A detailed theoretical study of hydrogen-bond formation in different polyethylene glycol + water complex and dipropylene glycol + water have been performed by Hartree Fock (HF) method, second-order Møller-Plesset perturbation theory (MP2), and density functional theory (DFT) using 6-31++G(d,p) basis set. B3LYP DFT-D, WB97XD, M06, and M06-2X functionals have been used to describe highly dispersive hydrogen-bond formation appropriately. Geometrical parameters, interaction energies, deformation energies, deviation of potential energy curves of hydrogen bonded O–H from that of free O–H, frontier orbitals, and charge transfer have been studied to analyze stability and nature of hydrogen bond formation of various glycol and water complexes. It is found that WB97XD is best among all the applied DFT functionals to describe hydrogen bond interaction, and intermolecular hydrogen bonds have higher covalent character and accordingly higher strength when glycol acts as proton donor for glycol + 1 water complex system.
Polyethylene glycol and its derivatives are applied extensively as drag delivering medium in medical industry [
A detail theoretical analysis is reported here to comprehend the electronic nature of the hydrogen-bond formation in various polyethylene glycol-water and dipropylene glycol-water systems, and its property using Hartree Fock, Møller-Plesset is truncated at second-order (MP2), density function theory (DFT), and density functional theory with dispersion function (DFT-D). The detail study of geometrical parameters of optimized structures, interaction energies, deformation energies, relaxation energies, many body energy contributions, charge transfer, potential energy plots, and frontier orbitals reported in this paper should provide electronic structure-based insights on hydrogen-bond formation in glycol-water complex and scientific understanding on application of different glycols as a gas hydrate inhibitors.
Geometry optimization and interaction energy calculation have been carried out using Hartree Fock (HF) [
Interaction energy (
The optimized structures of ethylene glycol (EG), diethylene glycol (DEG), triethylene glycol (TEG), and dipropylene glycol (DPG) molecule, their dimer, their complex with one and two water molecules have been obtained by HF, MP2, and DFT methods using 6-31++G(d,p) basis set and B3LYP DFT-D, WB97XD, M06, and M06-2X functionals, and the corresponding structures obtained by using WB97XD functional DFT method are shown in Figures
Calculated hydrogen-bond distances (
System | Parameters | Methods | ||||||
---|---|---|---|---|---|---|---|---|
MP2 | WB97XD | B3LYP |
MO62X | MO6 | B3LYP | HF | ||
