The vibrational frequencies and optimized structure parameters of 3DAU and 6AU’ s tautomers have been calculated by using ab initio Hartree-Fock (HF) and density function theory (B3LYP) methods at 6-311++G(d, p) basis set level. All computations have been performed using Gauss-View molecular visualization program^[15] and Gaussian 03 program package on personal computer^[16]. To close the calculated frequencies to the experimental ones the scale factors of 0.905 1 and 0.961 4 are used for HF and B3LYP with 6-311++G(d, p) basis set, respectively^[17]. Additionally, the calculated vibrational frequencies were clarified by means of the potential energy distribution (PED) analysis of all the fundamental vibrations modes by using VEDA 4 program^[18]. VEDA 4 program have been used in previous studies by many researchers for PED analysis of vibrational modes^{[19, 20, 21]}.

To our knowledge, there are no theoretical studies on the vibrational assignments of 3DAU and 6AU in the literature. So, in order to introduce detailed vibrational assignments, we have performed computational analysis done by using PED analysis and the visualization of modes.

3DAU is a molecule having 13 atoms, which belongs to the point group C_S. The three Cartesian displacements of the 13 atoms provide 39 internal modes, namely;

Γvib.=Γ39-Γtrans.-Γrot.=23A'+10A″

From the character table for the C_S point group, since Γ _trans.=2A'+A″ and Γ _rot.=A'+2A″, we get

Γinter.=22A'+11A″

normal modes of vibration. All the vibrations are active both in infrared (IR) and Raman (R). For an N-atomic molecule, 2N-3 of all vibrations is in plane and N-3 out of plane^[22]. So, for the title molecule, 6 of all the 23 vibrations are in plane and 10 are out of plane. Since the molecule is planer all the vibrations being anti-symmetric through the mirror plane of symmetry σ _h will belong to the species and A″ the others being symmetric through σ _h to the species A'. Thus, all the A' vibrations of thespecies will be in plane and those of the A″ species are out of plane. For 6AU, numbers of vibration modes is as follow

Γvib.=Γ33-Γtrans.-Γrot.=19A'+8A″

From the character table for the C_S point group, since Γ _trans.=2A'+A″ and Γ _rot.=A'+2A″, we get

The calculated optimized possible hydrogen conformations of the tautomers of all title molecules are given in Figure 1-2. Furthermore, the total energies (corrected by zero point energy), relative energies, vibrational deviations of all the conformations of the tautomers of all title molecules have summarized in Table 1-2. The relative energy values in the tables are respect to the conformer with minimum energy. As seen from Table 1-2, the relative energies between the conformers with maximum and minimum energy are 2.00 kcal· mol^-1 (HF) and 1.43 kcal· mol^-1 (B3LYP) for the 4-enol form and 6.23 kcal/mol^-1 (HF) and 5.92 kcal· mol^-1 (B3LYP) for the 2, 4-diol form of 3DAU and 6.73 kcal· mol^-1 (HF) and 6.03 kcal· mol^-1 (B3LYP) for 2, 4-diol form of 6AU. As seen from the tables the conformer 1 of each tautomeric form of all title molecules has minimum energy, since, we say that the conformer 1’ s are the most stable conformers of the tautomers. So, we only take into account the conformer 1 of the two tautomers of the all title molecules in the study.

Fig.1

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	Fig.1 Calculated optimized structures of possible conformers of 3DAU (a) 4-enol tautomer and (b) 2, 4-diol tautomer

Fig.2

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	Fig.2 Calculated optimized structures of possible conformers of 6AU (a) 4-enol tautomer and (b) 2, 4-diol tautomer

