Science Innovation
Volume 3, Issue 6, December 2015, Pages: 127-134

Tautomerism of 2-Azido-1, 3, 4-Thiadiazole Studied by Theoretical Methods in Gas Phase and Solution

Zeinab Dalirnasab1, *, Zeinab Suri2, Sudabeh Dalirnasab3

1Department of Chemistry, Faculty of science, Kangan Payam Noor University, Kangan, Iran

2Department of Chemistry, Faculty of science, Khorramabad Payam Noor University, Khorramabad, Iran

3Department of Chemistry, Faculty of Science, Yazd University, Yazd, Iran

Email address:

(Z. Dalirnasab)

To cite this article:

Zeinab Dalirnasab, Zeinab Suri, Sudabeh Dalirnasab. Tautomerism of 2-Azido-1, 3, 4-Thiadiazole Studied by Theoretical Methods in Gas Phase and Solution. Science Innovation. Vol. 3, No. 6, 2015, pp. 127-134. doi: 10.11648/j.si.20150306.21


Abstract: The tautomeric equilibrium of 2-azido-1, 3,4-thiadiazole and [1,3,4]thiadiazolo[3,2-e]tetrazole derivatives (5-H, 5-F, 5-Cl, 5-CH3, 5-CH2CH3, 5-NO2, 5-CN) has been investigated using HF, B3LYP and MP2 level of calculation with the 6-311G (d,p) in the gas phase and solution with full geometry optimization. The calculation results demonstrate 2-azido-1, 3, 4-thiadiazole derivatives are more stable. In addition variation of dipole moments, charges on atoms, HOMO, LUMO and the interfrontier molecular orbital energy gap are studied.

Keywords: 2-Azido-1, 3, 4-Thiadiazole, [1, 3, 4]Thiadiazolo[3,2-E]Tetrazole, Tautomerism, Polarizable Continuum Model (PCM), Tautomerism, Density Functional Theory (DFT)


1. Introduction

The [1,3,4]thiadiazoles heterocyclic core is a widespread subunit in numerous natural products (such as B6-vitamins pyridoxine, pyridoxamine, pyrodoxal and codecarbaxylase contain a thiadiazole nucleus) and synthetic compounds. The [1,3,4]thiadiazoles have recived the attention of medicinal chemists due to which include their broad spectrum of pharmacological actions such as anti-fungal, anti-inflammatory, analgesic, anti-anxiety, anti-viral, anti-depressant, anti-tubercular, analgesic and antibacterial activities. [1-5]

Tetrazoles are an important class of heterocycles in a wide range of applications, such as, organ catalysis and transition metal catalysis, propellants, explosives, and perhaps most commonly, as non-classical isosteres of carboxylic acids in medicinal chemistry.[6,7] [1,3,4]thiadiazoles azides are known for transformation to [1,3,4]thiadiazolo[3,2-e]tetrazole. Undoubtedly, This product can highly enhance biological activity of [1,3,4]thiadiazoles and Tetrazoles.

Tautomerism of five-membered heterocycles of importance for pharmacy (substituted diazoles and tetrazoles) was a subject of several theoretical and experimental papers. So, The aim of this study is systematic investigation of substituent effect and its influence on tautomerism of the C5-substituted [1,3,4]thiadiazoles azides and [1,3,4]thiadiazolo[3,2-e]tetrazole (Scheme 1).

Scheme 1. Tautomeric forms of [1,3,4]thiadiazoles azides and [1,3,4]thiadiazolo[3,2-e]tetrazole derivatives .

2. Computational Details

Quantum chemical calculations were performed with the use of the Gaussian 03 set of programs.[8] All structures were fully optimized with Hartree-Fock (RHF) and density functional theory (DFT) using Becke’s three parameter hybrid method [9] and correlation functional of Lee-Yang-Parr (B3LYP) [10]in conjunction at the level of 6-31++G** [11] basis sets. Atomic charges of the stationary points were obtained by using the natural bond orbital (NBO) approach.[12] The solvent effects have been considered by B3LYP/6-31G single point calculations over the gas phase optimized structures using a self-consistent reaction field [13] (SCRF) based on the PCM method of the Tomasi’s group.[14,15]

3. Results and Discussion

[1,3,4]thiadiazolo[3,2-e]tetrazole and 2-azido-1,3,4-thiadiazole derivatives are depicted in Scheme 1 and the results of calculated total energies in the different methods and using many basis sets presented in Table 1. The results of our calculations suggest that in the gas phase, B form is more stable. For example, based on the B3LYP/6311+ +G (d,p) calculations, the stability of B form over A form was found to be -5.83 kcal/mol (1 cal = 4.184 J). Consideration of the electron correlation effects did not change the stability order, and calculations at the MP2/6311++G (d,p) level showed B form favored by -0.094 kcal/mol over A form.