EG |
|
2.46 | 2.35 | 2.36 | 2.35 | 2.35 | 2.33 | 2.34 |
| ||||||||
EG + 1 water complex (GD) |
|
1.93 | 1.91 | 1.89 | 1.94 | 1.95 | 1.92 | 2.04 |
|
174.48 |
175.33 |
176.70 |
160.81 |
159.87 |
176.19 |
178.05 |
|
|
4.47 | 4.26 | 4.20 | 4.42 | 4.50 | 3.97 | 4.09 | |
| ||||||||
EG + 1 water complex (WD) |
|
1.93 | 1.89 | 1.89 | 1.96 | 1.92 | 1.90 | 2.03 |
|
153.39 |
158.14 |
154.63 |
144.61 |
151.63 |
162.56 |
163.87 |
|
|
2.46 | 2.35 | 2.36 | 2.35 | 2.35 | 2.33 | 2.34 | |
| ||||||||
EG + 2 water complex |
|
1.93 | 1.90 | 1.89 | 1.91 | 1.94 | 1.93 | 2.05 |
|
1.94 | 1.91 | 1.89 | 1.93 | 1.94 | 1.94 | 2.05 | |
|
178.40 | 177.47 | 174.49 | 177.35 | 164.04 | 173.9 | 177.04 | |
|
176.84 | 178.56 | 178.65 | 165.84 | 163.49 | 173.47 | 176.47 | |
|
2.57 | 2.48 | 2.49 | 2.81 | 2.60 | 2.03 | 1.94 | |
| ||||||||
EG dimer |
|
1.88 | 1.88 | 1.85 | 1.90 | 1.91 | 1.90 | 2.03 |
|
168.91 | 168.50 | 168.40 | 157.80 | 159.41 | 174.87 | 179.88 | |
|
4.82 | 4.27 | 4.04 | 5.07 | 5.02 | 3.68 | 4.08 |
Calculated hydrogen-bond distances (
System | Parameters | Methods | ||||||
---|---|---|---|---|---|---|---|---|
MP2 | WB97XD | B3LYP |
MO62X | MO6 | B3LYP | HF | ||
DEG |
|
1.14 | 0.96 | 1.05 | 0.97 | 1.04 | 1.02 | 0.93 |
| ||||||||
DEG + 1 water complex (GD) |
|
1.94 | 1.90 | 1.88 | 1.94 | 1.93 | 1.92 | 2.04 |
|
172.60 | 172.47 | 174.51 | 159.06 | 163.90 | 177.25 | 177.37 | |
|
3.64 | 3.48 | 3.59 | 3.33 | 3.47 | 3.52 | 3.32 | |
| ||||||||
DEG + 1 water complex (WD) |
|
1.91 | 1.88 | 1.86 | 1.90 | 1.91 | 1.90 | 2.02 |
|
160.25 |
162.39 |
162.09 |
152.65 |
154.61 |
164.61 |
166.90 |
|
|
1.88 | 1.59 | 1.69 | 1.91 | 1.78 | 1.53 | 1.58 | |
| ||||||||
DEG + 2 water complex |
|
1.91 | 1.89 | 1.86 | 1.90 | 1.90 | 1.89 | 2.02 |
|
1.91 | 1.89 | 1.86 | 1.90 | 1.90 | 1.89 | 2.02 | |
|
160.32 | 165.19 | 162.1 | 152.74 | 154.93 | 164.35 | 166.27 | |
|
160.31 | 165.30 | 162.05 | 152.74 | 154.94 | 164.43 | 166.26 | |
|
0.92 | 3.58 | 0.91 | 0.06 | 0.31 | 1.66 | 1.92 | |
| ||||||||
DEG dimer complex |
|
2.08 | 2.07 | 2.04 | 2.09 | 2.07 | 2.04 | 2.11 |
|
2.08 | 1.96 | 2.04 | 2.09 | 2.07 | 2.04 | 2.02 |
|
|
154.38 | 156.89 | 152.57 | 147.54 | 151.83 | 167.59 | 150.66 | |
|
154.37 | 157.17 | 152.58 | 147.53 | 151.78 | 167.58 | 173.49 | |
|
0.84 | 1.57 | 0.80 | 0.58 | 0.62 | 1.50 | 1.49 |
Calculated hydrogen-bond distances (
System | Parameters | Methods | ||||||
---|---|---|---|---|---|---|---|---|
MP2 | WB97XD | B3LYP |
MO62X | MO6 | B3LYP | HF | ||
TEG |
|
2.58 | 2.34 | 2.43 | 2.31 | 2.46 | 2.41 | 2.42 |
| ||||||||
TEG + 1 water complex (GD) |
|
1.94 |
1.90 |
1.89 |
1.94 |
1.93 |
1.92 | 2.04 |
|
173.13 |
172.71 |
175.39 |
159.79 |
164.13 |
177.01 |
178.10 |
|
|
