^{1}, Marcelo L. Lyra

^{1}, Kaline Coutinho

^{2}and Sylvio Canuto

^{2,a)}

### Abstract

A combination of the polarizable continuum model (PCM) and the hybrid quantum mechanics/molecular mechanics (QM/MM) methodology, PCM-MM/QM, is used to include the solute electronic polarization and then study the solvent effects on the low-lying n→π^{*} excitation energy and the ^{15}N nuclear magnetic shielding of pyrazine and pyridazine in aqueous environment. The results obtained with PCM-MM/QM are compared with two other procedures, i.e., the conventional PCM and the iterative and sequential QM/MM (I-QM/MM). The QM calculations are made using density functional theory in the three procedures. For the excitation energies, the time-dependent B3LYP/6-311+G(d) model is used. For the magnetic shielding, the B3LYP/aug-pcS2(N)/pcS2(C,O,H) is used with the gauge-including atomic orbitals. In both cases, i.e., PCM-MM/QM and I-QM/MM, that use a discrete model of the solvent, the solute is surrounded by a first shell of explicit water molecules embedded by an electrostatic field of point charges for the outer shells. The best results are obtained including 28 explicit water molecules for the spectral calculations and 9 explicit water molecules for the magnetic shielding. Using the PCM-MM/QM methodology the results for the n→π^{*} excitation energies of pyridazine and pyrazine are 32 070 ± 80 cm^{−1} and 32 675 ± 60 cm^{−1}, respectively, in good agreement with the corresponding I-MM/QM results of 32 540 ± 80 cm^{−1} and 32 710 ± 60 cm^{−1} and the experimental results of 33 450–33 580 cm^{−1} and 32 700–33 300 cm^{−1}. For the ^{15}N magnetic shielding, the corresponding numbers for the gas-water shifts obtained with PCM-MM/QM are 47.4 ± 1.3 ppm for pyridazine and 19.7 ± 1.1 ppm for pyrazine, compared with the I-QM/MM values of 53.4 ± 1.3 ppm and 19.5 ± 1.2 ppm and the experimental results of 42–54 ppm and 17–22 ppm, respectively. The agreement between the two procedures is found to be very good and both are in agreement with the experimental values. PCM-MM/QM approach gives a good solute polarization and could be considered in obtaining reliable results within the expected QM/MM accuracy. With this electronic polarization, the solvent effects on the electronic absorption spectra and the ^{15}N magnetic shielding of the diazines in water are well described by using only an electrostatic approximation. Finally, it is remarked that the experimental and theoretical results suggest that the ^{15}N nuclear magnetic shielding of any diazine has a clear dependence with the solvent polarity but not directly with the solute-solvent hydrogen bonds.

This work was partially supported by CNPq, CAPES, FAPESP, FAPEAL, INCT-FCx and nBioNet.

I. INTRODUCTION

II. CALCULATION DETAILS

III. RESULTS AND DISCUSSION

A. Electronic polarization of diazines in water

1. Pyridazine

2. Pyrazine

B. Structural analysis and solute-solvent hydrogen-bonded configurations

C. Spectroscopic properties in water

1. Absorption spectra

2. Nuclear magnetic shielding

IV. CONCLUSIONS

### Key Topics

- Polarization
- 60.0
- Solvents
- 43.0
- Magnetic shielding
- 26.0
- Electrostatics
- 23.0
- Electric dipole moments
- 12.0

## Figures

The structure of pyridazine and pyrazine molecules and the atomic labels.

The structure of pyridazine and pyrazine molecules and the atomic labels.

Calculated average values of the dipole moments of in-water pyridazine with respect to the number of iterations (filled square). Each point is obtained from an average involving 100 configurations. Also shown are the corresponding values using PCM (filled circle) and in values obtained after one MC simulation with the PCM polarization (open circle).

Calculated average values of the dipole moments of in-water pyridazine with respect to the number of iterations (filled square). Each point is obtained from an average involving 100 configurations. Also shown are the corresponding values using PCM (filled circle) and in values obtained after one MC simulation with the PCM polarization (open circle).

Calculated mean charges in atoms (a) N(1,2), (b) C(1,2,3,4), and (c) H(1,2,3,4) of pyrazine, and (d) N(1,2), (e) C(1,2), C(3,4), (f) H(1,4), and H(2,3) of pyridazine with respect to the number of iterations. Each set of charges in each iteration as obtained from an average involving 100 statistically uncorrelated configurations. The PCM charges are shown in the filled dark (red) circles and the open circles are the values obtained after one MC simulation with the PCM polarization. The dotted lines represent the converged values presented in Table I.

