QM calculations

As ab initio MD for all valence electrons [27] is not feasible for very large systems, QM calculations of an embedded quantum subsystem axe required. Since reviews of the various approaches that rely on the Born-Oppenheimer approximation and that are now in use or in development, are available (see Field [87], Merz ]88], Aqvist and Warshel [89], and Bakowies and Thiel [90] and references therein), only some summarizing opinions will be given here. 

MM methods are defined atom by atom. Thus, having a carbon atom without all its bonds does not have a significant affect on other atoms in the system. In contrast, QM calculations use a wave function that can incorporate second atom effects. An atom with a nonfilled valence will behave differently than with the valence filled. Because of this, the researcher must consider the way in which the QM portion of the calculation is truncated. 

FIGURE 23.1 Example of a QM/MM region partitioning for a S l reaction, (a) Entire molecule is shown with a dotted line denoting the QM region. (A) Molecule actually used for the QM calculation. 

Tliroughout this chapter and in Table 1 the inclusion of QM results as target data is evident, with the use of such data in the optimization of empirical forces fields leading to many improvements. Use of QM data alone, however, is insufficient for the optimization of parameters for condensed phase simulations. This is due to limitations in the ability to perform QM calculations at an adequate level combined with limitations in empirical force fields. As discussed above, QM data are insufficient for the treatment of dispersion... 

Step 1 of the parametrization process is the selection of the appropriate model compounds. In the case of small molecules, such as compounds of pharmaceutical interest, the model compound may be the desired molecule itself. In other cases it is desirable to select several small model compounds that can then be connected to create the final, desired molecule. Model compounds should be selected for which adequate experimental data exist, as listed in Table 1. Since in almost all cases QM data can be substimted when experimental data are absent (see comments on the use of QM data, above), the model compounds should be of a size that is accessible to QM calculations using a level of theory no lower than HE/6-31G. This ensures that geometries, vibrational spectra, conformational energetics, and model compound-water interaction energies can all be performed at a level of theory such that the data obtained are of high enough quality to accurately replace and... 

The MD/QM methodology [18] is likely the simplest approach for explicit consideration of quantum effects, and is related to the combination of classical Monte Carlo sampling with quantum mechanics used previously by Coutinho et al. [27] for the treatment of solvent effects in electronic spectra, but with the variation that the MD/QM method applies QM calculations to frames extracted from a classical MD trajectory according to their relative weights. 

In the MD/QM technique each tool is used separately, in an attempt to exploit their particular strengths. Classical molecular dynamics as a very fast sampling technique is first used for efficient sampling of the conformational space for the molecule of interest. A cluster analysis of the MD trajectory is then used to identify the main con-formers (clusters). Finally QM calculations, which provide a more accurate (albeit more computationally expensive) representation of the system, can be applied to just a small number of snapshots carefully extracted from each representative cluster from the MD-generated trajectory. 

ONIOM can combine two MO levels like ONIOM(QM QM), which is a unique feature that is not available to QM/MM methods. However, the most popular combination is ONIOM(QM MM), combining QM with MM. This is essentially equivalent to generic QM/MM. However, there are some subtle cancellation or double-counting differences for the case where a covalent bond is cut. For this, we refer to a detailed discussion published elsewhere [8], QM MM or QM/MM applications have typically been used without appropriate accuracy or S-value tests, as the benchmark full QM calculation for the real system is often impossible. In Section 2.2.2, we will examine one such test in detail. 

Figure 2-3. Protonated Schiff-base of retinal (PSBR) and computational models used in ONIOM QM QM calculations (left). Electrostatic effects of the surrounding protein on excitation energies in bacteriorhodopsin evaluated using TD-B3LYP Amber right). (Adapted from Vreven and Morokuma [37] (Copyright American Institute of Physics) and Vreven et al. [38], Reprinted with permission.)...

As discussed in many previous studies of biomolecules, the treatment of electrostatic interactions is an important issue [69, 70, 84], What is less widely appreciated in the QM/MM community, however, is that a balanced treatment of QM-MM electrostatics and MM-MM electrostatics is also an important issue. In many implementations, QM-MM electrostatic interactions are treated without any cut-off, in part because the computational cost is often negligible compared to the QM calculation itself. For MM-MM interactions, however, a cut-off scheme is often used, especially for finite-sphere type of boundary conditions. This imbalanced electrostatic treatment may cause over-polarization of the MM region, as was first discussed in the context of classical simulations with different cut-off values applied to solute-solvent and solvent-solvent interactions [85], For QM/MM simulations with only energy minimizations, the effect of over-polarization may not be large, which is perhaps why the issue has not been emphasized in the past. As MD simulations with QM/MM potential becomes more prevalent, this issue should be emphasized. 

In the AMOEBA force field the permanent atomic multipoles are determined from QM calculations [40], The prescription considers that the resulting multipoles on the atoms result from two components, the permanent and the induced moments ... 

Figure 19(a) shows the QM simulation of the differential cross-section (DCS) in the HF + D channel, over the same extended energy range as in Fig. 5. The agreement with experiment is seen to be qualitatively reasonable. The forward-backward peaking and direct reaction swathe observed in the experiment also occur in the QM calculation, although the relative magnitudes are not consistent. Thus fully quantitative agreement between QM calculations and experiment in all of the reaction attributes must await further refinements of the PES, and/or a more rigorous treatment of the open-shell character of the F(2P) atom.90...

Fig. 25. Comparison between the experimental abstraction reaction H + H2O(00)(0) cross-section (solid point with error bars), and the 5D QM calculations (solid line). The 6D QM cross-sections with the CS approximation (dotted line), and the QCT data using normal (o) and Gaussian (A) binning procedures are shown.

Fig. 1 N-formyltryptophanamide used for QM calculations on a tryptophan trimmed from a protein structure, also showing the two kinds of electron density shifts that control Trp fluorescence wavelength (red) and intensity/lifetime (green)...

Murphy et al. [34,45] have parameterized and extensively tested a QM/MM approach utilizing the frozen orbital method at the HF/6-31G and B3LYP/6-31G levels for amino acid side chains. They parameterized the van der Waals parameters of the QM atoms and molecular mechanical bond, angle and torsion angle parameters (Eq. 3, Hqm/mm (bonded int.)) acting across the covalent QM/MM boundary. High-level QM calculations were used as a reference in the parameterization and the molecular mechanical calculations were performed with the OPLS-AA force... 

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