Resonance Raman studies of imidazole, imidazolium, and their

Laura M. Markham, Leland C. Mayne,7 and Bruce S. Hudson* * ... Steacie Institute of Molecular Science, National Research Council of Canada,. Ottawa, O...
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J. Phys. Chem. 1993,97, 10319-10325

10319

Resonance Raman Studies of Imidazole, Imidazolium, and Their Derivatives: The Effect of Deuterium Substitution Laura M. Markham, Leland C. Mayne,' and Bruce S. Hudson' Department of Chemistry, Institute of Chemical Physics and Institute of Molecular Biology, University of Oregon, Eugene, Oregon 97403

Marek Z. Zgierski Steacie Institute of Molecular Science, National Research Council of Canada, Ottawa, Ontario Kl A OR6 Canada Received: May 24, 1993'

Resonance Raman spectra of imidazole, imidazolium cation, 4-methylimidazole, histidine, and their cations are presented for the proto and N-deutero forms. N-Deuteration greatly simplifies the resonance Raman spectra for all of these species. The deutero cations have only one strongly enhanced Raman band. This change in number of active vibrations is interpreted in terms of a change in the form of the ground electronic state normal modes of motion. The ground-state equilibrium geometry and vibrational force field are calculated at the 6-3 1++G**Hartree-Fock level for imidazole and imidazolium. The low-lying excited electronic states are calculated at the ground-state equilibrium geometry with configuration interaction involving singly excited states. A single state is expected to dominate the absorption and Raman spectral intensities. The equilibrium geometry of this state for imidazole and imidazolium at the 6-31+G/CIS level is calculated and expressed in terms of the displacement along each of the ground-state modes for each isotopic species. This ab initio procedure correctly predicts the intensity of the strongly enhanced normal modes of the neutral and cationic species including the large change in intensity observed with isotope exchange. It is found that the effect of replacement of N-H by N-D in the cation is to leave one of the two strong modes of the proto species the same in the dz species while the other active mode of the proto form becomes distributed among several modes in the deuterated species such that none has a significant displacement upon excitation and thus has a low Raman intensity. A quantitative comparison is made between theory and observations for imidazolium in its three N-proto isotopic forms.

Introduction The extension of the technique of resonance Raman spectroscopy into the far ultraviolet and vacuum ultraviolet region of the spectrum'-3 has resulted in the observation of several unusual phenomenona including considerable intensity in highly excited vibrational levels? strong enhancement of non-totally-symmetric vibronically active modes,s and large changes in intensity associated with deuterium isotope substitution.6 Imidazole, its cation, and their derivatives exhibit a vary large isotope effect of this type.2.3-7This phenomenon is documented and discussed in this paper in more detail than previously reported, and a theoretical treatment of this phenomenon is presented. The aromatic amino acid histidine is a substituted imidazole which plays a very important role in the proposed mechanism of many enzymes. In several cases, the state of protonation of the imidazole ring of a histidine residue is an important consideration in the hypothesized mechanism. Considerable effort has been expended on the determination of the state of ionization of activesite histidines and their interactions with neighboring residues. The development of a vibrational spectroscopic method for the determination of thestate of ionization of histidine residues could be of considerable importance in enzyme mechanism studies. There havebeen threerecent studiesslOoftheresonanceRaman spectroscopy of imidazole and imidazoliums and of these compounds plus 4-methylimidazole,histidine, and their cation^.^ The primary emphasis in these previous studies was on the excitation profile behavior, i.e., the variation in Raman intensity with t Present address: The Johnson Research Foundation, Department of Biochemistry and Biophysics, The University of Pennsylvania, Philadelphia, PA 19104. 0 Abstract published in Advonce ACS Abstracts. September 1, 1993.

0022-3654/93/2097-103 19$04.00/0

excitation wavelength. The spectral results of these prior studies and the present work are in substantive agreement so far as they concern the same chemical species. A recent paper10 includes a theoretical treatment of the enhancement of the Raman bands observedupon UV excitation for both imidazoleand imidazolium species. The major new aspect of this present paper is the demonstration and analysis of the effect of N-deuterium substitution of imidazole and imidazolium obtained by dissolution of these compounds in D20. Considerable simplification of the spectra results in a clear pattern emerging, which can be interpreted in terms of changes in the form of the normal modes of motion of these compounds.

