Identifying the Energy of the Hydrogen Bond Between Two Water Molecules

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Abstract

In this computational experiment the energy of the hydrogen bond between two water molecules was determined, using different density functionals. The proton affinity of water was also determined using different basis sets. The main goal was to look for the best density functional to determine the energy of the hydrogen bond and to determine what basis set is sufficient to calculate the proton affinity of water.

Introduction

For the calculation of the energy of the hydrogen bond between two water molecules different density functionals were used. Functionals with and without dispersion-correction were used. Also one hybrid functional was used. The calculated data can be compared with the experimental data. To calculate the proton affinity the energy of one water molecule, of one proton and of the oxonium ion had to be determined. Different basis sets were used. The less expensive basis set was determined using the converged method. Each calculation a more elaborate basis set was used. The most sufficient basis set is the basis set at which the calculated values don’t change if you use a higher basis set.

Computational method

For this experiment the software used was ADF. The density functionals used are GGA-BP, BLYP-D, B3LYP, GGA-HTBS and GGA-mPW. The different basis sets used to calculate the proton affinity are SZ, DZ, DZP, TZP, TZ2P and QZ4P.

Results and Discussion

One water molecule was optimized with the corresponding functional and the TZ2P basis set. The geometry and energy of the other water molecule was copied. The energies of the single water molecule are listed in Table 1. In Table 2 the energy of the hydrogen bond and the distance between the two oxygen’s are listed. The experimental value of the energy of the hydrogen bond was -21.05 kJ/mol, which corresponds to -5.031 kcal/mol. The O—O distance was determined experimentally at 292 pm.1 The calculated data of the energy from the BLYP-D functional corresponds most to the experimentally observed data. The O—O distance is best described with the GGA-mPW functional. The hybrid B3LYP functional was too expensive for this calculation and no data was obtained.

For the calculation of the proton affinity the GGA:BP functional was used. Different basis sets (Table 3) were used to calculate the energy of H2O, H+ and H3O+. The proton affinity is the energy released when water binds to a proton. This is always a positive value and equal to - ΔHr.2 It is the energy of the oxonium ion minus the energy of the proton and minus the energy of the water molecule (Table 3). According to the data the bond angle of H—O—H in water converged at the DZP basis set. The O—H bond length also converged at the DZP basis set. The basis set at which the proton affinity converged is hard to determine, but if the Q4ZP basis set is not taken into account, the proton affinity converged at the TZP basis set. Because the geometry of water is sufficient described with the DZP basis set, the DZP basis set is sufficient for the geometry of larger molecules. The TZP basis set is good enough for the calculation of the proton affinity on oxygen, because at this basis set the value of the proton affinity converged. The proton affinity on nitrogen will probably also be good described.

Table 1:Total bond energy of single water molecule with the basis set TZ2P.

Functional Total energy (kcal/mol)

GGA-BP -326.36

BLYP-D -317.78

B3LYP -393.71

GGA-HTBS -328.59

GGA-mPW -362.80

Table 2: Energy of water dimer, the hydrogen bond energy and the length of the hydrogen bond.

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Functional Total Energy (kcal/mol) Bond length of hydrogen bond (pm) O—O Distance (pm) Hydrogen bond Energy (kcal/mol)

GGA-BP -657.15 191.2 298.2 -4.43

BLYP-D -640.95 192.7 289.8 -5.39

B3LYP - - - -

GGA-HTBS -660.33 205.1 302.6 -3.15

GGA-mPW -658.1 194.0 291.8 -67.5

Table 3: Total energy of H2O, H+ and H3O+ and the proton affinity of water using different basis sets

Basis set Total energy H2O(kcal/mol) O—H Distance (pm) H—O—H Angle Total energy H+ (kcal/mol) Total energy H3O+(kcal/mol) Proton Affinity (kcal/mol)

SZ -333.89 103.6 96.1 264.17 -295.97 226.25

DZ -299.44 99.7 108.0 291.91 -179.23 171.70

DZP -321.23 97.7 103.5 291.91 -192.26 162.94

TZP -324.16 97.4 103.5 291.96 -201.03 168.93

TZ2P -326.36 97.1 104.4 291.96 -204.15 169.75

QZ4P -344.55 97.0 104.9 291.96 -206.97 154.38

Conclusion

The best and less expensive density functional to describe the hydrogen bond between two water molecules was the BLYP-D functional. The hybrid functional was to expensive for this type of calculation and the amount of atoms involved. The GGA-mPW functional describes the geometry of the dimer better than the other functionals compared with the experimental results.

For the calculation of the H—O—H bond angle and the length of the O—H bond the DZP basis set was good enough to give an adequate value. For the calculation of the proton affinity, the TZP basis set is good enough.

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