4.61 | 4.30 | 4.33 | 4.51 | 4.61 | 4.08 | 4.18 | |
| ||||||||
TEG + 1 water complex (WD) |
|
1.90 |
1.88 |
1.85 |
1.90 |
1.913 |
1.89 |
2.02 |
|
160.76 |
162.44 |
162.64 | 153.65 |
154.59 |
165.46 |
168.99 |
|
|
1.72 | 1.56 | 1.5 | 1.76 | 1.77 | 1.56 | 1.94 | |
| ||||||||
TEG + 2 water complex |
|
1.94 | 1.90 | 1.89 | 1.94 | 1.93 | 1.92 | 2.04 |
|
1.92 | 1.89 | 1.87 | 1.90 | 1.92 | 1.91 | 2.04 | |
|
173.07 | 174.19 | 175.47 | 160.52 | 164.03 | 176.55 | 178.99 | |
|
179.34 | 178.75 | 176.76 | 171.22 | 161.78 | 175.54 | 179.45 | |
|
5.40 | 4.80 | 4.64 | 5.66 | 5.80 | 4.08 | 4.69 |
Calculated hydrogen-bond distances (
System | Parameters | Methods | ||||||
---|---|---|---|---|---|---|---|---|
MP2 | WB97XD | B3LYP |
MO62X | MO6 | B3LYP | HF | ||
DPG | D | 5.01 | 4.47 | 4.46 | 4.40 | 4.30 | 4.43 | 4.69 |
| ||||||||
DPG + 1 water complex (GD) |
|
1.93 | 1.90 | 1.88 | 1.91 | 1.93 | 1.93 | 2.05 |
|
178.60 | 176.25 | 175.19 | 176.23 | 164.79 | 174.44 | 177.44 | |
D | 5.48 | 4.67 | 4.62 | 5.23 | 5.75 | 4.61 | 5.00 | |
| ||||||||
DPG + 1 water complex (WD) |
|
1.90 | 1.88 | 1.86 | 1.91 | 1.91 | 1.90 | 2.03 |
|
162.78 | 166.07 | 161.8 | 151.04 | 155.18 | 167.98 | 171.36 | |
D | 4.03 | 4.17 | 3.68 | 2.99 | 3.17 | 4.29 | 4.99 | |
| ||||||||
DPG + 2 water complex |
|
1.90 | 1.89 | 1.86 | 1.92 | 1.91 | 1.90 | 2.03 |
|
1.90 | 1.89 | 1.86 | 1.92 | 1.91 | 1.90 | 2.03 | |
|
162.54 | 161.59 | 161.55 | 149.65 | 154.93 | 167.89 | 170.64 | |
|
162.54 | 161.60 | 161.68 | 149.66 | 154.94 | 167.88 | 170.64 | |
D | 4.65 | 4.21 | 4.18 | 2.45 | 3.29 | 5.47 | 6.04 | |
| ||||||||
DPG dimer |
|
1.89 | 1.87 | 1.90 | 1.91 | 1.91 | 2.04 | |
|
— | 171.89 | 167.63 | 170.67 | 167.46 | 171.92 | 172.87 | |
D | 7.09 | 5.83 | 6.93 | 7.04 | 5.19 | 5.65 |
Optimized structures using WB97XD/6-31++G(d,p) of (a) ethylene glycol (EG), (b) diethylene glycol (DEG), (c) triethylene glycol (TEG), and (d) dipropylene glycol molecule (DPG) (colour legend: red = oxygen, black = carbon, and whitish grey = hydrogen).
Optimized structures using WB97XD/6-31++G(d,p) of (a) ethylene glycol (EG) dimer, (b) diethylene glycol (DEG) dimer, (c) triethylene glycol (TEG) dimer, and (d) dipropylene glycol (DPG) dimer (colour legend: red = oxygen, black = carbon, whitish grey = hydrogen, and black-dotted line is hydrogen-bond).
Optimized structures using WB97XD/6-31++G(d,p) of (a) water dimer [
Optimized structures using WB97XD/6-31++G(d,p) of (a) ethylene glycol (EG) + 2 water, (b) diethylene glycol (DEG) + 2 water, (c) triethylene glycol (TEG) + 2 water, and (d) dipropylene glycol (DPG) + 2 water, (colour legend: red = oxygen, black = carbon, whitish grey = hydrogen, and black-dotted line is hydrogen-bond).
