Chemical problems, electron correlation

The GIAO-MP2/TZP calculated 13C NMR chemical shifts of the cyclopropylidene substituted dienyl cation 27 show for almost all carbon positions larger deviations from the experimental shifts than the other cations 22-26. The GIAO-MP2/TZP method overestimates the influence of cr-delocalization of the positive charge into the cyclopropane subunit on the chemical shifts. Electron correlation corrections for cyclopropylidenemethyl cations such as 27 and 28 are too large to be adequately described by the GIAO-MP2 perturbation theory method and higher hierarchies of approximations such as coupled cluster models are required to rectify the problem. 

So far only a start has been made (mainly by G. E. K. Branch and G. Schwarzenbach) on the problem of correlating the acidity or basicity of a substance with its resonating electronic structure. It should be possible to develop the theory of molecular structure to such an extent as to permit the reliable prediction of the behavior of substances with respect to this property and other physical and chemical properties. 

Nonrelativistic quantum chemistry has been discussed so far. But transition metal (starting already from the first row) and actinide compounds cannot be studied theoretically without a detailed account of relativity. Thus, the multiconfigurational method needs to be extended to the relativistic regime. Can this be done with enough accuracy for chemical applications without using the four-component Dirac theory Much work has also been done in recent years to develop a reliable and computationally efficient four-component quantum chemistry.25,26 Nowadays it can be combined, for example, with the CC approach for electron correlation. The problem is that an extension to multiconfigurational... 

During the last decade MO-theory became by far the most well developed quantum mechanical method for numerical calculations on molecules. Small molecules, mainly diatomics, or highly symmetric structures were treated most accurately. Now applicability and limitations of the independent particle, or Hartree-Fock (H. F.), approximation in calculations of molecular properties are well understood. An impressive number of molecular calculations including electron correlation is available today. Around the equilibrium geometries of molecules, electron-pair theories were found to be the most economical for actual calculations of correlation effects ). Unfortunately, accurate calculations as mentioned above are beyond the present computational possibilities for larger molecular structures. Therefore approximations have to be introduced in the investigation of problems of chemical interest. Consequently the reliability of calculated results has to be checked carefully for every kind of application. Three types of approximations are of interest in connection with this article. 

Many-body effects play a leading role in the description of chemical phenomena, and there is little point advancing detailed relativistic theories which cannot treat the electron correlation problem. A major advan-... 

Density-Functional Theory. Transition metals pose a problem for classical quantum chemical methods like self-consistent field (SCF), perturbation theory, configuration interaction (Cl), and variations on these methods, because of the very large electron correlation. SCF underestimates binding substantially, and post-SCF methods are so expensive for transition metals that one can do a calculation only on models with few atoms. DFT on the other hand is relatively cheap it is about as expensive as SCF. Moreover, with the development of the generalized-gradient approximations it is also reasonably accurate. A large majority of quantum chemical... 

In the last section of this review, we elaborated on the relevance and consequences of these concepts for transition-metal cluster chemistry on the basis of new results. We discussed problems and pitfalls that may arise in present-day quantum chemical DFT calculations on open-shell clusters. Clearly, these obstacles point to the necessity of developing improved density functionals and also new ab initio electron correlation methods, like, for example, the density renormalization group algorithm (151). 

Jiri Cizek s research program centers on the quantum theory of molecular electronic structure and related developments in quantum chemical methodology, coupled-cluster approaches to many-electron correlation problems,105 large-order perturbation theory,106 dynamical groups and exactly solvable models, lower bounds, and the use of symbolic computation language in physics and in chemistry. 

The mathematical term functional, which is akin to function, is explained in Section 7.2.3.1. To the chemist, the main advantage of DFT is that in about the same time needed for an HF calculation one can often obtain results of about the same quality as from MP2 calculations (cf. e.g. Sections 5.5.1 and 5.5.2). Chemical applications of DFT are but one aspect of an ambitious project to recast conventional quantum mechanics, i.e. wave mechanics, in a form in which the electron density, and only the electron density, plays the key role [5]. It is noteworthy that the 1998 Nobel Prize in chemistry was awarded to John Pople (Section 5.3.3), largely for his role in developing practical wavefunction-based methods, and Walter Kohn,1 for the development of density functional methods [6]. The wave-function is the quantum mechanical analogue of the analytically intractable multibody problem (n-body problem) in astronomy [7], and indeed electron-electron interaction, electron correlation, is at the heart of the major problems encountered in... 

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