Interplay of Experiment and Theory: Determination of an Accurate

Article pubs.acs.org/JPCA

Interplay of Experiment and Theory: Determination of an Accurate Equilibrium Structure of 1‑Methyluracil by the Gas Electron Diffraction Method and Coupled-Cluster Computations Natalja Vogt,*,†,‡ Ilya I. Marochkin,‡ Anatolii N. Rykov,‡ and Olga V. Dorofeeva‡ †

Chemieinformationssysteme, University of Ulm, 89069 Ulm, Germany Department of Chemistry, Moscow State University, 119992 Lomonosov Moscow, Russia

‡

S Supporting Information *

ABSTRACT: As far as fundamental knowledge is concerned, the methyl derivatives of uracil can be considered as the simplest objects for studying the structural effects due to the substitution in the pyrimidyne nucleobases. From this point of view, 1-methyluracil is of special importance in biochemistry because uracil attaches ribose in ribonucleic acid (RNA) just precisely at the N1 atom. The semi-experimental equilibrium structure (rse e ) of 1methyluracil has been determined for the first time by the gas electron diffraction (GED) method taking into account rovibrational corrections to the thermal-average internuclear distances calculated with harmonic and anharmonic (cubic) MP2/cc-pVTZ force constants with consideration of the methyl torsion as a large-amplitude motion. For the first time, the structure of the molecule has been optimized by the very time-consuming coupled-cluster method with single and double excitations and perturbative treatment of connected triples using the correlation-consistent polarized weighted core−valence triple-ζ basis set with all electrons being correlated (CCSD(T)(all)/cc-pwCVTZ) and extrapolated to the complete basis set (CBS) with the help of the MP2 calculations. Small differences between similar bond lengths of equilibrium configurations were assumed in the GED analysis at the CCSD(T)(all)/CBS values. A remarkable agreement between the semi-experimental and computed equilibrium structures points out the high accuracy of both the GED determination and the coupled-cluster computations. The effect of methylation on the structure of uracil has been analyzed.

1. INTODUCTION After uracil,1 thymine,2 and adenine,3 1-methyluracil (see Figure 1 for atom numbering) is the next topic of our systematic

attaches ribose in ribonucleic acid (RNA) just precisely at the N1 atom. The equilibrium molecular structure of the non-substituted uracil has already been determined with high accuracy both from experimental data (GED1 and microwave spectroscopy (MW)6) and by high-level theoretical computations.1,6 In contrast, the structure of 1-methyluracil has neither been investigated in the gas phase nor computed at the level of coupled-cluster theory. Among the four methyl derivatives of uracil, only the molecular structure of two of them with the methyl group at the C atom (5-methyluracil (thymine)2,7 and 6-methyluracil8) has been studied previously by MW and/or GED as well as theoretical methods. According to the results of these studies,2,7,8 both C-substituted uracils have a planar ring and Cs total symmetry. Moreover, the ring in the thymine molecule is a rigid one with the lowest harmonic vibrational frequency ν39 (ring torsion) of 112.5 cm−1 (MP2(full)/ cc-pVTZ),2 and the methyl group is stabilized because of a relatively large barrier to internal rotation of 6.3 kJ mol−1 (MW7 and MP2(full)/cc-pVTZ2) as well as by two weak hydrogen bonds (GED2) between the methyl hydrogen and oxygen atoms. In contrast, N1-substituted uracil, 1-methyluracil, seems to be more

Figure 1. Molecular model of 1-methyluracil with atom numbering.

investigations of the molecular structure of nucleobases and their derivatives by the gas electron diffraction (GED) method. It is known as a component of some natural products which can be isolated (see, for example, ref 4). Along with other pyrimidine bases, the uracil derivatives are used for the production of many drugs which have a wide use in medicine.5 As far as fundamental knowledge is concerned, the methyl derivatives of uracil can be considered as the simplest objects for studying the structural effects due to the substitution in the pyrimidyne nucleobases. From this point of view, the determination of molecular structure of 1-methyluracil is of special importance because uracil © 2013 American Chemical Society

Received: August 19, 2013 Revised: October 4, 2013 Published: October 29, 2013 11374

dx.doi.org/10.1021/jp408297f | J. Phys. Chem. A 2013, 117, 11374−11381

The Journal of Physical Chemistry A

Article

flexible molecule because it has a large-amplitude motion with ν39(A″) = 46 cm−1 (B3LYP/6-31G(d,p)).9 It should be noted, that the torsion of the methyl group at the same nitrogen atom of the pyrimidine ring in the caffeine molecule has been successfully described in ref 10 as a large-amplitude motion by application of a dynamic model (so-called pseudo-conformer model). Besides the thermal-average (ra)2 and isotopic substitution (rs)7 structures, the accurate semi-experimental equilibrium 2 structure (rse e ) has been determined for thymine, whereas only the ra structural parameters have been obtained for 6methyluracil.8 However, because the structural changes due to the substitution by the methyl group are expected to be of the same order of magnitude as the vibrational contributions to the thermal-average bond lengths, the determination of the equilibrium structure is required. Moreover, for the correct comparison of the structural data from different experimental methods, they should be of the same type. In this respect, the equilibrium structure seems to be very convenient since it is also a result of quantum-chemical optimization. Concerning the structure of 1-methyluracil, there are only a few data derived from experiments. Thus, the infrared (IR) matrix isolation spectra of this molecule have been successfully analyzed under the assumption of the Cs total symmetry (see ref 9 and references therein). The crystal structure of 1methyluracil has been determined by X-ray11 and neutron diffraction12 methods, but as usual it is expected to be very different from the structure of a free molecule. The purpose of the present work is the determination of a reliable and accurate structure of 1-methyluracil by the GED method and coupled-cluster computations. Moreover, the problem of complementary use of experimental and computational results will be discussed. The structural changes due to methyl substitution in uracil will be also analyzed.

