Conventional ab initio methods

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. 

Modeling of biological systems frequently requires that the accuracy of calculated energy differences are at the kT level (which amounts to less than 1.0 kcal/mol in room temperature). In conventional ab initio methods, such accuracy has been achieved because of effective error cancelation, which is not always the case for the Kohn-Sham calculations. 

In addition to conventional ab initio methods, techniques based on the density functional theory (DFT) have also been used to study the Diels-Alder reaction between butadiene and ethylene97-99. With these kinds of methods, a concerted mechanism through a symmetric transition state is also predicted. Several kinds of density functionals have been used. The simplest one is based on the Local Density Approach (LDA), in which all the potentials depend only on the density. More sophisticated functionals include a dependence on the gradient of the density, such as that of Becke, Lee, Yang and Parr (BLYP). 

A selfconsistent treatment of the transverse interaction in conventional ab initio methods is often based on the Gaunt approximation [48], There are, however, no density functionals available within this approximation. 

Isomerization energies (in kcal/mol) for the reaction XHCO+ -> XCOH+ calculated with several DFT and conventional ab initio methods (67). Values in parenthesis imply that the geometry of the molecules were not optimized at that level. 

In spite of the impressive progress which has been achieved with conventional ab-initio methods as the Configuration-Interaction or Coupled-Cluster schemes in recent years density functional theory (DFT) still represents the method of choice for the study of complex many-electron systems (for an overview of DFT see [1]). Today DFT covers an enormous variety of fields, ranging from atomic [2,3], cluster [4,5] and surface physics [6,7] to the material sciences [8-10]. and theoretical biophysics [11-13]. Moreover, since the introduction of the generalized gradient approximation DFT has become an accepted method also for standard quantum chemical applications [14,15]. Given this tremendous success of nonrelativistic DFT the question for a relativistic extension (RDFT) arises quite naturally in view of the large number of problems in which relativistic effects play an important role (see e.g. Refs.[16,17]). 

Density functional theory is now an established alternative to conventional ab initio methods. It is well documented that with DFT calculations, geometries, bonding... 

To make matters worse, the use of a uniform gas model for electron density does not enable one to carry out accurate calculations. Instead, ripples must be introduced into the uniform electron gas distribution. The way in which this has been implemented has typically been in a semiempirical manner by working backward from the known results on a particular system, usually taken to be the hehum atom. In this way, it has been possible to obtain an approximate set of functions that ako give successful approximate calculations in many other atoms and molecules. By carrying out this combination of a semiempirical approach and retreating from the pure Thomas-Fermi ideal of a uniform gas, it has actually been possible to obtain computationally better results, in many cases, than with conventional ab initio methods using orbitak and wavefunctions. ... 

The various computational schemes based on DFT are attractive alternatives to conventional ab initio methods and particularly for the study of large dusters since the computational effort increases with the number of basis functions as roughly A. Th allow an accurate treatment of transition metal dusters where the standard HF technique is not easily applicable. Furthermore, they provide a natural way for describing the transition from the molecular to the metallic regime since DFT theory underlies most of the first prindple methods for solid state band structure calculations. [47] Although the method is still restricted to ground state properties, possible extensions for the treatment of exdted states are under discussion. [34]... 

This failure of most DFT exchange functionals, which can be traced back to an incorrect dissociation behavior of symmetric radical ions, is unfortunate, because the inability of DFT methods to localize spin and charge means that they are unlikely to give highly accurate transition state geometries for reactions of radical ions where this occurs. Until this problem of DFT methods has been remedied, the use of conventional ab initio methods will be necessary for geometry optimizations of such transition states. 

Methods for calculating dynamic properties of molecules are not nearly as well developed as tho.se for static properties. It is necessary to use very large basis sets and to treat correlation properly to get reasonable results from conventional ab initio methods. Density functional methods show promise, but they are still at an early stage in their evolution. In order to get really accurate results, it is necessary to include vibrational effects and the effects of intermolecular interactions. 

Conventional ab initio methods have been used in the study of reactions of unsymmetrical dienes and/or dienophi-les. These calculations predict concerted asynchronous mechanisms. The values of the potential energy barriers are very sensitive to the level of calculation, and reasonable values are only obtained when electron correlation is included up to the MP3 level. DFT calculations also predict concerted mechanisms, the transition states being more asynchronous than those obtained at the HF or MP2 levels. The potential energy barriers obtained with GGA and hybrid functionals are in excellent agreement with those obtained with high level ab initio methods. ... 

All calculations reported in the following sections have been performed with quantum chemical methods easily accessible via the widely used GAUSSIAN suite of programs. See GAUSSIAN 98 [34] and GAUSSIAN 03 [35]. This arsenal includes conventional ab initio methods and density functional theory (DFT) approaches. We wiU not give further details about the structure and predictive capability of these methods here. For the interested reader, extensive presentations of the above classes of methods are clearly presented in standard references [36-39]. 

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