Double Proton Transfer: From the Formamide Dimer to the Adenine

Christian Kramer , Peter Gedeck , and Markus Meuwly ... Jacqueline C. Hargis , Esteban Vöhringer-Martinez , H. Lee Woodcock , Alejandro Toro-Labbé ,...
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J. Phys. Chem. 1994,98, 4142-4141

4142

Double Proton Transfer: From the Formamide Dimer to the Adenine-Thymine Base Pair Vojtech Hrouda,? Jan FloriBn,S Martin Polt%ek,t and Pave1 Hobza'J J . Heyrovsk$ Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, Dolejjkova 3, 182 23 Prague 8, Czech Republic, and Institute of Physics, Charles University, Ke Karlovu 5, 121 16 Prague 2, Czech Republic

Received: November 29, 1993; In Final Form: February 15, 1994"

The cylic formamide dimer was used as a model system for the investigation of proton-transfer phenomena in D N A base pairs. The section of the potential energy surface (PES) in the coordinates of transferring protons was studied using a wide set of computational methods, from semiempirical (PM3,MNDO-M) to the ab initio MP2/DZ+2P level of theory. Three qualitatively different patterns of stationary points wereobtained, depending on the computational method used. The MP2/DZ+2P calculation resulted in two minima on the PES, corresponding to the amino-keto and iminc-enol tautomeric forms, separated by a low-lying transition state. The amino-keto tautomer was found to be more stable than the imino-enol one by 15.6 kcal/mol.

Introduction The undoubted biological importance of hydrogen-bonded systems is reflected in a growing quantum-chemical interest in proton-transfer phenomena.' In particular, an exceedingly important role is played by those complexes which are stabilized by several hydrogen bonds. In these bonds multiple proton transfer may occur and this is believed to form a physical ground for numerous processes of biological importance including enzymatic reactions2s3and transport phenomena in biological membranes.4~5 Moreover, double proton transfer (DPT) in DNA base pairs has been hypothesized as a possible source of spontaneous point mutations in DNA.6J Naturally, among nucleic acid base pairs the guanine-cytosine (GC) and the adenine-thymine (AT) complexes have been studied most extensively (only a few representative papers for tha AT are citeds-20). Because of the size of the AT and G C base pairs, however, merely gross approximations could be applied to them and lower computational levels could have been used. Obviously, precise solutions to the problem of the kinetics and dynamics of double proton transfer in its complexity may be found only by using a background of the anharmonic vibrational approach with sufficient dimensionality of the coordinate space. Keeping this "exact" description of the multiple proton transfer as an ultimate goal, we have been proceeding in the following steps. First, we studied the structures, interaction energies, and harmonic vibrational spectra of the AT and A*T* (iminwnol tautomeric structure) base pairs using semiempirical (AMl,PM3) and ab initio (HF/MINI-1) methods.2' Second, we located the transition state for the DPT in the AT molecule at the HF/MINI-1 level.22 The energy barrier between the canonical and tautomeric minima was found to be very low. We interpreted this fact as a clear argument against the possible role of the DPT in the point mutagenesis, as was suggeted by LOwdin.6~7 We are aware of the fact that the H F / MINI- 1 level is not sophisticated enough to investigate the proton transfer in the AT base pair. The role of a basis set saturation as well as of the inclusion of correlation energy should be elucidated. Such a study would be prohibitively expensive for the nucleic acid base pairs. We therefore decided to study the cyclic formamide dimer as a suitable model system which would efficiently simulate two hydrogen bonds of the AT molecule. Indeed, this system has previously been investigated23-27 as a benchmark for processes connected with the DPT in a pair of

* To whom correspondence should be addressed.

+ Academy of Sciences. 8 Charles University.

Abstract published in Advance ACS Abstracts, April 1, 1994.