Table 1

Table 1

Table 1 Total energies, relative energies and vibrational deviations for optimized conformations of 4-enol and 2, 4-diol tautomers of 3DAU HF [6-311++G(d, p)] B3LYP [6-311++G(d, p)] Total energy (Hartree/Particle) Relative Energy /(kcal· mol-1) |Δ ν |ave Total energy (Hartree/Particle) Relative Energy /(kcal· mol-1) |Δ ν |ave 4-enol Conformer 1 -396.436 862 0.00 0.000 -398.769 823 0.00 0 Conformer 2 -396.433 667 2.00 5.636 -398.767 540 1.43 5.485 2, 4-diol Conformer 1 -396.436 763 0.00 0.000 -398.766 951 0.00 0.000 Conformer 2 -396.436 223 0.34 1.430 -398.766 628 0.20 1.657 Conformer 3 -396.427 635 5.73 5.764 -398.758 360 5.39 6.446 Conformer 4 -396.426 827 6.23 6.281 -398.757 516 5.92 6.384

Table 1 Total energies, relative energies and vibrational deviations for optimized conformations of 4-enol and 2, 4-diol tautomers of 3DAU

Table 2

Table 2

Table 2 Total energies, relative energies and vibrational deviations for optimized conformations of 4-enol and 2, 4-diol tautomers of 6AU HF [6-311++G(d, p)] B3LYP [6-311++G(d, p)] Total energy (Hartree/Particle) Relative Energy /(kcal· mol-1) |Δ ν |ave Total energy (Hartree/Particle) Relative Energy /(kcal· mol-1) |Δ ν |ave 4-enol Conformer 1 -428.465 148 0.00 0.000 -430.884 246 0.00 0 2, 4-diol Conformer 1 -428.431 682 0.01 0.000 -430.851 303 0.00 0.000 Conformer 2 -428.427 897 2.38 4.808 -430.847 768 2.22 4.175 Conformer 3 -428.422 857 5.54 5.879 -430.843 491 4.90 5.008 Conformer 4 -428.420 955 6.73 8.670 -430.841 608 6.08 7.315

Table 2 Total energies, relative energies and vibrational deviations for optimized conformations of 4-enol and 2, 4-diol tautomers of 6AU

If the total energies of the two tautomeric forms of 3DAU and 6AU in Table 1-2 are compared we can see the ground state conformer of the 4-enol form of the molecules are more stable than that of the 2, 4-diol form, with a relative energy 0.06 kcal· mol^-1 (HF) and 1.80 kcal· mol^-1 (B3LYP) for 3DAU and 21.00 kcal· mol^-1 (HF) and 20.67 (B3LYP) for 6AU. This situation shows 4-enol tautomer of 3DAU and 6AU is more stable than 2, 4-diol tautomer. The mean vibrational deviations (|Δ ν |_ave) in Table 1-2 are between the calculated vibrational frequency values of the ground state conformer and the mentioned conformer. As seen the mean vibrational deviation increases while the relative energy increases. Therefore, we state that the more different the molecular structure of the conformers is the higher the relative energy is between them, and thus, a bigger mean vibrational deviation^{[23, 24]}.

The resulting vibrationam frequencies and proposed vibrational assignments with PED’ s analysis of the ground state conformers (conformers 1) of the 4-enol and 2, 4-diol tautomers of the title molecule are given in Table 3-4, respectively. The tables also show the experimental vibrational frequencies of the compounds. The experimental (FT-IR or FT-R) vibrational frequency values have been found from the spectra obtained by the web pages of SDBS (National Institute of Advanced Industrial Science and Technology)^[25]. The calculated vibrational frequencies in the tables are scaled and their symmetry species are written in the first column of the tables. As we said before all the vibrations of thespecies are in plane and those of!the species are out of plane. This was corrected by the visual inspection of all the vibrations on the Gauss-Wiev Program. As seen from Table 3-4, the calculated frequencies are in good agreement with the experimental ones. Additionally, from the correlation values in the last lines of the tables it has been clearly seen that the B3LYP method gives better correlation values than the HF method for the vibrational frequencies. The theoretical infrared intensities and Raman activities can also be seen in the tables.

