Analysis of the vibrational spectra of 1-methyluracil and its isotopic derivatives by ab initio calculations

Journal of Molecular Structure (Theochem), 139 (1986) 283-303 Elsevier Science Publishers B.V., Amsterdam -Printed in The Netherlands

ANALYSIS OF THE VIBRATIONAL SPECTRA OF l-METHYLURACIL AND ITS ISOTOPIC DERIVATIVES BY AB INITIO CALCULATIONS

KANGNIAN FAN* and JAMES E. BOGGS Department

of Chemistry, The University of Texas, Austin, TX 78712 (U.S.A.)

(Received 24 April 1986)

ABSTRACT The vibrational spectrum of 1-methyluracil trapped in an argon matrix has been analysed based on ab initio Hartree-Fock SCF calculations with a split-valence 4-21 basis set. The directly computed theoretical harmonic force field was scaled with empirical scale factors which were transferred from uracil (except for the methyl vibrational modes) to provide an a priori prediction of fundamental frequencies and intensities. The average deviations between experiment and prediction were 9.8 cm-’ for the in-plane vibrations and 16.3 cm-’ for the ring out-of-plane modes. After a few corrections of assignment of the observed spectrum, a new set of scale factors was optimized to give the best force field available from combined consideration of the experimental and theoretical information. These scale factors reduced the average deviations to 6.7 cm-’ for the in-plane modes and to 11.7 cm-’ for the out-of-plane ones. The vibrational spectra of seven isotopic derivatives (-2180, -4**O, -3d, -5d, -6d, -5, 6d, and CD,) of 1-methyluracil were predicted with the force field resulting from the optimized set of scale factors, and compared with the crystal-phase experimental data. A few misassignments in the experimental isotopic spectra have been corrected. Vibrational absorption intensities have been computed and compared with experiment and with an earlier calculation. INTRODUCTION

Due to the essential biological importance of uracil derivatives, several studies of the vibrational spectroscopy of 1-methyluracil (l-MeU) have been reported recently. The published results include an earlier study of the inplane fundamentals of polycrystalline l-MeU by Susi and Ard [l],the infrared and Raman spectra and vibrational assignments of crystal l-MeU and its seven isotopic derivatives obtained by Lewis et al. [2] , and the experimental infrared matrix isolation spectra and ab initio calculations of l-MeU by Szczesniak et al. [3, 41, as well as a study of the effect of intermolecular interactions on the infrared spectrum of l-MeU by the same research group

151.

Examination of the available experimental data [l-5] on the spectra of l-MeU reveals some uncertainty in a few of the assignments of fundamental *Permanent address: Republic of China. 0166-1280/86/$03.50

Department

of Chemistry,

Fudan University, Shanghai, People’s

0 1986 Elsevier Science Publishers B.V.

284

modes and also, to a lesser extent, in the direct experimental observation of fundamental frequencies and intensities. The variations in the experimental results are presumably due to the different sample states in which intermolecular interactions are quite different. Only incomplete data are available for the isolated molecule in the gas phase, so that the best presently available frequencies for the free molecule come from the observed spectra in argon matrices [3-51. Spectra in inert gas matrices are, indeed, better resolved than those in the gas-phase since the low temperature of the matrix minimizes the rotational motion of the molecules and sharpens the absorption bands. There are, however, frequency shifts and intensity variations arising from interaction with the host matrix which must be considered in any precise discussion of fundamental vibrational frequencies. In many cases, these frequency shifts amount to only a few wavenumbers and can be ignored, although in some cases (particularly for low frequency out-of-plane vibrations) they are known to be comparable to the 10 cm-’ precision sought here. Szczesniak et al. [3] have presented theoretical predictions of the vibrational fundamentals and intensities of l-MeU, based on the assumption that force constants could be transferred unchanged from those obtained for the parent uracil molecule by Chin et al. [6] with a point mass taken for the methyl group. The philosophy of such a procedure may be questioned, since it obviates any possibility of determining specific effects of methylation on the vibrational behavior, which must surely be the main reason for studying the methylated compound. The uracil force field used for transfer [6] was based on STO-3G calculations with a compliant scaling procedure by Nishimura et al. [7]. The level of calculation used is not fully adequate to give the best possible theoretical prediction of the fundamental frequencies, as has been shown in more recent, similar work on uracil [8]. The final computed frequencies of Szczesniak et al. [3] for l-MeU show an average deviation of 27 cm-l from the matrix experimental values for the in-plane vibrations (omitting four fundamentals for which no experimental matrix data are available), with the maximum deviation as large as 73 cm-‘. This was of great help in assigning the spectra, but it does not approach the level of accuracy which we have found to be possible from similar computations with scaling by the methods described below. Choices between alternative possible assignments for a given fundamental often require selection between observed bands which are quite close together, so that it is useful to obtain the maximum feasible precision from the theoretical predictions [ 91. Considerable success has recently been obtained with a computational procedure based on the transferability of scale factors rather than force constants and emphasizing adequate attention to those factors which significantly affect the accuracy of the force field obtained. The method is outlined briefly below and full details have been presented previously [lo] . The procedure has been applied to benzene [ll],pyridine [12, 131, napththalene [ 141, aniline [ 151, cubane [ 161, triprismane [ 171, pyrrole [ 181, imidazole [19], pyrazole [20], maleimide [21], y-pyrone [22], 4-methylpyridine [ 231 and uracil [ 81, as well as to a variety of smaller molecules [lo]. In all

of these cases, agreement between predicted and experimental data was at approximately the level of accuracy of the independent harmonic oscillator approximation. A deviation of 215 cm-’ between theory and a reported observed frequency was considered sufficient reason to look carefully at the experimental assignment. This wide range of successful experience, coupled with the fundamental importance of the l-MeU molecule, has induced us to obtain a theoretical prediction of its harmonic vibrational force field and carry out a critical assignment of the observed spectra and the corresponding assignment of vibrational fundamentals. COMPUTATIONAL DETAILS

Our basic procedure [lo] consists of the following steps. (1) The harmonic force field of one or more reference molecules is computed ab initio at a sufficiently high level of approximation, typically approximately double zeta Hartree-Fock. (2) The spectra of vibrational fundamentals predicted from the computed force fields are least-squares fit to the observed spectra of the reference molecules, for which the experimental assignment is reasonably secure. Elements of the force constant matrix are scaled as flyled = (CiCj)l/2F;Peor where groups of related vibrational modes are given a common value of C. Thus there are several independent values of Ci, but the number is kept small. For details, see the individual papers. (3) The harmonic force field of the unknown molecule is now calculated at exactly the same level of quantum mechanical approximation as was used for the reference molecules. (4) The scale factors derived groups of types the reference are transferred to the molecule and to scale its force field. (5) The resulting scaled quantum-mechanical (SQM) force field is used to compute the vibrational spectra of the new molecule. Comparison with experimental infrared or Raman spectra can identify fundamental transition frequencies and verify empirical assignments. It should be noted that it is not assumed that the molecule under study has the same force constants as the reference molecules, but only that the error in the calculation of similar types of vibration in the two molecules is identical. This higher-order approximation is demonstrably more accurate. The energy-optimized geometries and force fields have been computed by methods described earlier [ 10, 241, using the ab initio gradient program TEXAS [25] and the 4-21 basis set [24] of Gaussian orbitals. A complete, non-redundant set of internal coordinates (Fig. 1 and Table l), chosen in accordance with our previous recommendations [ 241 to minimize the contribution of off-diagonal elements in the force constant matrix, was used for the calculations. The matrix of force constants was determined from gradients calculated at displaced geometries and scaled by a procedure identical to that used previously [lo-231. Infrared absorption intensities were also evaluated from computed dipole moment derivatives. Our procedure strictly calculates the force field and vibrational spectra of

286 010

I

1

06/c2\N/c6\H,2

I’

H,/TQH,5 14

Fig. 1. Labeling of the atoms in 1-methyluracil. uracil ring plane.

