1649
J. Phys. Chem. 1992, 96, 1649-1653
Tautomerism of Uracil: The Final Chapter? Fourth-Order Electron Correlation Contributions to the Relative Energies of Tautomerstis Jerzy Leszczyiiski Department of Chemistry, Jackson State University, 1400 Lynch Street, Jackson, Mississippi 3921 7 (Received: July 29, 1991)
Four of the most important tautomers of uracil were studied by the ab initio LCAO-MO method at the MP2/6-31G**/ /HF/6-31G1* approximation. All calculated structures are minima at the HF/3-21G and HF/6-31G** potential energy surfaces with the dioxo tautomer 1 being the global minimum. Also in a polar environment 1 is predicted to be a predominant form. The stability order of three of the most stable tautomers was determined by using MP4(SDTQ)/6-31G**//HF/6-31G** and CISD/6-3 lG**//HF/6-31G** approximations with inclusion of the HF/6-31G** zero-point-energy (ZPE) corrections. The relative energies of 2-hydroxy-4-oxo (dihydroxy) tautomers amount to 48.0 kJ mol-' (53.8 kJ mol-') and 56.8 kJ mol-' (71.5 kJ mol-') at the MP4 and CISD levels, respectively. The relative tautomers' energies are rather sensitive to the theory level; however, ZPE contributions calculated at the HF/6-31G** approximation are negligible. For the 1 2 transition, at the CISD level), which strongly the calculated MP4 energy gap corresponds to the equilibrium constant of 4 X ol+' suggests that the reported UV detections of the rare uracil tautomer were due to an experimental error.
-
Introduction The essential biological importance of uracil and its derivatives, as well as the relatively small size of the parent uracil molecule, has motivated a number of experimental and theoretical studies of this species. Uracil occurs naturally in RNA, while in DNA it is replaced by thymine, its 5-methyl derivative.' In the Watson-Crick model of the R N A helix, uracil in uridine must adopt the dioxo tautomeric form to be in complementary conformation to the normal, amino tautomer of adenosine. However, in principle, six tautomeric forms of uracil are p o s ~ i b l e . ~Due *~ to the feasible relationship between the occurrence of the rare enol tautomeric forms of uracil and point mutations developing during RNA replications$ a numerous number of studies on all tautomers of uracil have been reported. A recent electron diffractional study has concluded that in the gas-phase uracil exists as planar or near planar dioxo tautomer (l).5Also earlier X-ray crystallographical data available for uracil demonstrates the existence of 1 in the solid state and reveals the major impact of the strong intermolecular hydrogen bonds causing noticeable distortions in molecular geometrya6 The importance of the intermolecular bonds has been confirmed by the recent IR study of crystalline uracil.' Currently, a theoretical study on the basis set dependence of the calculated molecular parameters and one-electron properties of uracil and (di)thiouracils has determined the essential role of the basis set d polarization functions on the second row elements in the molecular geometry optimization and has confirmed that the planar geometry of 1 corresponds to a minimum structure a t all basis sets appliedS8 Examination of the experimental NMR9, UV,'"-'* and IR13J4 data strongly suggests that the dioxo tautomer 1 is stable both in the polar solvents and in the gas phase. The calorimetric measurements of the heats of isomerization by Beak and White provide estimates of the enthalpy difference of 79.4 f 25.5 kJ mol-' (92.0 f 41.8 kJ mol-') between 1 and 4-hydroxy-2-oxo (2,4-dihydroxy) taut o m e r ~ . ' ~However, due to large experimental errors, these data must be examined with caution. The IR studies of uracil in the vapor phase and in the argon and nitrogen inert matrices detected existence of only the dioxo tautomer under the experimental condition^.'^ The theoretical, HF/6-31G* and HF/6-31G** harmonic vibrational frequencies and intensities calculated for 1 are in excellent agreement with the experimental data.16 A variety of theoretical methods have been used to study the tautomerism of the uracil molecule. Among them, semiempirical calculations predict the dioxo tautomer to be the most stable 'This paper is dedicated to Professor Klaus Ruedenberg. *Presentedat the Ab Initio Methods in Quantum Chemistry. An International Symposium in Honor of Professor Klaus Ruedenberg, Ames, Iowa, May 1991.