Methods The experimental methods used in the present study have, for the most part, been described previous1y.l4 The basic procedure consists of the generation of ultraviolet radiation using stimulated Raman shifting of the harmonic frequencies of a Q-switched Nd:YAG laser. The solution samples are streams circulated by a pump. The ab initio calculations were performed using Gaussian9211 with the 6-31++G** basis set at the HF level for the groundstate geometry and modes of vibration and for the electronic excitation energies at the CIS level. The 6-31+G basis set including configuration interaction involving all singly excited configurations outside the frozen core (1s on C and N) was used for excited-state geometry optimization and for normal mode analysis of the excited states. Experimental and Theoretical Results Figure 1 shows resonance Raman spectra of imidazole, 4-methylimidazole, histidine, and their N-deuterium isotopic 0 1993 American Chemical Society

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10320 The Journal of Physical Chemistry, Vol. 97, No. 40, 1993 I

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Figure 1. ResonanceRaman spectra of (A) imidazole,(B) N-deuteroimidazole,(C) 4-methylimidazole,(D) N-deutero-4-methylimidazolc, (E) histidine, and (F) N-deuterohistidine in H20 or D20 solution at pH 2.5 obtained with excitation at 218 nm. Solution concentrations were 10 mM. I

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a

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Figure 2. Resonance Raman spectra of (A) imidazolium, (B)N-deuteroimidazolium, (C) 4-methylimidazolium,(D) N-deutero-4-methylimidazolium, (E)histidine, and (F)N-deuterohistidine in H20 or DzO solution at pH 2.5 obtained with excitation at 218 nm. Solution concentrations were 10 mM. The solution was made acidic by addition of HCI.

forms obtained with excitation at 218 nm; Figure 2 shows the corresponding spectra for the protonated forms obtained at low pH (pD). We will be interested only in the strongest bands in these spectra and, particularly, the change in pattern associated with replacement of deuterium by protons. In previous work, it was shown that the major bands observed in the resonance Raman spectrumof imidazoleremain in roughly constant relative intensity as the excitation wavelength is changed from 229 to 218 nm. Thus, the present spectra are typical of thoseobtained throughout this excitation region. Themajor observationofthisstudy is that theresonanceRaman spectra of the deuterated cationic forms are dominated by one

strong band at 1394-1410 cm-l. This is a totally symmetric (al for the CZ,imidazolium ion) in-plane ring deformation mode. Alkyl substitution of the symmetric protonated imidazole ring results in only a minor change in the spectrum with an increase in intensity of some of the minor bands and what appears to be a redistribution of intensity from one to two active components. A dramatic effect is seen when the two deuterium atoms are replaced by hydrogen atoms. Even though the Cb symmetry of the species is maintained, there is a clear redistribution of the intensity of the major band into two components of roughly equal intensity at 1209 and 1449 cm-l. It is interesting to note that

Resonance Raman Studies of Imidazoles

The Journal of Physical Chemistry, Vol. 97, No. 40, 1993 10321

TABLE I: Vibrational Frequencies of Imidazolium-4 and Imidazolium-& Calculated with the HF/631++G** Basis Set’ imidazolium-do sYm

a

freq 3859 3484 3459 1787 1627 1322 1220 1169 1007 3851 3464 1709 1590 1445 1286 1134 989 1010 754 670 1041 861 793 666

assign NH stretch CH stretch C(+)Hstretch C=C stretch C(+)N+ CN stretch ring exp. NH wag C(+)N st. + C(+)H wag CN stretch ring deformation NH stretch CH stretch C(+)N stretch C(+)N CN stretch CH wag C(+)Nst. C(+)Hwag CN stretch ring deformation CH o.p,bends NH o.p,bends CH 0.p. bend ring torsion C(+)H0.p. bend CHo.p.bends NHo.p.bends ring puckering

+

+

+

+

4 2

freq 2845 3484 3459 1743 1570 1244 1196 929 1005 2832 3464 1694 1492 1408 1184 1010 956 1009 564 680 1034 860 578 667

Optimized geometry (CZ,symmetry): r(CC) = 1.3410 A, r(C(+)N)

= 1.3135 A, r(CN) = 1.3816 A, CCN = 106.49’, NCN = 107.99O,

CNC = 109.51’. The axis convention used is consistent with that used for the electronic-statesymmetry labels. The usual convention used in vibrational analyses interchanges the bl and b2 labels.