Table 1. Calculated relative instabilities of A form over B form in the gas phase.

    A B ΔE(B-A)
HF 6–311G(d) -746.0386482 -746.0432189 -2.89
  6–311+G(d) -746.0475718 7-746.0520187 -2.79
  6-311++(d,p) -746.0493644 -746.0538495 -2.81
DFT 6–311G(d) -748.7522259 -748.7619111 -6.08
  6–311+G(d) -748.7627467 -748.7719908 -5.80
  6-311++(d,p) -748.764434 -748.7737262 -5.83
MP2 6–311G(d) -746.0256874 -746.0257692 -0.051
  6–311+G(d) -746.0339809 -746.0341500 -0.106
  6-311++(d,p) -746.0358793 -746.0360288 -0.094

The results of energy comparisons of two tautomers in the gas phase and different solvents are given in Table 2. It is easily seen that in the gas phase all (B) forms are more stable than (A) forms. The major difference between (B) and (A) form in gas phase was found for 5-NO2 2-azido-1, 3, 4-thiadiazole with -9.54 kcal mol-1. By glancing at the table, we can notice that the stability of (B) tautomer relates to the nature of substituents.

Obviously, the solvent molecules play an important role in tautomer stability, Here, the solvent effects were calculated by PCM/B3LYP calculations (which is widely used for investigation of the solute-solvent interactions) to analyze the solvent effects on tautomerism of [1,3,4]thiadiazolo[3,2-e]tetrazole and 2-azido-1,3,4-thiadiazole derivatives. The data presented in Table 1 show that polar solvents increase the stability of derivatives of two forms in compare to gas phase.

Table 2. Calculated total energiesa at B3LYP/6-311++G** and relative stabilityv in the gas phase and solvents.

R   Gas Benzene THF Ethanol Dmso Water
CH3 A -788.1008843 -788.1086744 -788.113921 -788.1157318 -788.1161062 -788.1162782
B -788.1080242 -788.1125702 -788.1155352 -788.1165443 -788.1167523 -788.1168477
ΔE(B-A) -4.48 -2.44 -1.01 -0.51 -0.40 -0.36
CH2CH3 A -827.4253493 -827.4329168 -827.4379859 -827.4397281 -827.4400886 -827.4402542
B -827.4322643 -827.4366759 -827.4395399 -827.4405127 -827.4407128 -827.440805
ΔE(B-A) -4.34 -2.36 -0.97 -0.49 -0.39 -0.34
H A -748.76443 -748.7722345 -748.7774966 -748.7793131 -748.7796883 -748.7798612
  B -748.7737262 -748.7783719 -748.781384 -748.7824046 -748.7826148 -748.782711
  ΔE(B-A) -5.83 -3.85 -2.44 -1.94 -1.84 -1.79
F A -848.0235647 -848.030326 -848.0348274 -848.036372 -848.0366905 -848.0368371
  B -848.0338839 -848.0379412 -848.0405625 -848.0414517 -848.0416344 -848.0417181
  ΔE(B-A) -6.47 -4.78 -3.60 -3.19 -3.10 -3.06
Cl A -1208.3792004 -1208.3857656 -1208.3901442 -1208.3916476 -1208.3919588 -1208.3921014
  B -1208.3898749 -1208.3937667 -1208.3962814 -1208.397133 -1208.3973087 -1208.397389
  ΔE(B-A) -6.70 -5.02 -3.85 -3.44 -3.36 -3.32
NO2 A -953.3045945 -953.3127692 -953.3180451 -953.319824 -953.3201889 -953.3203562
B -953.3198031 -953.3262439 -953.3303823 -953.3317793 -953.3320664 -953.332198
ΔE(B-A) -9.54 -8.45 -7.74 -7.50 -7.45 -7.43
CN A -841.0148361 -841.0227068 -841.0279177 -841.0296984 -841.0300659 -841.0302335
B -841.0298493 -841.0355616 -841.0392779 -841.0405388 -841.040798 -841.040917
ΔE(B-A) -9.42 -8.07 -7.13 -6.80 -6.73 -6.70

a Hartree.

b Relative stabilities in kcal mol_1.

The plots of relative stability of two tautomers separately are depicted in Fig. 1. The electron donating and electron withdrawing groups show a regular decrease of in the difference between two forms from gas phase to most polar solvents (water).