species (AMl," MIND0/3,I8 INDOI9); however, MND020and MIND0/2*' methods estimate the hydroxy tautomers to be the most stable forms. Quite accurate, the recent AM1 study predicts 1 to be the global minimum with the next stable 2-hydroxy-4-oxo tautomer 2 lying 39 kJ mol-' above, on the uracil potential energy surface.22 However, the same study estimates the next most stable 4-hydroxy-2-oxo species 4 to be more than 13 kJ mol-' higher in energy than 2 and the dihydroxy tautomer 3 to be the fifth lowest energy species, lying 23 kJ mol-' above that of 2. We believe that in spite of some success of semiempirical methods in proper prediction of the global minimum tautomers, the relative stability order and energy of the rare forms might not be reliable at these approximations.
(1) See, for example: Saenger, W. Principles of Nucleic Acid Structure; Springer-Verlag: New York, 1984. (2) Kwiatkowski, J. S.;Zielinski, T. J.; Rein, R. Adu. Quantum Chem. 1986, 18, 85. (3) Les, A.; Adamowicz, L. J . Phys. Chem. 1990, 94, 7021. (4) Lowdin, P. 0. Rev. Mod. Phys. 1963, 35, 724. (5) Ferenczy, G.; Harsanyi, L.; Romndai, B.; Hargittai, I. J. Mol. Srrucr. 1986, 140, 71. (6) Voet, D.; Rich, A. Prog. Nucleic Acid Res. Mol. Biol. 1970, 10, 247. (7) (a) Wojcik, M. J. J . Mol. Srrucr. 1988, 189,239. (b) Piskorz, P. J.; Wojcik, M. J. J . Mol. Srrucr. 1991, 242, 263. (8) Leszczynski, J. Inr. J . Quantum Chem., Quantum Biol. Symp. 1991, 18, 9. (9) Ruterjans, H.; Kaun, E.; Hull, W. E.; Limbach, H. H. Nucleic Acids Res. 1982, 10, 7027. (10) Nowak, M. J.; Szczepaniak, K.; Barski, A,; Shugar, D. 2.Narurforsch. 1978, C33, 876. (11) (a) Fujii, M.; Tamura, T.; Mikami, N.; Ito, M. Chem. Phys. Lerr. 1986, 126, 583. (b) Tsuchiya, Y.; Tamura, T.; Fuji, M.; Ito, M. J . Phys. Chem. 1988, 92, 1760. (12) Brady, B. B.; Peteanu, L. A.; Leavy, D. H. Chem. Phys. Lett. 1988, 147, 538. (13) (a) Shugar, D.; Szczepaniak, K. Inr. J . Quantum. Chem. 1981,20, 573. (b) Szczesniak, M.; Nowak, M. J.; Szczepaniak, K.; Person, W. B.; Shugar, D. J . Am. Chem. Soc. 1983, 105, 5969. (c) Chin, S.;Scot, I.; Szczepaniak, K.; Person, W. B. J . Am. Chem. SOC.1984, 106, 3415. (14) Radchenko, Ye. D.; Scheina, G. G.; Smorygo, N. A.; Blagoi, Yu. P. J . Mol. Strucr. 1984, 116, 387. (15) Beak, P.; White, J. M. J . Am. Chem. SOC.1982, 104, 7073. (16) Szczepaniak, K.; Leszczynski, J.; Person, W. B. Manuscript in preparation. (17) Norinder, U.J. J . Mol. Srrucr. 1987, 151, 259. (18) Czerminski, R.; Lesyng, B.; Pohorille, A. Inr. J . Quantum Chem. 1979, 16, 605. (19) Saunders, M.; Webb, G. A.; Tute, M. S.J . Mol. Srrucr. 1987, 158, 69. (20) Buda, A.; Sygula, A. J. Mol. Strucr. (THEOCHEM) 1983,92, 255. (21) Zielinski, T. J.; Rein, R. Inr. J . Quantum Chem. 1978, 14, 851. (22) Katritzky, A. R.; Karelson, M. J . Am. Chem. Soc. 1991. 113, 1561.