One methyl C-H bond (C,H,,)

is in the

independent isolated molecules, while the experimental results with which we wish to make comparison are obtained in a low-temperature matrix. Exactly the same situation prevailed in the study of uracil [8] . We can therefore expect that scaling the computed force field of l-MeU with factors optimized to fit the computed spectra of uracil to matrix frequencies will transfer some part of the small error from the matrix interaction, as well as the similar computational errors in the two closely related molecules [4]. The vibrational spectra of seven l-MeU isotopic derivatives (two mono-l*0 species, MeU-Z1*O and MeU-4l*O, three monodeuterio species, MeU-3d, MeU-5d and MeU-Gd, a dideuterio species MeU-5, 6dz and the deuteriomethyl derivative CD3U) have also been computed and compared with experimental data to test the scale factors optimized on the normal l-MeU spectrum and confirm the accuracy of assignments in the isotopic species. RESULTS AND DISCUSSION

Geometry It is very important in force field calculations to choose a proper reference around which the energy surface is expanded. This reference point should be the best approximation that can be made, either from experiment or from theory, to the true equilibrium geometry of the molecule [lo, 241. The sensitivity of the results to this factor is illustrated by the observation that a computed C-H stretching frequency is shifted approximately 10 cm-’ (0.3%) for every 0.001 A error in the length used for the C-H bond [14]. Since no complete experimental geometry for l-MeU has been reported, the geometry in this case is best approximated by using the computed minimumenergy geometry, with suitable small corrections for consistent computational geometry

287 TABLE 1 Internal coordinate No. in-plane l-3,6 495 7 8, 10 9 11,12 13 14 15 16 17 18 19,21 20 22,23 24 25,26

systema Description

Internal coordinate

q1 = R(l, 2); qz = R(2,3); ~4 I ;I;, ;;; qg = R(5,6)

CN stretch CC stretch Me-N stretch 00 stretch N-H stretch C-H stretch

q3 = R(3, 4); qs = R(6,l)

q: = R(8: 2); qla = R(lO, 4) qs = R(9,3) qll = R(ll,5); qla = R(l2,6) qls = R(13,7) + R(l4,7) + R(l5,7) q14 = 2R(13,7)-R(l4,7)-R(l5,7) q15 =oL1 -oL* +(Y,-o14 +(Y,-ffG q1s = 2(Y1-oLz -(Yj + 2aq --es --a6 417 = (Y2- oLj + 415-(Ye q18 = ~(7,1,2) - L(7,1,6) Ql$l= 08, 2, 3) - L(8,2,1); QZl = QlO, 4, 5) - L( 10,4, 3) 410 = L(9,3,4) - 09,332) qz2 = ~(11,5,6)-~(11, 5,4);q,, = L(l2,6,1) --(12, 6,5) q2.$=01 +oz +&--P1--Pz--PJ 425 = 2@, -&-@3;426 = 2P, -01--b,

Out-of-plane qzs =@3-@2;4,9 =82 -83 28,29 qz, = R(14,7) - R(15,7) 27 930 = T1 - T2 + T3 - r4 + r5 - T6 30 q31 = T1 - ,r3 + 74 - 76 31 432 = 272 - T1 - Tg + 276 - 74 - 76 32 q33 = 7 out of (2, 6,1) plane 33 qs4 = 8 out of (3,1,2) plane; qs6 = 10 out of (5, 3, 4) 34,36 plane qa5 = 9 out of (4,2,3) plane 35 plane; q3* = 12 out of (1, 5,6) 37,38 q37 = 11 out of (6,4,5) plane qs9 = sum of all possible dihedral angles XiC,N, Yj 39

C-H stretch (Me)

1

Ring deformation Me-N deformation C=O deformation N-H deformation C-H deformation

>

C-H bend (Me)

C-H bend (Me) C-H stretch (Me) Ring torsion Me-N wagging C=O wagging N-H wagging C-H wagging Me-ring

twisting

aSee Fig. 1 for labeling of atoms. a, = ~(6, 1, 2);or, = L(1, 2, 3);...a, = L(5,6,1). o, = L(14, 7, 15); I& = L(13, 7, 14); @J3= L(13, 7, 15). P1 = L(13, 7,l);P, = Q14,7,1);Ps = = dQ6, 5, 4, 3). T = L(15, 7, 1). 7, = dihedral ~(1, 6, 5, 4); 71 = c&(2, 1, 6, 5);...~~ dL(a, b, c, d) is defined as the angle between the planes abc and bed. r is positive if a is in the direction of the vector product cb * cd.

errors arising from neglect of electron correlation and use of a finite basis set [ 10, 241. A similar procedure was used for work on the parent molecule uracil [8]. Optimization of the geometry of l-MeU under the assumption that all heavy atoms are coplanar gave two minimum-energy conformations. One, (form A) has the methyl group oriented with one hydrogen in the ring plane

and pointing toward the carbonyl group CZ=O, as shown in Fig. 1. The other (form B) is obtained by a 60” rotation of the methyl group and has the methyl hydrogen in the plane and pointing toward the C6H group. Form A (Fig. 1) is found to be more stable by 126 cal mol-‘, as calculated at the 4-21 level. We have therefore obtained our estimate of the true equilibrium geometry by the application of standard empirical corrections [24] to the more stable form A. The corrections amounted to -0.001 ,&for C4-C5, +0.019 A for CS-C6, +0.005 W for C-H and N-H, -0.010 i%for C-N, and -0.005 A for C=O, all of which are compatible with the corrections made to obtain the best estimate of the equilibrium geometry of uracil [8] . The resulting estimate of the true equilibrium geometry, which we have used as the reference state, is listed in Table 2 along with the original computed optimized geometry of the form A (Fig. 1). Scale factors and force fields Scaling a computed force field to correct for residual computational errors can be done for either of two reasons. First, if the experimental spectrum is unknown, or if there is a desire to test the assignment of fundamental frequencies that has been made from experiment, scale factors may be transferred from closely related molecules on the assumption (for which there is TABLE 2 Reference (equilibrium) geometry of 1-methyluracila Bond length (A)

Theoreticalb

CorrectedC

Bond angle (“)

Theoreticalb

CorrectedC

NI-C, G--N, K--C, G--c, G--C, C,--N, C--N, Q-G H,--N, 0,0-c, H,,-C, HI,-% H,,-C Hw--C, G-G

1.382 1.375 1.397 1.456 1.327 1.380 1.473 1.219 0.998 1.215 1.065 1.070 1.075 1.081 1.081

1.372 1.365 1.387 1.455 1.346 1.370 1.463 1.214 1.003 1.210 1.070 1.075 1.080 1.086 1.086

LN,CJ’J, ~C&C, WC,‘& LC4CSC6 LCSCP~ GN,C, LC,N,C, LC,CP, LHP,C, LC*,C,C, W,C,C, LH,,C,N, LH,,C,N, LH, ,C,N, LH&,NI LH,,C,H,, LH,,C,H,, 7 13 LH 15CH

114.1 128.4 113.0 119.7 123.6 121.3 118.5 122.7 116.4 126.2 122.2 114.5 107.5 110.0 110.0 109.8 109.8 109.8

114.6 128.8 112.9 119.2 123.2 121.4 118.4 122.4 116.2 126.2 122.4 114.7 107.5 110.0 110.0 109.8 109.8 109.8

Wee Fig. 1 for labeling of atoms. bComputed values, see text. CFor corrections see text.