0022-3654 /94/2098-4142%04.50/0

hydrogen bonds. Another fact supporting the choice is that an excellent quantum theory based on the Pauli master equation formalism and describing the interaction of transferring protons with a condensed-phase environment has been applied to the formamide dimer.2* We believe that a similar theoretical approach could subsequently be broadened for more complex systems such as the nucleic acid base pairs. In the present paper a wide set of computational methods (semiempirical, nonempirical, and nonempirical with inclusion of correlation energy) has been tested for the formamide dimer. A stability of the characteristics inherent in the PES for the DPT in the formamide dimer is discussed. The aim is to be able to make a qualitative estimate of both the reliability of the HF/ MINI-1 results obtained earlier for the AT molecule and the error which can be expected for higher computational levels. Computational Methods Ab initio Hartree-Fock (HF) calculations were performed with the MINI-1,29 MIDI-l,294-31G, 6-31G, 6-31G(*) (polarization functions only on 0 and N forming the H-bonds with exponents of 0.8), 6-31G*, and 6-31G** basis sets. For the post-HF calculations using the second-order Merller-Plesset perturbation theory (MP2), the 6-31G(*),6-31G*, and the full double-tbasis set of Dunning and Huzinaga3O (DZ+2P) wereused. TheDZ+2P basis set includes two sets of polarization d-functions on 0, N , and C and two sets of polarization p-functions on H. The Berny gradient optimization algorithm31 implemented in the GAUSSIAN 90 and GAUSSIAN 92 program packages3*was employed for optimizing stationary points. The default convergency criteria were used. At the semiempirical level of theory, the PM333 and modified MNDO-M34 methods implemented in the VAMP program package35were used. Gradients and second derivatives were calculated analytically (PM3) or numerically (MNDOM). All the structures were kept planar during the optimization. The character of the stationary points was verified by the subsequent calculation of vibrational frequencies a t all computational levels except the DZ+2P one. All the eigenvalues of the second derivative matrix were positive in the case of the minimum, one negative eigenvalue was found for the saddle point of the first order (SP(l)), and two negative eigenvalues were found for the saddle point of the second order (SP(2)). General Considerations on the Double Proton Transfer in the Cyclic Formamide Dimer and the Adenine-Thymine Base Pair Forming the complex, the adenine and thymine molecules are linked together by a pair of two parallel hydrogen bonds in a way 0 1994 American Chemical Society

Double Proton Transfer in the Formamide Dimer

The Journal of Physical Chemistry, Vol. 98. No. 17. 1994 4743

0 carbon nitrogen

@ oxygen

=.

o hydrogen

Figme 1. Molecular structure of the adenine-thymine base pair and of the cyclic formamide dimer; two internal coordinates, q and r ~are .

indicated.

0 I_.+

++

Figore 2. Important formamide dimer stationary point structures:

MI-aminc-keto (canonical) minimum, MI-imin-no1 (tautomeric) minimum, MI and Mpionic minima, and SPll-saddle point. similar to that of two molecules of formamide in the cyclic formamide dimer (cf. Figure 1). The collective interaction between two protons which can transfer along the hydrogen bonds and"static"ske1etonsof both subsystems is reflect d i n theshape of the PES. The correspondence between the mutual positions of both protons and stationary points on the PES is illustrated in Figure 2 for the formamide dimer. Out of the five structures in the figure only three were located by all the computational methods: M, and M1,which correspond to aminr+keto (canonical) and imin-no1 (tautomeric) minima, and the SPIz,which is a saddle point lying on the minimum-energy path between them. The remaining two stationary points, M, and M4, which can be assigned to ionic minima, as well as additional saddle points appearing on the reaction paths between MI, MI, MI, and M4, were located only by some of the computational methods. A two-dimensional section of the PES built up on the rI and r2 coordinates (cf. Figure 1) turns out to exhibit three different characteristic shap& (i)'DPT of type I (cf. Figure 3a) is of a one-valley character with two minima, canonical (MI) and tautomeric (Mz) ones separated by a saddle point of the first order (SPlz(1)). (ii) DPTof type II (cf. Figure 3b) is of a twovalley character with the same two minima as in the previous case, which are, however, separated by two saddle points of the first order (SP!z( 1)); one saddle point of the second order (SPll(2)) lieson theconnecting path between them. (iii) DPTof iype

Fiyre3. Two-dimensional PES sections obtained by scanning from the optimizedSP1zstructuresforthecyclicformamidedimer;the HF/MINI-I (a. top), HF/6-31Gt*' (b, middle). and PM3 (Cs bottom) surfaw demonstratetheDPToftypeI-III,respectively. Positionsofthestationary pints in the figure correspond only schematically to fully (cf, I and 3).

III (cf. Figure 3c) is characterized by four minima; two ionic minima (M,, M4) appear in addition to MI and Mz; the pattern

4744 The Journal of Physical Chemistry, Vol. 98, No. 17, 1994

Hrouda et al.