Interaction energies for glycols (including dimers) and water systems with and without BSSE correction have been summarized in Tables
Calculated energy of interaction energy without correction (
Systems | Calculation methods |
|
|
---|---|---|---|
EG + 1 water complex (GD) | MP2 | −7.01 | −4.94 |
WB97XD | −6.78 | −5.86 | |
B3LYP DFT-D | −7.09 | −6.10 | |
M062X | −7.14 | −6.18 | |
M06 | −6.72 | −5.82 | |
B3LYP | −5.92 | −4.99 | |
HF | −5.08 | −4.38 | |
| |||
EG + 1 water complex (WD) | MP2 | −7.55 | −5.49 |
WB97XD | −7.50 | −6.72 | |
B3LYP DFT-D | −8.38 | −7.49 | |
M062X | −8.06 | −7.23 | |
M06 | −7.28 | −6.50 | |
B3LYP | −6.14 | −5.34 | |
HF | −4.94 | −4.35 | |
| |||
EG + 2 water complex | MP2 | −13.40 | −9.40 |
WB97XD | −12.96 | −11.19 | |
B3LYP DFT-D | −13.62 | −11.72 | |
M062X | −13.43 | −11.49 | |
M06 | −12.41 | −10.66 | |
B3LYP | −11.47 | −9.67 | |
HF | −9.72 | −8.35 | |
| |||
EG dimer | MP2 | −7.69 | −4.98 |
WB97XD | −7.62 | −6.78 | |
B3LYP DFT-D | −8.36 | −7.38 | |
M062X | −7.50 | −6.60 | |
M06 | −7.05 | −6.26 | |
B3LYP | −5.55 | −4.77 | |
HF | −4.60 | −3.95 | |
| |||
Water dimer | MP2 | −6.39 | −4.83 |
WB97XD | −6.71 | −5.95 | |
B3LYP DFT-D | −5.97 | −5.19 | |
M062X | −6.58 | −5.80 | |
M06 | −5.99 | −5.25 | |
B3LYP | −6.35 | −5.61 | |
HF | −5.01 | −4.36 |
Calculated energy of interaction energy without correction (
Systems | Calculation methods |
|
|
---|---|---|---|
DEG + 1 water complex (GD) | MP2 | −7.24 | −5.13 |
WB97XD | −7.00 | −6.09 | |
B3LYP DFT-D | −7.28 | −6.28 | |
M062X | −7.41 | −6.44 | |
M06 | −6.90 | −6.01 | |
B3LYP | −6.06 | −5.14 | |
HF | −5.20 | −4.51 | |
| |||
DEG + 1 water complex (WD) | MP2 | −7.56 | −5.53 |
WB97XD | −7.51 | −6.75 | |
B3LYP DFT-D | −8.35 | −7.51 | |
M062X | −7.85 | −7.05 | |
M06 | −7.07 | −6.32 | |
B3LYP | −6.19 | −5.44 | |
HF | −5.13 | −4.59 | |
| |||
DEG + 2 water complex | MP2 | −15.08 | −11.04 |
WB97XD | −14.12 | −12.60 | |
B3LYP DFT-D | −16.64 | −14.98 | |
M062X | −15.61 | −13.99 | |
M06 | −14.15 | −12.65 | |
B3LYP | −12.33 | −10.83 | |
HF | −10.23 | −9.15 | |
| |||
DEG dimer complex |
MP2 | −13.93 | −8.53 |
WB97XD | −9.69 | −8.71 | |
B3LYP DFT-D | −16.08 | −14.71 | |
M062X | −14.80 | −13.41 | |
M06 | −13.85 | −12.55 | |
B3LYP | −6.44 | −5.32 | |
HF | −5.04 | −4.39 |
Calculated energy of interaction-energy without correction (
Systems | Calculation methods |
|
|
---|---|---|---|
TEG + 1 water complex (GD) | MP2 | −7.16 | −5.03 |
WB97XD | −6.95 | −6.03 | |
B3LYP DFT-D | −7.19 | −6.19 | |
M062X | −7.34 | −6.37 | |
M06 | −6.80 | −5.90 | |
B3LYP | −5.98 | −5.07 | |
HF | −5.12 | −4.43 | |
| |||
TEG + 1 water complex (WD) | MP2 | −7.45 | −5.39 |
WB97XD | −7.43 | −6.67 | |
B3LYP DFT-D | −8.22 | −7.38 | |
M062X | −7.73 | −6.92 | |
M06 | −6.93 | −6.19 | |
B3LYP | −6.09 | −5.35 | |
HF | −5.05 | −4.51 | |
| |||
TEG + 2 water complex |
MP2 | −13.95 | −9.84 |
WB97XD | −13.51 | −11.69 | |