289

now much reassuring evidence [ 11-231) that the computational error is similar for similar vibrational types in related molecules. This leads to an a priori prediction of the spectrum and can be used to make or correct assignments of the fundamental modes. Alternatively, if there is a reliable experimental spectrum of the molecule under study, the computed force field may be scaled by a set of factors newly optimized to give the best fit of the computed spectrum to the observed spectrum, or to some portion of the latter that is known with certainty. The object in this case is to obtain the best possible force field from a combination of all the available evidence, both experimental and theoretical. Both procedures have been used in the present study. One major goal is to test the available experimental assignments, so an a priori spectral prediction was made by transfer of scale factors from other molecules. Then, having achieved confidence in the complete assignment, we obtained the best available force field by scaling directly to the observed spectra. Since the molecule of l-MeU has the same ring structure as that of uracil, the scale factors transferred from uracil [S] were used for all the ring vibrational modes, using the same value for the Me-N stretch as was found for the C-N stretch in uracil [S], and an estimated value of 0.8 was taken for the methyl group vibrational modes. The Me-N torsional mode cannot be predicted with any accuracy because it is at a very low frequency, of anharmanic character and is not known from experiment. Consequently, a scale factor of unity was used for this vibration and left unchanged through later work, and the corresponding predicted frequency is assumed to be highly inaccurate. The scaled force fields obtained in this manner were used to make a priori predictions of the spectra of, l-MeU, with the results described below, to test and complete the fundamental mode assignments which have been previously proposed. In order to obtain the best possible force field for l-MeU to assist in the prediction of other vibrational properties, the full set of scale factors was optimized to give the best least-squares fit between the computed spectra and the experimental frequencies, taking into account the corrections in assignments which are discussed below. These optimized scale factors are also shown in Table 3. Tables 4 and 5 give the force fields directly computed and the scaled (SQM) force fields resulting from scaling with the optimized factors of Table 3. The SQM force fields are believed to be the best force fields currently available for l-MeU based on simultaneous consideration of all the available experimental and theoretical information. A consideration of the transferred and newly optimized scale factors in Table 3 is informative. For the ring in-plane modes, with the exception of the N-H and GO deformations, the scale factors agree within 2%, corresponding to a 1% difference in predicted frequencies, which reveals a high degree of uniformity of the scale factors of uracil and l-MeU. This, of course, indicates a similar effect of computational error in the two molecules as well as similar compensation for any matrix effects on the observed spectra. For

290 TABLE 3 Scale factors for 1-methyluracil Description

Uracil

Optimized

C-N stretch C-C stretch C=C stretch Me-N stretch C=O stretch N-H stretch C-H stretch C-H(Me) stretch Ring deformation Me-N deformation N-H deformation C=O deformation C-H deformation C-H(Me) bend N-H wagging C-H wagging GO wagging Ring torsion C-H(Me) stretch (out of plane) C-H(Me) bend (out of plane) Me-N wagging Me-Ring torsion

0.842 0.896 0.909 _a

0.849 0.921 0.921 0.833 0.821 0.844 0.820 0.797 0.828 0.925 0.749 0.794 0.772 0.790 0.599 0.707 0.701 0.817 0.834 0.758 0.907 l.OOOC

aTaken as 0.842 mated values of modes, of 0.900 ing mode were constants.

0.831 0.850 0.822 4 0.813 -b

0.793 0.847 0.768 4

0.583 0.733 0.765 0.791 -b -b

-b 4

in this work, identical with the C-N stretching mode of uracil. bEsti0.800 for the C-H(Me) stretching and bending and Me-N wagging for the Me-N deformation mode, and of 1.000 for the Me-Ring twistused. Yf’his value was held constant during optimization of the other

three out-of-plane modes, the N-H wagging, ring torsion and C-H wagging, the scale factors differ by 2.7 to 3.5% between l-MeU and uracil. However, the C=O wagging mode has a somewhat larger difference of 8.4%. For this mode, the transfer of computational error (or perhaps of matrix interaction) seems to be less accurate, although the results have an accuracy sufficient that the a priori prediction would have been useful in an original assignment of the spectrum or in later correction of a misassignment. Assignment of in-plane fundamentals modes The fundamental vibrational frequencies of l-MeU, as calculated with the transferred uracil scale factors and with the scale factors optimized for l-MeU, are reported in Tables 6 and 7. As described above, we have chosen the matrix isolation data [3--51 to compare with our results. In addition to being the best available approximation to the experimental vibrational spectra

291

of the free molecule, the a priori predictions of the vibrational spectrum of l-MeU were made using the uracil scale factors which had been optimized to the observed uracil matrix spectrum, thereby to some extent absorbing whatever matrix perturbations may exist. The overall assignment of the in-plane modes from our calculation is highly consistent with that made by Szczesniak et al. [4, 51, except for a few fundamentals discussed below. First, the three fundamentals that were not observed in the matrix spectrum (vZ6 Me-N deformation, v5 and v4 methyl C-H stretch) calculated at 350,2827 and 2962 cm-’ agree well with the frequencies of 353,284O and 2948 cm-’ , observed in the crystal Raman spectrum and assigned to these modes by Lewis et al. [2]. We have therefore taken the latter values as the experimental frequencies for these modes in spite of the difference in physical state of the sample. Szczesniak et al. could not distinguish between bands at 712 and at 749 cm-l for the v21 ring stretching mode and also assigned 749 cm-’ for the vzo ring deformation. Our predictions of 740 cm-’ for u21 and 794 cm-’ for v20 indicate that 749 cm-’ is the preferred choice for vzl. However, the computed value for v20 is clearly incompatible with the simultaneous assignment of this mode at 749 cm-‘. Guided by the computed difference between vzl and ~20 of 54 cm-l, we reassign the vzo fundamental as the 804 cm-’ band observed in the crystal Raman spectrum of Lewis et al. [2]. The corresponding weak band in the absorption spectrum at 804 cm-’ may well be hidden in the strong band at 802 cm-’ observed for vgl in the matrix spectrum. It should be emphasized that assignment questions such as those discussed here are made solely with the spectra predicted a priori based on transferred scale factors and do not rely on any re-optimization of the scale factors to fit the observed spectra of l-MeU. The average difference between the in-plane frequencies predicted by the transferred scale factors and the experimental matrix frequencies (with the assignment clarifications presented here) is 9.8 cm-‘, an acceptable value. If comparison is made between the experimental in-plane frequencies and those computed with the optimized scale factors, as shown in Table 6, the average deviation is reduced to 6.7 cm-‘, an improvement which we consider to be negligible. This again indicates that the direct transfer of scale factors between related molecules is highly successful in producing a highly accurate force field and set of predicted vibrational fundamental frequencies. Assignment of out-of-plane fundamentals modes The previous assignment of the out-of-plane fundamental modes based on experiments is less complete than for the in-plane modes. Only six of the thirteen fundamentals were observed in the matrix spectra of l-MeU, although more information can be obtained from the crystal spectra of Lewis et al. [ 21. These and our computed results are shown in Table 7. The fundamental mode v30, the C-H wagging mode, has been assigned [4]