Table 3

Table 3

Table 3 Experimental and calculated vibrational frequencies of the ground state conformer of 4-enol tautomer of 3DAU Sym. Assignments (%PEDa) Experimentalb frequencies IR Calculated 6-311++G(d, p) HF B3LYP IR IR int. R act. IR IR int. R act. A' ν OH(100) - 3 770 106.4 64.5 3 672 69.7 95.4 A' ν NH(100) - 3 490 97.7 76.3 3 465 71.9 99.4 A' ν CH(94) 3 112 3 072 1.7 113.1 3 109 0.5 123.6 A' ν CH(100) - 3 047 2.1 66.9 3 079 1.9 91.1 A' ν CH(97) 2 989 3 032 3.0 74.1 3 065 2.6 80.0 A' ν O=C(60)+δ CNC(18) 1 655 1 721 1 157.0 18.7 1 675 853.3 30.3 A' ν CC(54) 1 626 1 654 198.3 14.0 1 605 125.1 17.0 A' ν CC(59) 1 530 1 572 177.3 66.2 1 532 89.8 45.0 A' δ HCC(42)+ν NC(12)+ν OC(12) 1 464 1 476 52.2 18.0 1 453 53.8 9.9 A' δ HNC(41)+ν O=C(13)+ν NC(10) 1 404 1 435 38.0 14.3 1 404 11.3 11.9 A' δ HCC(52)+δ HOC(13)+δ HNC(10) 1 360 1 349 3.9 16.3 1 319 4.3 8.1 A' δ HCC(36)+ν OC(26) 1 217 1 237 176.0 13.4 1 206 78.6 8.9 A' ν NC(19)+ν OC(13)+δ HOC(12)+δ CNC(11) - 1 227 19.7 17.4 1 191 29.0 7.6 A' δ HCC(39)+δ HNC(13) - 1 179 56.6 6.6 1 164 67.8 9.7 A' δ HOC(45)+δ HCC(13) - 1 166 173.9 11.2 1 145 193.8 1.8 A' δ HCC(39)+ν NC(25)+ν CC(13) 1 093 1 077 24.7 4.4 1 066 17.6 4.6 A' ν CC(47)+δ CCC(16)+δ NCC(11) 965 977 0.2 2.4 966 4.4 8.3 A″ τ HCCC(80)+τ NCCC(10) - 972 5.2 7.4 903 0.2 0.7 A' δ CCC(22)+δ NCC(18)+ν OC(12)+ν NC(11) 886 911 6.4 3.0 894 6.5 2.2 A″ τ HCCC(52)+γ ONCC(25) 803 812 103.7 2.2 789 57.6 0.5 A″ τ HCCC(68) 796 773 23.2 0.3 739 19.4 ~0 A' ν NC(19)+δ CNC(18)+δ CCC(15)+ν CC(13)+δ NCC(10) 779 745 8.8 17.4 737 11.0 25.4 A″ γ ONCC(57)+τ HCCC(23)+τ HNCC(13) - 729 11.6 0.1 697 18.3 0.2 A″ τ HNCC(23)+γ OCCC(19)+τ CNCC(15)+τ HCCC(14) - 682 17.6 1.3 661 25.2 0.7 A″ τ HNCC(60)+γ OCCC(22) 595 594 73.0 0.1 595 42.1 0.1 A' δ NCC(26)+ν NC(15)+δ CNC(10) 573 547 9.1 4.7 538 6.6 6.9 A' δ OCC(36)+δ CCC(26) 518 509 4.4 3.4 502 6.1 3.7 A' δ OCC(37)+δ CCC(36)+δ CNC(10) - 481 6.5 0.9 476 2.4 0.9 A″ τ HOCC(56)+τ NCCC(20)+τ HCCC(11)+δ CNC(10) - 422 2.6 2.7 418 16.0 2.0 A″ τ HOCC(42)+τ NCCC(26)+γ OCCC(15)+τ HCCC(10) - 394 150.0 0.6 399 120.1 0.5 A' δ OCC(73)+δ CCC(11) - 355 24.7 0.9 346 19.4 1.4 A″ τ CCCC(65)+γ OCCC(14)+τ NCCC(10) - 203 3.0 0.5 201 2.7 0.5 A″ τ CNCC(67)+τ NCCC(17)+τ CCCC(10) - 167 2.6 0.3 163 3.1 0.4 Scalingfactor 0.905 1 0.9614 Correlation value 0.998 5 0.999 0 a Potential Energy Distribution (PED), less then 10% are not shown.b Taken from Ref. [25].ν : stretching; δ : bending; γ : out of plane bending; τ : torsion

