J. Phys. Chem. 1991, 95,6447-6454
6447
Ring Current Contributions to Vibrational Circular Dichroism? Ab Initio Calculations for Methyl Glycolate-d, and -dJ R. Bursi and P.J. Stephens; Department of Chemistry, University of Southern California. Los Angeles, Cali/ornia 90089-0482 (Received: November 15, 1990; In Final Form: February 27, 1991)
Vibrational rotational strengths are predicted for the hydrogenic stretching transitions of methyl glycolate-dl (*CHD(OH).COOCH,) and -d4 (*CHD(OH)COOCD3) using Stephens' a priori theory, implemented at the SCF level of approximation using the 6-31G* basis set. Five conformations are studied; four contain internally hydrogen-bonded rings, one does not. Predicted rotational strengths vary substantially with conformationalstructure but, for the *C-H and *C-D stretching modes, show no significant correlation with the existence of an internally hydrogen-bonded ring. For each isotopomer a detailed analysis of the rotational strengths of the *C-H and *C-D stretching transitions of two structures, with and without a hydrogen-bonded ring and differing in geometry only in the position of the OH H atom, shows that formation of the ring does not lead to significant enhancement in the magnetic dipole transition moment component perpendicular to the ring for these transitions. Our results are contrary to the expectations of the ring current hypothesis of Nafie and co-workers and lead to the conclusion that this hypothesis does not provide a sound foundation for the interpretation of VCD spectra.
Introduction A number of approaches to the prediction of the vibrational circular dichroism (VCD) spectra of chiral molecules have been proposed.' In our laboratories, we have recently developed and implemented an a priori theory of magnetic dipole vibrational transition moments and vibrational rotational strengths, permitting the prediction of VCD ~ p e c t r a . ~ In - ~ addition to the molecular geometry and vibrational force field, calculations of rotational strengths require the calculation of two sets of molecular tensors, e 0 and Mk8, termed atomic polar and axial tensors. The former are required for the calculation of vibrational electric dipole transition moments and absorption intensities and are well-known. The latter are new. Calculations of VCD spectra for several small chiral molecules, using and Mt8 tensors calculated at the ab initio S C F level of approximation, have exhibited substantial overall agreement with experiment.+I2 Despite the emergence of a reliable theory of vibrational rotational strengths, other approaches to the prediction and analysis of VCD spectra continue to be developed and employed. It is clearly of interest to examine the relationship of these approaches to our a priori theory and to explore their reliability. We have already reported such comparative studies of the fixed partial charge, atomic polar tensor, coupled oscillator, and localized molecular orbital models.13 In the present paper, we examine an approach proposed by Nafie and co-workers for molecules containing rings in which vibrational magnetic dipole transition moments and rotational strengths are related to vibrationally induced ring current^.'^'^ Nafie and co-workers propose that the vibration of an atom at the periphery of a ring can induce in this ring a current giving rise in turn to a magnetic dipole moment perpendicular to the ring. The rotational strength of a normal mode involving this vibrational motion then possesses a contribution arising from the induced ring current. Nafie and coworkers have identified ring current contributions to the VCD of a wide variety of molecules. A major focus has been the C-H stretching transitions of methine groups whose C atoms participate in hydrogen-bonded rings. Simply put, it is proposed that large VCD associated with the stretching mode of a methine group attached to a hydrogen-bonded ring is predominantly due to an induced ring current. Conversely, it is assumed that the VCD of a methine stretching mode can be used to elucidate the existence of a hydrogen-bonded ring in the structure of a molecule. On this basis, hydrogen-bonded ring structures have been proposed for a number of molecules. To date, the identification of ring current contributions to VCD spectra is empirical and is not based on 'First reported at the 10th Canadian Symposium on Theoretical Chemistry, August 1989, Banff, Paper T6.1.
reliable calculations of vibrationally induced ring In addition, in a number of molecules it has been necessary to postulate rather unusual and otherwise unsupported conformations in order to generate rings around which currents can flow. If ring currents are to be routinely introduced into the analysis of VCD spectra, it is clearly important that their existence be more securely established. To this end we are examining the predictions of our theory of vibrational rotational strengths for a number of molecules in the light of the expectations of the ring current hypothesis.
(1) Stephens, P. J.; Lowe, M. A. Annu. Reu. Phys. Chem. 1985,36,213. (2) Stephens, P. J. (a) J . Phys. Chem. 1985,89,748;(b) 1987.91, 1712. (3) Lowe, M. A.; Segal, G.A.; Stephens, P. J. J . Am. Chem. Soc. 1986, 108, 248. (4) Amos, R. D.; Handy, N . C.; Jalkanen, K. J.; Stephens, P. J. Chem. Phys. Lett. 1987, 133, 21. (5) Amos, R. D.; Jalkanen, K. J.; Stephens, P. J. J . Phys. Chem. 1w)8,92, 5571. (6) Lowe, M. A.; Stephens, P. J.; Segal, G. A. Chem. Phys. Len. 1986, 123, 108. (7) Jalkanen, K. J.; Stephens, P. J.; Amos, R. D.; Handy, N. C. J . Am. Chem. Soc. 1987, 109, 7193. (8) Jalkanen, K. J.; Stephens, P. J.; Amos, R. D.; Handy, N. C. J . Am. Chem. SOC.1988,110,2012. (9) Kawiecki, R. W.; Devlin, F. J.; Stephens, P. J.; Amos, R. D.; Handy, N. C. Chem. Phys. Leu. 1988, 145,411. (10) Jalkanen, K. J.; Devlin, F. J.; Polonski,T.; Amos, R. D.; Stephens, P. J. Forty-Third Symposium on Molecular Spectroscopy; The Ohio State University, 1988, paper RH5, and to be submitted. Bursi, R.; Stephens, P. J., paper RH6. and to be submitted. Jalkanen, K. J.; Stephens, P. J.; ElAzhary, A.; Keiderling, T. A., to be submitted. (1 1) Lowe, M. A.; Alper, J. S. J. Phys. Chem., 1988,92,4035. Dothe, H., Lowe, M. A.; Alper, J. S.J . Phys. Chem. 1988, 92,6246. (12) Amos, R. D.; Handy, N. C.; Drake, A. F.; Palmieri, P. J. Chem. Phys. 1988,89, 7287. (13) Stephens, P. J.; Jalkanen, K. J.; Kawiecki, R. W. J . Am. Chem. Soc. 1990,112,6518. Annamalai, A.; Jalkanen, K. J.; Narayanan, U.; Tissot, M. C.; Keiderling, T. A.; Stephens, P. J. J . Phys. Chem. 1990, 94, 194. (14) Nafie, L. A.; Oboodi, M. R.; Freedman, T. B. J . Am. Chem. Soc. 1983, 105, 7449. (IS) Oboodi, M. R.; Lal, B. B.; Young, D. A.; Freedman, T. B.; Nafie, L. A. J . Am. Chem. Soc. 1985. 107, 1547. (16) Freedman, T. B.; Balukjian, G. A.; Nafie, L. A. J . Am. Chem. Soc. 1985, 107, 6213. (17) Freedman, T. B.; Nafie, L. A. In Topics in Stereochemistry; Eliel, E. L., Wilen, S. H., Eds.; Wiley: New York, 1987; Vol. 17, pp 113-206 and references therein. (18) Freedman, T. B.; Chernovitz, A. C.; Zuk, W. M.; Paterlini, M. G.; Nafie, L. A. J . Am. Chem. Soc. 1988,110,6970. (19) Zuk, W. M.; Freedman, T. B.; Nafie, L. A. J . Phys. Chem. 1989,93, 1771.
