HF dimer

Data computed for the intramolecular vibrational modes of HF and its dimer are reported in Table 3.43. Taking the values in the last row, computed with a very extended basis set, as a benchmark, it is immediately apparent that frequencies computed with small unpolarized basis sets are several hundred cm too small. 3-21G is probably the worst offender in this regard. Once polarization functions have been added, even a single set, the frequencies are more in line with those of the better basis sets. The same patterns are observed in the intensities which are significantly underestimated with the small unpolarized basis sets. 

The limits of accuracy were probed in a study which focused on the gradient and force constants in diatomics like FIF. As more basis functions are added to one of 6-31G type, changes of the order of 1 % occur in the force constant, at both correlated and SCF levels. The superposition contribution to the gradient is fairly large, and can account for variation of as much as 0.004 A in the bond length. 

If one concedes that SCF vibrational spectra, with no correction for anharmonicity, are unlikely to reproduce experiment, the next question would concern whether such calculations are capable of reproducing changes that occur in each molecule upon formation of the H-bond. Table 3.44 lists the shifts in the HF stretching frequency that result upon dimerization, along with the intensification, expressed as a ratio between that of the dimer versus that of the monomer. The results are in many ways a confirmation of the absolute val- 

The water dimer adds a number of new dimensions to the problem since each water molecule contains three vibrational frequencies instead of one. The two stretching modes are labeled V, and Vji Vj refers to the symmetric bending motion. The frequencies computed for the water monomer are reported in the first three columns of Table 3.45, followed by the corresponding frequencies in the dimer. As in the case of (HF)2, the unpolarized basis sets strongly underestimate the stretching frequencies in the monomer. On the other hand, the bending frequency is computed reasonably well with all of the sets, albeit the small unpolarized sets do yield a bit of an overestimate. Rather similar patterns are evident in the dimer as well. The unpolarized sets underestimate v and Vj and yield a small overestimate, by less than 100 cm of the frequency for V2. 

As in the case of (HF)2, the shifts are larger in the donor molecule. All basis sets, even the smallest, agree that both stretches suffer a red shift and that the frequency of the bend is increased. There is discrepancy concerning the magnitudes of these shifts. The three polarized sets concur that the red shifts are some 40-50 cm for v and 20-30 cm for Vj. The shifts predicted by the three smaller basis sets are erratic and generally undependable. 

While orbitals may be useful for qualitative understanding of some molecules, it is important to remember that they are merely mathematical functions that represent solutions to the Hartree-Fock equations for a given molecule. Other orbitals exist which will produce the same energy and properties and which may look quite different. There is ultimately no physical reality which can be associated with these images. In short, individual orbitals are mathematical not physical constructs. 

Semi-empirical methods may only be used for systems where parameters have been developed for all of their component atoms. In addition to this, semi-empirical models have a number of well-known limitations. Types of problems on which they do not perform well include hydrogen bonding, transition structures, molecules containing atoms for which they are poorly parametrized, and so on. We consider one such case in the following example, and the exercises will discuss others. 

we optimize the structure of the HF HF complex. The following table lists the results for our AMI, PM3 and HF/6-31+G(d) optimizations as well as an MP2/ 6-31 l-F-tG(2d,2p) tight-convergence optimization taken from the Gaussian Quantum Chemistry Archive  

Basis set keywords are not used for semi-empirical methods as they are inherent in the method s definition. 

Exploring Chemistry with Electronic Structure Methods 113 

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Huang Z S, Jucks K W and Miller R E 1986 The vibrational predissociation lifetime of the HF dimer upon exciting the free-H stretching vibration J. Cham. Phys. 85 3338-41... 

A nice example of this teclmique is the detennination of vibrational predissociation lifetimes of (HF)2 [55]. The HF dimer has a nonlinear hydrogen bonded structure, with nonequivalent FIF subunits. There is one free FIF stretch (v ), and one bound FIF stretch (V2), which rapidly interconvert. The vibrational predissociation lifetime was measured to be 24 ns when excitmg the free FIF stretch, but only 1 ns when exciting the bound FIF stretch. This makes sense, as one would expect the bound FIF vibration to be most strongly coupled to the weak intenuolecular bond. 

Figure C 1.3.5. Spectra of two different infrared bands of HF dimer, corresponding to excitation of the bound (lower panel) and free (upper panel) HF monomers in the complex. Note the additional line width for the bound HF, caused by vibrational predissociation with a lifetime of about 0.8 ns. (Taken from 1211.)...

Fig. 60. Configuration and relevant coordinates of the planar HF dimer in stable and transition configurations. The angles and intermolecular distance are = 9°, 6 = 116°, R = 2.673 A in the stable configuration 0, = 02 = 54.9°, R = 2.S61 k in the transition configuration. The HF bond lengths are constant within an accuracy of 0.003 A.