Table 3 Experimental and calculated vibrational frequencies of the ground state conformer of 4-enol tautomer of 3DAU

Table 4

Table 4

Table 4 Experimental and calculated vibrational frequencies of the ground state conformer of 4-enol tautomer of 6AU Sym. Assignments (%PEDa) Experimentalb frequencies Calculated 6-311++G(d, p) HF B3LYP IR Raman IR IR int. R act. IR IR int. R act. A' ν NH(100) 3 361 - 3 522 134.7 80.7 3 490 111.5 102.1 A' ν NH(100) 3 217 - 3 466 102.5 56.3 3 446 70.9 78.5 A' ν CH(100) 3 044 3 088 3 060 0.0 84.6 3 087 0.2 99.7 A' ν O=C(79) 1 755 1 730 1 805 309.9 64.0 1 742 553.0 29.4 A' ν O=C(80) 1 711 - 1 785 1 426.9 8.7 1 710 694.4 48.0 A' ν N=C(76) 1 599 1 599 1 684 12.5 60.7 1 578 32.8 24.3 A' δ HNN(66)+ν O=C(10) 1 408 1 408 1 469 53.0 18.9 1 411 28.5 15.6 A' δ HNC(42)+ν NC(20) 1 359 - 1 412 60.5 4.5 1 355 37.2 4.4 A' δ CNC(20)+ν NC(18)+δ HNC(18)+δ OCC(11) 1 336 - 1 398 149.4 11.1 1 334 112.5 7.9 A' δ HCN(75) 1 266 1 267 1 329 69.2 2.4 1 300 37.9 3.0 A' ν NC(49)+δ NNC(11)+δ HCN(10) 1 111 - 1 240 53.8 26.2 1176 60.5 26.0 A' ν NN(57)+ν NC(10) 1 021 1 023 1 113 52.9 0.4 1 079 23.8 1.9 A' δ CNN(36)+δ CNC(16)+ν NC(15) 996 - 987 16.5 2.2 965 11.5 2.7 A' δ CNN(21)+δ HNC(14)+δ NCN(14)+δ NNC(12) 902 - 960 26.5 4.1 935 29.6 5.7 A″ τ HCNN(85) 865 - 892 23.6 2.9 850 20.5 0.9 A″ γ ONNC(63)+τ HCNN(12) 746 749 758 61.1 0.2 722 9.3 0.5 A″ γ ONNC(89) - - 743 1.8 2.2 713 27.6 0.4 A' ν NC(34)+δ NNC(22)+ν NN(11) - - 722 13.6 10.7 710 10.9 16.8 A″ τ HNCN(89) - 676 641 178.0 0.5 655 146.0 0.5 A″ τ HNCN(90) 576 576 550 16.9 2.4 574 40.8 0.3 A' δ NCN(53)+δ CNC(14) 543 539 545 56.9 0.1 537 14.4 4.2 A' δ NNC(23)+δ OCN(22)+δ OCC(16) - - 534 31.2 0.3 518 26.1 0.4 A' δ CNC(25)+δ OCN(21)+δ OCC(16)+ν NC(10) - - 516 12.4 4.7 505 7.4 5.7 A″ τ CNNC(55)+τ NCNN(16) - 416 394 8.4 1.4 391 4.9 0.7 A' δ OCC(39)+δ OCN(27)+ν NC(17) - - 384 35.5 1.4 369 24.0 1.8 A″ τ NCNN(55)+τ CNNC(25)+τ CNCN(13) - 150 137 0.5 0.2 146 0.4 0.4 A″ τ CNCN(77)+τ NCNN(18) - 134 130 4.7 0.0 134 3.3 0.0 Scaling factor 0.905 1 0.961 4 Correlation value 0.997 0 0.997 7 a Potential Energy Distribution (PED), less then 10% are not shown.b Taken from Ref. [25].ν : stretching; δ : bending; γ : out of plane bending; τ : torsion.

