1066
J . Phys. Chem. 1988, 92, 1066-1070
Deuterlum and Nitrogen Quadrupole Coupling in Derivatives of Imidazole: An ab Initio SCF Study E. D. Millert and J. L. Ragle* Department of Chemistry, University of Massachusetts, Amherst, Massachusetts 01 003 (Received: July 17, 1987)
Quadrupole coupling constants at deuterium and nitrogen in compounds that contain the imidazole group are discussed in the light of ab initio SCF calculationsof field gradients in imidazole. In particular, estimates of the effect of hydrogen bonding to imino nitrogen on the field gradients at I4N and 2H are made by use of a point charge polarizing field. The calculations are intended to be relevant to experimental data on nucleosides and other biological species in which a significant feature of the structure is hydrogen bonding to imino nitrogen (-N:). The polarization density of imidazole in the point charge field is also discussed. The SCF calculations are at the level of Dunning-Hay + d,p polarization bases.
Introduction
It has been known qualitatively for a long time how field gradients respond to interactions such as hydrogen bonding. Changes in bond length and stretching frequency correlate with shifts in field gradients, illustrating the common origin of these effects, and a fundamental understanding of the interrelationship may be based on the work of Salem’ and of Anderson et al.* With the inception of precise and very sensitive methods for the measurement of quadrupole coupling strengths in solids, it has become possible to study the response of the field gradient at nitrogen and deuterium to changes in the environment caused by, e.g., chemical substitution or intermolecular or intramolecular hydrogen bonding. For example, Goldman et aL3 have recently discussed the changes in molecular charge distribution that accompany formation of a weak complex between chloroform and pyridine in terms of a simple a b initio model and Brown et aL4 have published similar measurements which bear on the perturbation of the structures of pyridine and pyrrole by complexation. Several studies of deuterium and nitrogen coupling in solids containing imidazole or its chemical relatives’~~ are available. In addition, deuterium coupling data are available from wet-spun’ and powders high-field N M R measurements on D N A and nucleosides, and the data are relevant to the dynamics of large biopolymer molecules in solution. One of us9 has recently published a field-cycled N Q R study of the nucleosides adenosine, guanosine, and inosine, in which deuterium coupling data were obtained for substitution at the C8 position, corresponding to C2 in imidazole. Since this position is useful as a marker for other studies, the present work was undertaken in an attempt to model the sensitivity (or lack of sensitivity) of this coupling constant to intermolecular hydrogen bonding. The effect of hydrogen bonding (and other intermolecular effects) is expected to be calculable by cluster models. Unfortunately, such calculations are well beyond our computational resources on a molecule the size of imidazole and at the degree of basis elaboration which we feel to be adequate, and thus some compromise is necessary. We have modeled hydrogen bonding at the -N: site by replacing the intermolecular proton by a distant unit point charge. In this model, no charge transfer is possible from donor to acceptor and also no representation is made of the polarization that accompanies -NH hydrogen bonding. In nucleosides, -NH hydrogen bonding is irrelevant since this is the point of attachment of the sugar residue. Clearly this model is at best qualitative, and one may attempt to characterize it as including those components of hydrogen-bond formation that Umeyama and MorokumaIo have called the electrostatic and polarization contributions to hydrogen bonding. In spirit it is ‘Taken in part from a Senior Honor’s Thesis submitted by E.D.M., University of Massachusetts, 1986. Present address: Department of Chemistry, University of Chicago. *Author to whom correspondence should be addressed.
