ORIENT [132] was used to derive the stable minima and their corresponding binding energies for each of the model potentials. The zero-point energies were also estimated from the 6 harmonic frequencies. The following tables (Table 6.7 and Table 6.8) show the minima and binding energies obtained along with the minima's intermolecular structural parameters. The first observation of the results is that none of the non-empirical model potentials is capable in producing all three minima as observed in our ab initio study and other simple models. The 7i-bonded minimum is not observed from the calculations in ORIENT.
Min 1 4 ., ^disp E,o.al (D .) ZPE
SU^ - - - -25.14 - HS -37.80 1.16 - -36.64 10.77 FIT -40.93 21.37 -10.95 -30.51 6.82 OPLS -36.79 - 5.99 -30.80 5.16 6 31 g ss_ rg -26.31 10.80 -8.54 -24.05 5.09 6 3 1 g ss_ rg n d -27.17 12.17 -9.73 -24.73 5.20 6 3 1gss_rm -28.07 11.96 -9.51 -25.62 5.33 6 3 1gss_rm n d -29.24 13.84 -11.14 -26.54 5.47 d(0p...0w) 3 Y d(Ow...Hp) A B C SU^ 2.78 137.66 108.75 1.82 4199.33 1162.02 913.97 HS 2.82 130.37 110.73 1.85 4243.73 1133.07 897.97 FIT 2.75 124.09 114.40 1.80 4379.04 1115.15 892.44 OPLS 2.73 135.05 113.24 1.77 4349.68 1130.79 901.17 63 1 g ss_ rg 3.10 134.99 110.09 2.13 4103.10 1069.71 851.80 6 3 1 g ss_ rg n d 3.07 133.39 110.39 2.11 4124.04 1073.68 855.22 631gss_rm 3.04 133.66 109.88 2.08 4119.37 1084.77 862.04 63 1gss_rm n d 3.01 131.69 110.25 2.05 4145.61 1089.62 866.25
Table 6.7 Table of results for global minimum, the phenol proton donor for the corresponding model potentials.
Note all energies are in kJ/mol, bond distances (d) in A, angles p and y in degrees and rotational constants A, B, C in MHz. ^SU is our best supermolecule calculations (Chapter 5).
New Models for intermolecular Repulsion and their Application to van der W aals Helen H.Y. Tsui
6 Model Intermolecular Potentials of Phenol-Water Complex I___________________________ 121
Min 2 E.S Ejisp EW (D .) ZPE d(0p...0w)
SU^ - - - -13.56 - 2.82 HS -23.62 0.75 - -22.87 10.90 2.83 FIT -20.90 11.93 -8.67 -17.64 5.92 2.89 OPLS -29.99 - 4.66 -25.33 8.26 2.76 631 g ss_ rg -13.68 7.23 -9.55 -16.00 5.09 3.01 631 g ss_ rg n d -13.86 7.71 -10.14 -16.28 5.01 3.00 631gss_rm -14.46 7.92 -10.51 -17.05 5.21 2.97 6 3 1gss_rm n d -14.69 8.54 -11.26 -17.42 5.07 2.96 P Y d(Op...Hv,i) d(0p...Hw2) A B C SU^ 53.04 112.10 1.88 3.20 4065.39 1186.22 922.95 HS 50.20 116.45 1.88 3.17 4199.08 1138.45 898.10 FIT 42.39 117.56 1.97 3.11 4192.33 1114.63 884.05 OPLS 48.35 118.28 1.81 3.08 4274.14 1139.95 903.16 6 3 lg s s _ r g 9.86 114.28 2.55 2.55 4054.90 1119.47 880.81 6 31 g ss_ rg n d 9.66 113.86 2.54 2.54 4047.31 1126.22 884.62 6 31gss_rm 9.99 113.51 2.51 2.51 4053.45 1139.18 892.89 631gss_rm n d 9.72 113.03 2.50 2.50 4045.11 1147.28 897.45
Table 6.8 Table of results for second stable minimum, the water proton donor for the corresponding model potentials.