B3LYP DFT-D | −14.11 | −12.15 | |
M062X | −14.11 | −12.18 | |
M06 | −12.97 | −11.24 | |
B3LYP | −11.89 | −10.06 | |
HF | −10.07 | −8.69 |
Calculated interaction-energy without correction (
Systems | Methods |
|
|
---|---|---|---|
DPG + 1 water complex (GD) | MP2 | −6.69 | −4.78 |
WB97XD | −6.49 | −5.59 | |
B3LYP DFT-D | −6.83 | −5.87 | |
M062X | −6.67 | −5.74 | |
M06 | −6.05 | −5.19 | |
B3LYP | −5.89 | −4.89 | |
HF | −4.90 | −4.20 | |
| |||
DPG + 1 water complex (WD) | MP2 | −7.39 | −5.28 |
WB97XD | −7.39 | −6.61 | |
B3LYP DFT-D | −8.10 | −7.23 | |
M062X | −7.55 | −6.71 | |
M06 | −6.77 | −6.02 | |
B3LYP | −6.09 | −5.31 | |
HF | −5.03 | −4.43 | |
| |||
DPG + 2 water complex | MP2 | −14.67 | −10.45 |
WB97XD | −14.53 | −12.97 | |
B3LYP DFT-D | −16.07 | −14.33 | |
M062X | −14.94 | −13.26 | |
M06 | −13.49 | −11.97 | |
B3LYP | −12.11 | −10.53 | |
HF | −9.95 | −8.74 | |
| |||
DPG dimer |
WB97XD | −8.14 | −7.33 |
B3LYP DFT-D | −8.85 | −7.93 | |
M062X | −7.53 | −6.67 | |
M06 | −6.81 | −6.07 | |
B3LYP | −5.78 | −5.05 | |
HF | −4.97 | −4.26 |
Calculated deformation energy (
Systems | Calculation methods |
|
|
---|---|---|---|
EG + 1 water complex (GD) | WB97XD | 0.09 | 0.09 |
B3LYP DFT-D | 0.08 | 0.09 | |
M062X | 0.13 | 0.12 | |
M06 | 0.12 | 0.12 | |
B3LYP | 0.08 | 0.09 | |
HF | 0.04 | 0.04 | |
| |||
EG + 1 water complex (WD) | WB97XD | 0.14 | 0.21 |
B3LYP DFT-D | 0.21 | 0.29 | |
M062X | 0.42 | 0.47 | |
M06 | 0.20 | 0.28 | |
B3LYP | 0.13 | 0.20 | |
HF | 0.11 | 0.13 | |
| |||
EG + 2 water complex | WB97XD | 0.10 | 0.10 |
B3LYP DFT-D | 0.12 | 0.13 | |
M062X | 0.11 | 0.09 | |
M06 | 0.17 | 0.18 | |
B3LYP | 0.11 | 0.11 | |
HF | 0.05 | 0.05 |
Calculated deformation energy (
Systems | Calculation methods |
|
|
---|---|---|---|
DEG + 1 water complex (GD) | WB97XD | 0.05 | 0.05 |
B3LYP DFT-D | 0.10 | 0.10 | |
M062X | 0.08 | 0.06 | |
M06 | 0.17 | 0.17 | |
B3LYP | 0.09 | 0.09 | |
HF | 0.04 | 0.05 | |
| |||
DEG + 1 water complex (WD) | WB97XD | 0.07 | 0.14 |
B3LYP DFT-D | 0.11 | 0.20 | |
M062X | 0.10 | 0.14 | |
M06 | 0.16 | 0.24 | |
B3LYP | 0.08 | 0.15 | |
HF | 0.05 | 0.07 | |
| |||
DEG + 2 water complex |
WB97XD | 0.09 | 0.23 |
B3LYP DFT-D | 0.22 | 0.39 | |
M062X | 0.24 | 0.32 | |
M06 | 0.25 | 0.40 | |
B3LYP | 0.16 | 0.29 | |
HF | 0.09 | 0.13 |
Calculated deformation energy (
Systems | Calculation methods |
|
|
---|---|---|---|
TEG + 1 water complex (GD) | WB97XD | 0.02 | 0.02 |
B3LYP DFT-D | 0.09 | 0.09 | |
M062X | 0.04 | 0.02 | |
M06 | 0.17 | 0.17 | |
B3LYP | 0.08 | 0.09 | |
HF | 0.04 | 0.05 | |
| |||
TEG + 1 water complex (WD) | WB97XD | 0.03 | 0.10 |
B3LYP DFT-D | 0.11 | 0.19 | |
M062X | 0.05 | 0.09 | |
M06 | 0.13 | 0.20 | |
B3LYP | 0.07 | 0.14 | |
HF | 0.04 | 0.06 | |
| |||
TEG + 2 water complex |
WB97XD | 0.10 | 0.10 |
B3LYP DFT-D | 0.16 | 0.17 | |
M062X | 0.12 | 0.10 | |
M06 | 0.32 | 0.32 | |
B3LYP | 0.15 | 0.15 | |
HF | 0.07 | 0.07 |