0022-3654/88/2092-1066$01.50/0
similar to a calculation of the Sternheimer polarization of an ion in the field of neighboring point charge counterions, except that the full molecular wave function is used and the polarization arises from a single charge. Calculations were performed either on a Celerity C1200 minicomputer using GAMESS Ver. 1.02 provided by M. Schmidt and S. Elbert or on a Tandy 3000HD microcomputer using appropriate parts of the Polyatom-60 package. Choice of Basis Set for SCF Calculations
The ingredients that constitute an attempt to calculate field gradients to experimental accuracy are well-known. Within the finite basis set single-configuration SCF modality, a property such as the field gradient at a nitrogen or oxygen nucleus must be calculated with a basis set which does not compromise the nuclear region in favor of flexibility in the valence shell, but which is reasonably well designed with respect to both regions. One must then attach to this S C F representation some correction for correlation. One must then average the field gradient over molecular vibrations using an accurate representation of the potential field. Sundholm et a1.l1 have addressed the magnitude of the correlation correction that needs to be applied to S C F field gradients. Cummins et a1.I2have more recently discussed this topic with a goal of obtaining nuclear scalar quadrupole moments from ab initio field gradients and present a detailed study of several small molecules containing nitrogen and hydrogen. If the experiment to which comparison is attempted is performed on a condensed phase, proper account must be taken of the medium and of any specific chemical effects that are present, as well as of additional vibrational averaging. This program is not a trivial task, nor is it within our means to perform for a molecule of the size of imidazole. Since experimental data on systems that incorporate this moiety are becoming available, it seems important to go (1) Salem, L. Ann. Phys. 1963, 8, 169. (2) Anderson, A. B.; Handy, N.; Parr, R. G. J . Chem. Phys. 1970, 53, 3375. (3) Goldman, E.; Ragle, J. L. J . Phys. Chem. 1986, 90, 6440. (4) Hiyama, Y.; Keiter, E. A.; Brown, T. L. J . Magn. Reson. 1986, 67, 202. See also Hiyama, Y . ;Butler, L. G . ;Olsen, W. A,; Brown, T. L. J . Magn. Reson. 1981, 44, 483. ( 5 ) Ashby, C. H.; Cheng, C. P.; Brown, T. L. J . A m . Chem. SOC.1978, 100,6057. (6) Garcia, M. L. S.; Smith, J. A. S.; Bavin, P. M. G.; Ganellin, C. R.J . Chem. SOC.,Perkin Trans. 2 1983, 1391. (7) Tsang, P.; Vold, R. R.; Vold, R. L. J . Magn. Reson. 1987, 71,276. (8) Vold, R. R.; Brands, R.; Tsang, P.; Kearns, D. R.; Vold, R. L. J. Am. Chem. SOC.1986, 108, 302. (9) Day, R.; Ragle, J. L.; Yoshida, Y . J . Magn. Reson. 1987, 7 2 , 562. (10) Umeyama, H.; Morokuma, K. J . A m . Chem. SOC.1977, 99, 1316. (1 I ) Sundholm, D.; Pyykko, P.; Laaksonen, L. Mol. Phys. 1985,56, 1411. Laaksonen, L.; Pyykko, P.; Sundholm, D. Comput. Phys. Rep. 1986,4, 313. (12) Cummins, P. L.; Bacskay, G. B.; Hush, N. S.; Ahlrichs, R. J . Chem. Phys. 1987, 86,6908.
0 1988 American Chemical Society
Quadrupole Coupling in Imidazole Derivatives
The Journal of Physical Chemistry, Vol. 92, No. 5, 1988 1067
TABLE I: Summary of Energy and Field Gradient Calculations on HCNI-” and N212-15 a
basis STO-3G STO-4/31G STO-6/3 1G Dunning/Hayb STO-6/31 IG Dunning [5s,3p] [3sle Dunning [5s,4p] [3sIc Dunning/Hay + polariznb [5s,4p9ld1[3s,1plN [5s,4p, Id] [ 3s, lple~’’f [5s,4~,2dl[3s,2plr MacLean/Yoshimine set l h
1
2 3 4 5
6 7 4a
8 9
10 11
basis from row 9 basis from row IO Cade et al.’ Sundholm et a l l
12 13 14
15
total E HCN -91.675 194 -92.731 295 -92.827 972 -92.837 110
-92.848 869 -92.855071 -92.856 571
-92.889 268 -92.905 000 -92.905 629 -92.907918 -92.908 684
N2 -108.981 178 -108.983 005 -108.992 8 -108.993 8
qN
9H
0.356 565 0.948 843
-0.362444 -0.358 498
0.900 575 0.823 5 15 1.119 478 1.133 128 1.064746 0.946 760 1.152 451 1.158238
-0.362 148 -0.361 770
1.162721
-0.356 354 -0.366 235 -0.357 982 -0.338 622
-0.341 702 -0.338 843 -0.340 250
1.3 I6 792 1.327 521 1.365 3
1.336 59