292 TABLE 4 SQM and directly computed in-plane force fields of l-methyluracil* Int.

1

2

3

4

5

6

I

8

9

10

11

12

coord. 1

6.312”

2

0.632 0.627

1.435

3 4 5

4.244 4.287 0.105 0.118 4.204 4.231

6.249

7.360 0.389 0.468 4.146 4.166

0.484 0.570

4.210 4.248

I

0.265 0.315

4.054 4.065

8

1.170 1.401 -0.039 4.046

0.420 0.475

0.138 4.173 0.157 4.195

6

9

5.487 6.463

4.090 4.107

4.082 4.098

-0.063 -0.076

11

4.007 4.008

-0.031 4.008 -0.037 4.010

12

4.038 4.045

4.016 4.019

13

4.079 4.096

14

4.088

4.107

4.056 4.064

1.179 1.412

4.021 4.025

8.713 9.460 0.696 0.787 4.063 4.060

-0.108 4.110 -0.124 4.127

0.083 4.029 0.098 4.033

10

0.006 0.001

0.429 0.466

0.218 4.318 0.256 4.360

1.098 4.092 1.315 4.110 0.063 0.015

5.210 5.657

4.026 4.028

0.739 -0.139 0.850 4.159 0.025 0.029 4.003 4.003

6.181 7.280 0.208 0.248

4.895 5.876

4.048 4.058

4.034 -0.041

10.874 13.244

4.015 4.018

4.000 4.000

4.025 4.030

0.014 -0.032 0.016 4.038

6.537 7.746

0.102 4.012 0.124 4.015

11.433 13.926

0.056 4.027 0.064 4.032

0.002 0.003

0.001 4.001 0.001 4.001

0.021 0.026

5.172 6.308

0.065 0.074

0.004 0.004

0.010 0.012

0.008 0,009

0.010 0.013

4.995

0.164 0.201

0.010 4.000 0.012 -0.001

0.008 0.010

0.000 0.000

0.008 0.010

0.086 0.103

0.015 4.022 0.018 -0.027

0.000 0.000

0.004 0.005

0.006 0.007

-0.010 4.012

0.013 0.016

0.025 4.001 0.029 4.001

4.007 4.074 -0.008 -0.091

0.003 0.003

0.267 -0.098 0.324 -0.118

0.001 4.004 0.002 4.005

4.000 4.000

6.091

4.006 4.007

15

0.009 0.010

4.023 4.027

0.011 0.013

0.045 4.012 0.052 4.014

-0.094 4.193 -0.112 -0.232

16

0.055 0.066

4.113 4.135

0.138 0.164

0.065 4.206 0.074 4.236

0.050 4.256 0.060 -0.308

17

0.098 0.117

4.028 4.033

4.090 4.107

0.247 0.283

0.134 4.245 0.153 4.293

0.006 -0.350 0.007 -0.425

0.082 0.098

0.002 4.072 0.003 4.087

0.068 0.082

18

0.467 0.528

4.011 4.013

4.043 4.049

4.047 -0.051

0.009 4.254 0.010 4.287

0.153 0.174

0.003 0.004

0.003 4.006 0.003 -0.007

0.020 0.023

19 20

4.618 -0.753 0.022 0.027

0.424 4.099 0.516 4.121 4.141 -0.176

0.098 4.035 0.114 4.041

0.087 -0.026 -0.022 0.109 -0.031 4.026

21

4.040 4.048

0.093 4.438 0.113 4.534

22

4.038 4.047

0.024 4.004 0.029 4.005

4.127 4.150

23

-0.008

-0.014 4.017 -0.018 4.022

4.003 4.004

4.010 24 25 26

0.043 0.063 4.031 4.037 0.039 0.048

0.006 0.007 4.004 4.005 4.032 4.039

0.008 0.009 4.000 4.000

0.217 4.049 0.253 4.057

0.070 0.085

0.060 0.069

0.005 4.007 -0.036 0.001 -0.009 4.043 -0.016 4.005 4.020 4.007

0.111 4.009 0.135 4.011

4.039 4.048

0.275 4.022 0.340 4.027

0.017 4.000 0.022 4.000

0.017 -0.541 4.059 0.021 4.667 4.073

0.007 4.002 0.008 4.003

0.000 0.001

4.002 4.002

0.002 0.002

0.077 -0.007 0.094 4.008

0.009 0.011 0.036 0.044

0.068 0.070

0.041 0.050

0.004 4.005 0.005 4.006

0.019 0.024

0.005 4.000 0.006 4.001

0.001 4.010 0.001 4.012 4.012 4.015

-0.001 4.006 -0.002 4.007 0.000 0.000 0.002 0.003

0.081 0.098

0.047 0.058

0.033 -0.084 4.022 0.040 4.104 4.026

0.001 4.001 4.003 0.001 -0.001 4.004

0.008 -0.019 0.010 4.022

0.009 4.026 0.011 4.031

0.055 -0.346 0.066 -0.419

0.036 4.003 0.046 4.004

0.174 4.005 0.201 -0.006 4.132 4.157

0.162 0.196

0.274 4.093 0.332 4.112

4.003 4.004 4.008 4.009

0.003 0.004 4.001 4.002

0.006 0.001 4.006 -0.007 0.002 0.003 4.007 4.009

0.000 0.001 0.000 0.001 0.001 4.009 0.001 -0.011

Wnits are such that Fij AqiAqj isin mdyn a, with distances in A and angles in radians. For notations constants, the second ones are the directly computed force constants. For meaning of SQM force

293

13

14

15

16

17

18

19

20

21

22

23

24

25

26

4.665 5.853 0.123 0.154 -0.007 -0.009

4.674 5.865 0.009 0.011

1.507 1.820

0.004 0.005

0.023 0.028

0.057 0.069

0.008 0.010

0.020 -0.059 -0.086 0.025 -0.072-0.104

1.462 1.765

-0.043 -0.110 -0.0504.090 -0.051 -0.128 -0.057-0.102 0.034 0.042

1.340 1.618 0.044 0.051

0.063 0.079

0.017 -0.0504.000 0.021-0.062-0.000

-0.001 -0.001

0.001 0.002

0.008 0.010

-0.000 -0.000

0.001 -0.059 0.001 -0.073

0.001 0.002

0.000 0.000

1.177 1.272 -0.138 -0.161

1.226 1.545

0.102-0.072 -0.012 0.129 -0.092 -0.015

0.047 0.061

0.091 0.112

0.131 0.161

0.002-0.059 0.002-0.075

0.007 -0.081 -0.048 -0.010-0.008 0.009 -0.101-0.060 -0.011-0.010

0.469 0.626 0.057 0.074 -0.010 -0.013

0.984 1.239 0.035 0.045

0.443 0.574

0.004 -0.005 0.005 -0.006

0.027 0.034

0.078 -0.002 -0.014-0.018 -0.0004.017 0.098 -0.002 -0.016 -0.023 -0.000-0.022

0.089 -0.031 0.112 -0.039

0.040 0.050

0.039 -0.009 -0.001-0.011 0.048 -0.012 -0.0014.014

0.003+X001-0.002 0.003 -0.0014.003

0.003 0.003

0.000-0.0024.000 0.0014.0024.000

0.021 -0.132 -0.001 0.027 4.167 -0.001 0.016 0.021

0.006 -0.036 0.007 4.042

0.110 4.027 4.035-0.024 0.138 4.033-0.043 4.030

of internal coordinates field see text.