0022-3654/92/2096-1649%03.00/0 0 1992 American Chemical Society
1650 The Journal of Physical Chemistry, Vol. 96, No. 4, 1992
Leszczy Aski
n
W 2
1
W 4
3 Figure 1. 2,4-Dioxo (l),2-hydroxy-4-oxo (2), 2,4-dihydroxy (3), and 2-oxo-4-hydroxy (4) tautomers of uracil.
More accurate data conceming uracil tautomerism are expected to arise from ab initio calculations. Low-level, STO-3G//STO-3G calculations predict the energy gap of 28 kJ mol-] between 1 and 4,23while the 3-21G//3-21G theory level estimates relative energies of 2 and 4 to be equal to 72 and 82 kJ mol-', respecti~ely.~~ Recently, a few more rigorous ab initio studies, including electron correlation effects at the second-order perturbation theory, have been p u b l i ~ h e d . ~ The ~ - ~ estimated ~ at this level relative energy of 2 is in the range of 4 4 4 6 kJ In spite of the theoretical and experimental predictions that the most stable tautomer is the dioxo form either in the gas phase or in the polar environment, it is not clear what is the relative stability of the rare tautomers. Recently Fujii et al. provided UV spectroscopic indications of the rare tautomers of uracil." Later however, Brady et al. claimed their observed spectra resulted from unidentified impurities.I2 The IR study on uracil in the gas phase and in the inert matrices reported the exclusive presence of 1," but this spectroscopic method is incapable of detecting rare forms in amounts less than ca. 0.1-1.0%,'3a and, indeed, on the basis of this data, the presence of the rare species under the IR experimental conditions cannot be ruled out. Very recent theoretical studies on 2-thio-, 4-thio- and dithio~ r a c i l s ~ have ~ ~ *raised - ~ ~ the question, what is the relative stability (23) Zielinski, T. J. Inr. J . Quanrum Chem. 1982, 22, 639. (24) (a) Scanlan, M. J.; Hillier, I. H. Chem. Phys. Lea. 1983, 98, 545. (b) Scanlan, M. J.; Hillier, I. H. J . Am. Chem. SOC.1984, 106, 3737. (25) Kwiatkowski, J. S.;Bartlett, R. J.; Person W. B. J . Am. Chem. Soc. 1988, 110. 2353. (26) Les, A.; Adamowicz, L. J . Phys. Chem. 1989, 93, 7078. (27) Gould, I. R.; Hillier, I. H. J . Chem. Soc., Perkin Trans. 2 1990, 329. (28) Rostkowska, H.; Szczepaniak, K.; Nowak, J. M.; Leszczynski, J.; KuBulat, K.; Person, W. B. J . Am. Chem. SOC.1990, 112, 2147. (29) Leszczynski, J.; Lammertsma, K. J . Phys. Chem. 1991, 95, 3128.
order of uracil tautomers? These calculations indicate that the relative energies of thiouracils, especially the order of the second and third most stable tautomers, are very sensitive on the theory level. While at the HF/3-21G* level (all calculations reported were carried out at HF/3-21* geometries), the second most stable tautomers are mercaptwthione and mercapto-hydroxy forms for dithio- and thiouracils, respecti~ely;~~-~O at the MP2/6-31* zero-point energy ( D E ) (dithi~uracil)~~ or MBPT(Z)/DZ + ZPE thiouracil^)'^ levels, the relative energy orders change and the dimercapto (mercapto-hydroxy) tautomer becomes the next most stable form instead, with the relative energy of 28 kJ mol- (dit h i ~ u r a c i l ) ,27 ~ ~kJ mol-] (2-thio~racil),~O and 38 kJ mol- (4thiouracil)?0 respectively. The fact that the uracil moiety occurs in a new, nonclassical nucleic acid base pyrazolo[4,3-d]pyrimidine5,7(4H,6H)-dione (designated as A) deserves the comparison between these systems. Our recent ab initio study on A indicates a very high sensitivity of the dihydroxy tautomer on the applied theory level.32 While at the HF/3-21G//HF/3-21G level, this tautomer is the fourth most stable structure, lying 112 kJ mol-' above the global minimum energy of the dioxo species; the MP2/6-3lG**//HF/3-21G ZPE approximation reverses the stability order and sets the dihydroxy tautomer as the third most stable species with the relative energy of 71 kJ Limitations in computer resources prohibited geometry optimization and further studies of A at the higher levels of theory. Since the dihydroxy tautomer of uracil has not been considered by any of the recent studies, the question arises whether a reported
+
+
(30) Les, A.; Adamowicz, L. J . Am. Chem. SOC.1990, 112, 1504. (31) (a) Katritzky, A. R.; Bakut, G.; Rachwal, S.; Szafran, M.; Caster, K. C.; Eyler, J. J . Chem. Soc., Perkin Trans 2 1989, 1499. (b) Katritzky, A. R.; Szafran, M.; Stevens, J. J . Chem. Soc., Perkin Trans 2 1989, 1507. (32) Leszczynski, J. Chem. Phys. Lett. 1991, 181, 123.
