm-l for the crystal structure and 9.7 cm-I for the tetrahedral structure. For epi-inositol, the average error of the frequencies was 9.7 cm-' for the crystal structure and 8.5 ern-' for the tetrahedral structure. The comparison is particularly significant in the case of epiinositol which has two axial hydroxyl groups in the 1:3 relative positions on the ring, resulting in substantial distortion from the tetrahedral model. The assumption of tetrahedral geometry, thus, seems a fairly good one. The exception, previously noted for cis-inositol should be kept in mind, however. The convergence properties of the Fletcher-Powell method in the present context were also tested. It was reasoned that if the Fletcher-Powell method can lead to descent into false minima, this would happen irrespective of whether the set of frequencies used as the target frequencies were observed experimental frequencies or frequencies calculated from an arbritary harmonic force field. Thus, two refinements were carried out where the observed frequencies were replaced by frequencies calculated by using harmonic force fields differing to varying degrees from the final force field shown in Table I. In both of the trial refinements the Fletcher-Powell algorithm reduced the average errors by more than 95%, suggesting that the method will very nearly fully minimize the least-squares difference between the assigned and calculated frequencies, rather than settling into a false minimum. The residual error remaining at the termination of the two trial refinements was finite but quite small when compared to average errors found in the genuine refinements. It should be kept in mind, however, that application of the Fletcher-Powell method is predicated on the assumption that the initial point for the refinement is sufficiently close to the
J . Phys. Chem. 1984, 88, 519-521 final minimum that a search based on an approximation to the Hessian matrix can be developed. It is clear that neither the assumption of tetrahedral geometries nor the residual errors from the Fletcher-Powell algorithm can account for a major portion of the average errors in the fit to the observed spectra of the inositols. Thus, it appears that these errors must be attributed to second-order effects such as intermolecular interactions and anharmonicities in the true potential energy functions. Conclusions The most significant conclusion from the present study, which is an extension of some of our earlier findings, is that in spite of the high degree of coupling involved in the majority of the vibrational modes, it is possible to account for most of the differences between the spectra of the individual inositols on the basis of a relatively simple force field and the differences between the G matrices. Thus, the isolated molecule approximation seems to be a valid basis for interpreting most features in the spectra of complex carbohydrates. It was found that the different hydrogen-bonding patterns may influence some of the bands in the region between 300 and 750 cm-', but the majority of the skeletal bands in the region appear insensitive. The validity of the isolated molecule approximation is further supported by the degree to
519
which activity of the spectra is governed by selection rules based on the symmetry of the molecular skeletons. With respect to the broader objectives of our work, the results of our study of the inositols suggest that the spectra of complex carbohydrates can be interpreted on the basis of differences in their G matrices, together with a relatively simple force field, and that the isolated molecule approximation is a reasonably good one, particularly for the skeletal modes. In systems where conformational transformations are of interest the corresponding changes in the vibrational spectra can be understood to at first approximation on the basis of differences in the G matrices arising from conformation change.
Acknowledgment. The authors acknowledge with great appreciation the help of Professor L. Anderson and Professor F. Angyal in the acquistion of the samples of the inositols. Portions of this work were used by R. M. Williams as partial fulfillment of the requirements for the Ph.D. degree at The Institute of Paper Chemistry. Support of the work from the Institute research fund is gratefully acknowledged. Registry No. sycllo-Inositol, 488-59-5; cis-inositol, 576-63-6; neoinositol, 488-54-0; myo-inositol, 87-89-8; epi-inositol,488-58-4; mucoinositol, 488-55-1; L-chiro-inositol,551-72-4; o-chiro-inositol,643-1 2-9; allo-inositol, 643-10-7.
