In the original studies o f the overlap model [3], W heatley and P rice pointed out that the interm olecular repulsion energy is related to the overlap betw een the unperturbed charge densities o f the interacting m olecules by a relationship o f the form = KS^ , w here y is less than the value o f 1. This will m ainly have the effect o f flattening the exponential decay o f the potential with distance, to give m ore realistic repulsion energy. This is show by a pow er trend line in the follow ing plot, show ing how our 6311 gss_rpcni m odel com pared with the theory. T here is a discrepancy betw een our current model and the above relationship that is clearly visible from the follow ing plot (Figure 7.9).
120 B E 100
0.000 0.002 0 .0 0 4 0 .0 0 6 0 .0 0 8 0.010 0.012
Model O verlap / a.u.
Linear (ex-rep + pen + ct) — - - Pow er (ex-rep 4- pen + ct)
Figure 7.9 IMPT exchange-repulsion + penetration + charge-transfer energy against model overlap for 631 ]gss_rpcm model.
The r^ for the linear trendline is 0.8698 and the r^ for the pow er trendline is 0.8947. This clearly shows that our model underestim ated the repulsion energy at sm all overlaps (long distances), and overestim ated the repulsion energy at large overlaps (short distances). W e m ust find a way to prevent this from happening, so that we can obtained a m ore realistic repulsion m odel. T here is also the problem o f additivity and we do not wish to follow elaborate analyses as in M itchell and Price's study [113]. A nother reason for not using the pow er relation is that it would be good to obtain an optim al value o f K that is transferable, because o f the lim itation o f the IM PT calculations. H ence it is best not to increase the com plexity o f the fitting. T herefore we m ust use another m ore pragm atic method to eradicate the problem s. O ne m ethod is to re-fit our model using a sm aller and m ore realistic range o f sam pling o f the repulsion regions. In our original fittings, 69 geom etries are used and som e o f them could well be too repulsive and also could be sam pling unrealistic regions. T herefore we have reduced the geom etries that we sam pled from 69 dow n to 62 (7 that are with IM PT (6 -3 IG**)
N e w M odels for Interm olecular R epulsion an d their Application to van d er W a a ls C o m p lexes and Crystals of O rg anic M olecules
H e le n H .Y . Tsui August 2001
7 Model Intermolecular Potentials of Phenol-Water Complex II 142 exchange-repulsion energies betw een -100 and -136 kJ/m ol were expelled, geom etry 23, 29, 30, 38, 39. 52, 53 are om itted), with IM PT exchange-repulsion energy less than 100 kJ/m ol. H ere below are the analyses o f the newly fitted m odels denoted as 631gss__rpcmn, 6311 gss_rpcm n and ccpvdz_rpcm n.
7.6.1 Analyses of the newly fitted repulsion model
The follow ing tables are the new K values, the r^ o f the fit and correlation for the different m odels (See Table 7.15 and Table 7.16). If we com pare the plot o f the 631 lg ss_ rp cm m odel (Figure 7.9) and the im proved plot o f the 6 3 IIgss_rpcm n model (Figure 7.10), it can be observed that the sam pling region has been im proved, with m ore realistic sam pling. The trendline (r^ = 0.8409) actually is m ore closely aligned to the pow er trendline (r^ = 0.8839), and the points are m ore evenly distributed.
60 40 C LU 30 20 ^ O 0.007 0.000 0.001 0.002 0.003 0.004
Model Overlap / a.u.
0.005 0.006
Linear (ex-rep + pen + ct) Pow er (ex-rep + pen + ct)
Figure 7.10 Graph of IMPT energy against model overlap for the 6311 gss_rpcmn model.
Energy Overlap Correlation (basis set 6-3IG**)
Correlation (basis set 6-31 IG**)
Correlation (basis set cc-pVDZ) Penetration GMUL -0.9848 -0.9811 -0.9828 Penetration model -0.9565 -0.8994 -0.9179 Charge-transfer GMUL -0.9143 -0.8471 -0.8702 Charge-transfer model -0.8969 -0.8537 -0.8656
Table 7.15 Table of r of fit and correlation for penetration and charge-transfer energy with the corresponding overlap using the same basis sets with 62 geometries.
Model Correlation K r^ of fit 631gss_rpcmn 0.9529 4.4504 0.8409 631 lgss_rpcmn 0.9538 4.0134 0.8145 ccpvdz_rpcmn 0.9527 4.3768 0.8230
Table 7.16 Table of proportionality constant ( K ), correlation coefficients for exchange-repulsion with overlap and 1^ of fit for K with 62 geometries.
N e w M odels for Interm olecular Repulsion and their Application to van d er W a a ls Co m p lex es and Crystals ot O rg anic M olecules
H e len H .Y . Tsui August 2001
7 Model Intermolecular Potentials of Phenol-Water Complex II 143 Charge densitv Atom pairs MP2 6-31G** (= MP2 6-311G** A. (= K "^' M P2 cc-pV D Z (= Cfi.-.Ow 5.05 4 5 2 5675 6.17 104572478 5.42 14273571 Cg. Hw 4.71 9 9 3 3 4 5.81 1465419 4 .8 6 24 5 1 7 8 5.01 4 2 7 9043 5.11 5058231 5.18 4 1 7 2 4 3 4 ..Hw 4.71 126259 4.85 159765 4 .7 2 137194 Hp... Ow 4 .6 4 9 0 2 7 6 4 .7 6 106006 4 .5 4 747 6 3 Hp.. .Hw 4 .4 6 4415 5.97 86027 4.55 7 7 8 2 C...ÜW 4.39 1927199 4.33 1417951 4.45 2 1 1 4 2 9 9 C ...H w 4.17 70459 4.11 5 1 3 8 4 4.15 846 3 8 .. ^3w 5.00 9 2 0 7 1 9 4 5.56 4 0 6 6 8 3 9 9 5 .74 6 2 8 5 8 8 4 7 C4. . .Hw 4.72 261 2 1 6 5.35 1240748 5.21 1286312 H ...O w 4.51 146518 4.42 104865 4 .3 4 9 8 8 0 4 H ...H w 4.32 5938 4.53 8779 4 .2 2 7451
Table 7.17 Table of model repulsion parameters derived from the (62 geom) fitted overlap of MP2 6-3 IG**, 6- 3IIG** and cc-pVDZ charge densities of phenol-water ( with ).