The Journal of Physical Chemistry, Vol. 96, No. 4, 1992 1651
Tautomerism of Uracil TABLE I: Total Enerdes (-a111of Uracil Tautomers HF/3-21G//HF/3-21G HF/6-31G**//HF/3-21G HF/6-3 lG**//HF/6-3 1G** ZPEa(HF/3-21G) ZPEa(HF/6-3 1G**) CISD/6-31G**d MP2/6-3 lG**d MP3/6-3 lG**d MP4(D)/6-31G**d MP4(DQ)/6-3 1GSSd MP4(SDQ)/6-31G**d MP4(SDTQ)/6-31GSSd
1 410.163 10 412.480 43 412.481 83 -0.095 32 -0.094 49b 413.289 17 41 3.660 8 1 4 13.674 02 413.699 52 413.675 89 413.69241 413.742 19
2 410.13568 412.46099 412.463 42 -0.094 03 -0.094 51' 413.267 53 413.643 43 413.65739 413.68234 413.65774 413.673 20 413.723 87
3 410.124 62 412.458 16 412.461 78 -0.093 02 -0.09441 413.261 93 413.64305 413.656 78 413.681 40 413.65571 41 3.669 7 1 413.721 63
a Zero-point energies (uncorrected). bGould and Hillier calculated ZPE(HF/6-31G**) to be equal to 0.094 60 au.*' dCalculated at the HF/6-31GS* geometries.
previouslyzstautomers' order is an artifact of the older, lowquality calculations. Moreover, an accurate prediction of the relative energies of the rare uracil tautomers is crucial for the determination of whether the minor tautomer can be observed by experimental methods and what is the probability of the formation of mispairs which involve the rare tautomers of the uracil nucleotide. Also such a rigorous study can help understand the oxo-hydroxy tautomerism of the larger systems for which uracil might be considered as a parent compound. It is the goal of our research to examine the tautomerism of the uracil molecule. In this paper we are presenting the results of the high-quality ab initio study on the basis set and electron correlation contribution (up to the full fourth-order Moller-Plesset theory and configuration interaction approximation including all single and double excitations) effects on the relative stability of the four uracil tautomers (Figure l), including dihydroxy uracil. Recently, we applied the ab initio method to study the tautomeric equilibria of 2,4-dithioura~il,~~ guanine,33 9-meth~lguanine,~~ adenine,33av35 2,6-diamino~yrimidine,~~ pyrazolo[4,3-d]pyrimidine-S,7(4H,6H)-di0ne,~* and 2-mercapto~yrimidine.~~
Method The ab initio LCAO-MO method3*was used for the study of the four tautomers of uracil. All calculations reported were performed with the GAUSSIANE~program.39 The optimizations of molecular geometries were carried out within C, symmetry, at the HF/3-21G and HF/6-31G** levels, by the gradient procedure.40 All optimized structures were checked by analysis of harmonic vibrational frequencies obtained from diagonalization of force constant matrices at the 3-21G level. Additonally, harmonic vibrational frequencies were calculated for 1 and 3 at the 6-31G** level, while those for 2 and 4 were taken from Gould and Hillier's papereZ7 Excluding translational and rotational motions, only positive eigenvalues of the Hessian matrix were obtained, proving that the calculated tautomer geometries are minima on the HF/3-21G and HF/6-31G** potential energy surfaces of uracil. The sum of zero-point energies for all nor(33) (a) Kwiatkowski, J. S.; Leszczynski, J. J . Mol. Struct. ( T H E 0 CHEM) 1990,208,35. (b) Leszczynski, J. Chem. Phys. Lett. 1990,174,347. (34) Szczepaniak, K.; Szczcsniak, M.; Szajda W.; Leszczynski, J.; Person, W. B. Can. J. Chem. 1991, 69, 1705. (35) Nowak, M. J.; Lapinski, L.; Kwiatkowski, J. S.; Leszczynski, J. Spectrochim. Acta 1991, 47A, 87. (36) Leszczynski, J. Chem. Phys. Lett. 1990, 173, 371. (37) Nowak, M. J.; Rostkowska, H.; Lapinski, L.; Leszczynski, J.; Kwiatkowski, J. S. Spectrochim. Acta 1991, 47A, 339. (38) k, for example: Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbital Theory; John Wiley and Sons: New York, 1986. (39) Frisch, M. J.; Head-Gordon, M.; Schlegel, H. B.; Raghavachari, K.; Binkley, J. S.; Gonzales, C.; DeFrees, D. J.; Fox, D. J.; Whiteside, H. B.; Seeger, R.; Melius, C. F.; Baker, J.; Martin, L.; Kahn, L. R.;Stewart, J. J. P.; Fluder, E. M.; Topiol, s.; Pople, J. A. GAUSSIANSS; Gaussian, Inc.: Pittsburgh, PA, 1988. (40) Schlegel, H. B. J . Comput. Chem. 1982, 3, 314.