treatment of connected triples17 (CCSD(T)) using the correlation-consistent polarized weighted core−valence tripleζ basis set (cc-pwCVTZ),18 with all electrons being correlated (denoted as all). The coupled-cluster diagnostic,19 T1, was calculated at the same level of theory. The structure optimizations were also carried out at the level of the second-order Møller−Plesset perturbation theory (MP2)20 with (all) or frozen core (fc) approximation (in the following “fc” is the default) with Dunning’s correlationconsistent polarized valence double-, triple-, and quadruple-ζ (cc-pVnZ (n = D, T, Q))21 and core−valence cc-pwCVnZ (n = T, Q)18 basis sets as well as at the level of the Kohn−Sham density functional theory (DFT) with Becke’s three-parameter hybrid exchange functional22 and the Lee−Yang−Parr correlation functional23 (together denoted as B3LYP) with the cc-pVTZ basis set. The harmonic and anharmonic (cubic) force constants were calculated in the MP2/cc-pVnZ (n = D, T) approximations. All the CCSD(T) calculations were performed with the MOLPRO program package. 24 The MP2 and B3LYP calculations were performed with the GAUSSIAN03 (Rev.E.01)25 or GAUSSIAN09 (Rev.C.01)26 program packages. The calculations were carried out on the computer cluster with quad-, six-, and sixteen-core processors.

4. RESULTS OF THEORETICAL CALCULATIONS AND DISCUSSION The potential energy (PE) of the molecule as a function of the torsional coordinate φ(C6−N1−C7−H10) describing the rotation of the methyl group around the N1−C7 bond was calculated in the interval from 0 to 60° with steps of 10° and with optimization of all other geometrical parameters in the B3LYP/cc-pVTZ and MP2/cc-pVnZ (n = D, T) approximations. The theoretical results (see Figure 2) are apparently somewhat conflicting.

2. GED EXPERIMENT A commercial sample (Aldrich) with a purity ≥99% was used without further purification. The GED experiment was carried out at the Moscow State University on the EG-100 M apparatus at an electron beam current of 1.9 and 2.0 μA for the long (LD = 362.28 mm) and short (SD = 193.94 mm) nozzle-to-film distances, respectively, and with a vacuum of 2 × 10−5 mm Hg. The diffraction patterns were recorded on photo films (MACO EM-FILM EMS). The necessary sample pressure of a few Torr was reached at 446(3) K. The wavelength of electrons was calibrated by means of CCl4 whose structural parameters are accurately determined.13 Its fluctuation during the experiments at LD and SD distances was about 0.1% and 0.02%, respectively. The diffraction patterns were scanned at the University of Ulm using the EPSON PERFECTION V750 PRO commercial scanner in the 16-bit/300dpi scanning mode. The calibration of the scanner was carried out using a gray scale for Kodak ektachrome films. The scanned data were transformed into intensity curves I(s) using the UNEX program14 which follows the method described in ref 15. The background lines were approximated by cubic splines. The experimental intensities I(s) were averaged in the ranges of s = 3.5−18.0 Å−1 (LD) and s = 8.25−32.0 Å−1 (SD) in steps of 0.125 Å−1. The averaged I(s) curves are presented in the Supporting Information, Figure 1S and Table 1S.

Figure 2. Calculated PE function of internal rotation of methyl group around the N1−C7 bond (relative energy in kJ mol−1, coordinate φ(C6−N1−C7−H10) in deg) for 1-methyluracil.

Thus, the PE function in the MP2/cc-pVTZ approximation has only one minimum at φ = 0°, whereas at the B3LYP/ccpVTZ and MP2/cc-pVDZ levels, besides the global minimum, it has also a very small second minimum with depth of a few cm−1 at φ = 60°. However, the cc-pVDZ basis set is too small to give reliable results. On the other hand, the effects of van der Waals dispersion forces27 are not taken into account by the B3LYP method. For these reasons, the second minimum might

3. COMPUTATIONAL DETAILS The molecular structure was optimized by the coupled-cluster method with single and double excitation16 and a perturbative 11375



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Table 1. Experimental and Computed Structural Parameters of 1-Methyluracila parameter