Infrared Intensities: Charge Flux Parameters for Fluorine and Their Transferability P. L. Polavarapu Department of Chemistry, Vanderbilt University, Nashville, Tennessee 37235 (Received: April 20, 1983)
In the analysis of infrared intensities, it is well-known that the number of unknown parameters exceeds the number of independent equations. If the interference contributions [W. T. King and G. B. Mast, J . Phys. Chem., 80, 2521 (1976)l and effective atomic charge are of the same order of magnitude and tend to cancel each other in atomic polar tensor (APT) equations, then the number of unknown parameters equals the number of independent equations. Under this assumption, it is found that the charge flux parameters for the fluorine atom in BF,, NF,, and CF4 are remarkably identical. This indicates that fluorine charge flux parameters are transferable, at least among these three molecules, with the aforementioned assumption.
Introduction The evaluation of a set of parameters, from infrared intensities that describe the properties of the subunits (atoms or bonds) of a molecule, has special significance. Such parameters are useful in understanding the magnitude and direction of charge flow from a given unit during molecular vibrations. In addition it is possible to estimate, from such quantities, the absorption intensities of related molecular systems. To predict absorption intensities, significant contributions have been made by Person, Overend, and their co-workers14 by examining the transferability of atomic polar tensors (AFTs) among related molecular systems. Their extensive investigations included the prediction of the infrared absorption intensities by transferring the polar tensors of hydrogen and fluorine atoms along with their comparison to the experimental values. A good agreement between the predicted and experimental (1) (a) J. F. Biarge, J. Herranz, and J. Morcillo, An. R.SOC.Esp. Fis. Quim., Ser. A, 57, 81 (1961). (b) W. B. Person and J. H. Newton, J . Chem. Phys., 61, 1040 (1974). (2) J. H. Newton and W. B. Person, J . Chem. Phys., 64, 3036 (1976). (3) B. J. Krohn, W. B. Person, and J. Overend, J . Chem. Phys., 65, 969 (1976). (4) W. B. Person and J. Overend, J . Chem. Phys., 66, 1442 (1977). (5) J. H. Newton, R. A. Levine, and W. B. Person, J . Chem. Phys., 67, 3282 (1977). (6) B. J. Krohn, W. B. Person, and J. Overend, J . Chem. Phys., 67, 5091 (1977). ( 7 ) J. H. Newton, and W. B. Person, J . Chem. Phys., 68, 2799 (1978). (8) J. H. Newton and W . B. Person, Appl. Spectrosc., 32, 290 (1978). (9) W. G. Golden, D. A. Horner, and J. Overend, J . Chem. Phys., 68,964 (1978).
0022-3654/84/2088-0519$01 .50/0
TABLE I: Equations Relating APT Elements to Charge Flux Parametersa
sy in
spccies
APT equations
I'
planar A B , molecules [A(O, 0, 0), B ( ~ A - B , 0, O ) ] apc,,'aXg = f ~ +' rA-Bk, a p y i a ) ' B = ZB' f 3 1 ' 2 r , 4 - ~ k 2
E
pyramidal A B molecules [ A(0, 0, 0 ) , B(-~A-B cos 4 , rA-B sin 0, o)] apylaxB = -'rA-B COS p sin p [ k , t ((1 - cos o)/ sin @)kz] aPy1al.B = f B e 7 rA-B Sin2 p [ k , - ( ( ' 1 2 f cos o)/ sin O)k, I (here p is the angle between C , :)\is a n d A-B bond. 0 is the angle L B A B )
F
tetrahedral AB, molecules [A(O, 0, 0), B ( ~ A - B / 3 I ' rA-B/3 "*,rA-B/3 ) ] b 3
apx/axB = rB' t
'A-B cos' p [ k , t 2 ( 2 " ' ) k 2 ] apix/a,i'B = rA-B COS2 p [ k , *- ( 2 1 ' 2 ) k , ]
(here p is half of the tetrahedral angle) The definitions of charge tlux parameters are k , = ( a p ~ / - (atg!arA-B');k? = ( a f B / a G , , ) -~( a f g / a a a ) , wherca,, i S the angle opposite to bond A-B and aa is the angle adjacent to bond A-B. b The values in parcntheses are atomic coordinates a n d define the employed molecular coordinate system. a
3rA-B)
intensities was f o ~ n d ~ for- ~some molecules and marked disagreement was noticed9 for some other molecules.
0 1984 American Chemical Society