4 4 10.132 00 412.45763 412.460 12 -0.094 07 -0.094 SO' 413.641 18
From Gould and Hillier.27
TABLE 11: Relative Enereies (kJ mol-') of Uracil Tautomers 1 2 3 4 HF/3-21G//HF/3-21G 0 72.1 101.2 81.8 HF/6-31G**//HF/3-21G 0 51.0 58.5 59.9 HF/6-31G**//HF/6-31G** 0 48.3 52.6 56.9 MP2/6-31G**" 0 43.5 44.5 49.4 TOTb 0 43.3 44.3 49.5 TOT' 0 45.7 51.7 CISD/6-31GS*' 0 56.8 71.5 MP3/6-3 lG**" 0 43.7 45.3 MP4(D)/6-3lG**" 0 45.1 47.6 MP4(DQ)/6-31G**a 0 47.6 53.0 MP4(SDQ)/6-3 lG**" 0 50.4 59.6 MP4(SDTQ)/6-3 1G* *' 0 48.1 54.0 TOTd 0 48.0 53.8 "Calculated at the HF/6-3lG** geometries. MP2/6-31GS*// HF/6-31G** energies corrected for 0.9 scaled ZPE(HF/6-31G**). 'Could and Hillier:27 MP2(FULL)/6-31G**//HF/6-3lG** energies corrected for ZPE(HF/6-31G**). dMP4(SDTQ)/6-31G**//HF/631G** energies corrected for 0.9 scaled ZPE(HF/6-31G**).
mal-mode vibrations scaled by a recommended factor of 0.941 approximates the ZPE contribution. The calculations of total electronic energies of all of the tautomers were performed at the level of second-order Moller-Plesset perturbation theory (MP2)42using the frozen core approximation, with Pople's split valence basis set augmented by two sets of polarization functions, d-orbitals on each second-row atom and p-orbitals on hydrogens (MP2/6-31G**//HF/6-3 1G** level). Additionally, for three of the most stable tautomers at this level, electron correlation contributions were calculated at the full fourth-order level of MP theory (MP4(SDTQ) level). Also configuration interaction (CI) calculations were performed for 1-3, including all single and double excitations (CISD). In all calculations, a frozen-core approximation was used to prevent electronic excitations from inner-shell orbitals. Our final set of relative energies was corrected for scaled ZPE energy differences. Results and Discussion The total internal energy (PT of) a molecule can be calculated at its optimum geometry on the potential energy surface as a sum of the energy calculated at the Hartree-Fock level (EHF),the electron correlation energy contributions (ECO"), and scaled zero-point vibrational energy (ZPE) ETOT = EHF + E m " + ZPE
We carried out two sets of calculations, at the HF/3-21G and HF/6-3 1G** geometries, followed by computations of the harmonic vibrational frequencies, to study the basis set dependence of the energy of the four uracil tautomers (Figure 1). Table I (41) (a) Pople, J. A.; Schlegel, H. B.; Krishnan, R.; DeFrees, D. J.; Binkley, J. S.; Frisch, M. J.; Whiteside, R. A.; Hout, R. F.; Hehre, W. J. Int. J. Quantum Chem. Symp. 1981, I S , 269. (b) DeFrees, D. J.; McLean, A. D. J. Chem. Phys. 1985, 82, 33. (42) Mdler, C.; Plesset, M. S. Phys. Reu. 1934, 46, 618.