Note all energies are in kJ/mol, bond distances (d) in Â, angles P and y in degrees and rotational constants A, B, C in MHz. ^SU is our own supermolecule calculations.
The results show that none of the non-empirical models can provide a good description of the intermolecular forces for the phenol-water system to reproduce the 7i-bonded minimum as observed in our supermolecule calculations and also from the OPLS and FIT models. Nevertheless, the results for the hydrogen-bonded complex is comparable, with slight lengthening of the Op...Ow bond distance. The Dg energies are more positive than those obtained from the FIT and OPLS models, and if we include the estimated harmonic zero-point energies, the harmonic Dq are still too positive to be comparable with the experimental determined value of -23.45 ± 0.48 kJ/mol [8]. The inclusion of the damping function appeared to only cause minor deviations of the structures and energies. Hence, the
Tang-Toennies damping function has shown to be suitable to apply in our model potential. Since we only have experimental data on the global minimum, we cannot judge on the quality of the second stable minima produced from the models.
6.5 Discussion
Our best non-empirical model potential, the 631gss_rm model, performed relatively well, but we need to find out why it did not produce the 7t-bonded minimum as observed in our supermolecule study and results from the OPLS and FIT models. We may need to adjust the fitting to derive another proportionality constant K in order to compensate for neglect of deficiency. Note that the range of repulsion energies included in our sample could be too large. Fitting with energies less than 100 kJ/mol should provide a more physical sampling. We have not considered testing the sensitivity of the overlap model upon the choice of basis sets used. Nobeli and Price carried out tests in their study of oxalic acids [101] and suggested that the larger the basis set used, the better the modelling of the repulsion using the overlap model. It would be of interest to probe this for our phenol-water system. Concurrent study by Mitchell and Price [113] has shown that it would be possible to include penetration and charge-transfer contributions by combining it with the repulsion term. Their study was Ne w M odels for Intermolecular Repulsion and their Application to van der W aals Helen H.Y. Tsui
6 Model Intermolecular Potentials of Phenol-Water Complex I___________________________ 122 on crystal structures of amines, and it would be of interest to know if the same procedure could be of benefit to be applied in the modelling of phenol-water complex. The next chapter will only concentrate on the improvements that can be applied to the repulsion term using the overlap model, since the electrostatic and the dispersion terms along with damping have been shown to produce good results.
New Models for Intermolecular Repulsion and their Application to van der W aals Helen H.Y. Tsui
7 Model Intermolecular Potentials of Phenol-Water Complex II__________________________ 123
7 Model Intermolecular Potentials of
Phenol-Water Complex II
7.1 Summary
The overlap model has demonstrated its capability in deriving a non-empirical repulsion model specifically for the phenol-water complex as shown in Chapter 6. However, there were some deficiencies in the model constructed, and further investigations on the capability of the overlap model were carried out in this chapter. The overlap model is tested using different basis sets in obtaining both the overlaps and the exchange-repulsion energies. The penetration and charge-transfer contributions can be included, by absorbing them into the repulsion term. This has been shown to improve the modelling by producing results that are comparable with results obtained from our supermolecule calculations. Detailed analyses have been carried out for the phenol-water complex, and it must be noted the choice of analytical methods and procedures are important to obtain a suitable repulsion model to describe the intermolecular forces sufficiently.