0.015 0.019

-0.0424.023 4.0494.029

0.002 0.003

0.009 0.011

0.005 0.006

0.529 0.686 -0.001 -0.001 0.003 0.004

0.650 0.822 0.003 0.004

0.551 0.697

0.004 4.004-0.0024.033 0.806 0.005 4.0054.003 -0.0421.021

see Fig. 1 and Table 1. bThe first entries in vertical pairs are the SQM force

5

4.661b 5.589 -0.152 -0.191 0.079 0.099 0.004 0.005 0.002 0.002 -0.006 -0.007 -0.012 -0.014 0.009 0.011 -0.000 -0.000 -0.000 -0.000 -0.001 -0.001 -0.009 -0.012 0.006 0.007

27

0.701 -0.016 -0.022 0.011 0.013 -0.011 -0.014 -0.009 -0.011 0.018 0.022 -0.026 -0.036 0.000 0.000 -0.000 -0.000 0.001 0.001 -0.002 -0.002 0.007 0.008

0.762 1.005 0.018 0.023 -0.010 -0.012 -0.011 -0.013 0.008 0.010 0.002 0.003 0.003 0.004 0.001 0.001 0.606 0.008 -0.001 -0.002 0.017 0.019

29

out-of-plane

0.532

28

computed

0.245 0.299 -0.052 -0.064 -0.063 -0.074 0.116 0.153 -0.059 -0.084 -0.007 -0.009 0.155 0.204 -0.109 -0.143 -0.002 -0.002

31

0.191 0.234 -0.077 -0.089 0.004 0.006 0.091 0.131 -0.100 -0.132 -0.059 -0.078 0.099 0.130 -0.002 -0.002

32

fields of 1-methyluraciP

0.245 0.300 0.045 0.055 -0.037 -0.046 0.096 0.112 -0.098 -0.130 0.103 0.148 -0.053 -0.071 0.144 0.189 -0.118 -0.156 0.001 0.001

30

force

0.340 0.375 -0.079 -0.099 0.013 0.017 -0.008 -0.010 0.018 0.023 -0.018 -0.023 0.010 0.011

33

0.749 1.068 -0.062 -0.096 -0.019 -9.027 -0.006 -0.008 -0.006 -0.008 -0.003 -0.004

34

0.232 0.388 -0.066 -0.101 0.002 0.003 -0.004 -0.007 0.000 0.000

35

0.656 0.935 -0.029 -0.041 -0.041 -0.059 -0.000 -0.000

36

0.367 0.519 -0.097 -0.137 -0.001 -0.002

37

0.003 0.003

39

see Fig. 1 constants.

0.435 0.615 -0.001 -0.001

38

aUnits are such that FijAqiAqj is in mdyn A, with distances in A and angles in radians. For notations of internal coordinates force and Table 1. bThe first entries in vertical pairs are the SQM force constants, the second ones are the directly computed For meaning of S&M force field see text.

39

38

37

36

35

34

33

32

31

30

29

28

27

Internal coordinates

SQM and directly

TABLE

Me-N & C=O def. C=O def. Ring def. C=O & ring def. & ring str. Ring, C=O & Me-N def. Ring & Me-N str. Ring def. & Me-N & ring str. Ring def. & str. C-H(Me), C-H def. & ring str. C-H & C-H(Me) def. Me-N & ring str. Ring str. & C-H def. Ring str. & C-H, C-H(Me) def. N-H def. & ring str. C-H, C-H(Me) def. & ring str. C-H(Me) def. & ring str. Ring str. & C-H(Me) def. C-H(Me) def. Ring str. & C-H def. C,=O & C,=O str. C,=O & C,=O str. C-H(Me) str. C-H(Me) str. C-H str _ C-H str. N-H str.

26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 350 399 461 543 622 740 794 958 1020 1151 1199 1239 1316 1374 1395 1428 1450 1495 1643 1723 1746 2827 2962 3023 3080 3444

352 392 462 539 620 742 794 960 1020 1151 1199 1239 1313 1360 1385 1425 1446 1487 1650 1716 1740 2822 2956 3020 3076 3432

Freq. 1.39 37.88 30.27 10.12 3.81 5.34 7.62 2.33 6.24 24.61 9.10 31.93 169.19 71.46 32.20 148.77 70.55 59.50 110.77 815.33 533.32 37.15 0.12 2.14 2.12 94.74

Int. (353 ww)” 388(24) 461(29) 538(10) 608(5) 749( 5) (804 w)” 963(13) 1027(19) 1150(48) 1188(17) 1224(52) 1320(142) 1358(52) 1386(56) 1432(101) 1445(104) 1482(67) 1650(57) 1704(406) 1738(782) (2840 ww)” (2948 w)” 3000( *)f 3092( *)f 3430(123) 3439

1739

1644

1442

1219 1312 1365

1021 1165

960

Vapor (IR)C

Matrix (Ar) (IR)C

(1) Freq.

(2)

Experimental data

Computed datab

vvw vw m m w vs w w vw vw w vs w w s m w w w VW vs ww w w w

353 394 478 547 626 773 804 995 1046 1162 1154 1228 1327 1418 1384 1432 1488 1468 1622 1718 1652 2840 2948 3077 3128

356 426 482 563 628 761 808 995 1048 1161 1146 1224 1331 1423 1379 1432 1486 1462 1623 1695 1660 2835 2950 3087 3147 3015 VW m m m vw w m w m w m w s s s m m w m vs vw w w w w m

(Raman)

(IR)

Crystald

3454(98)

315 7) 371(30) 444(13) 641(23) 616(11) 723(0.2) 777(6) 953(12) llOO(6) (1166)(42) 1222(13) 1253(103) 1270( 35) 1394(10) 1436(100) (1454)(51) 1451(168) (1495)(51) 1681(g) 1754(315) 1767(1046) (2881)(55) (2997)(O) 3033(9) 3070( 10)

PredictedC

aFrequencies in cm”, intensities in km mol“. b(l) Scaled with uracil scale factors, (2) scaled with optimized scale factors. CRef. 4. The values in parentheses after the frequencies are absorption intensities. dRef . 2 . eValues taken from the crystal Raman spectrum of ref. 2. fOnly a trace of absorbance is observed.

Approximate assignment

No.