TABLE 1: Geometries (in angstroms and degrees), Energies (for Nonem ' 'cal Methods, in au), or Heats of Formation (for Semiempirical Methods, in k 4 m o l ) and Imaginary Frequencies (in c m - l r f the MI, Mz, and SP12 Structures of the formamide Dimer Calculated by Various Methods (a) MI HF/MINI- 1 I

HF/MIDI-1

I

HF/4-31G I

-90.28 4.121 1.378 1.235 2.856 1.022 0.992 1.109 64.27 121.13 111.56 123.07 120.82 115.45 162.22

-335.433 826 4.033 1.430 1.313 2.754 1.075 1.043 1.162 59.77 124.60 119.25 120.87 117.97 114.32 177.35

-335.869 944 4.034 1.329 1.233 2.862 1.006 0.989 1.081 63.29 125.45 114.78 120.32 120.84 114.74 171.47

-337.390 637 4.072 1.328 1.230 2.899 1.006 0.990 1.080 64.48 125.13 113.02 120.27 120.95 114.97 168.92

PM3 111

MNDO-M

HF/MIDI-1 I

HF/4-3 1G I

HF/6-31G

I

HF/MINI-1 I

-71.84 4.075 1.300 1.331 2.748 1.771 0.990 1.098 56.19 119.16 126.01 125.03 114.83 129.97 177.25

-85.66 4.159 1.303 1.338 2.864 1.865 1.003 1.105 54.81 120.58 128.29 130.76 112.76 126.91 172.24

-335.427 329 3.988 1.349 1.417 2.687 1.632 1.060 1.157 55.92 123.00 128.09 128.25 110.36 124.59 179.59

-335.822 281 3.873 1.265 1.321 2.674 1.669 1.ooo 1.073 59.43 124.45 122.89 124.56 115.93 123.87 175.55

-337.340 941 3.903 1.265 1.317 2.696 1.702 0.999 1.074 59.66 124.01 122.38 124.10 116.34 124.03 175.33

-337.686 089 3.925 1.269 1.321 2.711 1.721 1.000 1.075 59.62 123.87 122.39 124.09 116.12 124.23 175.34

method: PES type:

PM3' 111

MNDO-M'

energy: 1-2 1-3 1-5 3-6 3-7 3-9 1-1 1 2-1-3 3-1-5 1-3-6 1-3-7 1-3-9 3-1-1 1 3-74

-87.08 4.153 1.377 1.232 2.816 1.01 1 0.989 1.101 58.59 118.25 119.13 122.20 119.34 119.40 175.22

method: PES type: energy: 1-2 1-3 1-5 3-6 3-7 3-9 1-1 1 2- 1-3 3-1-5 1-3-6 1-3-7 1-3-9 3-1-1 1 3-7-6

I

HF/6-31G i -337.736 363 4.088 1.332 1.234 2.910 1.006 0.990 1.081 64.93 124.94 112.35 120.20 120.84 115.21 168.05

0)M2 1

(4SP12 HF/MINI-1 I

HF/MIDI-1 I

HF/4-31G I

HF/6-3 1G

111

MNDO-M I

40.45 (-2548, -1873) 3.790 1.335 1.280 2.475 1.258 0.988 1.100 57.09 119.64 123.27 124.56 115.94 124.63 177.38

-71.56 (-1 7 18) 3.834 1.333 1.285 2.551 1.304 0.996 1.108 58.19 121.25 122.10 125.78 116.24 121.49 172.49

-335.420 292 (-1330) 3.774 1.379 1.365 2.504 1.285 1.051 1.161 58.17 124.66 123.68 124.36 112.93 119.32 178.59

-335.819 480 (-1 129) 3.706 1.279 1.296 2.513 1.398 0.997 1.075 60.57 124.72 120.63 122.53 116.95 121.45 175.73

-337.336 699 (-1254) 3.694 1.280 1.291 2.490 1.377 0.997 1.076 6 1.08 124.13 119.60 121.64 117.38 121.49 175.43

-337.681 327 (-1285) 3.697 1.285 1.294 2.486 1.373 0.997 1.077 61.14 123.97 119.45 121.52 117.20 121.61 175.37

method: PES type:

PM3

energy: img. freq: 1-2 1-3 1-5 3-6 3-7 3-9 1-1 1 2-1-3 3-1-5 1-3-6 1-3-7 1-3-9 3-1-1 1 3-7-6

