Ab initio accuracy

As a scientific tool, ab initio quantum chemistry is not yet as accurate as modem laser spectroscopic measurements, for example. Moreover, it is difficult to estimate the accuracies with which various methods predict bond energies and lengths, excitation energies and the like. In the opinion of tlie author, chemists who... 

The excellent agreement of the results of HCR ab initio studies with the corresponding experimental findings clearly shows that the strongest influence on the numerical accuracy of the vibronic levels have effects outside of the R-T effect, that is, primarly the replacement of the effective bending approaches employed in previous works by a full 3D treatment of the vibrational motions (for an analysis of this matter see, e.g., [17]). Let us note, however, that such a... 

The first point to remark is that methods that are to be incorporated in MD, and thus require frequent updates, must be both accurate and efficient. It is likely that only semi-empirical and density functional (DFT) methods are suitable for embedding. Semi-empirical methods include MO (molecular orbital) [90] and valence-bond methods [89], both being dependent on suitable parametrizations that can be validated by high-level ab initio QM. The quality of DFT has improved recently by refinements of the exchange density functional to such an extent that its accuracy rivals that of the best ab initio calculations [91]. DFT is quite suitable for embedding into a classical environment [92]. Therefore DFT is expected to have the best potential for future incorporation in embedded QM/MD. 

Having the Slater atomic orbitals, the linear combination approximation to molecular orbitals, and the SCF method as applied to the Fock matrix, we are in a position to calculate properties of atoms and molecules ab initio, at the Hartree-Fock level of accuracy. Before doing that, however, we shall continue in the spirit of semiempirical calculations by postponing the ab initio method to Chapter 10 and invoking a rather sophisticated set of approximations and empirical substitutions... 

Ab initio quantum mechanics methods have evolved for many decades. The speed and accuracy oiab initio calculations have been greatly improved by developing new algorithms and introducing better basis functions. 

Any set of one-electron functions can be a basis set in the LCAO approximation. However, a well-defined basis set will predict electronic properties using fewer terms than a poorly-defined basis set. So, choosing a proper basis set in ab initio calculations is critical to the reliability and accuracy of the calculated results. 

For small molecules, the accuracy of solutions to the Schrodinger equation competes with the accuracy of experimental results. However, these accurate ab initio calculations require enormous computation and are only suitable for the molecular systems with small or medium size. Ab initio calculations for very large molecules are beyond the realm of current computers, so HyperChem also supports semi-empirical quantum mechanics methods. Semi-empirical approximate solutions are appropriate and allow extensive chemical exploration. The inaccuracy of the approximations made in semi-empirical methods is offset to a degree by recourse to experimental data in defining the parameters of the method. Indeed, semi-empirical methods can sometimes be more accurate than some poorer ab initio methods, which require much longer computation times. 

To overcome these limitations, the hybrid QM-MM potential can employ ad initio or density function methods in the quantum region. Both of these methods can ensure a higher quantitative accuracy, and the density function methods offer a computaitonally less expensive procedure for including electron correlation [5]. Several groups have reported the development of QM-MM programs that employ ab initio [8,10,13,16] or density functional methods [10,41-43]. 

ES Huang, P Koehl, M Levitt, RV Pappu, JW Ponder. Accuracy of side-chain prediction upon near-native protein backbones generated by ab initio folding methods. Proteins 33 204-217, 1998. 

The relative merits of various MO methods have been discussed in die literature. In general, the ab initio type of calculations will be more reliable, but the semiempirical calculations are faster in terms of computer time. The complexity of calculation also increases rapidly as the number of atoms in the molecule increases. The choice of a method is normally made on the basis of evidence that the method is adequate for the problem at hand and the availability of appropriate computer programs and equipment. Results should be subjected to critical evaluation by comparison widi experimental data or checked by representative calculations using higher-level mediods. Table 1.12 lists some reported deviations from experimental AHf for some small hydrocarbons. The extent of deviation gives an indication of the accuracy of the various types of MO calculations in this application. 

Semi-empirical and ab initio methods differ in the trade-off made between computational cost and accuracy of result. Semi-empirical calculations are relatively inexpensive and provide reasonable qualitative descriptions of molecular systems and fairly accurate quantitative predictions of energies and structures for systems where good parameter sets exist. 

These can be determined experimentally to very high accuracy from the Stark effect and molecular beam studies. The experimental accuracy is far beyond the capabilities of ab initio studies. At the other extreme, the original route to these quantities was through studies of the dielectric polarization of species in solution, and there is currently interest in collision-induced dipole moments. In either case, the quantities deduced depend critically on the model used to interpret the experiment. 

The introduction of various empirical corrections, such as scale factors for frequencies and energy corrections based on the number of electrons and degree of spin contamination, blurs the distinction between whether they should be considered ab initio, or as belonging to the semi-empirical class of methods, such as AMI and PM3. Nevertheless, the accuracy tiiat tiiese methods are capable of delivering makes it possible to calculate absolute stabilities (heat of formation) for small and medium sized systems which rival (or surpass) experimental data, often at a substantial lower cost than for actually performing the experiments. 

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