‘RCN = 2.1791, RHc = 2.0143, R” = 2.068 Bohr. Series arranged in order of decreasing total energy. bContractionsand polarization exponents as given by Dunning and Hay, ref 16. CHydrogens scale factor optimized for the basis of calculation 6. “Hydrogen p scale factor from Dunning (optimum water value), ref 14. ‘Hydrogen p exponent = 1.00; hydrogen s scale factor from calculation 8. d exponents of carbon and nitrogen optimized. /Carbon and nitrogen d exponents = 2.214 and 0.656 (using Dunning’s one d-Gaussian and two d-Gaussian fits to a Slater d orbital and rescaling the value from set 1 accordingly. rd and p polarization functions uncontracted from calculation 9. MacLean and Yoshimine STO double f p,d N-D > C-D. The sign of the field gradient is also, as expected, negative, as the field gradient arises from an incomplete screening of the nuclear charge ofthe substituent heauy atom by the diffuse, nearly axially symmetric electron distribution. Using the numerical value of the nuclear scalar quadrupole moment given by Reid and Vaida?O which corresponds to 672.0 kHz of coupling constant per atomic unit of field gradient, one obtains deuteron coupling constants of 261.8 and 209.7 kHz for H1 and H2, respectively, from the final basis set of Table 11. These values are roughly 110 and 33 kHz higher than the observed values for the solid, respectively, in which molecular vibration and strong hydrogen bonding both operate to depress the coupling constant. Location H1 is expected to be much more sensitive to intermolecular effects in the condensed phase, and one can attribute the larger discrepancy at HI in part to this effect. The asymmetry of the deuterium field gradient also accords with the usual experimental experience: the departure from axiality is much more marked for N-D than for C-D. Unlike deuterium, a precise value for the scalar nuclear quadrupole moment of I4N is not available. The most recent value is that favored by Sundholm et al.,“ by Cummins et a1.,I2 and by Cernusak et al.:I3 Q = 2.05 fm2 (1 atomic unit of field gradient 4.82 MHz of coupling constant), although the older value of O’Konski and Ha,2’ Q = 1.56 fm2, forces the S C F field gradients into more “reasonable” agreement with experiments on solids.
-
(19) Craven, B. M.; McMullan, R. K.; Bell, J. D.; Freeman, H. C. Acta Crystallogr., Sect. B: Struct. Crystallogr. Cryst. Chem. 1977, 8 3 3 , 2585. (20) Reld, R. V., Jr.; Valda, M. L. Phys. Reu. Lett. 1972, 29, 494. (21) O’Konski, C. T.; Ha, T.-K. Int. J . Quanrum Chem. 1973, 7, 609
energy*
NlCvd
N3C3d
1.2906 0.1365 -223.54660 0.7212 0.0942 -223.549 11 0.6848 0.0669 -224.467 51 0.7524 0.0857 -224.706 53 0.7483 0.0716 -224.736 16 0.8283 0.0078 -224.75437 0.8482 0.0650 -224.769 97 0.7802 0.0632 -224.769 97 0.7801 0.0627 -224.769 68 0.7815 0.0750 -224.770 80 0.7747 0.0502 -224.857 18 0.7779 0.0782
0.8747 0.8043 0.9012 0.0533 0.9544 0.0914 0.9786 0.0506 0.9702 0.0320 1.0233 0.0653 1.0546 0.0102 1.0289 0.0478 1.0287 0.0478 1.0298 0.0508 1.0280 0.0511 0.9437 0.0045
-221.98799
6/311G Dunning (5,3)‘ Dunning (5,3)’ Dunning (5,318 Dunning (5,3)h DH d,p
+
HICsd
H2C,d
-0.3986 -0.3347 0.0512 0.1217 -0.4237 -0.3324 0.1360 0.0878 -0.4910 -0.3687 0.1262 0.0836 -0.4024 -0.3344 0.1 505 0.0806 -0.4007 -0.3378 0.1526 0.0779 -0.4131 -0.3378 0.1514 0.0704 -0.3970 -0.3352 0.1546 0.0759 -0.4034 -0.3404 0.1469 0.0744 -0.4033 -0.3403 0.1470 0.0744 -0.4052 -0.3422 0.1455 0.0755 -0.4050 -0.3410 0.1461 0.0773 -0.3895 -0.3120 0.0859 0.18 12
‘A calculation of the field gradients in imidazolium ion is given in Table 111. Two sets of numerical results are reported using the STO3/21G basis. The first is for the geometry of ref 18, and the second is for the energy-optimum geometry using the same basis. b R H F total energy in au. ‘Upper number is the major principal axis length of the field gradient. dLower number is the deviation from axial symmetry, the “asymmetry parameter”. ‘Dunning’s (5,3) set used for main atoms. For hydrogen, the unscaled Pople N/311G (3,1,1) set was used. fDunning’s (5,3) set used for main atoms. Dunning’s [3s] (3/1/1) set used for hydrogen. All contractions in hydrogen set unscaled. ZSame as e except hydrogen basis scaled by 1.20. *Same as e except hydrogen basis scaled by 1.49, the optimum value for HzO.