1

(a) MI

method: PES type: energy: 1-2 1-3 1-5 3-6 3-7 3-9 1-1 1 2-1-3 3-1-5 1-3-6 1-3-7

HF/6-3 1G(*) I1 -337.816 586 4.162 1.336 1.213 2.995 1.006 0.994 1.086 62.71 125.36 115.20 120.44

HF/6-3 1G* I1 -337.882 824 4.153 1.333 1.205 2.996 1.005 0.993 1.090 62.90 125.61 114.89 120.56

HF/6-31GS* I1 -337.902 337 4.153 1.332 1.205 2.995 1.004 0.991 1.091 63.06 125.56 114.67 120.29

MP2/6-3 1G(*) I -338.711 688 4.121 1.351 1.249 2.919 1.027 1.010 1.106 60.91 124.98 117.97 120.68

MP2/6-31G*' I -338.816 875 4.111 1.345 1.238 2.927 1.026 1.009 1.103 61.24 125.51 117.51 120.67

MP2/DZ+2Pd -339.023 010 4.010 1.346 1.237 2.822 1.026 1.004 1.099 62.62 125.20 115.42 120.04

exper.'

-

4.183 1.300 1.255 2.935 60.1 121.5 118.5

-

The Journal of Physical Chemistry, Vol. 98, No. 17, 1994 4145

Double Proton Transfer in the Formamide Dimer TABLE 1 (Continued) method: PES type:

HF/6-31G(*) I1

HF/6-31G* I1

HF/6-31G** I1

1-3-9 3-1-1 1 3-7-6

120.18 114.09 172.12

120.47 113.67 171.48

120.27 113.68 171.56

method: PES type:

HF/6-3 1G(*)

(a) MI MP2/6-31G(*) I

MP2/6-31G*C I

MP2/DZ+2Pd

exper.(

120.07 113.74 175.14

119.27 113.88 172.75

-

119.92 114.21 175.82

-

-

-

0)M2 HF/6-31G** I1

MP2/6-31G(*) I

MP2/6-31GS I

MP2/DZ+2P

I1

HF/6-3 1G* I1

energy: 1-2 1-3 1-5 3-6 3-7 3-9 1-1 1 2-1-3 3-1-5 1-3-6 1-3-7 1-3-9 3-1-1 1 3-7-6

-337.784 929 4.064 1.259 1.322 2.870 1.899 1.002 1.077 57.32 124.20 125.79 126.16 111.36 124.36 178.93

-337.843 020 4.027 1.258 1.306 2.844 1.872 1.001 1.080 57.57 124.51 125.24 125.82 111.68 124.01 178.32

-337.867 499 4.004 1.258 1.304 2.821 1.852 1.000 1.082 57.76 124.53 124.96 125.55 111.65 123.82 178.27

-338.680 626 3.994 1.292 1.339 2.765 1.752 1.020 1.096 56.44 123.58 126.82 126.64 110.78 124.75 179.50

-338.780 885 3.960 1.288 1.322 2.751 1.735 1.019 1.093 56.75 124.21 126.26 126.30 110.87 124.18 179.90

-338.998 080 3.822 1.294 1.313 2.616 1.588 1.014 1.089 57.26 124.46 125.41 125.48 110.21 122.93 179.82

method: PES type:

HF/6-3 1G(*)

(c) SP12 HF/6-31G** I1

MP2/6-3 1G(*) I

MP2/6-31G* I

MP2/DZ+2P

I1

HF/6-31G* I1

energy: img. freq: 1-2 1-3 1-5 3-6 3-7 3-9 1-1 1 2-1-3 3-1-5 1-3-6 1-3-7 1-3-9 3-1-1 1 3-7-6

-337.762 568 (-1907, -597) 3.654 1.287 1.272 2.474 1.303 0.999 1.081 59.02 124.96 122.33 123.18 114.46 119.82 178.20

-337.824 800 (-1838, -51 1) 3.647 1.284 1.262 2.475 1.318 0.998 1.083 59.13 125.11 122.04 123.17 114.66 119.74 177.59

-337.851 780 (-1748, -245) 3.639 1.285 1.261 2.466 1.309 0.997 1.085 59.33 125.08 121.70 122.85 114.44 119.58 177.57

-338.673 575 (-1366) 3.727 1.309 1.303 2.5 15 1.348 1.017 1.099 57.65 124.44 124.44 124.52 113.48 120.81 179.82

-338.775 524 (-1267)

-338.996 117

3.714 1.303 1.292 2.519 1.365 1.016 1.096 57.82 124.94 124.17 124.55 113.40 120.62 179.16