0022-3654191 /2095-6441%02.50/0 0 1991 American Chemical Society
Bursi and Stephens
6448 The Journal of Physical Chemisrry, Vol. 95, No. 17, 199'1 In this paper we present a theoretical study focusing on dl and d4 isotopomers of methyl glycolate CH2(OH)-COOCH3 (l), CHD(OH).COOCH3 (2), and CHD(OH).COOCD3 (3). Preliminary to studies of the VCD of a number of molecules containing internally hydrogen-bonded rings, we have examined the conformational structures and associated vibrational spectra of methyl glycolate (1) predicted at the ab initio SCF level. We have identified four conformations within an energy range of 10 kcal/mol, three possessing internally hydrogen-bonded rings and one without. The existence of a multiplicity of structures, both with and without internal hydrogen bonding, permits the relationship between VCD and ring structure to be examined. We have therefore carried out calculations of the VCD of dl and d4 isotopomers of methyl glycolate, 2 and 3, and examined the rotational strengths predicted for the *C-H and *C-D stretching modes (*C denoting the asymmetric C atom). These calculations permit the qualitariue expectations of the ring current hypothesis to be examined in two ways. First, we can determine whether large *C-H and *C-D stretching VCD is or is not correlated with the presence of an intramolecular ring. Second, in cases where large VCD is predicted, we can examine the directions of the electric and (particularly) magnetic dipole transition moments contributing predominantly to this VCD. Magnetic dipole transition moments originating in ring currents must be perpendicular to the ring in which current flows. In principle, our calculations also permit a quantirariue assessment of the current density at any point in space induced by vibrational motion of any atom. At this time, however, we have not attempted to derive or display such calculated current densities.
Methads Vibrational absorption and circular dichroism spectra, 4 ( ~ and ) A+), are given by
At@)
1
\'I
32n3N PZRJ;(F~,F) 3000hc(2.303) i
(OI(reJpl1
)i
= C[(fieJpIiX A
(OI(fimoS)pIl)i
=
C[(fimg)~l?( 5 ) A
where
[ (fimag)p]? = -(2 h 3@i)'I2CSAa,iM$ a
[Fell: and [Fmag]:are the contributions of nucleus X to the electric and magnetic dipole transition moments of the ith fundamental transition, respectively. The equilibrium geometry, vibrational force field and ?$@ and M$ tensors for 1 have been calculated ab initio at the SCF level of approximation. Geometry optimization was carried out at the 6-31G* basis set level using CRAY-XMP or Alliant FX-80 versions of GAUSSIAN 86 or a CRAY-XMP implementation of CADPAC (version 4.0).20 Four energy minima were found corresponding to structures henceforth labeled Ia, Ib, IC, and I1 (Figure 1). Structures Ia and Ib contain an internally hydrogen-bonded ring involving the carbonyl oxygen of the ester group. In Ia the methoxy group is cis to the carbonyl oxygen, in Ib it is trans. Structure IC is very similar to Ia except that no hydrogen-bonded ring is present. Structure I1 contains an intemally hydrogen-bonded ring involving the oxygen of the methoxy group. Cartesian force fields at each of these four energy minima were calculated using CADPAC and the 6-31G* basis set. Vibrational frequencies calculated thence verified that all geometries are true minima. In all cases the six lowest frequencies (zero at an exact minimum) were less than 5 cm-I. P$ and (I$) tensors were also calculated for all four structures using CADPAC and the 6-31G* basis set. ?$ tensors are obtained using standard analytical derivative metkds based on the coupled Hartree-Fock equations?' (It@)' tensors are obtained using the equation'
(7)
where Dl and Ri are the dipole and rotational strength of the ith transition of energy hcrf,andf,(vl,r) is the band shape of the ith transition? For a fundamental transition, 0 1, in the ith normal mode, Di and Ri are given by
-
Di = (OIi4111 ) A 1 I i W ) i
operator, and is the t$ tensor evaluated with the origin at the equilibrium position of nucleus A. The hf;@tensor of eq 4 is in the distributed origin gauge.2b Equation 3 can be rewritten:
Ri = Im [(OIji~il1 ) A 1lPmagP)iI ( 2 )
where2
(3) In eq 3, hw, is the energy of the ith mode, the S , matrix connects normal coordinates Qf with Cartesian displacement coordinates x, (A = nucleus, a = x, y, z ) , and t$@ and h f : ~are atomic polar and axial tensors, given by
(4)
In eq 4, fi denotes nucleal coordinates, & is the equilibrium molecular geometry, qo(R) is_the adiabatic electronic wave function of the ground state_G, *,is the position of nucleus A at the equilibrium geometry Ro, +G(&,H@) is the electronic wave function of G in the presence of the perturbation -(fi&)@H@, where ji",,, is the electronic contribution to the magnetic moment
where (I$" is the tensor of nucleus A, calculated with the origin at the molecular origin 0 for all nuclei, and Etd(.) is the electronic contribution to the momentum representation of the atomic polar tensor, ?$,,(n). The (f$)O and E:,(n) tensors are obtained using analytical derivative methods based on the coupled Hartree-Fock equations, as described previou~ly.~*~ In all cases, the molecular origin, 0, was chosen to be the center of mass of the most abundant isotopomer of methyl glycolate: l2CH2 160H.I2Cl6016012CH3.