TABLE 11: Vibrational Frequencies of Imidazole-& and Imidazole-h Calculated with the HF/631++G** Basis Set’ imidazole-& sym a’ a’ a’ a’ a’ a’ a’ a’ a’ a’ a’ a’ a’ a’ a’ a‘‘ a’’ a’’ a” a’’ a”

freq 3928 3458 3429 3428 1730 1652 1578 1497 1404 1250 1231 1183 1153 1018 982 998 967 836 727 686 551

assign. N I H stretch CH stretch CH stretch CH stretch CsC4 + C2N3 stretch C5H4 + C2N3 stretch CzNl+ C5Nl st. N H wag C2N3, C4N3 + CsN1 st. + CH wag CHwag C4C5 C2N1 st. CH wag C4N3 + C ~ Nstretch I C2N1, C4N3 + C4Ns st. + NH wag CsNl stretch CsNlC2 deformation ring deformation CH 0.p. bends C2H 0.p. bend C4H CsH 0.p. bends ring puckering ring puckering NH 0.p. bend

+

+

+

+

-di freq 2888 3458 3429 3428 1714 1644 1499 1480 1394 1235 1217 916 1155 1000 1009 998 967 835 723 662 427

a Optimized geometry (C, symmetry): r(CsN1) = 1.3720 A, r(C4Cs) = 1.3532 A, r(C2N3) = 1.3713 A, r(CsN2) = 1.2907 A, r(C2Nl) = 1.3502 A, C ~ C S N = ~105.23’, C S C ~ N= ~110.35’, NlC2N3 = 112.09’, C5NiC2 = 106.86’, C4N3C2 = 105.47’.

there is no appreciable change in the pattern or position of the weaker bands of the spectrum near 900, 1150, and 1550 cm-1. T h e results of the ab initio determination of the equilibrium geometry and the normal modes of vibration for the ground states of imidazole and imidazolium are given in Tables I and 11. T h e excited-state frequencies and displacement parameters for the most relevant low-lying excited state of each species a r e given in Tables I11 and V. Figure 3 shows the calculated geometries for the ground state and the relevant excited state for imidazole and imidazolium.

TABLE III: Excited-State Normal Mode Frequencies and Displacements for Imidazolium, Imidazolium-d~,and Imidazolium-dj sym (2A1)6-31+G (lA1)6-31++G** a B(2Al)* A. Imidazolium, 2Al State 3900 3859 (3473)‘ 0.143 3509 3459 (3113) 0.160 3486 3484 (3136j 0.020 1687 1787 (1608) [1560]e 1.116 1619 1627 (1464) [1454] 0.781 1169(1052) I10731 0.390 1299 1322(1190) [1216] 1202 1.296 1220 (1098) [1142] 1067 1.883 1007 (906) [902] 882 1.302 3892 3851 3464 347 1 1585 1709 (1538) [1528] 1527 1590 (1431) [1421] 1349 1445 (1300) [1256] 1286 1153 1134 1010 836 988 1010 1035 754 484 670 407 861 866 793 474 1041 2221 666 3861’ B. Imidazolium-d2, 2AI Statd 3509 3459 (3113)‘ 0.166 3486 3484 (3 136) 0.023 2870 2845 (2561) 0.204 1678 1743 (1569) [1550]e 1.274 1471 1570 (1413) [1395] 0.877 1244 (1120) [ii451 0.488 1211 1168 1196 (1076) (10851 1.509 920 929 (836) 1.546 1005 (905) [902] 1.333 862 3471 3464 2832 2857 1694 1555 1408 1383 1492 1277 1026 1184 1010 972 956 935 1009 1034 680 414 564 360 865 860 578 361 1034 215i 381i 667 C. Imidazolium-dl 3855 0.102 3896 2863 2838 0.144 3486 3483 0.021 347 1 3464 0.001 3509 3459 0.163 1682 1766 1.204 1601 1701 0.564 1552 1619 0.334 1414 1516 0.530 1339 1433 0.215 1231 0.212 1298 1193 1236 1.256 14111 1197 1.241 1008 1143 0.61 1 87 1 1020 1.322 0.036 835 980 1.228 947 948 2191 1037 1034 1010 865 860 479 774 36 1 570 41 1 677 666 3831 a

B(1AI)C B(1Al)z 0.196 0.115 0.173 0.490 1.994 0.263 2.303 0.479 1.077

0.038 0.013 0.030 0.240 3.976 0.069 5.304 0.229 1.160

0.181 0.123 0.349 0.076 2.525 0.984 0.828 0.379 1.645

0.033 0.015 0.122 0.006 6.376 0.968 0.686 0.144 2.706

0.140 0.247 0.119 0.005 0.177 0.336 0.028 1.872 1.283 0.707 1.537 0.314 0.656 0.384 1.277 0.569 0.267

0.020 0.061 0.014 O.Oo0

0.031 0.113 0.001 3.504 1.646 0.500 2.362 0.099 0.430 0.147 1.631 0.324 0.07 1

Ground-state frequencies for the most closely corresponding mode.