Winter and AndraZ2suggest the value 1.93 fm2. One may compare the field gradients calculated for N1 and N 3 from the final basis set with the experimental ratio, as there should be some mutual cancellation of neglected correction terms for the two sites, which should also be similar in their lattice dynamics. The work of Garcia et a1.6 is probably the most comprehensive recent experiment work on substituted imidazoles, and an examination of their measurements on 15 substituted imidazole derivatives shows this ratio to be N3/N1 = 1.9-2.3, much larger than that given by any of the basis sets in Table 11. The calculated field gradient asymmetries are also at variance with the experimental values, particularly for N1, for which the experiments of Garcia et al. give considerably larger values, and these authors have commented in detail on likely sources of this discrepancy. They argue that it is due to hydrogen-bonding interactions in the solid and point out that in the case of N-benzylimidazole the nonaxial character in the field gradient at N3 is in agreement with values calculated here. We take this to indicate that the disagreement between our calculations and experiment is, in major part, a real effect and not a deficiency of the basis sets. A simple model of this effect is described in the next section. Intermolecular Effects on Field Gradients in Imidazole As would be expected, the crystal structure of imidazole is
marked by strong, saturated hydrogen bonding involving both the proton donor (-NH) and acceptor (-N:) sites of the molecule. The differences in field gradients between the isolated molecule and the real systems studied by Garcia et al. are especially due, in large measure, to these hydrogen bonds. We have modeled hydrogen bonding at the -N: site by replacing the intermolecular proton by a distant unit point charge, while maintaining the basis set of the “target” molecule at the level of the final entry in Table (22) Winter, H.; Andra, H. J. Phys. Reo. A 1980, 21, 581.
The Journal of Physical Chemistry, Vol. 92, No. 5, 1988
Quadrupole Coupling in Imidazole Derivatives
TABLE 111: Computed Field Gradients at Selected Sites in Imidazole Polarized by a Point Charge” site ionb 5 bohr 10 bohr 15 bohr 20 bohr
50 bohr
molecule
1069
~
N1 0.5926 0.3 16
0.7146 0.087
0.7527 0.040
0.7643 0.055
0.7694 0.063
0.7762 0.075
0.078
0.5926 0.316
0.6280 0.293
0.8838 0.046
0.9197 0.020
0.9310 0.012
0.9419 0.006
0.9437 0.004
-0.3481 0.181
-0.3817 0.179
-0.3862 0.180
-0.3877 0.181
-0.3883 0.181
-0.3893 0.181
-0.3895 0.181
-0.4221 0.066
-0.3060 0.086
-0.3114 0.099
-0.3 121 0.090
-0.3122
-0.3145 0.087
-0.3 120 0.106
N3 HI H2
0.088
0.7779
“Upper quantities are field gradients in atomic units, and lower quantities are asymmetry parameters. Field gradients in imidazolium ion calculated with the same basis set and using the geometry of ref 17. N3 and N1 are equivalent, as are H1 and H3.
//-’ /-----e--
1.
1
-0,3t “
-0.4
R
7\10
d
KHZ i n O C C ~
I
I
IO
Y. 00
, 5.m
I
6.m
2-RxIS 0
.CH
= =
.
electronic charge in the polarized molecule, are at 0.010, 0.020, 0.030, and 0.040 electron/bohr3.