1652 The Journal of Physical Chemistry, Vol. 96, No. 4, 1992 I
120.0
100.0
Leszczydski
n-i
I I
I I
/
80.0
I
i
I
w.0
40.0
20.0
0.0
0.0 c
I c
-. I
.20.0
MP2
Figure 2. Plot of the relative energies versus theoretical levels. A11 energies are relative to that of 1. TOT are the MP2/6-31G**//HF/631G** + 0.9 ZPE(HF/6-31G**) relative energies.
presents the H F energies, determined at different theory levels, as well as various electron correlation and ZPE contributions, while the relative energies are given in Table 11. All electron correlation contributions were calculated at the HF/6-31G** geometries with the 6-31G** basis set. Clearly, the dioxo tautomer 1 is the most stable species at all theoretical levels. Simultaneously, the relative stabilities of the other tautomers are basis set and correlation energy dependent (Figure 2). As the theory level improves, all rare tautomers are stabilized; however, the most pronounced basis set effect is observed on the relative energy of the dihydroxy tautomer 3. This observation is in line with the previous study on thiouracils (dithiouracils), where the single-point MP2/DZ (MP2/6-3 1G*) calculations carried out a t the HF/3-21G* geometries reversed the relative stabilities of the hydroxy-thione vs hydroxy-mercapto (dithione vs dimercapto) tautomers calculated at the HF/32 1G*//HF/3-2 1G* levels and placed hydroxy-mercapto (dimercapto) species as the second most stable tautomers on the potential energy surface of 2-thi0-~Oand 4 - t h i o u r a ~ i l s(dithio~~ uracils29). Although uracil tautomer 3 is the fourth most stable species at the HF/3-21G//HF/3-21G approximation with the relative energy of 101 kJ mol-], improvement of the theoretical level significantly reduces this number to 44 kJ mol-I at the MP2/6-31G**//HF/6-31G** level. At this level 3 lies 1 kJ mol-I above the second most stable tautomer 2; moreover, zero-pointenergy corrections at the HF/6-31G1* geometry decrease this estimate by some 0.1 kJ mol-I. Interestingly, if the ZPE corrections were calculated at HF/3-21G geometries (routine procedure in less rigorous calculations), 3 would be the second most stable tautomer lying 0.6 kJ mol-' below 2. It should be noted that while ZPE corrections calculated at the HF/3-21G geometries stabilize relative energies of rare tautomers by as much as 3 kJ mol-] (4), this effect is significantly reduced at the HF/6-31G** level, and, as it was argued recently by Kwiatkowski et al.25and Gould and Hiller,27we found out that for all considered species ZPE corrections are negligible, being equal to or less than 0.2 kJ mol-'. At this level our relative energy of 2 (43 kJ mol-') is very close to those calculated by Gould and Hillier (46 kJ mol-') at the MP2(Fu11)/6-31G**//HF/6-3lG** ZPE(HF/6-31G**) level2' and by Les and Adamowicz (44 kJ mol-') at the MBPT( 2)/DZP//HF/3-2 1G + ZPE( HF/3-2 1G) leveLZ6 Since at the MP2 level the relative energies of 2 and 3 are virtually the same, we carried out further, more rigorous calculations of the electron correlation energy contributions for the three most stable tautomers 1-3 up to the full fourth-order MrallerPlesset theory (MP4(SDTQ)) level and also through a variational configuration-interaction scheme (CI). Therefore, we can conclude
+
MP4(D)
MP4(SOP)
161
Figure 3. Plot of the relative energies versus CISD and higher-order electron correlation contributions for dioxo, 2-hydroxy-44x0, and dihydroxy tautomers. All energies are relative to that of 1. TOT are the MP4/6-31G**//HF/6-31G** + 0.9 ZPE(HF/6-31G**) relative ener-
gies.