3.686 1.306 1.289 2.490 1.344 1.012 1.091 58.10 124.9 1 123.66 123.98 112.29 120.20 179.29

-

-

-

0 Heat of formation of the ionic minimum M3 is -54.87 kcal/mol, and heats of formation and imaginary frequencies of the SPl3 and SP14 saddle points are -54.45 (-1 164) and -49.13 (-21 15) kcal/mol (cm-I). The norm of the gradient for the PM3 and MNDO-M methods was below 0.03 and 2.74 kcal/mol/A for minima and transition states, respectively. Such large gradient values are typical for the semiempirical methods in qucstion.35 We are aware that this degree of accuracy of optimized structures is insufficient for drawing quantitative conclusions on energy barriers. Despite this we decided to include these energies in the table to assist quantitative considerations. Torsion angle 1-3-7-6 is always Oo with exception of the M2(PM3) and Mz(MP2/6-31G(*) structures, where it is 180O. Single-point MP4 energies are -338.877 200, -338.847 580, and -338.840 053 au. MP2/DZ+2P vibrational analysis was not performed. e See ref 24.

of saddle points involves four saddle points of the first order (SP13( l ) , SP14(l), SPZ3(1), SPz4(1)) connecting appropriate minima along rl and rz axes of the diagram and one saddle point of the second order (SPIz(2)) located in the center of the diagram. Results DFT Types Given by Various Methods for Formamide Dimer. Comparing the semiempirical and nonempirical methods (cf. Table 1) revealed that the former provided the DPT of type I11 (PM3) or DPT of type I (MNDO-M) while the latter provided the DPT of type I or 11. The nonempirical ab initio results can be summarized as follows: (i) the PES obtained at the H F level with a basis set without polarization functions refers to the type I, (ii) the addition of polarization functions is reflected in the appearance of "lateral" saddle points SP12( 1) (cf. Figure4) which are characteristic for the DPT of type 11, and finally, (iii) the MP2 level provides again the PES of type I. Energy Differences between Stationary Points. The relative stability of both the minima and the saddle points is the most important characteristic for qualitative energy consideration of

the proton transfer; the energy differences among MI, Mz, and SP12 stationary points for the formamide dimer are collected in Table 2. The MP2/DZ+2P level is taken as a reference to which other levels are related. The canonical minimum (MI) always represents the global minimum. Furthermore, the SPlz saddle point is considerably closer to the tautomeric minimum (M2) than to the canonical minimum (MI) at any theoretical level, the reference MP2/DZ+2P value of the SPIz-Mz barrier being only about 1 kcal/mol! The energy differences obtained by semiempirical methods are a long way from the reference values. The ab initio energy differences give evidence that the role of polarization functions on carbons (6-31G(*)) as well as the role of second polarization functions (6-3 1G**) is not negligible. The MP4/6-3 lG* single-point calculation performed on the MP2/ 6-3 lG* optimal geometries does not substantially change the energy differences. Geometry. The MI, M2, and SPlz structures optimized at various computational levels for the formamide dimer are summarized in Tables 1 and 3. As expected, the semiempirical

Hrouda et al.

4746 The Journal of Physical Chemistry, Vol. 98, No. 17, 1994 10

i

I1 n Y

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

1

0.2

u(Ang)

Figure4. One-dimensionalcut through the PES for the formamidedimer

obtained by scanning from the SPl2 structure along the mass-weighted - (1) the HF/6-31G(*) level vibrational coordinate u = ( 2 m ~ ) l / ~ ( r 2rl): with optimizationof all the coordinatesexcept the scanned u coordinate; (2) the MP2/6-3 1G(*) level (single-point calculation on the points of curve 1). Energies are taken as relative with respect to the local minima of both curves.

TABLE 2 Energy Differences AE (in kcalhol) for the Cvclic Formamide Dimer Calculated bv Various Methods PM3 MNDO-M HF/MINI- 1 HF/MIDI- 1 HF/4-3 1G HF/6-31G HF/6-31G(*) HF/6-31G* HF/6-3 1G** MP2/6-3 1G(*) MP2/6-31G* MP4/6-31G* (SP) MP2/DZ+2P

-15.24 -4.62 -4.08 -29.91 -31.18 -31.55 -19.87 -24.98 -21.86 -19.49 -22.58 -18.59 -15.64