GEDb (static(−1)) se rse e /∠e

GEDb (dynamic) se rse e /∠e

GEDb (static(−1)) rg

B3LYP/ VTZc re/∠e

MP2/ VTZc re/∠e

MP2(all)/ wCVTZc re/∠e

MP2(all) /wCVQZc re/∠e

CCSD(T)(all) /wCVTZc re/∠e

CCSD(T)(all) /CBSd re/∠e

r(N1−C2) r(C2−N3) r(N3−C4) r(C4−C5) r(N1−C6) r(N1−C7) r(C2O8) r(C4O9) r(C7−H10) r(C7−H11,12) r(N3−H13) r(C5−H14) r(C6−H15) r(C5C6) ∠(N1−C2−N3) ∠(C2−N3−C4) ∠(N3−C4−C5) ∠(C2−N1−C6) ∠(C2−N1−C7) ∠(N1−C2O8) ∠(N3−C4O9) ∠(N1−C7−H10) ∠(N1−C7−H11,12) ∠(C4−C5−H14) ∠(C5C6−H15) ∠(C2−N3−H13) ∠(C4−C5C6) ∠(N1−C6C5) ∠(C6−N1−C7) ∠(N3−C2O8) ∠(C5−C4O9) ∠(C6−N1−C7−H11) Rf(LD)k Rf(SD)k Rf,totk

1.382(1)e 1.375(1)e 1.394(1)e 1.447(3)f 1.372(1)e 1.451(3)f 1.210(1)g 1.211(1)g 1.086(4)h 1.087(4)h 1.009(4)h 1.076(4)h 1.081(4)h 1.343(24)i 114.5(5) 128.2(2) 113.1(3) 121.3(4) 116.3(6) 122.6(7) 120.3(5) 108.4j 110.2j 118.9j 121.9j 115.3j 119.9(6)i 123.0(9)i 122.4(7)i 123.0(8)i 126.6(6)i 120.2j 1.69 3.26 2.25

1.383(2)e 1.376(2)e 1.395(2)e 1.451(3)f 1.374(2)e 1.455(3)f 1.211(1)g 1.213(1)g 1.090(4)h 1.092(4)h 1.013(4)h 1.081(4)h 1.085(4)h 1.352(33)i 114.7(6) 127.8(3) 113.1(3) 122.2(6) 113.3(7) 122.9(9) 120.2(8) 108.4j 110.2j 118.9j 121.9j 115.3j 120.7(6)i 121.5(10)i 124.5(9)i 122.4(12)i 126.7(9)i 120.2j 1.59 3.81 2.44

1.394(1) 1.386(1) 1.406(1) 1.458(3) 1.383(1) 1.464(3) 1.215(1) 1.216(1) 1.107(4) 1.108(4) 1.029(4) 1.097(4) 1.101(4) 1.351(24)

1.395 1.379 1.406 1.451 1.371 1.461 1.213 1.214 1.086 1.088 1.010 1.077 1.081 1.346 114.2 128.4 112.8 121.2 116.8 122.3 120.5 108.6 110.4 118.5 121.7 115.3 119.8 123.3 122.2 123.7 126.6 120.2

1.388 1.379 1.402 1.449 1.369 1.456 1.218 1.219 1.085 1.087 1.011 1.076 1.081 1.351 113.9 128.8 112.7 121.5 116.3 122.4 120.7 108.3 110.2 119.0 121.8 115.0 120.0 123.5 122.0 123.5 126.7 120.2

1.3841 1.3751 1.3978 1.4452 1.3655 1.4516 1.2148 1.2161 1.0833 1.0849 1.0095 1.0750 1.0791 1.3460 113.94 128.76 112.68 121.48 116.35 122.36 120.71 108.37 110.22 118.95 121.73 115.07 119.84 123.31 122.17 123.70 126.61 120.24

1.3814 1.3732 1.3952 1.4431 1.3642 1.4502 1.2138 1.2152 1.0825 1.0840 1.0091 1.0743 1.0785 1.3448 114.08 128.59 112.83 121.46 116.38 122.35 120.62 108.37 110.28 118.94 121.74 115.16 119.78 123.27 122.17 123.57 126.55 120.24

1.3870 1.3784 1.3984 1.4538 1.3747 1.4570 1.2133 1.2145 1.0865 1.0876 1.0089 1.0766 1.0806 1.3479 113.99 128.61 113.13 121.49 116.51 122.47 120.58 108.33 110.26 118.89 121.87 115.18 119.39 123.39 122.00 123.54 126.29 120.17

1.3823 1.3751 1.3939 1.4501 1.3724 1.4546 1.2115 1.2129 1.0851 1.0860 1.0082 1.0754 1.0795 1.3457 114.23 128.32 113.39 121.45 116.57 122.45 120.43 108.35 110.19 118.88 121.89 115.33 119.29 123.32 121.98 123.32 126.18 120.18

a

Bond lengths in Å, bond angles in deg. bUncertainties given in parentheses are 3σ. cBasis sets cc-pVTZ, cc-pwCVTZ and cc-pwCVQZ denoted as VTZ, wCVTZ and wCVQZ, respectively. dCCSD(T)(all)/cc-pwCVTZ structure after extrapolation to CBS, see text. e,f,g,hParameters with the same superscript were refined in one group. Differences between parameters in each group were assumed at the value of the CCSD(T)(all)/CBS structure. iDependent parameter. jAssumed according to the CCSD(T)(all)/CBS structure. kRf factors for the LD and SD nozzle-to-film distances and total Rf (in %), respectively.