Fig. 1. Relative stability of [1,3,4]thiadiazolo[3,2-e]tetrazole tautomers (left) and 2-azido-1,3,4-thiadiazole tautomers (right) of tetrazole derivatives.

The thermodynamics parameters, E, H and G, of each tautomer were calculated at B3LYP/6-311G (d,p) level according to the formulas [16]

H = E + RT                               (1)

G = H −TS                               (2)

E is the thermal energy

H is the enthalpy

G is the Gibbs free energy

For comparison, the relative values, ΔE, ΔH and ΔG are collected and shown with E, H and G in Table 3. The calculation results confirm that form B is more stable than form A.

Table3. The thermodynamics parameters, E, H and G, of each tautomer were calculated by DFT/6-311G** level.

    EO H G ΔE ΔH ΔG
A Gas -748.711359 -748.710415 -748.746553 -6.32 -6.32 -8.09
  Water -748.726465 -748.725521 -748.761530 -2.48 -2.48 -4.35
B Gas -748.721428 -748.720484 -748.759448 0 0 0
  Water -748.730412 -748.729468 -748.768461 0 0 0

Equilibrium constants [17] between the tautomeric forms A and B were calculated in gas phase and in water from Gibbs free energies using

ΔG= -RT ln Keq.                            (3)

The R value is equal to 1.987 cal K-1mol-1, ΔG the Gibbs free energy difference between the A and B tautomers and T is 298.15K. The result of the calculated equilibrium constant for the B→A conversions in the gas phase and with water as the solvent is tabulated in Table 4. As seen in the table, from gas phase to the water solvent phase, the equilibrium constants decreased.

Table 4. Calculated equilibrium constants in the gas phase and water solvent phase using DFT methods using 6311++G (d,p) basis function.

B→A DFT
Gas 1.15
Water 0.932

The calculated dipole moments of two tautomeric are presented in Table 5. It is notable that dipolemoments significantly relate to the nature of substituents at the 5th position. In the A tautomers, electron withdrawing derivatives have smaller dipole moments than electron releasing ones; however in B forms electron donating derivatives have lower dipole moments values than electron withdrawing substituents.

Table 5. Calculated dipole moments of optimized tautomers of tetrazoles (Debye).

R Tautomer Gas Benzene THF Ethanol Dmso Water
CH3 A 7.11 8.29 9.14 9.44 9.50 9.53
B 3.30 3.93 4.41 4.59 4.62 4.64
CH2CH3 A 7.35 8.51 9.34 9.63 9.69 9.72
B 3.39 4.01 4.49 4.66 4.69 4.71
H A 6.13 7.23 8.02 8.30 8.36 8.38
  B 2.95 3.54 3.98 4.14 4.18 4.19
F A 4.79 5.71 6.39 6.63 6.68 6.70
B 2.85 3.42 3.85 4.00 4.02 4.03
Cl A 5.35 6.34 7.06 7.32 7.38 7.40
B 2.67 3.23 3.66 3.81 3.84 3.86
NO2 A 2.63 3.27 3.77 3.95 3.99 4.00
B 4.46 5.29 5.91 6.13 6.18 6.20
CN A 2.95 3.64 4.16 4.35 4.39 4.40
B 4.24 4.98 5.53 5.71 5.75 5.77

For example for methyl and Cl derivatives difference between dipole moment of A and B is 3.81 and 2.68 D but for NO2 and CN the values are -1.83 and -1.29, respectively. The results of calculations show that dipole moments of the A and B forms is affected by variation of polarity of the medium, and in all tautomers a regular increase in the dipole moment when using more polar solvents was observed. Plot of dipole moment of tetrazole derivatives vs. dielectric constants are given in Fig. 2.

Fig. 2. Dielectric constant dependence of the dipole moments of [1,3,4]thiadiazolo[3,2-e]tetrazole (left) and 2-azido-1,3,4-thiadiazole (right).

The atomic charges for all the atoms of the title compound calculated by DFT method in gas phase and solutions are listed in Table 6. As seen from this table, Nitrogens atoms of the tautomer A carry negative charge and the sulfur atom S has positive atomic charge with values as 0.397, 0.395, 0.413, 0.398, 0.444, 0.495 and 0.475 units for CH3, CH2CH3, H, F, Cl, NO2and CN respectively. Negative charge was found for C2 atom in A forms when substituent are CH3, CH2CH3, Cl and NO2. However as it can be seen from Table 3 S1, C2, C5, N7 and N8 in the derivatives of B forms have positive charge values but N3, N4 and N6 have negative charge. From Table 3, it is clear that substituents have some influence on charge in two tautomers. The charge at the S1, C2, N3, N4, C5, N6, N7, and N8 atoms differs a little from that in unsubstituted forms solely for electron donating or electron withdrawing groups. Unexpectedly, the substituents, which have lone electron pair(s), generate increase of charge at the C2 atom. This phenomenon can be related to electron flow from the substituent to the p-electron systems of the five-membered system. The charge at this atom of the substituent is also quite negative for electron drawing group CN.