I
20
I
I
30
~
I
40
;
I
~
50 BOHl
Figure 2. Response of field gradients at selected locations in imidazole to the polarization induced by a point charge located as described in the text. The ordinate of this plot is the field gradient in atomic units, and corresponding scales of quadruple coupling in frequency units are shown in the body of the plot. Note the discontinuity in the ordinate scale. The abscissa is the distance, in atomic units, of the polarizing charge from
nitrogen N3.
I1 (set 4a of Table I), since an adequate representation of the -N: nitrogen (and all heavy atoms) is necessary if an assessment of the “through-bond” modification of the properties is to be possible. This model ignores charge transfer from donor to acceptor. The calculations were done by adding a hydrogen atom at a specified distance from -N: and with a basis that consisted of a single s Gaussian with a very large exponent. Because of its scale, at hydrogen-bonding distances and beyond, this basis function cannot participate in the occupied SCF orbitals and never contains population; the calculation therefore mocks a point charge calculation which converges smoothly to the isolated imidazole molecule a t large distances. There are two aspects of these calculations on which we wish to comment. Of direct interest is the way in which the field gradients at N1, N3, and ring deuterons respond to the polarization. Second, it is instructive to view the overall difference charge density, especially around these sites. HermanssonZ3and
Krijn and Fellz4 have recently commented on the complexity of the polarization difference density of small molecules in point charge fields, and we present here section maps of the response of the imidazole molecule.to the same type of perturbation. Table I11 and Figure 2 give the calculated field gradients at selected sites in imidazole as a function of the separation between N 3 and the polarizing charge. The latter is located on an axis which is in the molecular plane, which bisects the C2-N3-C4 angle and which passes through N3. This is intended to resemble the actual situation in crystalline imidazole, in which the -NH donor lies on an axis that makes an angle of about 10’ to the ring plane of the acceptor. As pointed out above, the electronic population a t the “point charge” is frozen at zero; at a given distance it therefore produces an electric field somewhat larger than would be produced by a hydrogen donor. For this and other reasons, it overestimates the effect of intermolecular hydrogen bonding, unless one scales the distance. The lower end of the separation range used here, 5 bohr, was chosen with this fact in mind, and the remaining, larger, separations are included for the sake of continuity. At a distance of 5 bohr the field experienced by N 3 from the bare point charge is ca. 2 X lo8 V/cm and, at 20 bohr, ca. 1.3 X lo7 V/cm. The electric field strength calculated at the location of N 3 from the neighboring imidazole molecular charge distribution located at the hydrogen bonding (Nl’-H-N3) distance and with the final wave function above is 0.0266 atomic unit or 1.37 X los V/cm. The direct contributions of the point charge to the field gradient are very small at N3, on the order ~~~
(23) Hermansson, K. Sweden, 1984.
3.00
Figure 3. Polarization density in the region around N3 and in the ring plane. The polarizing charge is located 5.0 bohr from N3. The map is computed on a 49 X 48 uniformly spaced grid. The units are electrons per bohr3. The dashed contours, which represent a depletion region for
:
I
I
2.m
Doctoral Thesis, University of Uppsala, Uppsala,
~
(24) Krijn, M. P. C. M.; Fell, D. J . Phys. Chem. 1987, 91, 540. Krijn, M. P. C. M.; Fell, D.J . Chem. Phys. 1986, 85, 319.
J . Phys. Chem. 1988, 92, 1070-1075
1070
ni 8
8 1.00
2.00
3. m 1.00 IdXIS 0
s.m
6. m
Figure 4. Polarization density in the region around C2 and H2 in the ring plane. The polarizing charge is located as in Figure 3. The map is computed on a 50 X 50 uniformly spaced grid. The zero contour is labeled in the plot, and the remaining solid contours are as in Figure 3. The dashed contours, showing the depletion of electronic charge in the polarized molecule, are at 0.002, 0.004, and 0.006 electron/bohr3.