Calculated deformation energy (
Systems | Methods |
|
|
---|---|---|---|
DPG +1 water complex (GD) | WB97XD | 0.07 | 0.07 |
B3LYP DFT-D | 0.07 | 0.07 | |
M062X | 0.05 | 0.04 | |
M06 | 0.15 | 0.16 | |
B3LYP | 0.06 | 0.06 | |
HF | 0.03 | 0.03 | |
| |||
DPG + 1 water complex (WD) | WB97XD | 0.01 | 0.02 |
B3LYP DFT-D | 0.11 | 0.19 | |
M062X | 0.10 | 0.15 | |
M06 | 0.14 | 0.22 | |
B3LYP | 0.10 | 0.16 | |
HF | 0.05 | 0.07 | |
| |||
DPG + 2 water complex | WB97XD | 0.17 | 0.31 |
B3LYP DFT-D | 0.22 | 0.38 | |
M062X | 0.27 | 0.36 | |
M06 | 0.29 | 0.46 | |
B3LYP | 0.15 | 0.27 | |
HF | 0.10 | 0.14 | |
| |||
DPG dimer |
WB97XD | 0.05 | 0.01 |
0.06 | |||
B3LYP DFT-D | 0.11 | 0.26 | |
0.16 | |||
M062X | 0.06 | 0.11 | |
0.05 | |||
M06 | 0.13 | 0.31 | |
0.18 | |||
B3LYP | 0.08 | 0.16 | |
0.08 | |||
HF | 0.05 | 0.08 | |
0.03 |
Calculated two-body energy
System |
|
|
---|---|---|
EG + 2 water complex | −13.33 | 2.04 |
DEG + 2 water complex | −15.03 | 2.20 |
TEG + 2 water complex | −13.67 | 1.88 |
DPG + 2 water complex | −14.83 | 1.85 |
The potential energy curves for a free O–H bond of single DEG, TEG, and DPG molecule are represented in Figures
Calculated energy (kcal/mol) curve using WB97XD/6-31++G(d,p) of for (a) a free bond of O–H (
Highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) of different glycol molecules and glycols + 1 water systems (both GD and WD complex), simulated by WB97XD/6-31++G(d,p) method, have been shown in Figure
Frontier orbitals (HOMO, LUMO energies are atomic unit) simulated by WB97XD/6-31++G(d,p) theory for (a) water molecule, (b) EG molecule, (c) DEG molecule, (d) TEG molecule, (e) DPG molecule, (f) EG + 1 water complex (WD), (g) EG + 1 water complex (GD), (h) DEG + 1 water complex (WD), (i) DEG + 1 water complex (GD), (j) TEG + 1 water complex (WD), (k) TEG + 1 water complex (GD), (l) DPG + 1 water complex (WD), and (m) DPG + 1 water complex (GD).
The charge transfer (CT) energies calculated using natural energy decomposition analysis (NEDA) for different glycol + 1 water complex and glycol dimer are summarized in Table
Calculated Charge transfer (CT, kcal/mol) for glycol + 1 water complex and glycol dimers using WB97XD/6-31++G(d,p).
System | CT |
---|---|
EG + 1 water complex (GD) | −31.55 |
EG + 1 water complex (WD) | −35.98 |
DEG + 1 water complex (GD) | −30.38 |
DEG + 1 water complex (WD) | −36.93 |
TEG + 1 water complex (GD) | −14.83 |
TEG + 1 water complex (WD) | −17.85 |
DPG + 1 water complex (GD) | −10.57 |
DPG + 1 water complex (WD) | −39.47 |
EG dimer | −44.14 |
DEG dimer | −48.59 |
TEG dimer | −15.78 |
DPG dimer | −17.12 |
A thorough analysis of hydrogen-bond formation in polyethylene glycol +
This work is financially supported by Ministry of Earth Science, India (Project no. MoES/16/48/09—RDEAS (MRDM5)). The authors also acknowledge accelrys Inc. for providing free Discovery Studio 3.1 visualization tool.