Results and Discussion Our eventual goal in studying methyl glycolate, 1, is to establish its conformation in dilute solution Le., under those conditions in which intermolecular hydrogen bonding is absent. To this end we are comparing predictions of vibrational absorption and circular dichroism spectra of isotopomers of 1 for obvious possible structures with experimental spectra. The structures we have chosen to examine, as shown in Figure 1, are the conformations involving a five-membered hydrogen-bonded ring, in which the OH is hydrogen bonded to either the carbonyl or the methoxy oxygen of the ester group. In the case of hydrogen-bonding to the carbonyl group we have examined the two options of a cis or trans methoxy methyl group. In addition, one alternative structure in which the OH group is "free", i.e., not hydrogen-bonded, has been examined. Geometry optimization at the SCF level, using the 6-31G* basis set, shows that each of these four structures constitutes a minimum on the conformational potential surface of methyl glycolate. The SCF energies and selected geometrical ~
(20) Amos, R. D.; Rice, J. E. The Cambridge Analytic Derivatives Package, Version 4.0, Cambridge, 1987. ( 2 1 ) Amos, R. D. Adv. Chem. Phys. 1987,67, 99.
The Journal of Physical Chemistry, Vol. 95, No. 17, 1991 6449
Ring Current Contributions to VCD -HI
Y
1
u7
la
Ib
IC
Figure 1. Conformationsof methyl glycolate (1). The R enantiomers of the Ia, Ib, IC,and IIa conformationsof 2 are obtained by substitution of HI, by deuterium. The S enantiomer of the IIb conformation of 2 is obtained by substitution of H12in I1 by deuterium. In the case of 3, He, H,, and HBare also substituted by deuterium.
TABLE I:
Energies of Conformations of 1
la Ib IC
Ewd
AEb
-341.683 941 -341.669 069 -341.675 91 7 -341.680537
0.00 9.34 5.04 2.14
I1 aSCF energy in atomic units. bEnergy relative to structure Ia in kcal/mol . parameters of the four structures, Ia, Ib, IC, and 11, are given in Tables 1-111. The relative energies are Ia < I1 < IC < Ib, structures 11, IC,and Ib lying 2.14, 5.04, and 9.34 kcal/mol above structure Ia, respectively. Internal hydrogen bonding is thus predicted to be slightly more stable when the carbonyl oxygen is involved than when the methoxy oxygen is employed. The cismethyl geometry of structure Ia is substantially more stable than the trans-methyl structure Ib. Breaking the hydrogen bond of structure Ia leads to a conformation approximately 5 kcal/mol higher in energy. These results support the expectation that structure la will be the preferred conformation in the gas phase or in dilute solution (in innocuous solvents). However, since the SCF energies are not close to the HartretFock limit and neither correlation nor solvents effects are included, a defnitiue conclusion regarding the structure of 1 is certainly not possible. An interesting feature of structure Ia is that all of the atoms participating in the hydrogen-bonded ring and in addition the 0,C, and one H of the
TABLE II: Mbednl Angles .ad I0”deeulrr Hydrogen B o d Lennths of Conformations of 1” T(02CIO3CJb 0.0 180.0 0.0 1.5 7(0$1C409)’ 180.0 180.0 180.0 27.9 0.0 0.0 155.1 f(02CIC409)d 0.0 0.0 180.0 48.5 ~(CIC409HlO) 0.0 3.640 2.289 2.137 2.065 R(02***Hio) “Dihedral angles are in degrees. Bond lengths arc in angstroms. br(03C102Cs) in II. CT(O~C~C,O~) in II. d7(03clc409)in 11. methoxy group are (to a very good approximation) coplanar. This planarity also exists in structure Ib. While it is natural to attribute the planarity of the ring to hydrogen-bond formation, the maintenance of planarity in structure IC shows that this is not a necessary requirement. This conclusion is strengthened by the significant nonplanarity of the hydrogen-bonded ring in structure 11. The coplanarity of all atoms in 1 save four hydrogen atoms in the three structures Ia, Ib, and IC must then be attributed to an intrinsic preference for planarity of the C and 0 atoms of this molecule, when the carbonyl 0 is cis to the hydroxyl 0, irrespective of the presence of hydrogen bonding. Vibrational frequencies of methyl glycolate-dl and -d4 ( 2 and 3) obtained from 6-31G’ SCF Cartesian force fields calculated for structures Ia, Ib, IC, and I1 are given in Table IV and V. In the case of structure 11, “axial” and “equatorial” conformations
6450 The Journal of Physical Chemistry, Vol. 95, No. 17, 1991 TABLE III: Ring Cartesian Coordinates of Conformations of 1' la Ib atom Y Z X X Y 0.000 0.007 0.000 0.000 CI 0.049 -0.001 2.257 0.000 0.000 0 2 0.056 0.000 -1.547 -2.474 0.OOO -2.347 C, 09
Hi0
-4.472 -3.943
-0.001 -0.002
-0.016 1.700
-4.512 -3.883
0.OOO 0.000
Bursi and Stephens
IC
I1
z
X
Y
Z
X
Y
0.000 2.242 -1.465 0.169 1.855
o.Oo0 0.000 -2.300 -4.470 -5.908
o.Oo0
o.Oo0 2.234 -1.696 -0.224 -1.289
0.001 0.001 -2.653 -4.470 -4.293
-0.047 -0.023 -0.004 -1.072 -0.411
O.Oo0
0.000 0.000 0.000
z -0.001 2.500 -1.077 0.489 2.144
'Cartesian coordinates are in au. TABLE IV: Vibratioarl Frequencies of Conformations of 2* freq la Ib IC Hab IIbb mode VI 4062 4043 4118 4111 4111 OH 3351 3356 3356 CH, asym u2 3359 3353 3334 3341 3341 CH3 asym u3 3340 3310 3252 3323 3256 CH, symC v4 3257 3239 3216 3256 3195 C-H' ~g 3239 3224 2361 2344 2446 C-D V6 2380 2369
Ila
*
400
IC
'Frequencies are in cm-'. See Figure 1 for definitions of a and b conformations of 11. The inequivalence of HI, and HI, in I1 is quantitated by the HlIC409Hlo and HI2C4O9Hl0 dihedral angles, which are and u5 are inverted in conformation 73.0' and 168.5', respectively. Ha. loot
(x 10 E'4)
TABLE V Vibrational Frequencies of Conformrtions of 3' freq la Ib IC Ilab IIbb mode 4118 4111 4111 CbH uI 4062 4043 3216 3323 3195 C-H u2 3239 3226 2490 2494 2494 CD, asym v3 2497 2489 2417 2482 2482 CD, asym u4 2482 2459 2361 2344 2446 C-D US 2380 2369 2329 2331 v6 2331 2320 2331 CD3 Sym a Frequencies are in cm-l. bSee Figure 1 for definitions of a and b conformations of 11. The inequivalence of H I I and HI, in I1 is quantitated by the HIIC409Hlo and HI2C4O9HIO dihedral angles, which are 73.0' and 168.5', respectively.