of 0.01-0.02 au a t 5 bohr, when compared to the effect of the molecular polarization. The effect of the polarizing charge on the field gradients in the molecule qualitatively matches what is found in experimental work on solids. In the limit in which proton transfer is complete (imidazolium ion) the two nitrogen and hydrogen pairs are equivalent, and the coupling constant at nitrogen is observed and calculated to be somewhat lower than the amino nitrogen in imidazole. As is reasonable, the imino nitrogen is the most strongly depressed of the two. A comparison between the calculations and experiment for imidazolium ion is difficult because of the effects of hydrogen bonding, but both nitrogen and -ND deuterium quadrupole coupling constants seem to be somewhat smaller in imidazolium salts than in the neutral molecule.6 As shown in Table 111, the coupling constant at H 2 is calculated to increase substantially in
magnitude when complete proton transfer occurs to form imidazolium ion. This is in accord with preliminary measurements on a series of inorganic imidazolium salts made in this laboratory. It is of some interest to examine the polarization density of the molecule. Selected cuts through the polarization density of imidazole are shown in Figures 3 and 4. The polarization density in the ring plane and centered on N3 is shown in the first of these. In addition to the expected simple dipolar response at the outer parts of the charge distribution there are complex regions around N 3 and in the N3-C2 and N3-C4 bonds which are roughly quadrupolar in character. These regions are qualitatively the largest contributors to the change in field gradient on polarization. At the deuteron bonded to C2 there is essentially no change in charge density, although a small decrease is exhibited in the C2-H2 bond near C2. This is shown in Figure 4, which is a cut through the ring plane, centered around C2. At N1 there is also a substantial change in density; this is the precursor polarization to the limit case of imidazolium ion, in which the two nitrogen centers have become equivalent. The complexity of the polarization density observed with the present, reasonably flexible, basis set points out graphically a justification for unease which one may have in attaching physical meaning to simple (e.g., Townes-Dailey) models of quadrupole coupling. Much of the detail present in these maps, especially close to N 3 where it has a strong effect on the field gradient, will be smeared out and lost if smaller basis sets are used. As mentioned in the Introduction, the deuteron at C2 has been used as a marker for studies of the solution dynamics of large biological polymers. According to the usual numbering scheme, this carbon is labeled C8 in a nucleoside. A primary reason for these calculations was to determine the sensitivity of the coupling constant of deuterium bonded to C8 to hydrogen bonding at N7 ( N 3 in the notation of this work). We have recently measured this coupling constant in solid adenosine, inosine, and quanosine: where it is essentially invariant except for small crystal effects. The present calculations confirm the expectation on chemical grounds that this location is relatively unchanged by hydrogen bonding and that it may therefore be used with some impunity in studies of solution dynamics in which the composition and degree of chain folding are variable.
Acknowledgment. We thank Paul E. Cade for a number of useful conversations during this work and for pointing out several pertinent literature articles. Registry No. D,,7782-39-0; N, 17778-88-0; imidazole, 288-32-4.
Raman Line Shapes of the vi Stretching Mode in Orientationally Disordered N,O Crystals J.-P. Lemaistre,* R. Ouillon, and P. Ranson Dspartement de Recherches Physiques, Uniuersitd P. et M . Curie, UA 71 du CNRS, Tour 22, 4, Place Jussieu, 75252 Paris Cedex 05, France (Received: July 17, 1987) An analysis of orientational disorder in nitrous oxide crystals is reported. A model based on the exciton theory with dipoledipole interactions is used to derive an expression of the Raman intensity availablefor a random distributionof the molecular orientations N-N-0 and 0-N-N. A small deviation from the equiprobability of these molecular orientations leads to a drastic effect on the spontaneous Raman scattering line shapes. Our theory is checked against experiment for the v, stretching mode. We conclude that N 2 0 crystals grown from the gas phase are not totally disordered.
Introduction During the past 10 years a lot of experimental and theoretical work has been devoted to the study of vibrational relaxation and dephasing in molecular crystals. Coherent time-resolved techniques together with high-resolution spontaneous Raman scattering have allowed accurate measurements of the vibron-state dynamics
to be carried out. Particular attention has been paid to crystals of diatomics (H2, Nz) O r triatomics (co2, NzO, c s 2 ) mokcules for which the number of fundamental modes is limited.’-6 (1) Abram, I. I.; Hochstrasser, R. M.; Kohl, J. E.;Semack, M. G.; White, D.Chem. Phys. Lett. 1980, 71, 405; J . Chem. P h p . 1979, 71, 153.
0022-3654/88/2092-1070$01.50/0 0 1988 American Chemical Society