that at the MP2 level over 93% of the MP4(SDTQ) electron correlation energy has been recovered (93.5%, 93.6%, and 93.8% for 1-3, respectively), while at the relatively inexpensive version of the MP4 approximation without triple substitutions (MP4(DSQ)) almost 96% of full MP4 energy has been recovered. Although at the CISD level only about 64% of the MP4(SDTQ) correlation energy has been recovered, one should realize deficiencies of both approximations. While the Morller-Plesset perturbation theory is not variational and can produce an energy below the true energy, CI calculations are variational, but at the S D approximation are not size consistent. Indeed, more important than the calculated absolute percentages of the electron correlation energy are descriptions of molecular potential surfaces. Figure 3 graphically illustrates the dependence of the relative energies of 2 and 3 upon different contributions to the electron correlation energies. Higher-order contributions stabilize the dioxo tautomer 1; however, this effect is the most pronounced at the CISD approximations where relative energies of 2 and 3 are 56.8 and 71.5 kJ mol-', respectively. Similar observation has been made in the energy evaluation of 2-pyridone and 2-hydroxpyridine systems. CISD calculations at the DZP (DZP = double-{ basis set augmented with polarization functions) level stabilize the oxo opposite to the trends observed when the correlation energy was introduced within MP2 theory." Also the recent coupled-cluster study on the same species with single, double, and triple excitations concludes that the higherorder corrections stabilize the oxo Contrary to the second-order correlation energy correction effects, the relative energies of the rare forms of uracil increase upon including higher-order contributions (except the triple substitutions) to the Mraller-Plesset energy, resulting in the "best estimate" of the MP4 results of 48 and 54 kJ mol-' for 2 and 3, respectively. At this level the energy gap between 2 and 3 amounts to 6 kJ mol-'. Our results are in line with the recent coupledcluster studies by Adamowicz et al. toward the estimation of the higher-order-correlation effects on the position of the tautomeric equilibria for cytosine& and 2-hydro~ypyridine.~~ In both cases the higher-order effects are not negligible, and they shift the tautomeric equilibrium toward the oxo form^.',*^,^^ The relative stabilities of the different tautomeric forms are of fundamental importance for a prediction of the probability of (43) Moreno, M.;Miller, W. H.Chem. Phys. Left. 1990, 171, 475. (44) Schlegel, H. B.; Gund, P.; Flueder, E. M. J . Am. Chem. SOC.1982, 104, 5347. (45) Adamowicz, L. Chem. Phys. Lett. 1989, 161, 73. (46) Les, A.; Adamowicz, L.; Bartlett, R. J. J . Phys. Chem. 1989, 93, 4001.
The Journal of Physical Chemistry, Vol. 96, No. 4, 1992 1653
Tautomerism of Uracil TABLE III: Dipole Moments (D) of Uracil Tautomers species 1
HF/3-21G//HF/3-21G 4.79
HF/6-31G**//HF/3-21G 4.86
HF/6-31G**//HF/6-31GS* 4.72
2 3 4
3.41 1.55 5.15
3.61 1.29 5.25
3.49 1.31 5.25
MP2/6-31G*//MP2/6-31G* 4.21
exp 3.86O 4.16b
"Reference 48. Derived from the microwave spectrum of uracil. bReference 49. Measured in dioxane solution.
spontaneous mutations.47 The 2.3 kJ mol-' increase in the tautomerization energy calculated by us, relative to the results of G~uld-Hiller,~~ corresponds to a prediction of a reduction in the relative concentration of the rare tautomer by a factor of 2.5 (4 X lo4 vs lo-*). Calculated at the CISD approximation, relative concentration of the rare tautomer is even smaller and amounts to 1O-Io. These results strongly support the theoretical26 and experimental conclusions12that UV detections of the rare uracil tautomer by Tsuchiya et al.II were due to an experimental error. In Table I11 we gathered calculated and experimental dipole moments. Our best theoretical dipole moment for 1 (4.72 D), calculated at the HF/6-31G**//HF/6-3 1G** approximation, overestimates by 22% the gas-phase value,48 which indicates perhaps the limitations of the HF geometry optimization with a medium-size basis set. The difference between the gas-phase dipole moment available for and the ab initio data is larger than in the case of the comparison with the value from dioxane solut i ~ (1 n 3%). ~ ~ Interestingly, our calculated dipole moment is in better agreement with the experimental data than that calculated recently at the experimental uracil geometry by Basch et al. (5.67 and 4.85 D a t the HF/DZ and MP2/DZ levels, respecti~ely).