equation from ref 28), whereas its eclipsed position is less stable because the single hydrogen bond O8···H10 of 2.26 Å has energy only 12.5 kJ mol−1. It should be noted that the molecular configuration with two weak hydrogen bonds H···O= has been found to be preferable also for thymine.2 Finally, the structural parameters of 1-methyluracil were optimized for the Cs molecular configuration by the very timeconsuming CCSD(T)(all)/cc-pwCVTZ method (one step of optimization needed about 10 days on a 12-core PC). The results are presented in Table 1. The T1 diagnostic of 0.014 calculated at the same level is less than 0.02. Therefore, the nondynamic electron correlation is not very important,19 and the computed CCSD(T)(all)/cc-pwCVTZ structure is expected to be reliable. The small structural changes due to the extrapolation to the higher or complete basis set (CBS) as well as due to the inclusion of the diffuse-function effects can be estimated for the CCSD(T) structure rather well at the MP2 level (see, for example, refs 1, 6, 29, 30.). Therefore, the structural parameters

be an artifact. Furthermore, the low barrier to internal rotation (ca. 0.4, 0.8, and 1.2 kJ mol−1 in the B3LYP/cc-pVTZ, MP2/ cc-pVDZ, and MP2/cc-pVTZ calculations, respectively, that is, less than 1/2 RT = 1.9 kJ mol−1) points to an almost free rotation of the methyl group at the experimental temperature. The results of the structure optimization at the B3LYP and MP2 levels are presented in Table 1. The stability of the optimized structure was confirmed by frequency calculations, all of which were found to have non-imaginary values at these levels. The harmonic vibrational frequencies are listed in Supporting Information, Table 2S and compared with the experimental values from IR (Ar) spectra.9 Thus, in the equilibrium configuration, the molecule has a planar ring and the methyl group possesses a staggered configuration relative to the N1−C2 bond (Cs total symmetry). The staggered configuration of the CH3 group is stabilized because of two weak hydrogen bonds H11···O8 and H12···O8 of about 2.68 Å with energy of 15 kJ mol−1 (estimated according to the 11376



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the molecule. In the last one, the large-amplitude torsion of the methyl group was considered separately as governed by the computed PE function. It was revealed that the GED model was not sensitive to the form of the functions shown in Figure 2. Therefore, the following simple expression was applied:

computed in the CCSD(T)(all)/cc-pwCVTZ approximation were extrapolated to the the CBS using results of MP2(all)/ cc-pwCVTZ and MP2(all)/cc-pwCVQZ calculations presented in Table 1. The extrapolation was performed according to Helgaker’s formula:31 re(MP2(all)/CBS) =

n3r(n) − (n − 1)3 r(n − 1) n3 − (n − 1)3

V (φ ) = (1)

(3)

where the constant V3 was assumed at the value of 1.2 kJ mol−1 from MP2/cc-pVTZ calculation. The kinetic energy function was calculated for seven points of the coordinate φ(C6−N1−C7− H10) in the interval from 0 to 60° with a step of 10°, that is, for the equilibrium configuration and six pseudo-conformers. The parameters of each of the pseudo-conformers were refined together with the corresponding parameters of the equilibrium configuration assuming differences between them (so-called relaxation effects) at the values from MP2/cc-pVTZ calculation (see Figure 3).

where n = 4, r(n) and r(n − 1) denote the MP2(all)/ cc-pwCVQZ and MP2(all)/cc-pwCVTZ structural parameters. Thus, the re(CCSD(T)(all)/CBS) structure was estimated according to the following expression: re(CCSD(T)(all)/CBS) = re(CCSD(T)(all)/cc‐pwCVTZ) + re(MP2(all)/CBS) − re(MP2(all)/cc‐pwCVTZ)

1 V3(1 − cos 3φ) 2

(2) 1

As it has been shown for uracil, at the MP2(all)/ccpwCVQZ level, the diffuse-function32 effects are negligibly small for the bond lengths between the C, N, and O atoms, except for the CO ones, for which they reach only 0.001 Å. Therefore, they were not calculated for 1-methyluracil. The CCSD(T)(all)/CBS structure presented in Table 1 seems to be very accurate as it is derived by considering practically all computational effects of significant level. For organic molecules, the accuracy of such a structure, named, as best ab initio,1,6 is estimated to be of the order of a few thousandths of Å units for the bond lengths and a few tenths of degree for the bond angles (see, for example, refs 1, 6, 33.), that is, it is even better than that of the GED method.1