IIa and IIb are considered separately. Our study here focuses on the *C-H and *C-D stretching modes; accordingly, only hydrogenic stretching frequencies are listed in Tables IV and V. Examination of the L and potential energy distribution matrices of the five conformations of 2 identifies ul as the 0 - H stretch, u2 and v3 as asymmetric CH3 stretches, u4 as the symmetric CH3 stretch, us as the *C-H methine stretch, and v6 as the *C-D stretch in all structures except Ha, in which u4 and u5 are inverted. In the case of 3, v, is identified as the 0 - H stretch, v2 as the *C-H methine stretch, u3 and u4 as asymmetric CD3 stretches, us as the *C-D stretch, and v6 as the symmetric CD3 stretch in all structures. For both 2 and 3, in all conformations the *C-H and *C-D coordinates are quite pure: according to the potential energy distribution these modes involve *C-H or *C-D stretching coordinates to 290%. This is not surprising in view of the considerable separation of the CH3 and CD3 moieties of 2 and 3 from their CHD groups. The purity of the *C-H and *C-D stretching modes of 2 and 3 makes these molecules optimal for our purposes. The vibrational frequencies given in Table IV and V (and the remaining 24 frequencies not given there) are not accurate frequencies, of course. SCF calculations are well-known to give vibrational frequencies 10-1 5% too high on averageF2 In work to be reported elsewherez3we are using our 6-31G* SCF force fields as the starting point for the derivation of more accurate force fields, following the scaling methodology of h l a y and co-workemN While for some modes this process will significantlymodify their normal coordinates, the purity of the *C-H and *C-D modes of 2 and 3 guarantees that these coordinates will change very little (22) Hehre, W. J.; Radom, L.; Schleyer, P. v. R.;Pople, J. A. Ab Initio Moleculor Orbital Theory: Wiley: New York, 1986. (23) Bursi, R.; Devlin, F. J.; Stephens, P. J., to be submitted. (24) Fogarasi, G.; Pulay, P. Annu. Reo. Phys. Chem. 1984,35, 191; Vib.
Spectro Slruci. 1985, 14, 125.
-100' 3450
1
I
Y
I
I
3250
3050
(em-l )
Figure 2. VCD spectra predicted for (R)-methyl glycolatedl in the C-H stretching region. The arrow marks the methine stretch. Ilb
Ila IC
100
c
-501
-100'
2600
Ib
V I
I
2400
I
I
J
2200
v (cm-')
Figure 3. VCD spectra predicted for (R)-methyl glycolatedl in the C-D stretching region.
as a result of such scaling. For our purposes here, therefore, the use of unscaled SCF force fields is not a significant limitation. The dipole and rotational strengths of the modes of 2 and 3 calculated for structures Ia, Ib, IC, Ha, and IIb are given in Tables VI and VII. As is to be expected, the C-H and C-D stretching modes exhibit somewhat smaller dipole strengths than the 0 - H stretching modes. The predicted dipole strengths of all
The Journal of Physical Chemistry, Vol. 95, No. 17, 1991 6451
Ring Current Contributions to VCD TABLE V I Dipole and Rotational Strengths of 2#
la mode
Ib R
D 96.5 28.0 32.8 37.5 39.5 35.1
VI "2
y3 y4 y5
y6
D 110.7 26.6 49.0 52.3 26.1 38.2
-1 .o -0.1 0.2 0.0 11.7 -16.6
IC
IIa
R
D
R
-1.2 -0.4 4.2 -24.0 39.8 -23.4
61.1 33.4 36.9 42.2 50.5 45.6
0.0 -0.2 0.2 0.0 3.2 -10.1
IIb R
D 65.7 29.3 32.5 17.7 39.5 50.6
R
D 66.2 29.1 32.6 39.2 54.1 17.9
10.7 -0.5 0.5 2.4 0.9 -5.6
-1 1.0 0.4 -0.2 -1
.o
3.6 -4.5
#Dipolestrengths, D, and rotational strengths, R, are in 10" and 10- esu2cm2,respectively. Rotational strengths are for R absolute configuration. TABLE VII: Dipole and Rotational Strengths of 3 O
la
Ib
IC
IIa
IIb
mode
D
R
D
R
D
R
D
R
D
R
VI
96.5 39.7 28.5 30.3 35.1 42.7
-1 .o 11.8 -0.1 -0.3 -16.2 0.0
110.6 45.2 25.5 41.1 40.0 30.8
-1.2 19.5 0.4 -2.6 -18.2 -3.0
61.1 50.7 33.7 33.5 45.6 47.9
0.0 3.3 -0.2 -0.2 -9.7 0.0
65.6 18.1 30.1 30.4 49.9 45.1
10.7 2.7 -0.3 0.2 -4.8 -1.0
66.2 54.3 30.1 30.0 17.7 44.9
-11.0 3.4 0.4 -0.8 -4.1 0.1
y2
y3 y4
V5 y6
#Dipolestrengths, D, and rotational strengths, R, are in 10" and IO" esu2cm2,respectively. Rotational strengths are for R absolute configuration. TABLE VIII: Contributions to the Electric and Magnetic Transition Moments end Rotational Strengths of the *C-H and *C-D Stretching Modes of Conformations of 2 O ~
Ia C-H
x y z
C-D
x y
z
Ib
IC
~~~~
IIa
IIb
CC~I
pmg
Raab
pel
Pmg
%ab
fid
pmag
Raab
Pel
Pmg
Raab
Pel
-1.36 4.69 3.96 1.45 4.28 -3.83
7.20 6.23 -1.96 3.34 -5.56 -0.63
-9.79 29.22 -7.76 4.84 -23.80 2.41
-1.71 4.21 2.34 -1.65 -4.30 4.12
4.34 13.32 -3.75 -2.22 7.65 1.43
-7.42 56.08 -8.78 3.66 -32.89 5.89
-1.93 5.44 4.15 2.49 4.86 -3.97
8.31 4.94 -1.83 4.05 -4.55 -0.50
-16.04 26.87 -7.59 10.08 -22.11 1.99
0.49 -1.62 -3.85 -0.36 -6.50 2.86
-3.48 -6.21 1.54 -3.36 2.55 3.39
-1.71 10.06 -5.93 1.21 -16.58 9.70
-0.37 6.85 -2.65 -0.76 1.17 4.00
O p d and pmg are in product of Eel and pmr
and
esu cm, respectively. Rotational strengths are in IO" (esu cm)2. b
~ y y ,~and,
zz
p m ~
-7.74 2.38 5.87 -0.19 -5.48 0.43
&ob 2.86 16.30 -15.56 0.14 -6.41 1.72
contributions to the scalar
TABLE IX: Contributions to the Electric and Magnetic Transition Moments and Rotational Strengths of the *C-H and *C-D Stretching Modes of Conformations of 3" ~
la 'C-H
x y
z
*C-D
x
y
z
Ib
IC
~~
IIa
IIb
pel
pmg
Raob
pel
fimg
Raab
Pel
C(mq
Raa'
pel
pmg
Raab
pel
~Lmrg
Raab
1.29 -4.70 -3.99 1.44 4.26 -3.85
-7.20 -6.09 1.91 3.34 -5.52 -0.66
-9.29 28.62 -7.62 4.82 -23.53 2.55
-1.51 4.84 4.41 1.68 4.09 -4.52
5.83 8.83 -3.27 1.81 -7.03 -1.67
-8.80 42.74 -14.42 3.04 -28.75 7.55
-1.88 5.45 4.17 -2.48 -4.85 3.99
8.31 4.85 -1.79 -4.05 4.49 0.53
-15.62 26.45 -7.46 10.04 -21.78 2.11
-0.47 1.64 3.90 0.47 6.48 -2.78
3.44 6.18 -1.50 3.39 -2.45 -3.41