The charge distributions of dipolar compounds are often altered significantly in the presence of a solvent reaction field. [18] We have examined the charge distribution of tautomers in the solvent as well as gas phase by using calculated NBO charges. The charge distribution in solvents with increase of polarity differently varies for any atoms. For example, a regular increase of positive charge was found for S1 atom in A and B forms when passing from gas phase to more polar solvent water, In N3, N6, N7 and N8 position the negative charge of A isomers from gas phase to polar solvents increased drastically. When passing from gas phase to polar solvents a regular increase of negative charge in the C5 position in A and B tautomers was found. In C2 position in B tautomers with increase of polarity an increase of negative charge was observed.

Table 6. Calculated NBO charges on ring atoms of [1,3,4]thiadiazolo[3,2-e]tetrazole and 2-azido-1,3,4-thiadiazole derivatives.

  Form A           B          
  ε (1.0) (2.2) (7.6) (24.3) (47.2) (78.4) (1.0) (2.2) (7.6) (24.3) (47.2) (78.4)
  Atom                        
CH3 S1 0.397 0.423 0.443 0.450 0.452 0.453 0.367 0.386 0.402 0.408 0.409 0.409
  C2 0.107 0.121 0.129 0.133 0.134 0.134 0.063 0.071 0.077 0.078 0.078 0.079
  N3 -0.250 -0.264 -0.272 -0.276 -0.277 -0.277 -0.277 -0.299 -0.315 -0.320 -0.321 -0.322
  N4 -0.075 -0.067 -0.062 -0.060 -0.060 -0.060 -0.323 -0.340 -0.353 -0.357 -0.358 -0.359
  C5 0.167 0.173 0.175 0.176 0.176 0.176 0.191 0.193 0.195 0.195 0.195 0.195
  N6 -0.322 -0.337 -0.347 -0.351 -0.352 -0.352 -0.365 -0.365 -0.363 -0.363 -0.362 -0.362
  N7 -0.056 -0.077 -0.093 -0.098 -0.099 -0.100 0.257 0.263 0.266 0.267 0.267 0.267
  N8 -0.052 -0.066 -0.076 -0.080 -0.081 -0.081 0.022 0.017 0.013 0.012 0.011 0.011
CH2CH3 S1 0.395 0.420 0.441 0.448 0.449 0.450 0.366 0.385 0.400 0.406 0.407 0.407
  C2 0.118 0.131 0.138 0.141 0.142 0.142 0.072 0.080 0.084 0.085 0.086 0.086
  N3 -0.250 -0.263 -0.271 -0.274 -0.274 -0.275 -0.276 -0.297 -0.312 -0.317 -0.318 -0.319
  N4 -0.075 -0.067 -0.062 -0.061 -0.060 -0.060 -0.324 -0.341 -0.353 -0.357 -0.358 -0.359
  C5 0.166 0.172 0.175 0.176 0.176 0.176 0.189 0.192 0.193 0.194 0.194 0.194
  N6 -0.323 -0.338 -0.348 -0.351 -0.352 -0.352 -0.365 -0.365 -0.363 -0.363 -0.363 -0.363
  N7 -0.057 -0.077 -0.092 -0.098 -0.099 -0.099 0.257 0.263 0.266 0.267 0.267 0.267
  N8 -0.053 -0.067 -0.077 -0.080 -0.081 -0.081 0.021 0.016 0.013 0.011 0.011 0.011
H S1 0.413 0.440 0.461 0.469 0.471 0.471 0.380 0.400 0.416 0.422 0.424 0.424
C2 -0.089 -0.075 -0.066 -0.062 -0.062 -0.061 -0.132 -0.126 -0.122 -0.120 -0.120 -0.120
N3 -0.217 -0.233 -0.244 -0.274 -0.248 -0.248 -0.252 -0.275 -0.291 -0.297 -0.298 -0.299
N4 -0.079 -0.071 -0.066 -0.064 -0.064 -0.064 -0.324 -0.341 -0.353 -0.357 -0.358 -0.358
C5 0.163 0.169 0.172 0.173 0.173 0.174 0.187 0.190 0.192 0.192 0.192 0.192