5. GED STRUCTURAL ANALYSIS AND DISCUSSION Being very close to each other (see Table 1), some bond lengths in the 1-methyluracil molecule could not be separated by the GED method. Therefore, they were refined in groups with differences assumed at the theoretical values. The molecular model of Cs total symmetry was described by 24 equilibrium structural parameters (bond lengths re and bond angles ∠e) with some of them being combined in the groups as follows: (1) r(N1−C2), r(C2−N3), r(N3−C4), and r(N1− C6); (2) r(C4−C5) and r(N1−C7); (3) r(C2O8) and r(C4O9); (4) r(N3−H13), r(C5−H14), r(C6−H15), r(C7−H10), and r(C7−H11,12); (5) ∠(N1−C2−N3); (6) ∠N3−C4−C5; (7)∠(C2−N3−C4); (8) ∠(C2−N1−C6); (9) ∠(C2−N1−C7); (10) ∠(N1−C2O8); (11) ∠(N3−C4 O9); (12) ∠(N1−C7−H10); (13) ∠(N1−C7−H11,12); (14) ∠(C4−C5−H14); and (15) ∠(C5−C6−H15). The C5C6 bond length was determined as a dependent parameter. Because of weak electron scattering on the light atoms, the positions of the hydrogen atoms could not be determined. Therefore, the equilibrium bond angles involving these atoms were fixed at the theoretical values as shown in Table 1. The equilibrium bond lengths of each group were refined simultaneously with differences between them assumed at the values of CCSD(T)(all)/CBS structure. According to the results of theoretical calculations (see above), the methyl group undergoes an almost free rotation. As it was shown in ref 10 (see Introduction), this large-amplitude motion can be described by the model of pseudo-conformers with different torsional angles of methyl group. Therefore, the structural analysis of 1-methyluracil was carried out in the present work using both the static and the dynamic models of

Figure 3. Changes of some structural parameters (so-called, relaxation effects) during rotation of the methyl group in 1-methyluracil (bond lengths in Å, bond angle in deg) according to MP2/cc-pVTZ calculations.

The rovibrational corrections to the experimental bond lengths ra, Δ(ra − re), were calculated at the level of the firstorder perturbation theory taking into account nonlinear kinematic effects34,35 by means of the SHRINK program.34,36 The harmonic (including also centrifugal distortions due to vibrations37) and anharmonic vibrational contributions were calculated with quadratic and cubic force constants, respectively, in the MP2/cc-pVTZ or MP2/cc-pVDZ approximation. Corrections for the centrifugal distortion effect due to overall rotation38 and rotational−vibrational interaction39,40 were also included. It was revealed that the rovibrational corrections calculated with MP2/cc-pVTZ and MP2/cc-pVDZ force constants are relatively close to each other. Therefore, for the equilibrium configuration, they were calculated with the MP2/cc-pVTZ force field, whereas for each of the pseudo-conformers, they were estimated using the less time-consuming MP2/cc-pVDZ approximation. 11377



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Table 2. Vibrational Corrections Δ(ra − re) to Internuclear Distances ra, Calculated uh1, and Experimental uexp rms Vibrational Amplitudes (in Å) of 1-Methyluracil (static(−1) model) term N3−H13 C5−H14 C6−H15 C7−H10 C7−H12 C7−H11 C2O8 C4O9 C5C6 N1−C6 C2−N3 N1−C2 N3−C4 C4−C5 N1−C7 H11···H12 H10···H12 H10···H11 C2···H13 C4···H13 N1···H10 N1···H15 N1···H12 N1···H11 C6···H14 C5···H15 C4···H14 H10···H15 N3···O9 N3···O8 N1···O8 N1···N3 N3···C5 C5···O9 N1···C5 C2···C6 C2···C7 C4···C6 O8···H13 O9···H13 H14···H15 C6···C7 C2···C4 C6···H10 C7···H15 N3···C6 O8···H12 O8···H11 O9···H14 C2···H12 C2···H11 C7···O8 N1···C4

ra 1.024 1.092 1.096 1.102 1.103 1.103 1.213 1.215 1.349 1.382 1.385 1.393 1.404 1.456 1.462 1.780 1.793 1.793 2.032 2.063 2.087 2.093 2.111 2.111 2.123 2.133 2.192 2.231 2.275 2.279 2.289 2.332 2.384 2.385 2.399 2.412 2.418 2.425 2.468 2.471 2.479 2.488 2.500 2.545 2.639 2.679 2.691 2.691 2.695 2.705 2.705 2.708 2.825

Δ(ra − re)a 0.0152 0.0155 0.0154 0.0155 0.0160 0.0160 0.0034 0.0035 0.0062 0.0095 0.0097 0.0105 0.0104 0.0089 0.0109 0.0172 0.0164 0.0164 0.0088 0.0094 0.0201 0.0163 0.0185 0.0185 0.0112 0.0106 0.0111 0.0174 0.0120 0.0086 0.0120 0.0137 0.0110 0.0089 0.0118 0.0090 0.0135 0.0086 0.0045 0.0090 0.0073 0.0100 0.0090 0.0108 0.0145 0.0103 0.0155 0.0155 0.0080 0.0152 0.0152 0.0178 0.0117

uh1b 0.070 0.074 0.075 0.076 0.076 0.076 0.038 0.038 0.043 0.045 0.046 0.047 0.048 0.048 0.049 0.123 0.123 0.123 0.100 0.102 0.103 0.098 0.103 0.103 0.099 0.096 0.103 0.202 0.058 0.056 0.056 0.056 0.059 0.060 0.054 0.057 0.069 0.057 0.136 0.139 0.161 0.067 0.059 0.143 0.139 0.066 0.204 0.204 0.140 0.159 0.159 0.104 0.064