7.2 Introduction
We have already demonstrated that the overlap model [3] is capable in producing non-empirically derived repulsion parameters that can provide reasonable repulsion as shown in the blind crystal structure prediction in Chapter 4. This is an exceptionally good method in deriving parameters that are difficult to obtain, or repulsion parameters that are not suitable for use because of transferability New Models for Intermolecular Repulsion and their Application to van der W aals Helen H.Y. Tsui
7 Model Intermolecular Potentials of Phenol-Water Complex II__________________________ 124 problems [33] (See Chapter 4). Along with the repulsion model, the electrostatic model [1], and the inclusion of a suitable dispersion model [51] with damping effect [57] taken into account; non- empirically derived model potentials have been constructed for the phenol-water complex and tested using ORIENT [132] in Chapter 6. However, the results have shown that the hydrogen bonds between the phenol molecule and the water molecule are too long. This suggests that our model repulsion could well be too repulsive, and this will be the main area that needs further study. Another major problem was that our model potentials were unable to reproduce all three minima as observed in our
ab initio studies (See Chapter 5). It was known in an earlier stage that the assumption of the charge overlap proportional to the exchange-repulsion energy is only an approximation [3]. Therefore we need to investigate the alternative ways, or any improvements that can be implemented on the existing repulsion model. In order to improve our model potential, it is sensible to carry out detailed analyses to determine the origin of the problem. These analyses should provide us insights into the sensitivity of the repulsion model, and hence it can aid us in further understanding and development of utilising the overlap model. Similar tests have been reported in earlier studies by Nobeli and Price [lOI], which showed that a slightly larger basis set than 6-31G** [207] such as the 6-31 IG** [208] basis set, can produce better results using the overlap model. Therefore it is essential to test whether the same observations may occur in our system.
In most model potentials, the main components consist of the exchange-repulsion model, the electrostatic and the dispersion models, but they only account for the main contributions to the intermolecular interactions. For the empirically fitted model, the other short-range contributions such as the penetration and charge-transfer energy terms are absorbed in the parameterisation. However, in a non-empirical model potential, such contributions are either neglected or explicitly modelled. In order to take these into account without needing to create more parameters for either the penetration or the charge-transfer terms, a novel method has been recently developed by Mitchell and Price [113] for model systems of formamide, acetamide and rra/i^-N-methylacetamide. The method used was the incorporation of the penetration and charge-transfer explicitly along with the exchange-repulsion into the repulsion term in a non-empirical model potential. The approximation procedure was also illustrated by Fraschini and Stone [208] who have studied and constructed an H ...H model potential for exchange-repulsion energy of methane dimer. In their studies, they have divided the electrostatic energy into two contributions. The two contributions consist of a long-range part arising from the multipolar expansion of the separated charge distributions of the monomers, and a short-range part called electrostatic penetration, which corrects for the effects due to the overlap of the two charge distributions at medium and short range. The exchange-repulsion and the electrostatic-penetration show an ex p (-/?) behaviour with respect to the interatomic distance R , and for this reason they can be combined to yield an exchange-repulsion-penetration energy of exponential form. We could apply the same methodology by using the existing overlap model we constructed as shown in Chapter 6
(631gss_rm). One can easily perform simple calculations to determine the charge-transfer energies from IMPT calculations [4,55], and the penetration energies which is the difference of electrostatic energies from IMPT and DMA energies from GMUL [3,116]. This method can be implemented into our existing repulsion model to give the same number of parameters. The model overlap remained the
New Models for Intermolecular Repulsion and their Application to van der W aals Helen H.Y. Tsui
7 Model Intermolecular Potentials of Phenol-Water Complex II__________________________ 125 same, only the pre-exponential K value is scaled, to absorb the penetration and charge-transfer. This will be carried out in full analysis using the overlap models based on MP2 6-31G**, MP2 6-311(1** and MP2 cc-pVDZ charge densities. The quality of the new models will be tested in terms of correlation coefficients between the energies and overlaps, and the fit for the proportional constant
K, and also their capabilities in reproducing the three possible minima using ORIENT [132], Ultimately, the quality of the model potential will have to be determined by its ability to reproduce experimental data by including the anharmonic zero-point motion, by diffusion Monte Carlo (DMC) [31] simulations (Chapter 8). Since it is very expensive to carry out DMC simulations, we can only choose one model as the best model potential for the simulation. Hence, detailed analyses are essential, so we could judge on the quality of the model based on the structural parameters and the harmonic zero-point energies estimated from the vibrational frequencies.