N6 -0.319 -0.334 -0.344 -0.347 -0.348 -0.348 -0.365 -0.364 -0.363 -0.362 -0.362 -0.362
N7 -0.050 -0.071 -0.087 -0.092 -0.093 -0.094 0.257 0.263 0.266 0.267 0.267 0.268
N8 -0.050 -0.064 -0.074 -0.078 -0.079 -0.079 0.029 0.024 0.020 0.019 0.018 0.018
F S1 0.398 0.430 0.453 0.461 0.463 0.464 0.357 0.382 0.402 0.408 0.409 0.410
C2 0.480 0.489 0.495 0.497 0.495 0.498 0.448 0.451 0.450 0.451 0.451 0.451
N3 -0.275 -0.287 -0.295 -0.298 -0.296 -0.298 -0.707 -0.326 -0.338 -0.343 -0.344 -0.344
N4 -0.076 -0.067 -0.062 -0.060 -0.059 -0.059 -0.317 -0.332 -0.343 -0.347 -0.348 -0.348
C5 0.171 0.178 0.182 0.184 0.184 0.184 0.200 0.205 0.208 0.209 0.209 0.209
N6 -0.314 -0.328 -0.336 -0.340 -0.340 -0.340 -0.368 -0367 -0.365 -0.364 -0.363 -0.363
N7 -0.049 -0.070 -0.084 -0.089 -0.090 -0.091 0.257 0.263 0.267 0.268 0.268 0.269
N8 -0.042 -0.055 -0.065 -0.068 -0.069 -0.069 0.037 0.033 0.029 0.028 0.028 0.028
Cl S1 0.444 0.472 0.493 0.501 0.503 0.503 0.411 0.433 0.450 0.456 0.458 0.458
C2 -0.007 -0.000 0.004 0.005 0.005 0.005 -0.033 -0.031 -0.030 -0.030 -0.030 -0.030
N3 -0.251 -0.263 -0.272 -0.274 -0.275 -0.275 -0.280 -0.299 -0.313 -0.318 -0.319 -0.320
N4 -0.074 -0.065 -0.060 -0.058 -0.058 -0.058 -0.315 -0.330 -0.340 -0.344 -0.345 -0.345
C5 0.167 0.175 0.179 0.180 0.180 0.180 0.195 0.200 0.203 0.204 0.205 0.205
N6 -0.316 -0.329 -0.339 -0.342 -0.343 -0.343 -0.366 -0.365 -0.363 -0.362 -0.361 -0.361
N7 -0.048 -0.068 -0.082 -0.087 -0.088 -0.089 0.257 0.263 0.267 0.268 0.268 0.269
N8 -0.044 -0.057 -0.066 -0.069 -0.070 -0.071 0.037 0.033 0.030 0.029 0.029 0.028
NO2 S1 0.495 0.524 0.546 0.554 0.556 0.556 0.437 0.494 0.510 0.516 0.517 0.518
C2 0.159 0.168 0.174 0.176 0.176 0.176 0.121 0.124 0.124 0.124 0.124 0.124
N3 -0.178 -0.185 -0.190 -0.192 -0.192 -0.192 -0.203 -0.216 -0.225 -0.228 -0.229 -0.229
N4 -0.074 -0.064 -0.058 -0.057 -0.056 -0.056 -0.314 -0.323 -0.328 -0.330 -0.331 -0.331
  C5 0.167 0.178 0.184 0.187 0.186 0.187 0.198 0.207 0.213 0.215 0.215 0.215
N6 -0.309 -0.322 -0.330 -0.332 -0.333 -0.333 -0.361 -0.358 -0.355 -0.353 -0.353 -0.353
N7 -0.031 -0.049 -0.062 -0.066 -0.067 -0.067 0.257 0.264 0.269 0.270 0.271 0.271
N8 -0.036 -0.047 -0.054 -0.057 -0.058 -0.058 0.062 0.061 0.061 0.061 0.061 0.061
CN S1 0.475 0.510 0.536 0.546 0.547 0.548 0.450 0.478 0.449 0.506 0.508 0.509
C2 -0.037 -0.033 -0.031 -0.030 -0.030 -0.030 -0.085 -0.090 -0.094 -0.095 -0.095 -0.095
N3 -0.165 -0.172 -0.178 -0.179 -0.180 -0.180 -0.193 -0.270 -0.218 -0.221 -0.222 -0.222
N4 -0.072 -0.063 -0.057 -0.056 -0.055 -0.055 -0.311 -0.322 -0.330 -0.332 -0.333 -0.333
C5 0.166 0.174 0.179 0.180 0.181 0.181 0.196 0.202 0.206 0.207 0.208 0.208
N6 -0.311 -0.324 -0.332 -0.336 -0.336 -0.336 -0.362 -0.360 -0.357 -0.356 -0.356 -0.356
N7 -0.035 -0.054 -0.067 -0.072 -0.073 -0.073 0.257 0.264 0.268 0.270 0.270 0.270
N8 -0.040 -0.052 -0.060 -0.063 -0.064 -0.064 0.055 0.052 0.050 0.049 0.049 0.049