* Normalized displacement upon excitation in the excited-state mode

basis. Normalized displacement upon excitation in the ground-statemode basis. d Calculated frequenciesmultiplied by a uniform scaling factor of 0.9. e Experimental fr uencies. foptimized excited-state (2A1) geometry: r(CC) = 1.40867, CCN = 108.63’, r(C+N) = 1.4237 A, NC+N = 105.90’, r(CN) 3: 1.3521 A, CNC+ = 108.42’.

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TABLE I V Mode Rotation Matrix for Imidazolium-4 and Imidazolium-4 doJd2 1787 1627b 1322b 1220 1169 1007

1743 0.298 -0.314 -0.100 -0.077

157W 0.259 0.913 -0.264 -0.096 -0.139

1244

1196

-0.076 -0.677 0.681 0.250

-0.062 -0.371 -0.633 0.672

1005 0.089 0.111 0.328 0.182 0.330 0.850

929 -0,195 -0.241 -0.456 -0.300 -0.591 0.514

1 I

i

Most Raman-active band in d2 species. Most Raman-active bands in do species.

TABLE V Excited-State Normal Mode Frequencies and Displacements for Imidazole and Imidazole-dl sym (2Af)6-31+G (lA’)6-31++G** a’

a’’

a

B(2A’)b B(lA’)C B(1A’)2

Imidazole, 2A’ State (s3 for 6-31++G** and s2 for 6-31+G) 3951 3928 (3535)d 0.062 0.090 0.008 3526 0.155 0.078 0.006 3428 (3085) 3501 3457 (3111) 0.081 0.163 0.027 3488 3429 (3086) 0.022 0.129 0.017 1605 1496 (1346) [1331Ic 0.833 1.511 2.283 1558 1.202 1.445 1578 (1420) [1430] 0.636 1531 1652 (1487) [1491] 1.234 1.028 1.057 1377 1404 (1264) [1261] 0.329 0.943 0.889 1231 (1108) [1137] 0.098 0.331 1352 0.220 1160 1152(1037) [lo681 0.948 0.111 0.012 1135 1249(1124) [1163] 1.110 1.150 1.323 982 (884) [917] 1014 0.419 0.029 0.001 985 1729 (1553) [1537] 0.602 0.041 0.002 859 1018 (916) [932] 1.018 0.705 0.497 843 1183 (1065 [1100] 0.090 0.140 0.020 948 998 755 967 515 836 507 726 433 551 207i 686

Imidazole-dl, 2A’State (sa for 6-31++G** and s2 for 6-31+G) 3428 (3085)d 0.157 0.080 0.006 3526 3501 3458 (3112) 0.081 0.166 0.028 0.016 0.021 0.128 3488 3429 (3086) 0.080 0.149 0.022 2899 2888 (2599) 1.944 3.779 1603 1499 (1349) [132Ole 0.919 1527 1644(1480) [1490] 1.349 1.236 1.528 0.009 0.000 1403 1714(1543) [1540] 0.354 0.599 0.359 1375 1394 (1255) [1250] 0.229 1279 1480 (1332) [1355] 0.222 0.438 0.192 0.659 1140 1235 (1112) [1140] 1.395 0.812 1084 0.281 0.079 1155 (1040) [lo701 0.051 0.542 0.294 994 1217 (1095) [lo951 0.583 927 916 (824) [830] 0.514 0.286 0.082 842 1000 (900) [895] 0.460 0.658 0.433 828 1009 (908) [935] 0.908 0.502 0.252 a’’ 948 998 755 967 572 835 474 723 363 427 198i 662 a‘

a. Ground-state frequencies for the most closely corresponding mode. Normalized displacement upon excitation in the excited-state mode basis. Normalizeddisplacementupon excitationin the ground-statemode basis. Calculated frequencies multiplied by a uniform scaling factor of 0.9. Experimental frequencies. foptimized excited-state (2A’) geometry: r(C5Nl) = 1.3614 A, r(C4Cs) = 1.4544 A, r(C4N3) = 1.3133 A, r(CzN3) 1.3794 A, r(C2N1) 1.4180 A, C ~ C S N = ~105.32’, CsC4N3 = 110.89’, N I C ~ N 109.46’, ~ C ~ N I= C 107.23’, ~ C4N3C2 107.10’.