uexpc d

0.070 0.074d 0.075d 0.076d 0.076d 0.076d 0.041(1)e 0.041(1)e 0.046(1)e 0.048(1)e 0.049(1)e 0.050(1)e 0.051(1)e 0.051(1)e 0.052(1)e 0.123d 0.123d 0.123d 0.100d 0.102d 0.103d 0.098d 0.103d 0.103d 0.099d 0.096d 0.103d 0.202d 0.056(2)f 0.055(2)f 0.054(2)f 0.055(2)f 0.058(2)f 0.059(2)f 0.053(2)f 0.056(2)f 0.068(2)f 0.056(2)f 0.136d 0.139d 0.161d 0.066(2)f 0.058(2)f 0.143d 0.139d 0.065(2)f 0.204d 0.204d 0.140d 0.159d 0.159d 0.103(2)f 0.063(2)f

term

ra

Δ(ra − re)a

uh1b

uexpc

C2···C5 C6···H12 C6···H11 N1···H13 C5···H13 C2···H10 C2···H15 N3···H14 N1···H14 H12···H15 H11···H15 C4···H15 C6···O8 C6···O9 C2···O9 C4···O8 N3···C7 C6···H13 C5···C7 N3···H15 O8···H10 C5···H10 C2···H14 N3···H11 N3···H12 N1···O9 C5···O8 H13···H14 C4···C7 C5···H11 C5···H12 O8···H15 N3···H10 C7···H13 O9···H15 O8···O9 H10···H14 C7···H14 H11···H13 H12···H13 C4···H10 C4···H11 C4···H12 H13···H15 O8···H14 H12···H14 H11···H14 H10···H13 C7···O9 O9···H12 O9···H11 O9···H10

2.834 3.204 3.204 3.232 3.299 3.322 3.358 3.371 3.379 3.396 3.396 3.428 3.525 3.558 3.568 3.587 3.652 3.686 3.731 3.761 3.773 3.882 3.913 3.986 3.986 4.029 4.040 4.208 4.274 4.362 4.362 4.365 4.400 4.433 4.487 4.534 4.556 4.601 4.649 4.649 4.741 4.757 4.757 4.766 5.117 5.258 5.258 5.273 5.474 5.925 5.925 5.932

0.0091 0.0178 0.0178 0.0126 0.0100 0.0180 0.0157 0.0132 0.0163 0.0188 0.0188 0.0134 0.0081 0.0050 0.0064 0.0055 0.0139 0.0091 0.0096 0.0159 0.0207 0.0049 0.0122 0.0163 0.0163 0.0068 0.0056 0.0096 0.0096 0.0171 0.0171 0.0140 0.0143 0.0111 0.0072 0.0015 0.0057 0.0121 0.0125 0.0125 0.0042 0.0154 0.0154 0.0126 0.0065 0.0191 0.0191 0.0091 0.0017 0.0076 0.0076 −0.0078

0.064 0.113 0.113 0.094 0.095 0.102 0.097 0.096 0.174 0.174 0.094 0.095 0.060 0.061 0.063 0.064 0.068 0.095 0.068 0.097 0.122 0.146 0.095 0.167 0.167 0.065 0.066 0.129 0.072 0.127 0.127 0.107 0.113 0.112 0.103 0.076 0.186 0.113 0.209 0.209 0.134 0.158 0.158 0.118 0.097 0.152 0.152 0.136 0.073 0.173 0.173 0.137

0.063(2)f 0.113d 0.113d 0.094d 0.095d 0.102d 0.097d 0.096d 0.094d 0.174d 0.174d 0.095d 0.067(3)g 0.068(3)g 0.070(3)g 0.071(3)g 0.075(3)g 0.095d 0.076(3)g 0.097d 0.122d 0.146d 0.095d 0.167d 0.167d 0.074(3)h 0.074(3)h 0.129d 0.081(3)h 0.127d 0.127d 0.107d 0.113d 0.112d 0.103d 0.084(3)h 0.186d 0.113d 0.209d 0.209d 0.134d 0.158d 0.158d 0.118d 0.097d 0.152d 0.152d 0.136d 0.082(3)h 0.173d 0.173d 0.137d

a

Calculated with quadratic and cubic force constants in the MP2/cc-pVTZ approximation. bCalculated with quadratic MP2/cc-pVTZ force constants. cUncertainties given in parentheses are 3σ. dThe rms amplitudes for internuclear distances involving hydrogen atom(s) were assumed at the theoretical values. e,f,g,hAmplitudes with the same superscript were refined in one group. Differences between amplitudes in each group were fixed at the theoretical values.

applied method,34,35 and their errors can be several times larger than the calculated values themselves. Therefore, the vibrational

It should be noted, that the vibrational contributions of the large-amplitude motion cannot be accurately calculated by the 11378