46.63 18.72 8.49 3 1.67 33.85 34.54 33.90 36.41 3 1.73 23.92 25.95 23.31 16.88

3 1.39 14.10 4.42 1.76 2.66 2.99 14.03 11.43 9.86 4.42 3.36 4.72 1.23

OAll stationary points except the MP4/6-31G* (sp) which were calculated as single points on the MP2/6-31G* geometries were fully optimized. as well as nonempirical geometry characteristics do not differ dramatically and are in reasonable agreement with experiment" (only the M I experimental structure is available). A linearity of the intermolecular H-bonds is preserved in all stationary points with only slight deviation from the parallel arrangement. A lengthening of the H-bonds due to the polarization functions effect and subsequent MP2 shortening to an almost identical length as is found without polarization functions mimic the corresponding changes in energy differences. A planarity of all the stationary points was proved by harmonic vibrational analysis. Normal modes corresponding to the imaginary frequencies were found to possess planar symmetry. Discussion Let us first discuss the nonempirical results for theformamide dimer. The addition of the polarization functions to the "splitvalence" basis set changes the character of the PES considerably: the SPIZ(1) saddle point with one imaginary frequency corresponding to the symmetric rl r2 vibrational mode becomes the saddle point of the second-order SPlz(2) (cf. Figures 3 and 4 and Table 3). The second imaginary frequency of the rz - rl antisymmetric vibrational mode leads to an appearance of two "lateral" saddle points of the first order (SPl2( 1)). The artificial character of these two saddle points is proved when the effect of electron correlation is taken into account; the MP2 level of calculation exhibits again type I of the DPT. As expected, these changes of the PES quality are reflected in the magnitudes of the

+

TABLE 3: Geometries (in angstroms and degrees), Energies (in au), and Imaginary Frequencies (in cm-') of the formamide Dimer SPlz Structures Obtained for the Type I1 of the DPT (See Text and Figure 3 for Definition) method: HF/6-31G(*) HF/6-31GS HF/6-31GS* -337.851 798 -337.763 084 -337.825 137 energy: (-1553) (-1662) img. freq: (-1435) 1-2 1-3 2 4 1-5 2-6 3-6 4-5 3-7 4-8 3-9 4-1 0 1-1 1 2-12 2-1-3 1-2-4 3-1-5 4-2-6 1-3-6 2 4 5 1-3-7 2 4 8 1-3-9 2410 3-1-1 1 4-2- 12 3-74 5-8-4"

3.691 1.289 1.282 1.270 1.279 2.551 2.477 1.492 1.195 1.ooo 0.999 1.085 1.077 59.80 57.94 124.92 125.25 121.69 123.59 123.14 123.69 112.76 115.77 119.75 120.16 176.50 179.82

3.678 2.386 1.280 1.26 1 1.268 2.546 2.469 1.487 1.220 0.999 0.998 1.087 1.080 60.00 58.01 125.08 125.33 121.27 123.35 122.95 123.77 113.15 115.77 119.69 120.07 175.96 179.16

3.646 1.286 1.283 1.260 1.263 2.486 2.461 1.377 1.255 0.998 0.997 1.087 1.083 59.61 58.98 125.03 125.16 121.44 122.09 122.75 123.04 113.77 115.04 119.54 119.70 177.06 178.07

Torsion angles 1-3-7-5 and 2 4 8 - 5 are 0". energy differences. The SPlZ-MZ barrier follows the same trend as the DPT type (see Results, first paragraph). The inclusion of correlation energy compensates for the effect of polarization functions. The MP2 energy differences are comparable to the HF values with basis sets not containing polarization functions. On the other hand, the influence of the computational level on the M ( M I - M2) (cf. Table 2) is not correlated with changes of the DPT type. This energy difference is rather small at the HF/ MINI-1 level. Enlarging the basis set leads to an important increase in the M ( M 1 - M2) while a considerable decrease is observed when polarization functions are added. Inclusion of the correlation energy only slightly reduces the M ( M I - M2). The effect of the computational level on the M(SP12 - M I ) can be deduced from the M(SP12 - M2) and M ( M 1 - Mz). The use of semiempirical methods for such a small system as the formamide dimer seems to be inadequate. As mentioned above, we aim to pass from the formamide dimer to the AT base pair for which a "meaningful" semiempirical description is desirable and fully justified. The PM3 method seemed to be the best candidate for use in calculations on hydrogen-bonded systems such as the formamidedimer and the AT base pair.21~36However, we demonstrated (cf. Tables 1 and 4 and Figure 3) that this method provides qualitatively incorrect results if the whole section of the PES for the DPT is taken into account. We should mention at this point that the same incorrect characterization of the PES has been earlier obtained by Lune11 and Sperber9for the AT base pair using a semiempirical method developed by Rein and Harris.*Jo Another attempt to correct the deficiency of semiempirical methods in providing a proper description of hydrogenbonded systems has been made by Blizniuk and V o y t i ~ k , 3who ~ used a special parametrization of the MNDO repulsion term for atoms participating in hydrogen bonds. Their parametrization, called MNDO-M, seems to be an efficient tool for calculations on hydrogen-bonded systems. For the formamide dimer the MNDO-M method gives qualitatively correct type I PES (cf. Table 1).