Table 4 Experimental and calculated vibrational frequencies of the ground state conformer of 4-enol tautomer of 6AU

The calculated N— H stretching modes are in nearly 3 500 cm^-1 for the 4-enol tautomer of al title molecules. These

N— H stretching modes are observed in lover frequencies due to intermolecular hydrogen bonding in FTIR spectra. In plane and out of plane bending modes of N— H bonds are in good agreement with observed spectra. One of the most important mode observed in FTIR and FT-R spectra is O=C stretching mode in 1 655 cm^-1 for 3DAU and 1 755, 1 711 cm^-1 for 6AU. These modes are calculated in 1 675 cm^-1 for 3DAU and 1 742, 1 710 cm^-1 for 6AU. The calculations approach observed data quite well. This O=C modes indicate presence of 4-enol tautomer. Additionally, O— H stretching modes are not seen in experimental spectra for 6AU. All the vibrational assignments are in excellent agreement with our recent study on 5-Bromo-2'-deoxyuridine and related biomolecules in the literature^{[26, 27, 28, 29]}.

In Table 5-6 are given the calculated optimized structure parameters (bond lengths and bond angles) for the ground state conformers of both the two tautomers of the title molecules in accordance with the atom numbers in Figure 1-2. The table also compares the calculated structure parameters with those obtained experimentally from X-ray data for the geometric structure of 3DAU^[11] and 6AU^[12]. The correlation values between the experimental and calculated geometric parameters can be seen in the last line of the table. From these values we can say that there is also a good agreement between them, and furthermore, the B3LYP method is superior to the HF method as it was in the vibrational frequencies.

Table 5

Table 5

Table 5 Experimental and calculated geometric parameters of the ground state conformers of two tautomer of 3DAU Parameters Exp.a 4-enol 2, 4-diol HF B3LYP HF B3LYP Bond lenghts (Å ) O1-C2 1.271 1.200 1.225 1.332 1.354 O1-H1 0.944 0.968 O2-C4 1.337 1.334 1.358 1.336 1.358 O2-H2 0.970 0.942 0.964 0.942 0.964 N1-C6 1.359 1.357 1.361 1.331 1.345 N1-C2 1.367 1.387 1.414 1.306 1.326 N1-H1 0.890 0.995 1.011 C2-C3 1.412 1.446 1.442 1.393 1.398 C3-C4 1.375 1.350 1.370 1.377 1.389 C3-H3 1.000 1.074 1.084 1.074 1.084 C4-C5 1.419 1.436 1.427 1.398 1.401 C5-C6 1.352 1.338 1.358 1.370 1.384 C5-H5 1.000 1.071 1.080 1.072 1.082 C6-H6 0.980 1.074 1.082 1.076 1.085 Correlation value 0.943 5 0.955 6 0.941 8 0.945 7 Bond angles (° ) C4-O2-H2 107.8 111.3 109.9 111.4 110.1 C6-N1-C2 123.1 124.4 124.8 117.1 117.0 C6-N1-H1 120.3 120.3 120.6 C2-N1-H1 116.2 115.3 114.6 C2-O1-H1 108.3 106.5 O1-C2-N1 118.8 120.0 119.7 117.7 117.4 O1-C2-C3 124.5 125.8 126.9 124.6 124.5 N1-C2-C3 116.8 114.2 113.4 117.7 118.0 C4-C3-C2 120.5 121.4 121.6 122.8 122.5 C4-C3-H3 118.3 122.3 121.9 117.1 117.2 O2-C4-C3 123.3 123.6 123.4 122.8 122.8 O2-C4-C5 116.4 115.0 113.2 117.7 117.7 C3-C4-C5 120.3 121.4 121.4 119.5 119.5 C6-C5-C4 118.0 117.3 117.7 117.3 117.6 C6-C5-H5 125.0 122.3 121.8 122.1 121.9 C4-C5-H5 117.0 120.4 120.5 120.6 120.5 C5-C6-N1 121.3 121.6 121.1 119.9 120.1 C5-C6-H6 126.0 122.4 122.6 124.4 124.1 N1-C6-H6 112.6 116.0 116.3 115.6 115.8 C2-C3-H3 121.1 116.7 116.5 120.1 120.2 Correlation value 0.809 6 0.815 1 0.769 3 0.769 5 a Taken from Ref.[11]