Much additional work on HF-HF potentials, as discussed elsewhere (37.38). is directed very specifically at that part of the potential energy surface that governs the binding energy, geometry, and internal dynamics of the (HF) dimer near its... 

W. Klopper, M. Quack, and M. A. Suhm, HF dimer Empirically refined analytical potential energy and dipole hypersurfaces from ab initio calculations. J. Chem. Phys. 108, 10096 10115 (1998). 

Fig. 15. Counterpoise-corrected and uncorrected D, R (FF) and r (HF) for the HF dimer, computed with the aug-cc-pVnZ basis sets. The dashed lines represent the estimated CBS limit.

Fig. 1. Dissection of TSJ(F, F) PSO term into NLMOs contributions in the HF dimer at the DFT-B3LYP level. LP1, -A- LP2, - x LP3, Total.

Bond Lengths, Bond Angles, and Normal Vibration Frequencies in the Ground and Transition States of HF Dimer... 

Dayton, D.C., Jucks, K.W. and Miller, R.E. (1989). Photofragmentation angular distributions for HF dimer Scalar J-J correlations in state-to-state photodissociation, J. Chem. Phys. 90, 2631-2638. 

Unimolecular dynamics of smaller clusters has also been studied. The HF dimer provides a particularly interesting system because it involves a highly quantal degenerate rearrangement consisting of a concerted double hydrogen-bond switch (Quack and Suhm 1991 Truhlar 1990). 

Figure 2-4. A comparison of the experimental HF dimer angular distribution and those calculated by Zhang and Zhang (1993) using the potential energy surfaces of Bunker et al. (1988, 1990) (calculation A) and Quack and Suhm (1991) (calculation B).

However, the most extensive calculations on this problem are those using the IEPA, CEP A, and PNO-CI approaches,625 i.e. explicitly including correlation. The results of all three methods were in good agreement, and the effect of electron correlation is rather small for this system. There have been several other papers on hydrogen bonding, and Van Niessen626 has also studied the HF dimer. 

Rybak S, Jeziorski B, Szalewicz K (1991) Many-body symmetry-adapted perturbation theory of intermolecular interactions. H20 and HF dimers. J Chem Phys 95 6576-6601... 

Vissers GWM, Groenenboom GC, van der Avoird A (2003) Spectrum and vibrational predissociation of the HF dimer. I. Bound and quasibound states. J Chem Phys 119 277-285... 

The HF dimer is predicted to nearly perfect accuracy by this simple electrostatic prescription. The prediction deteriorates somewhat for the water dimer, but falls apart entirely for (NH3)2- The poor performance in the latter case is not surprising since the surface is extremely flat, even with the most precise full calculations available. Excellent agreement is obtained for the mixed dimers in the last two rows of Table 3. A later study, which carried the analysis one step further to R 6, indicated the series is not yet entirely stable, and changes of several degrees are to be expected at this level [39]. 

Aqueous HF dimers have been shown to exist by Warren (35) who measured a log K of 0.43 0.05 for the reaction ... 

More recent work has confirmed these conclusions The counterpoise method leads to an accurate description of the correlated interaction energies in the HF dimer, with the proviso that the basis set is capable of properly describing the physical forces involved . Even with an insufficiently flexible set, the counterpoise-corrected results are more stable with respect to basis set than uncorrected data. 

Table 1.8 Perturbation components to interaction energy of HF dimer at equilibrium geometry with various basis sets. ...

Table 2.17 Calculated binding energies of HF dimer (- AEj.[ ), in kcal/mol . ...

Changing the subunit from HX to H2Y adds a number of new vibrational modes to the dimer. Nonetheless, the D-bonded form of the water dimer is more stable than the H-bonded complex . The energy difference of 60 cm" is attributed chiefly to the out-of-plane motion that shears the bond which is of higher frequency for a proton than a deuteron, consistent with the observations for the HF dimer. 

Lischka, H., A note on the ab initio calculation of intermolecular potentials The HF dimer, Chem. Phys. Lett 66, 108-110 (1979). 

Peterson, K. A, and Dunning, T. H. J., Benchmark calculations with correlated molecular wave functions. VJI. Binding energy and structure of the HF dimer, J. Chem. Phys. 102, 2032-2041 (1995). 

Collins, C. L., Morihashi, K., Yamaguchi, Y, and Schaefer, H. R, Vibrational frequencies of the HF dimer from the coupled cluster method including all single and double excitations plus perturbative connected triple excitations, J. Chem. Phys. 103, 6051-6056 (1995). 

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