Discussion We begin this discussion with an intuitive explanation of the effects of deuterium substitution on the preresonance Raman intensities of these compounds. We then turn to a quantitative theoretical treatment based on ab initio calculations. These calculations result in intensities that are in good agreement with experiment and demonstrate that the reasonable intuitive picture

Figure 3. Geometry of imidazole (upper) and imidazolium (lower) in the ground and excited states. The solid line is for the ground state; the dashed line is for the excited state in each figure.

deduced directly from the experiments is incorrect. A further quantitativeexperiment is suggested by the ab initiocalculations, and this shows that the more complex picture presented by this treatment is substantially correct. We discuss the imidazolium species (proto and deutero) first because of the simplicity of their spectra. Some of these considerations, however, apply to all of the species studied. In the deuterated imidazolium species, there is only one strongly enhanced line. We begin with the assumption that the geometry change associated with electronicexcitation must belargely along the ground-state normal coordinate associated with this enhanced 1400-cm-l vibration. Since isotopic substitution is not expected to have a large effect on the geometry of either the ground or the excited states, the new pattern of intensity observed for the protocation must reflect a change in the form of the normal modes of motion. Since in the protoimidazolium species there are two strongly enhanced bands, the simplest explanation is that the normal mode correspondingto the 1400-cm-1 motion in the deutero species is, in the proto species, now distributed between two normal modes of motion. Thus, according to this explanation, the displacementof the molecular geometry associated with electronic excitation has a near unity projection on the 1400-cm-1 mode of deuteroimidazolium but nearly equal projections on the 1200and 1500-cm-1 modes of protoimidazolium. This is the same explanation that has been proposed for a similar effect of deuterium substitution for N-methylacetamide, NMA.68 In order to make this explanation more concrete, we present a possible physical picture that could form an underlying basis

Resonance Raman Studies of Imidazoles for a large change in the form of the normal modes upon deuterium substitution. Suppose that in the proto species there are valence motions corresponding to a ring expansion (or C-N stretch in NMA) and an in-plane N-H angle bending vibration that have intrinsically similar frequencies near 1340 cm-1. These local modes of motion are coupled dynamically. Further suppose that the symmetric ring expansion has all of the Raman activity. If the coupling between them is roughly 120cm-1, then the resulting splitting of the nearly degenerate motions will result in two bands at roughly the observed values for imidazolium ion. The relative intensitiesof the two bands will be sensitive to the initial splitting; if this is small, the bands will have nearly equal intensities. Deuterium substitution is expected to have a large effect on the frequency of the N-H bending local mode. If this is on the order of the factor of the square root of the ratio of the masses, then this local mode will move down to about 950 cm-1. The splitting of the two local modes will then be 1340- 940 = 400 cm-I, which is much larger than the off-diagonal matrix element of 120cm-I. This will result in normal modes that are similar to the local modes, and essentially all of the intensity will be in the highfrequency mode. This “two-mode” picture of the effect of isotopic substitution predicts that theintensityof thesingle band seenfor thedeuterated species will be distributed between the two bands seen for the protonated form with approximate conservation of intensity. This conservation of intensity is indeed observed for N-methylacetamide.6a This behavior is expected under preresonance conditions where the intensity is proportional to the square of the displacement for a given normal mode times the square of the frequency of that mode,l2 given that the mean frequencies of the active modes do not change appreciably. The main point is that this descriptionof the effect of isotopicsubstitutioncan be checked by a comparison of relative intensities. Ab initio computations were performed to see if this isotope effect on preresonance intensities could be reproduced and explained. Previous similar calculations have successfully accounted for the intensities of the normal modes of vibration that are enhanced for the proto forms of imidazole and imidazolium.IO The present calculations are performed with a much larger basis set. Furthermore, these previous calculations treated the electronic excitation only at the orbital level and further assumed that the major changes in the geometry were associated with bond length changes related to bond order changes. In the present work, we perform a CI calculation to improve the description of the excited electronic states and determine the minimum energy geometry with full optimization for the excited state dominating the absorption and resonance Raman spectra. The calculated excited-stategeometrychange is thenprojectedonto thecomputed ground-state normal modes of vibration. Under preresonance conditions, i.e., sufficiently close to resonance that the nearby electronicexcitationdominatesthe transition but outside the actual absorptionband, the intensityof a Raman transition is proportional to the square of this displacement times the square of the frequency. The equilibrium geometry and normal mode frequencies calculated with the 6-31++G** basis set for imidazolium and imidazolium-d2are given in Table I along with their approximate description and symmetry type. As is usual for such calculations, the calculated frequencies are somewhat higher than the experimental values. In Table 111, these values are multiplied by a uniform scaling factor of 0.9 and compared with experimental values for the totally symmetric ring vibrations of interest here. Reasonable agreement is observed. A much more elaborate scaling procedure has been employed elsewherewith optimization to fit experimentaldata.10 The correspondingresults for imidazole and imidazole-dl are given in Tables I1 and V. Calculations of the excited electronic states of imidazole and imidazolium at the 6-31++G**/CIS level clearly show, in each