Computed and experimental in-plane vibrational frequencies and intensities of 1-methyluracila

TABLE 6

E3,

;;;

Me-Ring twisting Ring torsion Ring torsion Me-N wagging Ring torsion N-H wagging C-H & C=O wagging C=O wagging C=O & C-H wagging C-H wagging C-H(Me) bend C-H(Me) bend C-H(Me) stretch

Approximate assignment

75 107 188 258 417 647 706 801 830 974 1145 1497 2884

75 109 190 269 421 657 688 780 807 952 1116 1457 2945 43.37

9.73

3.84 0.15 6.78 5.03 17.79 129.69 2.15 4.25 297.22 3.75 8.81 759 (121 m)e (195 w)” (267 XW)~ (446 w)~ 659(86) 712(5) 760( 56) 802(67) 963( 13) (1135 ww)” (1442 w)~ 2945(*)f

Freq.

Freq.

760 800 960

Vapor (IR)C

Matrix (Ar) (IR)=

(2)

(1) Int.

Experimental data

Computed datab

983 w

1438 2980 vw

723 vww

267 vw 446 s

177 w

1135 ww 1442 w 2980 w

w w vw m w m

(Raman)

990 w

195 257 448 869 124 757

(IR)

Clystald

519 669 754 813 921 1157 1505 2931

PredictedC

a-fFootnotes same as in Table 6. ( ) around frequencies means group frequency and intensity transferred for CH, group. Waiue taken from computed data.

38 37 36 35 34 33 32 31 30 29 28 27

39

No.

Computed and experimental out-of-plane vibrational frequencies and intensities of 1-methyluracil*

TABLE 1

297

as being either at 1270 cm-’ or at 963 cm-‘. Our prediction of 974 cm-‘, coupled with the suggestion of 983 cm-’ in the crystal infrared spectrum and of 990 cm-’ in Raman [2], gives unequivocal support to the assignment of the 963 cm-’ in the matrix as v30. For five of the seven fundamentals which were unobserved in the matrix spectra, we can find ready assignments by comparing our computed frequencies with the crystal Raman data, although the discrepancies are likely to be large because of interactions in the solid state. For v37, v3& v35, ~29 and v28, we can choose the crystal Raman frequencies of 195, 267, 446, 1135, and 1442 cm-‘, respectively, as shown in Table 7. There is little evidence to support the assignments of the lowest two absorption bands v3g and Vet. Our predicted intensity for v38 shows that it should not be observed under ordinary conditions in the infrared. It is possible that the 121 cm-’ band assigned to an out-of-plane lattice vibrational mode in the crystal Raman spectrum [2] is really v38 and we have listed it in Table 7 for lack of a better choice. Considering the low predicted intensity, it is also quite likely that this band has never been observed experimentally. For the lowest frequency mode, Vet, we can only take our computed frequency of 75 cm-‘, although errors in this prediction are expected to be large because of the extreme anharmonicity in this periodic motion. It has never been observed experimentally. As might be expected, the agreement between frequencies obtained by scaling the computations with factors transferred from the matrix spectrum of uracil and observed frequencies, taken from a mixture of matrix infrared and crystal Raman experiments is not as good as was found for the in-plane modes, where the experimental data were more satisfactory. The mean deviation for the out-of-plane modes is 18.3 cm-‘, a quantity which would be considered unacceptably large if comparison were possible entirely with matrix or gas-phase data. Optimization of the scale factors on the mixed l-MeU data reduced this value to 11.7 cm-‘, again a value appreciably larger than is customary and an indication that the experimental data from the solid and matrix are not mutually consistent. Nevertheless, within this larger frequency uncertainty, assignment of all except the lowest two out-of-plane vibrational fundamental modes should be considered as established. Is0 topic spectra As a test of the scale factors optimized on the normal l-MeU spectrum and a confirmation of the accuracy of assignments, the vibrational spectra of seven isotopic forms of l-MeU have also been calculated with the results shown in Tables 8 and 9. Neither vapor-phase nor complete matrix isotopic spectra are available, so in Tables 8 and 9 we made a comparison with the spectra of crystal l-MeU observed by Lewis et al. [2]. While the computed results will be most useful to assist in assignments from future matrix or vapor-phase experiments on these isotopic spectra, they can be used in a less

298 TABLE 8 Computed and experimental in-plane vibrational frequencies and isotopic shifts of 1-methyluracil No. Approximate assignment 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

Me-N, C=O def. C=O def. Ring def. C=O, ring def. Ring, C=O def. Ring, Me-N str. Ring def. & str. Ring str. & def. C--H(Me), C-Hdef. C-H.C-H(Me) def. Me-N, ring str. Ring str. Ring str. N-Hdef. C-H, C-H(Me) def. C-H(Me) def. Ring str. C-H(Me) def. Ring str. c,=o str. C,=O str. C-H(Me) str. C-H(Me) str. C-H str. C-H str. N-H str.

MeU Exp.

MeU-21s0 Camp.

356 352 426 392 482 462 563 539 628 620 761 742 808 794 995 960 1048 1020 1161 1151 1146 1199 1224 1239 1331 1313 1423 1360 1379 1385 1432 1425 1486 1446 1462 1487 1623 1650 1695 1716 1660 1740 2840132822 29481) 2956

3oM

3020

31281) 3076 3015 3432

EXP.

Camp.

349 419 480 560 623 755 807 995 1048 1161 1146 1224 1331 1422 1378 1425 1483 1459 1624 1675 1660

350 382 462 533 613 740 791 956 1019 1151 1199 1239 1311 1354 1384 1422 1445 1486 1649 1696 1740 2822 294713 2956 3o75” 3020 3128b 3076 (3015) 3432

MeU-4180 Shift

EXP.

MeU-3-d

Camp. Shift

354 348 418 387 472 455 561 536 626 618 758 742 807 786 993 960 1048 1019 1161 1151 1146 1199 1223 1239 1331 1313 1417 1355 1378 1382 1437 1424 1484 1445 1461 1487 1618 1645 1%/l% 1693 1715 1647 1719 2842b 2822 2947b 2956 3078133020 3128133076 (3015) 3432

Exp.

Camp.

355 352 422 391 480 459 556 531 624 615 752 720 794 771 914 880 1045 1016 1164 1150 1148 1211 127lb 1273 1336 1317 1119 1103 1379 1379 1427 1421 1486 1445 1456 1486 1620 1648 1691 1702 1%/l% 1638 1737 2841b 2822 2936132956 3085b 3020 3129133076 2235 2516

Shift

89618%

21%/19%

26%/27%

Vomputed data using optimized scale factors for 1-methyluracil; experimental data from crystal using the product rule to replace the experimental data which might be misassigned. dF&aasigned TABLE 9 Computed and experimental out-of-plane vibrational frequencies and isotopic shifts of l-methyl No. Approximate assignment 39 38 37 36 35 34 33 32 31 30 29 28 27

MeU-2’sO

MeU Exp.

Comp.

Me-Ring twisting 75 Ring torsion 177b 107 Ring torsion 195 188 Me-N wagging 257 258 Ring torsion 448 417 N-H wagging 869 657 C-H & C=O wagging 724 688 C=O wagging 757 780 C=O & C-H wagging 807 C-H wagging 990 952 C-H(Me) bend 1135b1116 C-H(Me) bend 1438 1457 C-H(Me) stretch 2980 2945

EXP.

Camp.

75 106 184 257 413 655 685 778 804 983b 954 1115 1437 1457 2980 2944 l73b (195 266 b 446b 865 723 755

MeU-4lsO Shift

EXP.