Double Proton Transfer in the Formamide Dimer

The Journal of Physical Chemisfry, Val. 98, No. 17, 1994 4141

TABLE 4 Relative Energies (in kcal/mol) of S t a t i o ~ ~Points y for the AT Complex Calculated by the P M 3 Method (the Energy of the Canonical Minimum (MI) Depicted in Figure 1 Is Taken as a Reference) stat. p i n t " Mlb Mz M3 M4 SP(2)C SPII(I) SP,4(1) SPZI(1) SPzr(1) energy 0.M) 12.65 14.66 32.01 38.41 16.90 32.94 28.01 33.29 img. frcq (-2324,-1750) (-1819) (-1559) (-2420) (-1565) 'The norm of the gradient was below 1.80 and 9.71 kcalftnol/A for minima and transition states, respectively (seeTable 1 for further comment). Heats of formation of the minima are -25.61, -12.96, -10.95, and 6.40 kcal/mol. Heats of formation of the saddle pints are (values in parenthesis mean imaginary frquencies in cm-I) 12.80 (-2324, -l749), -8.71 (-l819), 7.33 (-1559). 2.40 (-2420). and 7.68 (-1656) kcal/mol. (iii) For the formamide dimer, the canonical (MI) structure was always proved to be more stable than the tautomeric (M2) oneand theSPlrMzenergybarrierwasfound toberathersmall. These formamide dimer energy characteristics support the lowenergy barrier calculated previously between the transition state and tautomeric structures of the AT complex. (iv) On the basis of analogy between the formamide dimer and AT base pair we expect that the AT PES for the double proton transfer is also of the first type. Note Added in Proof: We investigated the PES for the GC base pair at the HF/MINI-1 level and located the transition state for the DPT.37 References and Notes ( I ) Proceedings of a NATO Advanced Research Workshop an Proton Transfer in Hydrogen-Bonded Systems: Plenum Press: New York, 1992. ( 2 ) Crsik, C. S.:Rocmiak, S.;Largman. C.; Rutter. W. Science 1981,

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Figure 5. PM3 two-dimensional PES section for the AT base pair constructed as a scan from the SP12(2)geametry.

The trends obtained for the formamide dimer can, in the first approximation, be extrapolated to the DPT in the adeninethymine molecule. Two minima and only one SPlrof the first orderwerefoundearlierfor the ATbasepair at theHF/MINI-1 level." Two minima and one SPI2of the first order were also located for the formamide dimer at the HF/MINI-1 and MP2 levels (see above). Consequently, the same type of the DPT can be expected to exist also for the AT complex at the high level of theory. We can also conclude that qualitatively correct energy barriers can be obtained only if the MP2 level with extended basis set (or a method of a comparable quality) is employed. Nonetheless, the most important conclusion of our previous study on the AT base i.e. the low energy barrier between the SP12(I)(AT*)andM2(A*T*) structures,seemstobeconfirmed bytbe presentstudy. On thebasisoftbehighest levelcalculations performed for the formamide dimer, we can even expect that the energy barrier found for the AT represents the upper limit. As mentioned above, a parallel between the formamide dimer and the AT base pair was found for the PM3 method (cf. Figures 3 and 5 and Table 4). However, this method does not provide qualitatively correct PES for the DPT in both complexes. We assume that the parallel between semiempirical and ob inifio resultscanalso beobtained in thecaseoftbe MNDO-M method, which seems tobe promising for the proper descriptionofhydrogen bonding in the AT base pair. Since this method has been parametrized for a very limited set of inorganic molecules, we suggest that a new parametrization covering the larger set of hydrogen-bonded biomolecules be carried out. Conclusions (i) The formamide dimer PES for the double proton transfer exhibits three different patterns. The character of the PES strongly depends on the theoretical level, and it is affected by the basis set as well as by the inclusion of correlation energy. The highest levels used support the expected double-well potential of the type I (Le. two minima separated by the saddle p i n t of the first order). (ii) Reasonable energy barriers for the double proton transfer in the formamide dimer are obtained only if both the correlation energy and extended basis sets are considered