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corrections were calculated with and without the contribution of the lowest-energy vibration with ν39(A″) = 64 cm−1 (MP2/ cc-pVTZ, see Supporting Information, Table 2S) and used in the models named as static(1) and static(−1), respectively. Fitting the theoretical model to the experimental molecular intensity sM(s) was carried out by means of the program UNEX.14 A strong decrease of the disagreement factor Rf from 4.3% (static(1) model) to 2.3% (static(−1) model) confirmed that the poorly estimated weak vibrational contributions should be omitted rather than used (see also ref 41). Following ref 10, in the applied dynamic model, the excluded lowest-energy vibration was replaced by the torsion of the methyl group around the N1−C7 bond. However, this coordinate is not a pure mode: its contribution to the PE distribution (PED) calculated with the SHRINK program34,36 is of 62%, whereas 16% of PED are contributed by the N1 outof-plane coordinate. Thus, the one-dimensional dynamic model, taking into account only the methyl torsion, seems to be not exact enough in the case of 1-methyluracil. The total rovibrational corrections Δ(ra − re) to the experimental internuclear distances ra for the static(−1) model are presented in the Table 2 together with rms vibrational amplitudes, uh1, calculated with the quadratic force constants (MP2/cc-pVTZ) using the SHRINK program.34,36 In the GED analysis, vibrational amplitudes for the atom pairs consisting of hydrogen atom(s) could not be determined accurately, and, therefore, they were fixed at the theoretical values. The calculated corrections Δ(ra − re) to the bond lengths ra(CO), ra(CC), ra(C−C), ra(C−N), ra(N−H), and ra(C−H) of the order of 0.003, 0.006, 0.009, 0.011, 0.015, and 0.016 Å, respectively, (see Table 2) are rather close to those for uracil1 and thymine.2 This fact confirms that the uncertainties in the rovibrational corrections for the middle-size organic molecules are about 10% of their values.42 The results of the GED analysis are presented in Table 1. The experimental molecular intensity curves sM(s) and their theoretical counterparts for the final structural model as well as the difference curves ΔsM(s) (experiment − theory) are shown in Figure 4, whereas the corresponding radial distribution curves f(r) and Δf(r) are shown in Figure 5.

Figure 5. Experimental (open circles) with damping factor of exp(−0.0015s2) and theoretical (solid line) radial distribution curves f(r) for the static(−1) model with vertical bars of the terms. Difference curve Δf(r) = f(r)exp − f(r)theor.

As it can be seen from Table 1, the dynamic model does not improve the quality of the experimental analysis in comparison to the static(−1) model: the experimental uncertainties of the structural parameters in this model are larger and the Rf factor is slightly higher than those in the static(−1) one. A strong relaxation of the C2−N1−C7 bond angle at the large-amplitude torsion of the methyl group (see Figure 3), not being compensated by its decrease due to the out-of-plane vibration of the N1 atom, leads to a decrease of the equilibrium value of this angle in the one-dimensional dynamic model. This is why this angle in the dynamic model is smaller than that in the static(−1) one as well as in the CCSD(T)(all)/CBS structure. Unfortunately, the two-dimensional dynamic model is still a challenge for the GED theory. Therefore, the structural parameters determined for the static(−1) model are preferable, and they are recommended as the final results (see column 1 in Table 1).

6. COMPARISON OF STRUCTURAL DATA FOR METHYL DERIVATIVES OF URACIL The comparison of the equilibrium structural parameters of the methyl derivatives of uracil with those of uracil (see Table 3) shows that the methyl group causes several changes in the pyrimidine ring, namely, the elongation of the adjacent equilibrium bond lengths, that is, r(N1−C2) and r(N1−C6) in 1-methyluracil and r(C4−C5) and r(C5C6) in 5methyluracil, as well as the decrease of the adjacent bond angle, that is, ∠(C2−N1−C6) and ∠(C4−C5C6) in 1methyluracil and 5-methyluracil, respectively. The decrease of the ring angle at the substituent leads to the corresponding increase of the other angles in the ring. Whereas the systematic changes in the bond lengths, being of the same order as the experimental uncertainties, can be seen well only in the computed values; the decrease of the bond angles is so strong that it can be observed also experimentally. Besides the experimental uncertainties, the vibrational effects disturb the observation of substitution effects in the thermal-average

Figure 4. Experimental (open circles) and theoretical (solid line) molecular intensity curves sM(s) for the long (above) and short (below) nozzle-to-film distances and difference curves ΔsM(s) = sM(s)exp − sM(s)theor. 11379



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Table 3. Comparison of Structural Parameters of Uracil and Its Methyl Derivativesa uracil

1-methyluracil

5-methyluracil (thymine)

parameter

b GED(rse e)

calc(re)b,c

d MW(rse e)

e GED(rse e)

calc(re)e,f

g (GED)(rse e)

N1−C2 N1−C6 C2−N3 N3−C4 C4−C5 C5C6 C2O C4O N1−C2−N3 C2−N3−C4 N3−C4−C5 C4−C5C6 N1−C6C5 C2−N1−C6 N1−C2O N3−C4O

1.381(2) 1.374(2) 1.379(2) 1.402(2) 1.454(8) 1.339(18) 1.210(1) 1.212(1) 113.0(2) 128.0(3) 113.6(3) 120.0(3) 121.6(4) 123.8(3) 122.6(5) 119.9(5)

1.380 1.373 1.378 1.401 1.458 1.345 1.211 1.213 113.5 127.7 113.8 119.7 121.7 123.6 122.8 120.4

1.38175(53) 1.37196(55) 1.3763 1.39793(40) 1.45500(57) 1.34496(59) 1.21025(21) 1.21278(24) 113.383 127.942 113.860(22) 119.516(16) 121.924(10) 123.374(19) 123.883(44)