The Journal of Physical Chemistry, Vol. 97, No. 40, 1993 10323

case, only one low energy electronic excitation with appreciable oscillator strength. For imidazolium,this state is the first singlet excitation with AI symmetry calculated to be at 7.54 eV with f = 0.27. A second state with B2 symmetry is calculated to lie about 0.7 eV higher in energy and to have f = 0.12. A very weak transition to a state of Bl symmetry lies between these two transitions. The transition from theground state to the Al excited state is expected to dominate the scattering at longer wavelengths. Presumably the B2 state is the major contributor to the second band, whch is seen in the absorption spectrum and in the excitation profile beha~ior.~ Theorbital compositionof this 2A1 (SI)excited state is 0.923 (HOMO to uLUMO) - 0.285 (HOMO to uLUM0+3). Thus, the single orbital approximation used in ref 10 is roughly valid in this case. For imidazole, the 6-31++G** level calculations give a state of A” symmetry as the lowest singlet excitation at 5.98 eV (with f = 0.006) followed by a second state of the same symmetry at 6.65 eV (with f = 0.038). A uu* state of A’ symmetry is then found at 6.95 eV with f = 0.22. This is presumably the state which dominates the first absorption band and the preresonance Raman intensity. This state has significant contribution from four configurations all of the type uHOMO u* with relative weights (in order of increasing u* orbital energy) of 0.87,0.26, 0.3 1, and 0.15. In this case, the use of a single configuration to represent the excited state is problematic. The optimum geometry for the 2A1state of imidazolium and the 2A’ state of imidazole was determined at the 6-3 l+G/CIS level. The results are shown in Tables I11 and V and Figure 3. For imidazolium, this excitation results in a lengthening of the C-C bond by 0.068 A, and the C(2)-N bonds increase by 0.1 10 A while the two C-N (1,s and 3,4) bonds decrease by 0.029 A. (To be sure that the geometry change associated with excitation was not sensitive to the particular choice of basis set, and to eliminate any effects due to the use of one basis set for the ground state and another for the excited state (where configuration interaction is necessary), we also calculated the ground-state geometry in the 6-31+G basis. This was found to be sufficiently similar to that obtained with the 6-31++G** basis: the most important geometry changes associated with excitation were the same to within a few percent.) Comparison of this set of displacements with the form of the normal mode calculated for the deuterated species to be at 1413 cm-* shows a high degree of coincidence. This is shown quantitatively in Table IIIB as the values of B(lA1), the dimensionlessdisplacement parameters for the geometry change on going from the ground to the excited state projected onto the normal modes of the ground state. The same projection for the protoimidazolium species given in Table IIIA shows that there is a large projection on two of the normal modes expected at 1464 and 1190 cm-l and observed (as strong bands) at 1454 and 1216 cm-I. We thus conclude that these calculations substantially reproduce both the observed intensitiesfor the imidazoliumspecies and the effect of change in intensities upon deuteration due to change in the normal modes of motion of the ground state. The forms of the most Raman active modes are given in Figure 4. Tables I11 and V also give the calculated frequencies for the normal modes of motion in the excited electronic states. These are, in general, fairly close to those of the ground state. Note, however, that there are two imaginary bl modes for imidazolium and one of a” symmetry for imidazole,indicating that these species are nonplanar in these excited electronic states. This is expected to have only a small effect on the resonance Raman spectra. Table IV presents an analysis of the normal modes of deuteroimidazolium in terms of the modes of motion of protoimidazolium (and vice versa), Only the ring (non-hydrogen) totally symmetric modes are shown, and these are labeled by their calculated frequencies. The most Raman-active modes are indicated. It is seen that the strong 1570-cm-I mode of