The optimized structural parameters (bond lengths, bond angles and dihedral angles) of the titled compound have been obtained at the B3LYP level of theory with a 6-311G (d,p) basis set are listed in table 8, To the best of our knowledge, there is no experimental report on the geometry of the titled compound isomers in the literature for comparison.

The calculated dihedral angles demonstrate that both tautomers are planar. From the table 7 the bond lengths S1-C2 and C2-N3 are in A-isomer 1.776, 1.290 and 1.74, 1.294 in B-isomer respectively.

Table 7. Calculated geometrical parameters of [1,3,4]thiadiazolo[3,2-e]tetrazole and 2-azido-1,3,4-thiadiazole in the gas phase and solution using the DFT/6311++G(d,p) level of theory.

  R S1-C2 C2-N3 N3-N4 N4-C5 C5-R C2-N6-N7 R-C5-N4 S1-C5-R N3-C2-N6-N7
A Gas CH3 1.738 1.355 1.359 1.293 1.491 104.191 123.227 120.943 0.00453
  benzen   1.735 1.353 1.343 1.294 1.489 104.34407 123.22790 120.91698 0.01734
  thf   1.733 1.352 1.359 1.296 1.488 104.390 123.290 120.876 -0.00655
  dmso   1.733 1.3513 1.3594 1.2967 1.4882 104.47061 123.27351 120.86751 -0.02671
  ethanol   1.733 1.351 1.359 1.297 1.488 104.441 123.313 120.860 0.00286
  water   1.733 1.351 1.359 1.297 1.488 104.454 123.294 120.868 -0.00282
B Gas   1.747 1.298 1.368 1.296 1.493 116.09685 123.97798 122.81229 -0.01015
  benzen   1.745 1.390 1.3700 1.2980 1.493 116.24493 124.12734 122.74003 -0.01113
  thf   1.744 1.390 1.371 1.299 1.492 116.323 124.218 122.665 0.01920
  dmso   1.743 1.300 1.372 1.299 1.492 116.372 124.283 122.624 -0.01739
  ethanol   1.743 1.300 1.372 1.300 1.492 116.356 124.276 122.619 0.02234
  water   1.743 1.301 1.372 1.300 1.492 116.365 124.272 122.627 -0.00513
A Gas CH2CH3 1.737 1.355 1.359 1.293 1.496 104.205 123.138 121.146 0.03122
  benzen   1.735 1.298 1.359 1.295 1.495 104.372 123.155 121.112 0.05461
  thf   1.733 1.352 1.359 1.296 1.495 104.415 123.208 121.063 0.01394
  dmso   1.732 1.351 1.359 1.297 1.494 104.426 123.229 121.0428 -0.04244
  ethanol   1.732 1.351 1.372 1.297 1.494 104.399 123.260 121.032 -0.01876
  water   1.732 1.351 1.359 1.297 1.494 104.452 123.225 121.047 0.01189
B Gas   1.747 1.299 1.367 1.297 1.498 123.931 116.090 122.976 0.01999
  benzen   1.745 1.299 1.369 1.298 1.498 116.208 124.045 122.923 0.03985
  thf   1.743 1.300 1.371 1.300 1.497 116.300 124.109 122.872 0.06273
  dmso   1.743 1.301 1.372 1.300 1.497 116.326 124.137 122.866 0.04077
  ethanol   1.743 1.309 1.372 1.300 1.497 116.317 124.140 122.864 0.05577
  water   1.742 1.301 1.372 1.300 1.497 116.324 124.151 122.854 0.05277
A Gas H 1.739 1.358 1.357 1.290 1.081 104.196 122.027 120.535 -0.00156
  benzen   1.737 1.356 1.358 1.291 1.081 104.381 122.041 120.431 -0.06582
  thf   1.735 1.354 1.358 1.293 1.080 104.399 122.169 120.266 0.02190
  dmso   1.734 1.354 1.358 1.293 1.080 104.472 122.173 120.208 0.04728
  ethanol   1.734 1.354 1.358 1.293 1.080 104.448 122.201 120.201 0.00101
  water   1.734 1.356 1.358 1.293 1.080 104.458 122.211 120.187 0.00081
B Gas   1.748 1.3018 1.367 1.294 1.081 -116.077 123.431 121.869 0.00497
  benzen   1.746 1.302 1.369 1.295 1.0801 116.202 123.543 121.814 -0.00588
  thf   1.744 1.303 1.370 1.296 1.081 116.275 123.630 121.713 0.00637
  dmso   1.744 1.304 1.371 1.297 1.081 -116.307 123.707 121.647 -0.00456
  ethanol   1.744 1.304 1.3701 1.297 1.081 116.302 123.698 121.652 0.02220
  water   1.744 1.304 1.371 1.297 1.080 116.307 123.707 121.646 -0.00458