(3) Bender, M. L.; Bergem, R. I.; Kamiyama, M. The Or@" Biwhemisfry o/Ewymotic Cotolysis; Wiley: New Yark, 1984. (4) Scarborough, G. A. Prm. Nall. Acod. Sei. U.S.A. 1986.83.3688. (5) Williams. R. J. P. In The Enzymes o/ Biologfcd Mcmbroncs; Manonmi, A. N., Ed:; Plenum: New York. 1984; Val. 4, pp 71-110. (6) Lawdin, P.-0. Rev. Mod. Phys. 1963, 35, 724. (7) L h d i n , P.-0. Adv. Qunnfum Chem. 1965. 2, 213. (8) Rein, R.; Harris, F E. J. Chem. Phys. 1964,41, 3393. (9) Lunell, S.: Sperber, G . J. Chem. Phyz. 1967,46,2119. (IO) Clementi, E.;Mehl, I.: van Niessen, W. J. Chem. Phys. 1971,54. 508. (11) Scheiner, S.; Kern. C. W. J. Am. Chem. Sm. 1919,101.4081. (12) Kong. Y. S.; Ihon. M. S.; Lbwdin, P.-0. Inf. J. Quontum Chem., Quantum Bid. Symp. 1987, 14, 189. (13) Lipidski, I. Chem. Phys. Leff. 1988,145, 227. (14) Kwiatkowski.. J. S.:. Ziclinski.. T. I.:. Rein.. R. Ad". Ouonfum Chem. 1986, 18, 85. (15) Czerminsld, R.; Szczepaniek, K.; Person, W. E.;Kwiatkowski, I. S. J. Mol. Struef. 1990, 237, 151. (16) Kwiatkowski, J. S.;Person, W. B. In Thcoreficol Biwhemistry ond Molecular Biophysics; Bevcridge. D. L.. Lavcry. R., Eds.: Academic Press: Guilderland, NY, 1990; Vol. I, p 153. (17) Grinberg, H.: Capparelli, A. L.; Spina, A,; Maralion. J.: Sorarrain. 0. M. J. Phys. Chem. 1981,85,2751. (18) Rein, R.: Ladik, I. J . Chem. Phys. 1964. 40, 2466. (19) Rein, R.; Harris, F. E. J. Chem. P h p . 1%5,42,2177. (20) Rein, R.; Harris, F. E. J. Chem. Phys. 1%5,43,4415. (21) Hrouda, V.; Flod6n. I.; Habza, P. J . Phya. Chem. 1993.97. 1542. (22) FIori4n. I.; Hrouda. V.: Hohza, P. J. Am. Chem. Sw. 1994. 116. 1457. (23) Del Re, G.: Adamo, C . J. Phys. Chem. 1991.95.423l. (24) Dreyfus, M.: Maigret. B.; Pullman, A. Theor. Chim. Acto 1910,17, 1"O ."I.

(25) Janaschek, R. Theor. Chim. Acfo 1973.32.49. (26) Yamak, S.;Kitaura. K.: Nishimoto, K. Theor. Chim. A m 19'18, 47.111. .. , ....

(27) (28) (29) , (30) chapter (31)

Ottersen, T.; Jcnsen, H. H. 1. Mol. Strucf. 1915,26,355. Maycr. R.: Emst, R. R. J. Chem. Phys 1981,86,784. Tatcwaki, H.; Hudnaga, S. J. Chem. Phys. 1919, 71, 4339. Dunning, T. H.; Hay, P. I. Plenum: New York. 1976: 111) 1-28, 1.

Schlegel, H. B. J. Compuf. Chem. 1982.3. 214

%AN 92: Gaussian. Inc.: Pittsburgh, PA,

(33) Stewart, J. 1. P. J. Compuf. Chsm. 1989. IO, 209. (34) Blizniuk, A. A,; Voytiuk, A. A. Zh. Strukt. Khim. 1988. 29, 31. (35) Clark. 7. Program VAMP-4, University of Erlangen. (36) Leach, A. R.: Kallman, P. A. 1. Am. Chem. Sw. 1992,114,3675. (37) Floriin, J.; Leszczynski, I.; Scheiner. S. Submitted for publication in Chem. Phys. Lett.