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10324 The Journal of Physical Chemistry, Vol. 97, No. 40, 1993 I

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800

1600

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1

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Figure 4. Form of the most Raman-active normal modes of motion of imidazolium-do and imidazolium-d2. The frequency labels refer to the scaled theoreticalvalues (see Table I11 for theunscaled and experimental values). I

deuteroimidazole has a 0.9 1 projection on the protoimidazole vibration at 1627 cm-1. These modes are substantially the same motion, and it is not surprising that they are strong in the spectra of both species. The other strong band in the proto species, with a calculated value of 1322 cm-l (expected with scaling at 1190 cm-1, observed at 1216 cm-l), is seen to have a projection of only 0.68 on the 1244-cm-1 deuteroimidazolium mode with significant projections on several other modes. This dilution of the displacement along the 1322-cm-l protoimidazolium mode by distribution among several deuteroimidazolium modes results in an apparent loss of intensity in the protoimidazolespectrum when only the strongest one or two bands are considered. This can be seen quantitatively in the last column of Table 111, in which the square of the displacement (which should be closely proportional to the Raman intensity) is given for the deutero and proto forms. The intensities of the two strongest bands of the proto species (4 and 5.3 units) are to be compared with the value of 6.4 units for the deuteroimidazolium species. This calculation makes a prediction that is at variance with the simple "twomode" argument given above in that it predicts that the two bands of the proto species will each be only slightly less intense than that of the deutero species,whereas the simple argument predicted a conservation of intensity within the space spanned by these two modes. (If they had equal intensity, they would each be half as intense as the strong band of the deuterated cation.) As a further test of the ability of this computational procedure to reproduce experimental resonance Raman data, we have calculated (and determined the spectrum for) the case of imidazolium with one deuterium and one proton (imidazoliumdl). These results are also presented in Table 111. This indicates that four bands in the 1100-1600-~m-~region are expected to have appreciable intensity. This is, in fact, what is seen in the experimental spectrum obtained by subtracting the imidazoliumdo and -d2 contributions from a spectrum obtained in a 50% mixture of acidified H2O and D20. A quantitative comparison is made between the predictions of this full ab initio study and experiment in Figure 5, where the dideutero-, diproto-, and monodeuteroimidazolium species are placed on the same intensity scale by the use of an internal standard. One common scale factor is used for the calculation in making this comparison. The degree of agreement is very good. The major deviation between the calculated and observed values is the relative intensity of the deutero vs the proto species, and this is quite minor.

1200

1400

1600

1800

Wavenumbem (cm-1)

Figure 5. Resonance Raman spectra of dideuteroimidazolium, ImD2+ (top); imidazolium, ImH2+ (middle); and monodeuteroimidazolium, ImHD+ (100 mM; pH 3) obtained with 228-nm excitationwith an internal reference of 2.2 M sodium perchlorate to provide a relative intensity standard. The spectrum of the mixed isotopic species was obtained by subtracting equal amounts of the top two spectra from the data obtained for a 5050 mixture of these species. The shaded bars are the intensities calculated as discussed in the text and arbitrarily scaled with one overall scale factor for all three spectra.

The same type of analysis for the neutral speciesimidazole and imidazole41 also shows reasonable agreement with experiment. Specifically, the proto species shows five moderate to strong lines (greater than 0.6 unit) while the deutero species has only three. The inner lines in each spectrum are, however, incorrectly predicted in terms of their relative intensities. For example, the two strong central lines of imidazole41 at 1320 and 1355 cm-1 are calculated to be very strong (3.8 units) and weak (0.19 unit) instead of roughly equal in intensity, as is observed. The origin of this discrepancy, as well as the smaller discrepancy seen for the cationic species, could be due to a small error in the forms of the normal modes or in the position of the excited-state equilibrium. The first possibility could be explored by utilizing either a more refined ground-statecalculation (probably involving electron correlation via MP2) or an empirically scaled force field as used in ref 10. The second possibility of a slightly incorrect excited-state positioning, which seems more likely, could be investigated by optimizationof theexcited stateat the 6-3l++G** level and, perhaps by the inclusion of doubly excited configurations. There is, however, the possibility that the difference between theory and experiment is related to the underlying assumption of preresonance domination of the Raman intensities by the single nearby excitation. This should be approached by further experiment and by additional calculations. Acknowledgment. This research was supported by NIH Grant GM32323 and NSF Grants CHESS16698 and 9207380. B.S.H. wishes to acknowledge the support of the Department of Energy (DOE) through the Molecular ScienceResearch Center of Pacific Northwest Laboratory (PNL). PNL is operated for the DOE by Battelle Memorial Institute under Contract DE-AC06-76RLO 1830. Support from the U.S.Department of Education Graduate

Resonance Raman Studies of Imidazoles

The Journal of Physical Chemistry, Vol. 97, No. 40, 1993 10325

Assistance in Areas of National Need Program for L.M.M. is gratefully acknowledged.