~~ However, inclusion by these authors of d-polarization basis functions with the exponents optimized to minimize the dipole moment magnitude significantly improves calculated dipole moments (5.20 and 4.43 D at the H F and MP2 levels, respecti~ely).~~ Also good agreement between the theoretical and the experimental data has been obtained by Jasien and Fitzgerald in the dipole moment from local density functional (LDF) calculations using a double numerical orbital basis set with d- (4.54 D) and p-,dpolarization (4.73 D) function^.^^ Somewhat disappointing, this minor improvement of the basis set quality in the LDF calculations significantly increases the calculated dipole moment. In contrast, inclusion of the correlation energy at the a b initio theory level allows for a significant refinement of the calculated dipole moment (4.21 D at the MP2/6-31G**//MP2/6-31G* To be able to analyze the dependence of calculated dipole moments upon the applied theory level, two contributions, arising as a result of the improvement of the basis set applied to the geometry optimization, should be separated. The effects of p,d-polarization functions on the calculated dipole moments can be studied by comparing the HF/3-21G//HF/3-21G and HF/ 6-3 lG**//HF/3-21G results, while the comparison between HF/6-31G**//HF/3-21G and HF/6-31G**//HF/6-31G** data allows for analysis of the molecular geometry dependence of the (47) Drake. J. W. Nature 1969. 221. 1132. (48) Brown; R. B.; Godfrey, P. D.; McNaughton, D.; Pierlot, A. P. J . Am. Chem. SOC.1988,110, 2329. (49) Kulakowska, I.; Geller, M.; Lesyng, . . B.; Wierzchowski, K. L. Biochim. Biophys. Acta 1974, 361 119. (50) Basch, H.; Garmer, D. R.; Jasien, P. G.; Krauss, M.; Stevens, W. J. Chem. Phys. Lett. 1989, 163, 514. (51) Jasien, P. G.; Fitzgerald, G. J . Chem. Phys. 1990, 93, 2554. (52) Leszczynski, J. To be published.
calculated dipole moments. The calculated dipole moments of all tautomers, given in Table 111, show little sensitivity to the theoretical level applied. This effect is the most pronounced in the case of 2, coincidently the most substantial basii set dependence of the relative energy observed for this tautomer. The knowledge of physicochemical properties of the isolated uracil is requested for prediction of the interactions of this species with various biochemical environments. Qualitatively, the interaction between different solutes (tautomers) and a constant polar solvent (environmental effects) can be correlated to the magnitude of the solute dipole moment. Although the calculated dipole moment of tautomer 4 is 0.5 D larger than that of 1, its high relative energy excludes this species from being observed in the polar solutions, and, consequently, the same order of the relative stability has been predicted for the gas phase and for the polar solutions.
Conclusions The important conclusions from the present study can be summarized as follows. (1) Dioxo tautomer 1 is the global uracil minimum with an energy difference of 48.0 kJ mol-' at the MP4/6-31G**// HF/6-31G** + ZPE level (56.8 kJ mol-l a t the CISD/631G**//HF//6-31G** level) with the oxo-hydroxy tautomer 2. Also in the polar solvents, 1 is predicted to be the most stable structure. (2) The relative energies of uracil tautomers, especially the order of the second, the third, and the fourth most stable tautomers, are very sensitive to the theory level. Our calculations have concluded that the third most stable species is dihydroxy tautomer 3, lying some 5.8 kJ mol-' above the 2-hydroxy-4-oxo species at the MP4 level (14.7 kJ mol-' a t the CISD approximation). (3) The dominant effects stabilizing the rare tautomers arise from the presence of the basis set polarization functions (especially d-orbitals on the second-row elements). Also electron correlation effects are essential for the accurate prediction of the relative energies. While MP2 corrections stabilize rare tautomers, higher-order corrections which are not negligible, as well as CISD approximation, shift the tautomeric equilibrium toward the dioxo form. However, at the HF/3-21G level, ZPE energies are of the order of a few kilojoules per mole; they are negligibly small (0.2 kJ mol-]) a t the HF/6-31G** level. (4) Calculated from the MP4 energy differences, the equilib rium constant for the room-temperature 1 2 transition is equal to 4 X (1O-Io at the CISD approximation). +
Acknowledgment. This study was supported by a contract (DAAL 03-89-0038) from the Army High Performance Computing Research Center. The Minnesota Supercomputer Institute and the Mississippi Center for Supercomputing Research are acknowledged for their generous allotments of computer time. Registry No. 1, 66-22-8; 2, 138260-29-4; 3, 51953-14-1; 4, 13828560-6.