-1.62 10.14 -5.85 1.59 -15.88 9.48
-0.35 6.87 -2.63 0.77 -1.13 -3.98
-7.69 2.34 5.84 0.25 5.48 -0.47
2.69 16.08 -15.36 0.19 -6.19 1.87
O b d and pmg are in product of jieland Pmg.
and IO-" esu cm, respectively. Rotational strengths are in 10- (esu cm)2. ' X X , y y , and zz contributions to the scalar
C-H and C-D stretching modes are similar. In contrast, there is much greater variation in rotational strengths, both among modes of the same structure and between analogous modes of different structures. The situation for the C-H and C-D stretching modes is presented graphically in Figures 2-4, where VCD spectra predicted from the rotational strengths of Tables VI and VI1 assuming Lorentzian band shapes9 (half-width at half-height equal to 8 cm-I) are shown. The contributions of individual Cartesian components of the electric and magnetic dipole transition moments to the rotational strengths of the *C-H and *C-D stretching transitions of 2 and 3 are given in Tables VI11 and IX. In all cases the yy term of the rotational strength (arising from the y components of the electric and magnetic dipole transition moments) is the largest. As seen from Table 111, they axis is essentially perpendicular to the planes best approximating the H1,,09C4C102 geometries of the various conformations. However, the variations in rotational strengths between conformations arise predominantly from change in all three x x , yy, and zz components. In particular, for both 2 and 3, it is noteworthy that the yy contributions to the *C-H
and *C-D rotational strengths of conformations Ia and ICare very similar and that the differences in rotational strengths arise predominantly from differences in the x x contributions. As shown by eqs 5 and 6,for any vibrational transition the electric and magnetic transition moments can be subdivided into atomic contributions. For the *C-H and *C-D stretching modes of conformations Ia and IC of 2 these contributions are listed in Tables X and XI. In both modes of both conformations, the contributions of the two atoms primarily involved in the stretching vibration are overwhelmingly dominant. The rotational strengths of these transitions thus do not depend significantly on the contributions to the *C-H or *C-D stretching normal coordinates by other atoms. Analysis of the *C-H and *C-D stretching modes of 3 leads to the same conclusion. In sum: the rotational strengths of the hydrogenic stretching transitions of 2 and 3 overall exhibit much greater variation with conformational structure than do the dipole strengths. Thus, as expected, predicted VCD spectra are much more sensitive to molecular geometry than predicted absorption spectra. The rotational strengths of *C-H and *C-D stretching transitions vary
6452 The Journal of Physical Chemistry, Vol. 95, No. 17, 1991 TABLE X Iwner Ia of 2. Atomic Contributioar [b,& (emcm) .ad [p&
Bursi and Stephens (esu em) for the us and the v6 M&
Y5
Y6
[Poll:
atom
X
CI 02 03 c4 c5 H6 H7 H8 09 HI0 DII HI2
-0.09
total
-0.01
-0.02 -0.43 -0.01 -0.02 -0.02 -0.02 0.05 0.08 0.02 -0.88 -1.36
Y 0.01 0.00 0.00 1.06 0.00 -0.03 0.02 0.00 0.02 0.06 0.04 3.52 4.69
tPe,lF
[Pmgl:
z
X
0.03 0.02 0.01 0.71 0.01 -0.02
-0.02 0.01 0.00 -0.90 0.00 0.02
-0.01
-0.01
0.01 -0.01 0.06 -0.02 3.19 3.96
0.00 -0.02 -0.09 0.15 8.06 7.20
TABLE XI: Isomer IC of 2. Atomic ContributioaP[j&
Y 0.01 0.00 0.02 1.88 0.03 0.09 0.06 -0.04 0.00 0.34 -0.04 3.89 6.23
z
0.02 0.00 0.01 0.90 -0.01 -0.11
0.08 0.00 -0.06 -0.13 -0.09 -2.56 -1.96
(esu cm) and [p&
X
0.21 0.00 0.09 0.81 0.01 0.00 0.00 0.00 -0.04 -0.37 0.69 0.05 1.45
Y -0.02 -0.01 0.00 1.65 0.00 0.00 0.00 0.00 0.05 0.05 2.11 -0.20 4.28
[PIMgIf
z
X
0.15 -0.02
0.04 0.05 -0.01 -1.03 0.00 0.00 0.00 0.00 -0.04 -0.06 4.67 -0.29 3.34
0.00 -1.34 0.00 0.00 0.00 0.00 -0.05 0.12 -2.51 -0.18 -3.83
V6
[Pcll:
c1 02 03 c4 c5 H6 H7 H8 09 HI0 D11 HI2
total
X
-0.10 -0.01 -0.02 -0.51 0.00 -0.01 -0.01 -0.01
0.04 -0.04 0.02 -1.27 -4.93
Y 0.01
0.00 0.00 1.13 0.00 -0.02 0.01 0.00 0.01 -0.02 -0.05 4.27 5.44
2
X
0.02 0.01 0.01 0.56 -0.01 -0.01 -0.01 0.01
-0.03
0.03 -0.03 3.57 4.15
Y 0.02 0.00 0.02 1.29 0.02 0.06 0.03 -0.02 -0.04 0.17 -0.03 3.43 4.94
0.01
0.01 -0.71 0.00 0.01 -0.01 0.00 0.00 -0.01 0.15
8.90 8.31
Ila 200
IC
501 0
3450
I
[Ped:
[Pmgl:
-0.01
I
3250
-5.56
z
-0.04 -0.01 0.00 1.02 0.00 0.00 0.00 0.00 -0.12 -0.09 -1.47 0.08 -0.63
(esu cm) for the us and u6 Modes
VII
atom
Y 0.00 0.00 -0.07 -2.60 0.00 0.00 0.00 0.00 -0.14 -0.34 -2.24 -0.16
I
la 3050
u (cm-')
Figure 4. VCD spectra predicted for (R)-methyl glycolate-d, in the C-H
stretching region.
less than the other C-H stretching and the 0-H stretching transitions. In particular, the signs are the same in all conformations. For both 2 and 3 the largest rotational strengths are found in structures Ia and Ib, and the smallest in structures IIa and IIb. Structure IC generates rotational strengths intermediate in size. Structures la, Ib, Ira, and IIb contain internally hydrogen-bonded rings; structure IC does not. No obvious relation between the predicted rotational strengths and the existence of a ring structure is apparent. Although the *C-H and *C-D stretching rotational strengths are smaller in structure IC than in structures la and Ib, they are not smaller than in structures IIa and IIb.
z
X
0.03 0.00 0.01 0.90 -0.01 -0.01 0.04 0.00 -0.03 0.05 -0.09 -2.65 -1.83
0.21 0.00 0.09 0.94 -0.01
0.00 0.00 0.00 0.02 0.16 1.00 0.09 2.49
Y -0.02 -0.01
0.00 1.76 0.00 0.00 0.00 0.00 0.04 -0.02 3.36 -0.25 4.86
[Pmgl:
z
X
0.25 0.03 0.00 -1.05
0.03 0.04 0.00 -0.81 0.00 0.00 0.00 0.00 -0.01
0.00 0.00 0.00 0.00 -0.05 -0.14 -2.82 -0.21 -3.97
-0.01
5.16 -0.34 4.05