(7) Mayne, L. C.; Harhay, G.; Hudson, B. Ultraviolet ResonanceRaman Studies of Protein Components: Proline Bonds and Histidine. Biophysical

References and Notes

(8) Asher, S. A.; Murtaugh, J. L. UV Raman Excitation Profiles of Imidazole, Imidazolium and Water. Appl. Specrrosc. 1988, 42, 83. (9) Caswell, D. S.; Spiro, T. G. Ultraviolet Resonance Raman Spectroscopyof Imidazole, Histidine and Cu(imidazo1e): Implications for Protein Studies. J. Am. Chem. Soc. 1986, 108,6470-6477. (10) Majoube, M.; Henry, M.; Chinsky, L.; Turpin, P. Y.Preresonance Raman spectra for imidazole and imidazolium ion: interpretation of the intensity enhancement from a precise assignment of normal modes. Chem. Phys. 1993, 169, 231. (11) Gaussian 92, Revision B, M. J. Frisch, G. W. Trucks, M. HeadGordon, P. M. W. Gill, M. W. Wong, J. B. Foresman, B. G. Johnson, H. B. Schlegel, M. A. Robb, E. S. Replogle, R. Gomperts, J. L. Andres, K. Raghavachari, J. S. Binkley, C. Gonzalez, R. L. Martin, D. J. Fox, D. J. Defreea, J. Baker, J. J. P.Stewart, and J. A. Pople, Gaussian, Inc.: Pittsburgh, PA, 1992. (12) Blazej, D. C.; Peticolas, W. L. Ultraviolet resonant Raman spectroscopy of nucleic acid components. Proc. Nutl. Acad. Sci. USA 1977,2639. Warshe1,A.; Dauber, P. CalculationsofresonanceRamanspectraofconjugated molecules. J. Chem. Phys. 1977, 66, 5477. (13) Zgierski, M.; Zerbetto, F. Franck-Condon structure of the SO-SI-S~ transitions in norbornadiene. J. Chem. Phys. 1993, 98, 14-20.

(1) Hudson, B.; Sension, R. J. Far Ultraviolet Resonance Raman Spectroscopy: Methodology and Applications. In Vibrationul Spectru und Srrucrure; Bist, H. D., Durig, J. R., Sullivan, J. F., Eds.;Elsevier: Amsterdam, 1989; Vol. 17A, pp 363-390. (2) Hudson, B.; Mayne, L. C. Ultraviolet Resonance Raman Studies of Protein Constituents. In Biological Applicutions of Raman Spectroscopy; Spiro, T. G., Ed.; Wiley: New York, 1987; pp 181-209. (3) Hudson, B.; Mayne, L. C. Ultraviolet RaonanceRamanSpcctroscopy of Bio-polymers. Methods in Enzymology 1986, 130, 331-350. (4) Sension,R. J.;Mayne,L. C.; Hudson, B. S.Far Ultraviolet Resonance Raman Scattering: Highly Excited Torsional Vibrations of Ethylene. J. Am. Chem. Sot. 1987, 109, 5036-5038. (5) Gerrity, D. P.; Ziegler, L. D.; Kelly, P. B.; Desiderio, R. A.; Hudson, B. S. Ultraviolet Resonance Raman Spectroscopy of Benzene Vapor with 220-184 nm Excitation. J. Chem. Phys. 1985,83, 3209-3213. ( 6 ) (a) Mayne, L. C.; Ziegler, L. D.; Hudson, B. Ultraviolet Resonance Raman Spectroscopyof N-methylacetamide. J. Phys. Chem. 1985,89,3395. (b) Mayne, L. C.; Hudson, B. Resonance Raman Spectroscopy of N-Methylacetamide: Overtonesand Combinationsof the C-N Stretch (Amide 11’) and Effect of Solvation on the C - 0 Stretch (Amide I) Intensity. J. Phys. Chem. 1991,95,2962.

J. 1986, 49, 330a.