Note A , in kJ/moI and a „ in  ' .
When the plots included the power trend line, one can see that most of the points lie more closely on the power trend line for all the models. The linear trendline is aligned more closely with the power trendline, this suggests that our repulsion energy is more realistic than before. In particular at large overlaps (short distances), the repulsion energy is almost exactly placed on the power trend line; this gives a very good estimate of the repulsion energy at short ranges. The overlaps are given more reasonable weighting, as the points are more spread out over the sampling region as shown in all the newly fitted models. The quality of these newly fitted repulsion models will be tested using ORIENT [132].
7.6.2 ORIENT results for newly fitted model potentials
The ORIENT results from the 6311gss_rpcmn model produced all three minima, and the total energy of the global minimum has been reduced. If we take into account the harmonic zero-point energy, the estimated Dq is -24.74 kJ/mol, in comparison with experimental energy of -23.45 ± 0.48 kJ/mol. This is regarded as very good results as the OPLS [5] only managed to give -25.50 kJ/mol of energy with an estimation of anharmonic zero-point energy derived from DMC [31]. However, the 0 . . . 0 distance has increased slightly, about 0.01 Â less than the experimental value. O f course, they are not directly comparable, as zero-point motion is not included in our case to derive the 0 . . . 0 distance. If we compared our 0 . . . 0 distance with our ab initio studies, the global minimum from the 631 Igssjrpcm
model is + 0.09 Â larger than our ab initio value. If we compare the 0 . . . 0 distance with Fang's [10]
ab initio value, it is 0.02 Â longer. The 631gss_rpcmn and the ccpvdz_rpcmn models failed to produce all three minima; they only managed to produce the global minimum and the water proton donor minimum. Hence these models are deemed to be less accurate in modelling the potential for phenol-water.
New Models for Intermolecular Repulsion and their Application to van der W aals Complexes and Crystals of Organic Molecules
Helen H.Y. Tsui August 2001
7 Model Intermolecular Potentials of Phenol-Water Complex II__________________________ 144
7.7 Discussion
The problems that we have encountered in Chapter 6 have been closely investigated. However, much of the work on the overlap model still relies on the choice of fittings in the analyses. The methods used in fittings may vary, and this will introduce different levels of errors into the model. There is no one single standard for analysing the data for the production of non-empirical repulsion parameters. In our studies, we mainly concentrated on the improvements of our model repulsion as studied in the previous chapter.
The testing of our repulsion model is based on the repulsion model with a combination of DMA [1] for the electrostatic model, and dispersion model derived using Slater-Kirkwood formula [51] with Miller's polarizabilities [170] unless where stated. Tests have been performed on the repulsion model used in previous chapter by fitting for new proportionality constants using IMPT exchange-repulsion energy (SCF 6-3IG**) with GMUL and model overlaps using charge densities from MP2 6-311G** and MP2 cc-pVDZ basis sets. The results from these tests have shown that it is inappropriate to mix the use of basis set in a model. This is shown clearly by the quality of fits and also their deficiency in improving the existing models to give good results using ORIENT [132].
The new models that included penetration and charge-transfer contributions performed reasonably well. Some of the models managed to produce all three minima as observed in our ab initio
studies. None of the models gave a very good energy and good 0 . . . 0 distance, but it is definitely an improvement from those obtained in the test. Modifying the dispersion model by using the effective Cg has made further improvements. This has significantly improved our 631 Igssjrpcm model to produce three fully distinguishable minima. The results improved when the geometries reduced to 62 geometries with energy sampling a more realistic repulsion region. The 631gss_rpcmn, 6311gss_rpcmn and ccpvdz_rpcmn were all tested but only the 6311gss_rpcmn produced three minima with a very good energy for the global minimum. The true quality of the model will need to be verified by performing DMC [31] calculations to determine the anharmonic energy and vibrationally averaged structure to enable a direct comparison with experiment to be carried out.
Overall, our studies have shown that not all systems perform in the same way using the overlap model. In particular, the choice of basis set used in the model is very important and we have shown that they are dependent on the system being investigated. There appeared to be no correlation on the quality o f the repulsion model with the size of the basis set used. It is of course inappropriate to conclude on this on just one system. More studies on a wide range of systems are needed in order to obtain a holistic view on the overlap model. Nevertheless, our refinements managed to improve our repulsion model, by including minor contributions of the penetration and charge-transfer energies. Such minor contributions could have important effects on the overall model as demonstrated in our studies. Despite the large number of refinements, this is a very good method to derive non-empirically repulsion parameters or those that are not widely available, as shown in our boron crystal structure prediction [33].
New Models for Intermolecular Repulsion and their Application to van d er W aals Helen H.Y. Tsui
8 Diffusion Monte Carlo Simulations for Phenol-Water Complex_________________________ 145