Y 0.04 0.01 -0.06 -1.77
0.00 0.00
0.00 0.00 -0.13 -0.50 -1.98 -0.15
-4.55
z
-0.03 0.00 0.00 1.02
0.00 0.00 0.00 0.00 -0.10 0.06 -1.53 0.10 -0.50
Our results are prima facie inconsistent with the expectations of the ring current hypothesis of Nafie and co-workers. These are that structures Ia, Ib, IIa, and IIb will exhibit larger rotational strengths than structure IC for the *C-H and *C-D stretching transitions as a result of their internally hydrogen-bonded rings. A more detailed examination of the origin of the rotational strengths of these transitions in structures Ia and IC further documents the inconsistency with the ring current hypothesis. Structures Ia and IC differ signifieantly only in the position of the hydroxyl H atom. Their comparison thus provides the cleanest assessment of the consequences of hydrogen bonding. Both *C-H and *C-D stretching rotational strengths are larger in structure Ia than in IC. In all cases the dominant contribution to the rotational strength involves the components of the electric and magnetic dipole transition moments perpendicular to the plane of the atoms HI0O9C4C1O2.However, for a given transition this contribution is very nearly identical in magnitude in the two structures. The variation between the two structures thus originates in the in-plane contributions. The ring current hypothesis predicts that structure Ia will exhibit larger *C-H and *C-D stretching rotational strengths than structure IC due to larger contributions from the electric and magnetic dipole transition moments perpendicular to the ring of structure Ia. This expectation is not borne out by our calculations. We conclude that contributions to the magnetic dipole transition moments of the *C-H and *C-D stretching transitions from vibrationally-induced ring currents are not important in determining their rotational strengths. The ring current hypothesis was first proposed by Nafie and co-workers to explain the VCD of the methine stretching modes of the a-amino a ~ i d s . ' ~The J ~ 'bias" of the C-H stretching VCD in this group of molecules was attributed to the VCD of this mode, whose magnitude was in turn related to the presence of a hydrogen-bonded ring involving the COO- and ND3+ (in D20) amino acid moieties in addition to the methine C. The existence of a "bias" of significant magnitude in the VCD of the C-H stretching modes is taken by Nafie and co-workers to indicate significant
Ring Current Contributions to VCD
The Journal of Physical Chemistry, Vol. 95, No. 17, 1991 6453
"charge flow". "Charge flow" is electronic redistribution attendant on vibrational motion over and above "perfect following" of the nuclear motion by the electrons. In the case of "perfect following", Nafie and co-workers expect that significant "bias" will be absent. The observation of significant "bias" in the C-H stretching VCD of the a-amino acids originating in the methine stretching mode was thus taken to indicate the generation of substantial "charge flow" by this vibrational motion. Nafie and co-workers then extrapolated further to the proposition that this "charge flow" was dominated by a contribution from a ring current around a closed ring formed, in the case of the a-amino acids, by hydrogen bonding between the amino and carboxyl groups. The corollary to this hypothesis is that in the absence of this ring the "charge flow" and "bias" arising from methine stretching would be much smaller. The idea that a significant C-H stretching VCD "bias", attributable to a methine stretching mode, could be explained in terms of electronic currents induced by the stretching vibration in rings involving the methine C was subsequently extended to a much wider variety of m o l e ~ u l e s . ' ~In' ~many cases, the rings invoked again involved some type of hydrogen bonding, varying from "classical" hydrogen bonding as in the a-hydroxy acids and their esters to less traditional hydrogen bonding to aromatic rings, as in a-phenylethanol. Related analyses, in which ring current are invoked to explain VCD sign and magnitude, have been proposed for N-H, 0-H, and non-methine C-H stretching modes, and (in a few cases) for modes not involving stretching motions of hydrogenic bonds. Examination of the specific molecules studied by Nafie and co-workers shows that in the majority of those cases where ring currents are associated with hydrogen-bonded rings, the hydrogen-bonded rings are postulated from the VCD data, rather than being independently known to exist, from other data or calculations. In many of these cases, the rings proposed are certainly plausible. However, in some cases such as those involving hydrogen bonding to phenyl and cyclopropyl rings the rings proposed are quite speculative. In addition, in those cases where experimental VCD data are obtained in aqueous solution, moleculesolvent hydrogen bonding has been ignored. The VCD data base for molecules containing independenrly well-characterized internally hydrogen-bondedring structures is thus extremely limited. Consequently, on a purely empirical level, the proposed correlation between VCD and hydrogen-bonded rings cannot be regarded as firmly established. Of course, even if all of the hydrogen-bonded ring structures proposed by Nafie and co-workers were to exist (i-e.,be the unique conformer) under the conditions of the VCD measurements, the question of the causal relation between VCD and ring remains. The observation of VCD of any given sign and magnitude for a vibrational mode of a molecule containing a ring does not in any way demonstrate that the VCD is caused by the ring. Likewise, in