171” 195 256 446b 868 723 758

MeU-3-d

Camp. Shift

1::

186 256 413 654 685 778 804 990 954 ll32b 1115 l443b 1457 2980 2944

aComputed data using optimized scale factors for 1-methyluracil;

Exp.

177b (195 b 264 446b 630 725 752 991 1448 2979

Camp.

Shift

1::

183 256 389 516 685 778 799 954 1115 1457 2944

28%/22%

experimental data from crystal

299

(MeU) and isotopic derivative8 MeUS-d

MeU-5-d EXP.

Comp.

353 423 480 547 614 757 807 995c 1045 861c 1151 1221 1330 1421 1358 1430 1485 1459 1615 1692 1662 2833b 2945b

352 391 461 524 601 739 785 957 1074 857 1193 1212 1311 1357 1369 1421 1441 1486 1638 1715 1737 2822 2956 3omb 3022 2336" 2279 (3015) 3432

Shift

26%/26%

25%/26%

Exp. 353 425 480 561 619 763 808 973d 1049 897d 1149 1219 1330 1420 1242C 1436 1485 1458 1600 1700 1660 2838" 294713 2297 312713 (3015)

CD,U

MeU-5.6-d Comp. 351 392 461 535 610 735 784 991 1026 876 1197 1268 1354 1361 1221 1423 1439 1487 1625 1715 1740 2822 2956 2244 3074 3432

Shift

26%/24%

10%/12%

25%/26%

EXP.

Camp.

350 422 478 543 608 748 800 92oc 1044 834 1157 1221 1349d 1418 1121c 1437 1484 1457 1601 1704 1673 2834" 2945" 2298b 2338" (3015)

351 390 459 520 600 732 780 886 1021 820 1200 1266 1336 1360 1099 1420 1436 1486 1614 1714 1737 2822 2956 2237 2286 3432

Shift

EXP. 313 422 472 564 617 754 808 995 840c

28%/29%

19%/21%

255126% 25%/26%

Camp. 318 387 450 538 609 727 779 967 848

112od

1111

115ld 1223 1317 1427 1387 1060 1465 1084 1624 169C 1659 212313 217313 3076" 3128" (3015)

1197 1236 1295 1361 1391 1063 1432 1086 1647 1714 1740 2026 2191 3020 3076 3432

Shift 14%/10%

20%/17% 4%/4%

2696125% 2696127%

25%/28% 27%/26%

infrared spectra in ref. 2 ; frequencies in cm -*. bRaman data from ref. 2. CThe values estimated by in this work, see text.

uracil (MeU) and isotopic derivative9 MeU-5-d Exp.

MeU-6-d Camp.

75 106 185 (195) 267b 252 446" 412 655 864 582 565 754 735 804 975 929 1115 144213 1457 2980 2944

Shift

EXP.

174’

170

(195)

267b 443b

20%/18%

2%/2%

(8641 717 757 854 1134" 1443b 2980

CD,U

MeU-5.6-d, Camp. 75 106 187 255 373 646 680 736 797 851 1114 1457 2944

Shift

1%/l%

14%/11%

EXP.

Comp.

17lb (195) 259 44213 869 583 755

1:: 187 250 373 646 565 130 814 763 1114 1457 2944

800 1437 2987

Shift

EXP.

19%/18%

54 100 187 247 411 653 686 770 802 956 877 893" 1044 1052 2241 2185

19%/18%

infrared spectra in ref. 2; frequencies in cm-‘. bRaman data from ref. 2.

Camp.

Shift 128%

17ob 195 251 443b 869 124 749

21%/21% 27%/28% 25%/26%

300

precise quantitative way to confirm the earlier assignments of spectra in other phases and to correct possible misassignments. The N-H and C4=0 vibrations are badly perturbed in the crystal by intermolecular hydrogen bonding. The crystal consists of cyclic hydrogen bonded dimers, held together by NB-H---O=C,, hydrogen bonds, as described by Green et al. [26], so the experimental N-H and C=O vibrational frequencies should not, and do not, agree with the frequencies computed for the isolated molecule. For these motions and a few others, we show in Tables 8 and 9 a comparison between the frequency shift on isotopic replacement, as predicted and as observed. The isotopic shifts are seen to be calculated with somewhat greater accuracy than are the absolute frequencies for these bands in the crystal state. In some cases, even the differences in the frequency shifts remain substantial, for example in the N-H wagging motion as disturbed by hydrogen bonding. The assignment of the two C=O stretching fundamentals, v6 and v7, presents an interesting problem. For the parent isotopic species, we predict v7, the mode with the larger contribution from the Cz=O motion, to be the lower frequency member of the pair; the experimental assignment and also work by Szczesniak et al. [4, 51 are in agreement. However, the assignment made by Lewis et al. [2] from the infrared and Raman crystal spectra, has these two modes in the inverse order. There is the possibility of major crystal interactions, further evidence of which is found in the large perturbation of the infrared intensity of v6 that apparently exists in the crystal (see Table 6). Table 8 shows that the inversion of the frequencies of the two modes persists through all of the isotopic species that have been reported. This behavior, coupled with the rather large frequency shift, about 78 cm-‘, observed between the crystal and matrix frequencies of v6 (Table 6), favors the interpretation that the effect is due to crystal interactions. Also, as mentioned above, the crystal structure is such that the C4=0 group is directly involved in hydrogen bonds, leading to dimeric units in the crystal. The assignment of the two C-H deformation modes also presents a special problem since there is a strong coupling between the C-H deformation and the ring stretch. One of the two C-H deformation modes, v17, was assigned at 1161 cm-’ in the crystal infrared spectrum of the parent species by Lewis et al. [2], in agreement with our calculation at 1151 cm-‘. These workers assigned the other C-H deformation mode, vl*, at an unusually low frequency of 995 cm-‘, but our calculated spectra of normal and isotopic species shows that this mode should be at 1385 cm-’ (computed), which can be related to the observed band at 1379 cm-’ in the normal isotopic crystal. This assignment is supported by the fact that the same C-H deformation mode in uracil is around 1360 cm-l, from both theory and experiment [8] . The misassignment of viz in the normal species apparently led to a number of misassignments of the C-H deformation modes in the isotopic spectra of MeU-5d, MeU-Gd, and MeU-5, 6-dz. For this reason, we have had to correct some fundamental frequency assignments and estimate a few frequencies

