Ab initio techniques

The problem with most quantum mechanical methods is that they scale badly. This means that, for instance, a calculation for twice as large a molecule does not require twice as much computer time and resources (this would be linear scaling), but rather 2" times as much, where n varies between about 3 for DFT calculations to 4 for Hartree-Fock and very large numbers for ab-initio techniques with explicit treatment of electron correlation. Thus, the size of the molecules that we can treat with conventional methods is limited. Linear scaling methods have been developed for ab-initio, DFT and semi-empirical methods, but only the latter are currently able to treat complete enzymes. There are two different approaches available. 

Each of these tools has advantages and limitations. Ab initio methods involve intensive computation and therefore tend to be limited, for practical reasons of computer time, to smaller atoms, molecules, radicals, and ions. Their CPU time needs usually vary with basis set size (M) as at least M correlated methods require time proportional to at least M because they involve transformation of the atomic-orbital-based two-electron integrals to the molecular orbital basis. As computers continue to advance in power and memory size, and as theoretical methods and algorithms continue to improve, ab initio techniques will be applied to larger and more complex species. When dealing with systems in which qualitatively new electronic environments and/or new bonding types arise, or excited electronic states that are unusual, ab initio methods are essential. Semi-empirical or empirical methods would be of little use on systems whose electronic properties have not been included in the data base used to construct the parameters of such models. 

HyperChem uses two types of methods in calculations molecular mechanics and quantum mechanics. The quantum mechanics methods implemented in HyperChem include semi-empirical quantum mechanics method and ab initio quantum mechanics method. The molecular mechanics and semi-empirical quantum mechanics methods have several advantages over ab initio methods. Most importantly, these methods are fast. While this may not be important for small molecules, it is certainly important for biomolecules. Another advantage is that for specific and well-parameterized molecular systems, these methods can calculate values that are closer to experiment than lower level ab initio techniques. 

J. B. Foresman, "Ab Initio Techniques in Chemistry Interpretation and Visualization, Chapter 14 in What Every Chemist Should Know About Computing, Bd. M. L Swift and T. J. Zielinski (ACS Books, Washington, D.C., 1996). 

J. B. Foresman, Ab Initio Techniques in Chemistry Interpretation and Visualiza-... 

Even though recent progress in hardware and software development has made it possible to study quite large molecules, systems of the size considered here do not lend themselves to studies with any ab initio technique. The Hartree-Fock method has the advantage of being size consistent, which Is a necessity for this type of study when results for molecules of vastly different size are to be compared. In addition, the method is technically and economically feasible for these large systems. 

The Onsager s reaction field theory [3] has been incorporated into MO calculations by Tapia and Goscinski [6], The model has been applied to different problems using either semiempirical [51] or ab-initio MO theory [52], or correlated ab-initio techniques [52],... 

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. 

It must be stressed that the use of GHOs in no way depends on this latter Gaussian expansion procedure since all molecular integrals reduce to standard STO forms. It has merely proved expedient to make use of the expansion method in calculations reported earlier. This ab initio technique provides the raw data with which to establish the patterns of behaviour of the GHOs. We can now address ourselves to one of our stated aims the development of approximation methods for a quantitative theory of valence. 

In this chapter, we look closely at the performance of several ab initio techniques in the prediction of radical thermochemistry with the aim of demonstrating which procedures are best suited in representative situations. We restrict our attention to several areas in which we have had a recent active interest, namely, the determination of radical heats of formation (AHf), bond dissociation energies (BDEs), radical stabilization energies (RSEs), and selected radical reaction barriers and reaction enthalpies. We focus particularly on the results of our recent studies. 

There is a wide variety of ab initio techniques available for the study of radical thermochemistry, ranging from quite cheap and approximate methods to much more expensive and accurate approaches. The quality of results yielded by these procedures depends on the size of the basis set used and on the degree of electron correlation included. In practice, it is necessary to strike a balance between the required accuracy and the computational cost that can be afforded. 

In the present paper we tried to demonstrate that the problems faced by most empirical and by (actual and so called) ab initio techniques when applied to modelling TMCs have deep roots in the specific features of the electronic structure of the latter and in approximations which tacitly drop the necessary elements of the theory required to reproduce these features. Of course, the EHCF approach whose success story is described here in details is not completely isolated from other methods. In general picture, the various CAS techniques must be mentioned in relation to it. The char-... 

These studies suggested a planar ylidic carbon and definite participation of the P d orbitals in the description of the HOMO. The earliest ab initio study of methylenephosphorane found a very small rotational barrier [0.003 kcal mol-1 (1 kcal = 4.184 kJ)] about the P=C double bond64. These three points, the degree of pyramidalization at the ylidic carbon, the role of the P d orbitals and the P=C rotational barrier, remain the focal points of all theoretical studies of the ylides. A summary of the theoretical structures determined using ab initio techniques is given in Table 7. 

The ab initio techniques have also been employed to estimate other molecular properties such as electronic spectra and ionization potentials. These studies have been performed on furan (84CPH(90)231, 85JCP(83)723, 89JCS(P2)263, 93JA6184), in comparison with other five-membered rings and (83JST(105)375) with benzoheterocyclic derivatives. These ab initio calculations provide values for molecular properties in accordance with experimental trends, but it is necessary to consider the effects of electron correlation for the calculations to quantitatively reproduce experimental values. 

Direct calculation of the ionization potential by LCAO-Xa, HAM/3 and Green s function techniques or via the Koopmans theorem by ab initio techniques. 

---