the cases of ring current contributions to VCD attributed to covalent rings, there is generally no uncertainty regarding the existence of the ring. However, the definite presence of a ring does not guarantee VCD originating in ring currents. More specifically, the conclusion that a large "charge flow" contribution to a vibrational rotational strength must arise from a ring current is currently a hypothesis without theoretical foundation. Further, the basis on which Nafie and co-workers deduce the existence of "charge flow" is also questionable. It is assumed that when all electronic redistribution concomitant with nuclear motion is "perfect following", significant "bias" does not exist. "Perfect following" is embodied in the theoretical model for vibrational rotational strengths known as the fixed partial charge (FPC) mode1.25*26"Charge flow" contributions are thus those not given by the FPC model, i.e., the difference between the FPC and the total rotational strengths. Calculations of C-H stretching VCD using the methodology employed in our study of 2 and 3 permit the differences from the predictions of the FPC model to be easily
evaluated. The use of eq 4 for atomic axial tensors gives rise to rotational strpgths that_ar$ the sum of two terms, which we have called the " P M ' and "P*L"terms, respectively?b36 The latter in the limit of constant, diagonal atomic polar tensors (P",$ = $84) reduces to the FPC expression for rotational strengths.: For a variety oJf molecules, we have tabulated separately the "h4"term and "P-L" contributions to :o$tional strengths and also evaluated the limiting values for the "P.L_"t p s in the Fpc approximation.26 Overall, we have found the " P - W terms to be dominant. In the language of Nafie and co-workers, "charge flow" contributions are thus the most important. However, in the case of the C-H stretching modes this does not necessarily lead to a signifi_ca_nt "bias". For example, in trarts-2,3-dideuteriooxiranethe "P-M" terms are the dominant contributors to the C-H and C-D stretching rotational strengths, yet in both C-H and C-D stretching regions the "bias" is very small.* The calculations are in excellent agreement with experimental VCD data. It can therefore be concluded that a unique relation between "bias" and "charge flow" does not exist. The fmn evaluation of the existence of ring current contributions to VCD can be carried out in one of two ways. First, one can compare the VCD of two molecular structures whose only difference is the presence or absence of a ring. Such comparison can be either experimental or, if a reliable theory is employed, theoretical. Second, one can examine a calculation of the VCD of a molecule containing a ring, probing the degree to which such a calculation exhibits evidence of ring currents. This requires a reliable theory of VCD. Both of these approaches have their difficulties. No matter how similar a pair of molecules, they can never be absolutely identical except for the existence or nonexistence of a ring. Consequently, differences may not be due to the difference in ring structure. From a theoretical standpoint, ring current contributions to VCD are not uniquely defined, and their importance will be a function of the specific algorithm employed to define them. To date, there have been no theoretical calculations of VCD that address the issue of ring current contributions. In our opinion, as discussed above, the experimental studies reported to date do not provide a definitive identification of ring current contributions to VCD. In particular, there have been no studies in which two structures, one possessing a ring and the other not but otherwise essentially identical, have been studied in parallel. The study reported here is thus the first study, experimental or theoretical,of a pair of molecular structures differing essentially only in the existence of a ring.27 We have made use of a molecule forming a ring via hydrogen bonding, since the breaking of a hydrogen-bonded ring is of much less consequence chemically than the breaking of a covalently bonded ring. This molecule, methyl glycolate, is also an excellent choice for this study in that multiple hydrogen-bonded ring structures exist. In the case of the pair of structures (Ia and IC) differing only in the presence of a hydrogen-bonded ring there is virtually no change in atomic positions with the exception of the hydrogen-bonding H. Their comparison provides as clean an evaluation of the consequences of the formation of the hydrogen-bonded ring as conceivably possible. We have made use of the theoretical methodology recently developed and implemented in our laboratories and that we have shown by comparison to the VCD spectra of molecules of known structure to provide a reliable basis for the prediction of VCD spectra. At the present time we have not attempted to separate out from our general theoretical algorithm for vibrational rotational strengths a ring current contribution. As pointed out above, this is not uniquely definable and alternative approaches can be envisaged. Instead, and to some degree more usefully, we have analyzed our predictions in a way that is more qualitative but also independent of the precise definition of a ring current contribution. Most importantly, a ring current contribution to the rotational strength of a vibrational mode arising from a planar ring must involve the magnetic dipole transition moment
(25) Schellman, J. A. J . Chrm. Phys. 1973,58, 2882. (26) Jalkanen, K. J.; Kawiecki, R. W.; Stephens, P. J.; Amos, R. D. J . Phys. Chrm. 1990, 94, 7040.