A Gas F 1.748 1.356 1.362 1.779 1.311 104.022 122.225 119.865 0.00248
  benzen   1.745 1.354 1.361 1.282 1.310 104.161 121.859 118.669 -0.01742
  thf   1.744 1.303 1.370 1.296 1.081 116.275 123.630 121.713 0.00637
  dmso   1.742 1.352 1.360 1.284 1.308 104.278 121.517 121.517 -0.03902
  ethanol   1.742 1.352 1.360 1.284 1.308 104.273 121.533 118.952 -0.00484
  water   1.742 1.352 1.360 1.284 1.308 104.301 121.516 118.948 -0.00663
B Gas   1.758 1.297 1.374 1.279 1.320 116.053 123.391 119.865 -0.01658
  benzen   1.756 1.299 1.375 1.280 1.321 116.191 123.027 120.148 -0.00311
  thf   1.754 1.300 1.377 1.281 1.321 116.311 122.663 120.453 -0.00801
  dmso   1.754 1.300 1.377 1.281 1.321 116.315 122.642 120.468 -0.00460
  ethanol   1.754 1.300 1.377 1.281 1.321 116.311 122.663 120.453 -0.00794
  water   1.754 1.300 1.377 1.281 1.321 116.315 122.642 120.468 -0.00460
A Gas Cl 1.742 1.357 1.358 1.288 1.711 104.090 122.448 119.804 0.05013
  benzen   1.740 1.355 1.358 1.290 1.709 104.235 122.227 119.964 -0.00195
  thf   1.754 1.300 1.377 1.281 1.321 116.311 122.663 120.453 -0.00801
  dmso   1.738 1.353 1.357 1.292 1.706 104.322 122.024 120.181 0.00066
  ethanol   1.737 1.353 1.357 1.292 1.706 104.270 122.0347 120.142 -0.01491
  water   1.737 1.353 1.357 1.292 1.706 104.322 122.024 120.181 -0.00270
B Gas   1.751 1.300 1.368 1.288 1.720 116.058 123.449 121.2552 -0.01221
  benzen   1.750 1.301 1.370 1.289 1.720 116.203 123.245 121.440 -0.00467
  thf   1.754 1.300 1.377 1.281 1.321 116.311 122.663 120.453 -0.00801
  dmso   1.748 1.303 1.371 1.291 1.720 116.341 123.038 121.604 -0.00273
  ethanol   1.748 1.303 1.371 1.291 1.720 116.332 123.052 121.586 -0.03502
  water   1.748 1.303 1.371 1.291 1.720 116.341 123.038 121.604 -0.00270
A Gas NO2 1.744 1.365 1.345 1.286 1.475 104.147 121.692 118.971 0.03754
  benzen   1.741 1.363 1.351 1.287 1.472 104.233 121.294 119.204 -0.01982
  thf   1.754 1.300 1.377 1.281 1.321 116.311 122.663 120.453 -0.00801
  dmso   1.739 1.362 1.344 1.288 1.471 104.296 120.833 119.547 0.00311
  ethanol   1.739 1.362 1.344 1.288 1.471 104.311 120.879 119.505 -0.00620
  water   1.739 1.362 1.344 1.288 1.471 104.296 120.833 119.547 0.00308
B Gas   1.745 1.313 1.354 1.288 1.466 116.066 123.248 120.389 -0.00261
  benzen   1.744 1.316 1.351 1.291 1.460 116.210 122.849 120.809 0.01141
  thf   1.754 1.300 1.377 1.281 1.321 116.311 122.663 120.453 -0.00801
  dmso   1.743 1.319 1.350 1.293 1.4557 116.389 122.412 121.212 -0.00620
  ethanol   1.743 1.319 1.350 1.293 1.456 116.380 122.452 121.191 0.01334
  water   1.742 1.319 1.350 1.293 1.455 116.393 122.411 121.228 0.01542
A Gas CN 1.736 1.363 1.345 1.299 1.419 108.763 122.732 120.234 0.00307
  benzen   1.734 1.361 1.344 1.300 1.420 104.295 122.1778 120.576 -0.00365
  thf   1.754 1.300 1.377 1.281 1.321 116.311 122.663 120.453 -0.00801
  dmso   1.731 1.359 1.343 1.301 1.421 104.361 121.580 120.976 -0.00042
  ethanol   1.732 1.359 1.343 1.302 1.421 104.352 121.602 120.980 -0.01304
  water   1.731 1.359 1.343 1.302 1.421 104.326 121.553 121.004 0.04256
B Gas   1.743 1.308 1.350 1.306 1.419 116.032 123.828 121.871 -0.00180
  benzen   1.742 1.311 1.3496 1.307 1.419 116.186 123.291 122.311 0.00237
  thf   1.754 1.300 1.377 1.281 1.321 116.311 122.663 120.453 -0.00801
  dmso   1.740 1.313 1.349 1.309 1.419 116.367 122.707 122.790 0.02259
  ethanol   1.740 1.309 1.349 1.309 1.419 116.36477 122.743 122.765 0.00122
  water   1.740 1.313 1.349 1.309 1.419 116.371 122.707 122.789 -0.00270