Table 5 Experimental and calculated geometric parameters of the ground state conformers of two tautomer of 3DAU

Table 6

Table 6

Table 6 Experimental and calculated geometric parameters of the ground state conformers of two tautomer of 6AU Parameters Exp.a 4-enol 2, 4-diol HF B3LYP HF B3LYP Bond lenghts (Å ) O1-C2 1.224 1.187 1.209 1.316 1.336 O1-H1 0.945 0.969 O2-C4 1.224 1.185 1.212 1.314 1.336 O2-H2 0.946 0.969 N1-N6 1.351 1.341 1.347 1.319 1.333 N1-C2 1.366 1.367 1.392 1.302 1.333 N1-H1 1.02 0.993 1.01 C2-N3 1.378 1.375 1.389 1.33 1.335 N3-C4 1.359 1.375 1.398 1.29 1.316 N3-H3 0.921 0.998 1.014 C4-C5 1.456 1.433 1.476 1.416 1.411 C5-N6 1.291 1.257 1.278 1.288 1.319 C5-H5 0.961 1.073 1.082 1.072 1.082 Correlation value 0.939 8 0.945 9 0.817 0 0.814 4 Bond angles (° ) C4-O2-H2 109.5 107.9 N6-N1-C2 125.4 126.4 127.1 117.7 117.6 N6-N1-H1 116.0 115.9 115.8 C2-N1-H1 118.0 117.7 117.1 C2-O1-H1 108.6 106.9 O1-C2-N1 123.2 123.2 123.2 117.7 117.0 O1-C2-N3 122.3 123.5 124.5 115.5 116.0 N1-C2-N3 114.5 113.3 112.3 126.8 127.0 C4-N3-C2 124.8 125.4 126.1 114.5 114.4 C4-N3-H3 115.0 118.1 117.6 O2-C4-N3 122.7 123.1 122.5 120.0 119.2 O2-C4-C5 123.3 124.0 125.0 118.6 119.4 N3-C4-C5 114.0 112.9 112.5 121.4 121.4 N6-C5-C4 123.4 123.0 123.9 119.2 120.0 N6-C5-H5 116.0 118.9 117.9 119.0 117.9 C4-C5-H5 121.0 118.1 118.2 121.8 122.1 C5-N6-N1 117.8 119.0 118.1 120.5 119.6 C2-N3-H3 120.0 116.4 116.3 Correlation value 0.967 4 0.963 4 0.712 3 0.660 1 a Taken from Ref. [12]

Table 6 Experimental and calculated geometric parameters of the ground state conformers of two tautomer of 6AU

From the discussion above we can say that the ground state conformer of the 4-enol tautomer is a lower energy than that of the 2, 4-diol tautomer. So, the most probably preferential tautomer of 3DAU and 6AU are the 4-enol form. The ground state conformer of the 2, 4-diol form has two O— H bonds which are oriented externally and the internally (to the N— H bond).

The ground state hydrogen conformations and vibrational analysis of 3DAU and 6AU tautomers (4-enol and 2, 4-diol forms) have been calculated by using ab initio Hartree-Fock (HF) and density functional theory (B3LYP) methods with 6-311++G(d, p) basis set level. The calculations have shown that the most probably preferential tautomer of 3DAU and 6AU are the 4-enol form. The vibrational frequencies and optimized geometry parameters (bond lengths and bond angles) of the ground state conformer of each tautomeric form of all title molecules were obtained and compared to the corresponding experimental data. It was also seen that the B3LYP method is superior to the HF method for both the vibrational frequencies and geometric parameters.