(27) Since completion of this work a similar study of methyl lactate (Bursi, R., Devlin, F. J.; Stephens, P. J. J. Am. Chrm. SOC.1990, 112,9430) has been carried out, leading to identical conclusions.
6454 The Journal of Physical Chemistry, Vol. 95, No. 17, 1991 perpendicular to this ring. It is clear from our calculations that the *C-H and *C-D stretching rotational strengths of 2 and 3 are not a simple function of its conformationalstructure and that, in particular, the rotational strengths for the non-hydrogen-bonded structure ICare not smaller than those of the structures containing rings. In addition, the variations that occur between structures Ia and ICdo not originate in changes in transition moment components perpendicular to the plane containing the hydrogen-bonded ring of Ia. Without more detailed calculations of the ring current contributions to rotational strengths, these results rule out significant contributions. Ring currents have been frequently invoked in the interpretation of magnetic susceptibilities and nuclear magnetic resonance chemical shifts of molecules containing aromatic rings and, therefore, delocalized electrons.28 In general the concept of ring currents is not introduced in the absence of aromatic rings. Even for molecules containing aromatic rings, the topic has been highly controversial. Recent ab initio calculations have tended to be unsupportive of the ring current c o n ~ e p t . * ~One . ~ ~could argue that ring currents induced by external magnetic fields, entering into magnetic susceptibilitiesand NMR chemical shifts, are not intrinsically related to ring currents induced by nuclear motion and that any conclusions arrived at in studies of susceptibilities and chemical shifts are irrelevant to the question of ring current contributions to VCD. This would be erroneous, however. It has recently been shown that the molecular paramagnetic susceptibility tensor is directly and linearly related to the set of molecular atomic axial tensors (more precisely, to the electronic parts Calculations of susceptibility tensors via this sum rule for two molecules have given results of excellent a ~ c u r a c y . ~It~ sfollows that if ring currents contribute to susceptibilities, they must also contribute to atomic axial tensors and consequently to VCD. Finally, therefore, the absence of significant literature supporting the existence of ring current contributions to magnetic susceptibilities in molecules not containing aromatic rings leads to scepticism regarding the probable existence of ring current contributions to VCD in such molecules, a category containing those molecules whose rings are formed by internal hydrogen bonding. (28) Haigh, C.W.;Mallion, R. B. Prog. NMRSpecrrosc. 1980, 13,303. (29) Lazzeretti, P.;Zanasi, R. Chem. Phys. Lerr. 1981, 80, 533. Lazzeretti, P.;Rossi, E.; Zanasi, R. J . Chem. Phys. 1982,77,3129. Lazzeretti, P.; Roasi, E.; Zanasi, R. 1983, 105, 12. (30) Hansen, A. E.;Bouman, T. D. J . Chem. Phys. 1985,82, 5035. (31) Laucretti, P.;Zanasi, R. Phys. Rev. A 1986, 33, 3727. (32) Buckingham, A. D.;Fowler, P. W.; Galwas, P. A. Chem. Phys. 1981, 112, 1. (33) Stephens, P. J.; Jalkanen, K. J.; Lazzeretti, P.; Zanasi, R. Chem. Phys. Lett. 1989, 156, 509. (34) Stephens, P. J.; Jalkanen, K. J. J . Chem. Phys. 1989, 91, 1379.
Bursi and Stephens Conclusion The rotational strength of a vibrational mode arises from its electric and magnetic dipole transition moments in combination. Magnetic dipole moments arise from the angular momentum of charges in motion. It is therefore natural in the case of a molecule containing a ring to imagine that charge flow around the ring, i.e., a ring current, contributes to magnetic dipole moments and, specifically, that there is a ring current contribution to vibrational magnetic dipole transition moments. However, such an expectation in no way prejudges the magnitude of a ring current induced by a specific vibration of a specific molecule, and the magnitude of its contribution to the magnetic dipole transition moment, relative to other contributions that inevitably exist. The ring current hypothesis of Nafie and co-workers is that a large rotational strength associated with a methine stretch in a ring-containing molecule arises predominantly from a ring current contribution to the magnetic dipole transition moment. This hypothesis has been applied to a variety of ring-containing molecules but particularly commonly to those in which internally hydrogen-bonded rings are anticipated. Our calculations for methyl glycolate-dl and -d4, *CHD(OH)COOCH3 ( 2 ) and *CHD(OH)COOCD3(3), find that for a strongly hydrogen-bonded conformation, Ia, a large *C-H stretching rotational strength is predicted but that the contribution to this rotational strength of the component of the magnetic dipole moment perpendicular to the hydrogen-bonded ring is essentially unchanged when the hydrogen-bonded ring is broken, as in conformation IC. We conclude that, in this case, a large methine stretch rotational strength does not arise from a ring current contribution. This result does not show that ring current contributions to VCD do not exist in any molecule. However, it does show that there is not a simple relationship between large methine stretching VCD and ring currents. The assumption that the relation between VCD and ring currents is simple has been fundamental to the application of the ring current hypothesis to the deduction of molecular conformational structure by Nafie and co-workers. The absence of any requirement for calculation of rotational strength, or even of normal coordinates, has been presented as a strength of the approach.I6 Since we cannot support the assumption on which applications of the ring current hypothesis are based, it follows that we cannot support the conclusions reached as a result of its application to VCD data.
Acknowledgment. We gratefully acknowledge support of our research by NSF, NIH, NATO, and the San Diego Supercomputer Center. Registry NO. CHD(OH)COOCH3,134653-67-1; CHD(0H)COOCDj, 134653-68-2.