Calculated mean charges in atoms (a) N(1,2), (b) C(1,2,3,4), and (c) H(1,2,3,4) of pyrazine, and (d) N(1,2), (e) C(1,2), C(3,4), (f) H(1,4), and H(2,3) of pyridazine with respect to the number of iterations. Each set of charges in each iteration as obtained from an average involving 100 statistically uncorrelated configurations. The PCM charges are shown in the filled dark (red) circles and the open circles are the values obtained after one MC simulation with the PCM polarization. The dotted lines represent the converged values presented in Table I.

Radial distribution functions between the (a) center of mass and the (b) nitrogen atom of solute and the oxygen or hydrogen atom of water molecules of the solvent for pyridazine. (c) The histogram of the pairwise energy interaction between pyridazine and the solvent water molecules in both polarization schemes.

Radial distribution functions between the (a) center of mass and the (b) nitrogen atom of solute and the oxygen or hydrogen atom of water molecules of the solvent for pyridazine. (c) The histogram of the pairwise energy interaction between pyridazine and the solvent water molecules in both polarization schemes.

Dependence of the experimental ^{15}N chemical shift of (a) pyridazine and (b) pyrazine with the Reichardt normalized polarity^{69} for 12 different solvents. Numerical values from the experiments of Witanowski *et al.* ^{68} with different solvents: 1 = cyclohexane, 2 = CCl_{4}, 3 = Et_{2}O, 4 = benzene, 5 = dioxane, 6 = acetone, 7 = DMSO, 8 = CH_{2}C1_{2}, 9 = CHCl_{3}, 10 = EtOH, 11 = MeOH, and 12 = H_{2}O.

Dependence of the experimental ^{15}N chemical shift of (a) pyridazine and (b) pyrazine with the Reichardt normalized polarity^{69} for 12 different solvents. Numerical values from the experiments of Witanowski *et al.* ^{68} with different solvents: 1 = cyclohexane, 2 = CCl_{4}, 3 = Et_{2}O, 4 = benzene, 5 = dioxane, 6 = acetone, 7 = DMSO, 8 = CH_{2}C1_{2}, 9 = CHCl_{3}, 10 = EtOH, 11 = MeOH, and 12 = H_{2}O.

## Tables

Atomic charges (*e*) of pyridazine and pyrazine obtained by PCM and iterative polarizations. The dipole moments for each type of polarization are also shown.

Atomic charges (*e*) of pyridazine and pyrazine obtained by PCM and iterative polarizations. The dipole moments for each type of polarization are also shown.

Statistics (in percentage) of solute-solvent hydrogen-bonding water molecules of pyridazine and pyrazine in water for both polarization schemes.

Statistics (in percentage) of solute-solvent hydrogen-bonding water molecules of pyridazine and pyrazine in water for both polarization schemes.

Experimental results for the lowest n → π* absorption transition (in cm^{−1}) of pyridazine and pyrazine in low polarity solvents and water.

Experimental results for the lowest n → π* absorption transition (in cm^{−1}) of pyridazine and pyrazine in low polarity solvents and water.

Calculated values for the lowest n → π* absorption transition (in cm^{−1}) of pyridazine and pyrazine using 100 statistically uncorrelated configurations obtained from the MC simulations. The absorption energies are calculated using TD DFT B3LYP/6-311+G(d) level and the error bars are the statistical error for the average values. Results in parenthesis were obtained using a geometry optimized with PCM.

Calculated values for the lowest n → π* absorption transition (in cm^{−1}) of pyridazine and pyrazine using 100 statistically uncorrelated configurations obtained from the MC simulations. The absorption energies are calculated using TD DFT B3LYP/6-311+G(d) level and the error bars are the statistical error for the average values. Results in parenthesis were obtained using a geometry optimized with PCM.

Theoretical values for the lowest n → π* absorption transition (in cm^{−1}) of pyridazine and pyrazine in water and the respective shifts with respect to the gas phase values.

Theoretical values for the lowest n → π* absorption transition (in cm^{−1}) of pyridazine and pyrazine in water and the respective shifts with respect to the gas phase values.

Theoretical values for the ^{15}N isotropic magnetic shielding and gas-water shift (in ppm) of pyridazine and pyrazine using 100 statistically uncorrelated configurations obtained by the MC simulations using the two polarization schemes. The magnetic shieldings are calculated using DFT/B3LYP/GIAO/aug-pcS2(N)/pcS2(C,O,H) level and the error bars are the statistical error for the average values. Results in parenthesis were obtained using a geometry optimized with PCM.

Theoretical values for the ^{15}N isotropic magnetic shielding and gas-water shift (in ppm) of pyridazine and pyrazine using 100 statistically uncorrelated configurations obtained by the MC simulations using the two polarization schemes. The magnetic shieldings are calculated using DFT/B3LYP/GIAO/aug-pcS2(N)/pcS2(C,O,H) level and the error bars are the statistical error for the average values. Results in parenthesis were obtained using a geometry optimized with PCM.

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