View of Ab Initio Methods

From a computational point of view, the heat of formation, which is derived from the electronic energy of the molecule molecule> is the most difficult thermochemical quantity to predict accurately. Entropies and heat capacities are derived from vibration and rotational constants, all of which can be predicted with considerable accuracy using relatively low levels of theory. Thus, the development of ab initio methods appropriate for a new class of compounds focuses primarily on identifying a level of theory and the basis set(s) needed to achieve sufficient accuracy in the electronic energy [67,68]. 

With regard to the electronic structure methodology, major obstacles must be surmounted before improvements can be made. Calculations with Coupled-Cluster methods, an obvious next step, are far more computationally costly than the presently used MP2, or B3LYP methods. In fact, there are extremely few direct ab initio calculations of anharmonic vibrational spectroscopy at higher than MP2 or DPT levels, even for small polyatomics. From the point of view of ab initio anharmonic spectroscopy, the leap from MP2 to the Coupled-Cluster method seems a bottleneck. One can draw encouragement from faster Coupled-Cluster implementations, so far employed with the perturbation theory anharmonic analysis [116,117]. 

While some attempts were made to parameterize such semiemprrical methods to reproduce the results of ab initio methods, Dewar insisted that we should not fit to the results that way, rather we should fit directly to experimental results. His view was that this would be the only approach actually useful to chemists. While ab initio methods might fit to experiment eventually, they did not fit at all well at the lower levels of calculation that were possible at the time. If semiempirical methods could be adequately developed and fit to experiment, perhaps one could really reach chemical accuracy with orders of magnitude with less work than would be required by strictly ab initio methods. 

First we discuss the QM methods of electronic structure calculation in view of the DSC procedure. In principle, any of the existing methods of quantum-chemical calculation of molecular systems may be used to treat the QM region different levels of ab initio methods, DFT methods, a variety of semiempirical versions. However, as mentioned above, even separate fragments of TMS may be relatively too large making the high-level ab initio methods impractical. 

The energies of several intermediates that could arise from the reaction of diazoazoles with alkenes have been estimated [90JCS(P2)1943] by means of the MNDO, AMI SCF-MO, and ab initio methods. The calculations suggest a 1,4-dipole behavior (also viewed as a 1,7-dipole) for most diazoazoles when reacting with electron-rich alkenes it is believed that the approach between 438 and alkenes is asynchronous. On the basis of that study, some errors have been corrected (Scheme 95). 

By carrying out this combination of semi-empirical procedures and retreating from the pure Thomas-Fermi notion of a uniform electron gas it has actually been possible, somewhat surprisingly, to obtain computationally better results in many cases of interest than with conventional ab initio methods. True enough, calculations have become increasingly accurate but if one examines them more closely one realizes that they include considerable semi-empirical elements at various levels. From the purist philosophical point of view, or what I call "super - ab initio" this means that not everything is being explained from first principles. 

As it is now very well known, accurate studies of the water-water interaction by means of ab-initio techniques require the use of larger and flexible basis sets and methods which consider correlation effects [85,94-96], Since high level ab-initio post-Hartree-Fock calculations are unfeasible because of their high computational cost for systems with many degrees of freedom, Density Functional Theory, more economical from the computational point of view, is being more and more considered as a viable alternative. Recently, we have presented [97] results of structural parameters and vibrational frequencies for the water clusters (H20) , n=2 to 8, using the DFT method with gradient corrected density functionals. 

Ab initio calculations are based on first principles using molecular orbital (MO) calculations based on Gaussian functions. Combinations of Gaussian functions yield Slater-type orbitals (STOs), also called Slater determinants. STOs are mathematical functions closely related to exact solutions for the hydrogen atom. In their ultimate applications, ab initio methods would use Gaussian-type wave functions rather than STOs. The ab initio method assumes that from the point of view of the electrons the nuclei are stationary, whereas... 

In summary, computational quantum mechanics has reached such a state that its use in chemical kinetics is possible. However, since these methods still are at various stages of development, their routine and direct use without carefully evaluating the reasonableness of predictions must be avoided. Since ab initio methods presently are far too expensive from the computational point of view, and still require the application of empirical corrections, semiempirical quantum chemical methods represent the most accessible option in chemical reaction engineering today. One productive approach is to use semiempirical methods to build systematically the necessary thermochemical and kinetic-parameter data bases for mechanism development. Following this, the mechanism would be subjected to sensitivity and reaction path analyses for the determination of the rank-order of importance of reactions. Important reactions and species can then be studied with greatest scrutiny using rigorous ab initio calculations, as well as by experiments. 

Figure 6-22 Generalized valence-bond orbitals calculated for ethene by the ab initio method. The nuclei are located in the x,y plane of the coordinate system at the positions indicated by crosses. The long dashes correspond to locations of change of phase. The dotted lines are contour lines of electron amplitude of opposite phase to the solid lines. Top shows both m-bonding carbon orbitals (almost sp2), middle-left is the carbon orbital and middle-right the hydrogen orbital of one of the C-H bonds, and bottom represents a side view of the ir orbitals in perpendicular section to the x,y plane. (Drawings furnished by Dr. W, A. Goddard, III.)...

HO-OH2+.14 This reaction forms two water molecules and a carbenium ion, which is then hydrated to form the protonated alcohol. The degenerate gas-phase reactions between HF and protonated alkyl fluorides RFH+ (R = Me, Et, i-Pr, r-Bu) were investigated by ab initio methods.15 With the exception of MeFFi+, the protonated alkyl fluorides can be viewed as weak complexes of the carbocation R+ and FiF. Both frontside and backside substitutions occur, supporting the proposal (see Introduction)8 that nucleophilic substitution reactions are better understood through such a competition as opposed to the traditional S /S 2 competition. 

The accuracy of ab initio geometries is astonishing, in view of the approximations present the 3-21G( ) basis set is small and the 6-31G is only moderately large, and so these probably cannot approximate closely the true wavefunction the HF method does not account properly for electron correlation, and the MP2 method is only the simplest approach to handling electron correlation the Hamiltonian in both the HF and the MP2 methods used here neglects relativity and spin-orbit coupling. Yet with all these approximations the largest error (Table 5.7) in bond... 

Another way of performing calculations using the cluster model is the use of a hybrid method. It is a theoretical method, which uses different approaches for different parts of the molecular system. The ONIOM method is one of the hybrid methods developed quite recently to facilitate accurate ab initio calculations of large chemical species. The ONIOM method (n-layered integrated molecular orbital and molecular mechanics approach) [29] is a multi-level extrapolation method, in which the studied molecular system is divided into two or more parts or layers. The most important part of the system from the chemical point of view (the inner part, IP) is treated at a high" level of theory (the HL method - a high level of ab initio molecular orbital method) and the rest of the system is described by a computationally less demanding method (the LL method - the lowest ab initio approximation or even semiempirical or molecular mechanic approximations) [30]. 

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