301

which were not available in ref. 2 by using product rules. These corrections and estimates are identified in Table 8. Infrared intensities Accurate absorption intensities cannot be calculated using a basis set of the size employed in this study. Nevertheless, the predicted intensities have at least qualitative or semi-quantitative significance, and a few comments can be made on their agreement with experiment and with earlier calculations for this molecule. The first conclusion to be drawn from the comparisons shown in Table 6 is that all predictions, in (1) and (2) and in ref. 4, give an intensity pattern for the in-plane modes that is in general agreement with that observed. Of course, the predicted force constants from the 4-21 calculation reported here are expected to be better than those from the STO-3G set, transferred to 1-methyluracil in ref. 4, giving better values for the normal coordinates of the vibrational modes. The difference is most apparent on comparison of the relative intensities of adjacent pairs of vibrations, for example the v14, v15 pair predicted here at 1316 and 1239 cm-‘. Our prediction is that v14 has about 5 times greater intensity than v15, whereas the earlier, more approximate calculation predicted that v 14 (at 1270 cm-‘) was 3 times less intense than v15 (at 1253 km mol-‘). Clearly the normal coordinates of these two modes have been predicted to be different in the two calculations. On the other hand, the intensity sum predicted for the in-plane modes in our calculation (2318 km mallI) is nearly identical with that from ref. 4 (2223 km mol-I),, indicating that the “effective charges” for the atoms are calculated to be nearly the same in both of these calculations. We believe that the primary effect of our improved calculation has been to yield a better set of force constants. These force constants not only predict frequencies in better agreement with experiment, but also predict normal coordinates that combine with atomic polar tensors to give predicted intensities that are in better agreement with experiment than those from earlier calculations. Nevertheless, the earlier predictions [4] are remarkably close to ours in spite of the approximations (primarily of transferability of force constants and intensity parameters) in that earlier calculation. If molecules are as similar as uracil and l-methyluracil, it appears that these parameters can be transferred very successfully. Nevertheless, it is important to point out that severe shortcomings persist at the level of calculation used here, and there are still rather serious discrepancies between the predicted spectral intensities and the experimental ones. For the in-plane modes in Table 6, the largest difference between the intensity pattern in the observed spectrum and that predicted in our calculation is in the predicted intensity ratio of v6 and v7, the C=O stretching modes. We do not believe this difference is very important, since there is considerable complication in the experimental spectrum due to Fermi resonance, which

302

has not yet been analyzed. Furthermore, the predicted intensity ratio depends very strongly on the exact normal coordinate in this region, as shown by the comparison of our predicted ratio A6/A7 = 0.65 with that of ref. 4, &IA, = 3.32. The total intensity predicted in our calculation for all of the carbonyl modes (vg, v7 and v8) is 1459 km mol-‘, in reasonable agreement with the experimental intensity of 1245 km mol-’ or the earlier calculated value [4] of 1370 km mol-‘. We believe this comparison suggests that any apparent discrepancy in this region between calculated and experimental intensities is less than 20%, and may be due either to the Fermi resonance or to errors in normal coordinate mixing. Aside from the carbonyl modes, the only serious errors in the intensity predictions for the in-plane modes in Table 6 are the consistent over-estimation of the intensities for the vibrations of the methyl group, vg, vll, and v14. Most of the difficulty, except for v5, is probably due to incorrect normal coordinates arising from an inadequate basis set. For the out-of-plane modes in Table 7, the intensities predicted here for and v31 are much too large. The worst problem is for vgl, where v27, v34, v35, the predicted intensity is 297 km mole1 compared with an observed relative intensity of only 67. The magnitude of the discrepancy is apparent when we compare the predicted intensity ratio of vjl to the adjacent ~32 to find = 74.2 in contrast with the observed ratio of 1.2. It would be interA31/A32 esting to see the effect of calculation on this ratio by using polarization functions on the heavy atoms. Incidentally, the approximate intensities listed in ref. 4 for the out-of-plane modes were taken from the CNDO calculations of Harsanyi and CsbszGr for uracil and so are not compared with ours in Table 7. Although those values are generally less accurate than the present ones, it is worth noting that the predicted relative intensities give a ratio of A3JA3Z = 0.86,which is in much better agreement with the experimental value than those presented here. ACKNOWLEDGEMENT

This work has been supported by a grant from the Robert A. Welch Foundation. We are grateful to Dr. W. B. Person and Dr. K. Szczepaniak for friendly discussion and helpful criticism. Their remarks on the intensity calculations are particularly illuminating. We also thank Dr. Pal Csiszar and Dr. L. Harsdnyi for their comments and advice. REFERENCES 1 H. Susi and J. S. Ard, Spectrochim. Acta, Part A: 30 (1974) 1843. 2 T. P. Lewis, H. T. Miles and D. Becker, J. Phys. Chem., 88 (1984) 3253. 3 K. Szczepaniak, M. Szczesniak, M. Nowak, I. Scott, S. Chin and W. B. Person, Int. J. Quantum Chem., Quantum Chem., Symp., 18 (1984) 547. 4 M. Szczesniak, M. J. Nowak, K. Szczepaniak, S. Chin, I. Scott and W. B. Person, Spectrochim. Acta, Part A: 41(1985) 223.

303 5 M. Szczesniak, M. J. Nowak, K. Szczepaniak and W. B. Person, Spectrochim. Acta, Part A: 41(1985) 231. 6 S. Chin, I. Scott., K. Szczepaniak and W. B. Person, J. Am. Chem. Sot., 106 (1984) 3415. 7 Y. Nishimura, M. Tsuboi, S. Kato and K. Morokuma, J. Am. Chem. Sot., 103 (1981) 1354. 8 L. Hars&nyi, P. C.&zar, A. Cs&%r and J. E. Boggs, Int. J. Quantum Chem., in press. 9 G. Fogarki and P. Pulay, in B. S. Rabinovitch (Ed.), Annu. Rev. Phys. Chem., Vol. 35, Reviews Inc., Palo Alto, CA, 1984, pp. 191-243. 10 P. Pulay, G. Fogarasi, G. Pongor, J. E. Boggs and A. Vargha, J. Am. Chem. Sot., 105 (1983) 7037. 11 P. Pulay, G. Fogarasi and J. E. Boggs, J. Chem. Phys., 74 (1981) 3999. 12 G. Pongor, P. PuIay, F. Fogarasi and J. E. Boggs, J. Am. Chem. Sot., 106 (1984) 2765. 13 G. Pongor, G. Fogarasi, J. E. Boggs and P. Pulay, J. Mol. Spectrosc., 114 (1985) 445. 14 H. Sellers, P. Puiay and J. E. Boggs, J. Am. Chem. Sot., in press. 15 Z. Niu, K. M. Dunn and J. E. Boggs, Mol. Phys., 55 (1985) 421. 16 K. M. Dunn, P. Pulay, C. Van AIsenoy and J. E. Boggs, J. Mol. Spectrosc., 103 (1984) 268. 17 Y. Dai, K. M. Dunn and J. E. Boggs, J. Mol. Struct. (Theochem), 109 (1984) 127. 18 Y. Kie, K. Fan and J. E. Boggs, Mol. Phys., 58 (1986) 401. 19 K. Fan, Y. Xie and J. E. Boggs, J. Mol. Struct. (Theochem), 138 (1986) 401. 20 K. Fan and J. E. Boggs, J. Mol. Struct. (Theochem), in press. 21 P. Cs&zar, A. C&z&r, L. Harsanyi and J. E. Boggs, J. Mol. Struct. (Theochem), 137 (1986) 207. 22 P. C&&r, A. Cs&szC, A. Somogyi, Z. Dinya, S. Holly, M. Gal and J. E. Boggs, Spectrochim. Acta, Part A: 42 (1986) 473. 23 K. Fan and J. E. Boggs, Tetrahedron, 42 (1986) 1265. 24 P. Pulay, G. Fogarbi, F. Pang and J. E. Boggs, J. Am. Chem. Sot., 101(1979) 2550. 25 P. Pulay, Theor. Chim. Acta (Berlin), 50 (1979) 299. 26 D. W. Green, F. S. Mathewsand A. Rich, J. Biol. Chem., 237 (1962) 3573.