Table 8 shows the HOMO, LUMO, and the interfrontier molecular orbital energy gap (Δε) values of two men-tioned isomers calculated at HF and DFT method using 6311++G(d,p) basis set. Three dimensional pictures of HOMO and LUMO of the studied molecules calculated at B3LYP/6311++G (d,p) level are shown in Fig. 3. Substituents Fand NO2 of Tautomers A and B are characterized with the lowest and highest lying HOMO energy values, respectively. The HOMOLUMO energy separation has been used as a simple indicator of kinetic stability. The HOMOLUMO gaps were found to be 150 and 158 kcal/mol for Substituents F of Tautomers A and B and 158 and 169 kcal/mol for Substituents F of tautomers A and B for DFT and HF methods, respectively. A large HOMOLUMO gap implies high kinetic stability and low chemical reactivity, because it is energetically unfavorable to add an electron to a high-lying LUMO or to extract electrons from a low-lying HOMO.

Table 8. The HOMO and LUMO energies (eV) and interfrontier energy gaps (Δε) of the structures considered.

R   HF DFT
    HOMO LUMO Δε HOMO LUMO Δε
CH3 A -0.146 -0.294 0.149 -0.151 -0.293 0.142
  B -0.135 -0.300 0.164 -0.141 -0.297 0.142
CH2CH3 A -0.148 -0.295 0.147 -0.153 -0.293 0.140
  B -0.137 -0.299 0.162 -0.142 -0.297 0.154
H A -0.149 -0.300 0.149 -0.153 -0. 296 0.143
B -0.136 -0.300 0.163 -0.141 -0.297 0.156
F A -0.135 -0.294 0.158 -0.142 -0.292 0.150
B -0.131 -0.300 0.169 -0.139 -0.297 0.158
Cl A -0.144 -0.295 0.151 -0.149 -0.293 0.144
B -0.134 -0.300 0.166 -0.141 -0.297 0.157
NO2 A -0.183 -0.299 0.115 -0.189 -0.297 0.108
B -0.179 -0.300 0.120 -0.186 -0.297 0.111
CN A -0.182 -0.298 0.116 -0.187 -0.296 0.109
B -0.174 -0.299 0.125 -0.179 -0.296 0.117

Figure 3. The HOMO and LUMO patterns of two tautomers.

4. Conclusion

Molecular orbital calculations to study of tautomerism of 2-azido-1, 3,4-thiadiazole and [1,3,4]thiadiazolo[3,2-e]tetrazole derivatives were performed using different calculation levels. In the gas phase, all calculations predict that 2-azido-1, 3,4-thiadiazole is more stable. The charge on all atoms in the two tautomers was calculated using an NBO method in the gas phase and in solution. The charge distribution in solvents with increase of polarity differently varies for any atoms.The dipole moments of the compounds were calculated in the gas phase and the solvent case and it was observed that they are affected by the solvent. The HOMOLUMO energy separation indicates kinetic stability of the title compound. A large HOMOLUMO gap implies high kinetic stability and low chemical reactivity

Acknowledgements

We gratefully acknowledge the financial support from the Research Council of kangan University.


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