1.382(1) 1.372(1) 1.375(1) 1.394(1) 1.447(3) 1.343(24) 1.210(1) 1.211(1) 114.5(5) 128.2(2) 113.1(3) 119.9(6) 123.0(9) 121.3(4) 122.6(7) 120.3(5)

1.382 1.372 1.375 1.394 1.450 1.347 1.212 1.213 114.2 128.3 113.4 119.3 123.3 121.5 122.5 120.4

1.377(3) 1.372(3) 1.378(3) 1.395(3) 1.466(9) 1.344(16) 1.210(1) 1.215(1) 112.8(5) 128.0(5) 114.8(5) 117.6(6) 123.1(5) 123.7(5) 123.1(9) 120.6(12)

6-methyluracil

MW(rs)h

GED(ra)i

1.34(5) 1.355(7) 1.42(2) 1.384(4) 1.457(4) 1.370(7)

1.390(3) 1.395(3) 1.384(3) 1.407(3) 1.455(10) 1.336(20) 1.225(5)f

113.7(8) 126(2) 115.5(3) 117.3(4) 122.8(3) 124.3(10)

114.1(5) 126.3(7) 114.3(5) 121.6(5) 119.7(5) 124.0(4) 123.5(15) 123.3(10)

a Bond lengths in Å, bond angles in deg. bRef 1. cCCSD(T)(all)/cc-pwCVTZ structure after extrapolation to the higher basis set, cc-pwCVQZ, and inclusion of diffuse-function effects. dRef 6. ePresent work. fCCSD(T)(all)/cc-pwCVTZ extrapolated to CBS at the MP2 level. gRef 2. hRef 7. iRef 8. j Average value of two CO bond lengths.

structure of 6-methyluracil.8 Nevertheless, the strong decrease of the angle ∠a(N1−C6C5) in the pyrimidine ring due to methyl substituent is observed also for this molecule.

from the experimental data permits to check the quality of theoretical calculations. On the other side, accurately computed molecular parameters can help to revise a theoretical model used in experimental analysis. Remarkable agreement between the equilibrium structure derived from the GED data (see first column of Table 1) and that one computed at the level of coupled-cluster theory CCSD(T)(all)/CBS (last column of Table 1) demonstrates the great success of complementary use of the experimental data with accurate theoretical predictions of the small changes in the similar bond lengths which cannot be determined by GED experiment. This success opens wide perspectives for the interplay of experiment and theory in the studies of other fine structural effects. The modern computational techniques enable to perform the accurate structure calculations for the middle-size bio-organic molecules at the very high level of theory (CCSD(T)(all)/ccpwCVTZ with extrapolation to the CBS at the MP2 level) with an accuracy rivaling the best GED determinations (see also ref 1).

7. INTERPLAY OF EXPERIMENT AND THEORY. CONCLUDING REMARKS As it was shown above (see GED structural analysis), the molecular structure of such a complex molecule as 1methyluracil with a large number of structural parameters cannot be determined completely from the GED data alone: very close bond lengths cannot be separated because of the low resolution of the method; the parameters involving hydrogen atom(s) cannot be determined because of weak electron scattering by the light atoms; some other parameters cannot be determined because of high correlation, and so on. Quantumchemical computations can support experiment if they yield the results of high accuracy. Otherwise, the theoretical assumptions will be a source of additional errors in the experimental analysis. For example, according to results of the B3LYP/cc-pVTZ and MP2/cc-pVTZ calculations (see Table 1), the difference between the N1−C2 and N1−C6 bond lengths, Δ(N1−C), is of 0.014 Å and 0.019 Å, respectively, whereas in the CCSD(T)(all)/CBS structure it is equal to 0.010 Å. Thus, in the GED structural analysis, the use of the Δ(N1−C) value from the B3LYP or MP2 (with cc-pVTZ basis set) calculations instead of that from the CCSD(T)(all)/CBS structure leads to an additional systematic error of up to 0.005 Å for each of these bond lengths. There is the same problem with the N1−C2 and C2−N3 bond lengths: their difference, Δ(C2−N), is equal to 0.016 Å in the B3LYP/cc-pVTZ approximation, whereas it is only 0.007 Å in the CCSD(T)(all)/CBS structure. It is remarkable that the use of the accurate values of the bond length differences from the CCSD(T)(all)/CBS structure instead of those from the B3LYP/cc-pVTZ or MP2/cc-pVTZ ones improved the fit with a decrease of the Rf factor from 4.8 to 4.3% (static(1) model). In other words, the GED experiment confirms that the CCSD(T)(all)/CBS structure is more accurate than that from the B3LYP and MP2 calculations. Thus, the determination of the accurate equilibrium structure

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ASSOCIATED CONTENT

S Supporting Information *

Complete references 24−26. Experimental total intensity curves I(s) and background lines for 1-methyluracil (Figure S1 and Table S1). Comparison of theoretical harmonic vibrational frequencies with experimental data for 1-methyluracil (Table S2). This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Prof. J. Demaison for helpful discussions. This study was supported by the Dr. Barbara Mez-Starck Foundation 11380



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(Germany) and the Russian Foundation for Basic Research (Grant Nos. 11_03_00716_a and 12_03_91330_HHNO_a).

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Interplay of Experiment and Theory: Determination of an Accurate

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