The Quantum-Chemical Approach

VLASTA BONACIC-KOUTECKt, JiftI PITTNER, DETLEF REICHARDT 

AIMD = ab initio molecular dynamics B-LYP = Becke-Lee-Yang-Parr CCSD = coupled cluster single double excitations CVC = core-valence correlation ECP = effective core potential DF = density functional GDA = gradient corrected density approximation MCLR = multiconfigurational linear response MP2 = M0ller-Plesset second-order (MRD)CI = multi-reference double-excitation configuration interaction RPA = random phase approximation TD-MCSCF = time-dependent multiconfigurational self-consistent field TD-SCF = time-dependent self-consistent field. 

Metal Clusters. Edited by W. Ekardt 1999 John Wiley Sons Ltd 

In this paper we will show that quantum chemistry provides suitable approaches to extracting the specific properties of small metallic and mixed nonstochiometric clusters which cannot be obtained by more approximate methods. This accuracy is needed for controlling the properties through size, shape and composition of the cluster. For this purpose the methodological aspects will be briefly sketched in Section 2.2. We will first address the methods used for the determination of cluster structures at zero temperature and outline the ab initio molecular dynamics method which we developed for the determination of temperature-dependent ground-state properties. Then, ab initio methods for calculation of excited states valid at T = 0 will be described. 

In Section 2.3 the structural and optical properties of neutral and cationic Na clusters at r = 0 K as functions of size are presented and compared with experimental data recorded at low temperature. The temperature-dependent line-broadening will be illustrated by the example of Na9, since in this case a comparison with experimental data at different temperatures is particularly instructive. In Section 2.4 the results of ab initio molecular dynamics (AIMD) studies on Li9 will serve to show different temperature behavior of distinct types of structures as well as their isomerization mechanisms. The study of possible metal-insulator transitions and segregation into metallic and ionic parts in finite systems carried out on prototypes of nonstoichiometric alkali halide and alkali hydride clusters with single and multiple excess electrons is presented in Section 2.5. A comparison of structural and optical characteristics of Na F and lAnUm (n m) series allows us to illustrate the influence of different bonding properties. 

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Equation (2) was also used to calculate quantum chemical approach. On the basis of previous results [19], calculated electrostatic potentials were computed from ab initio wave functions obtained in the framework of the HF/SCF method using a split-valence basis set (3-21G) and a split-valence basis set plus polarisation functions on atoms other than hydrogen (6-31G ). The GAUSSIAN 90 software package [20] was used. Since ab initio calculations of the molecular wave function for the whole... 

The complete theory of catalysis, which would start with the isolated reaction participants, was not available until now because of the lack of adequate knowledge of the participants themselves (even the complete theory of the isolated participants, starting from the first principles, is still lacking). However, in analogy with the homogeneous chemical reactions one can expect that the quantum chemical approach, based on the semiempirical quantum mechanical methods, could be a prospective one. 

Theoretical calculations are valuable tools for analysing solid-state 170 NMR spectra. As mentioned in Section 4.1, for example the absolute orientations of 170 NMR tensors in a molecular frame can be readily determined by ab initio calculations. However, a key problem of "accuracy" always receives attention. In many papers in the literature, the calculated results for the magnitudes of 170 CS tensors are compared with those of experimental data. It seems that the quantum chemical approach is the most frequently used and can yield reasonable... 

The ability of the quantum chemical approaches to analyze, interpret and rationalize all experimental observations on molecular processes in a unified language based on the primary principles of physics, represents an important asset in the study of biological systems where experimental data has to be obtained in a variety of forms and from many different sources. Taking advantage of this formal and anlytic power of the quantum chemical approaches, Lipscomb and his coworkers studied models of enzymatic mechanisms in chymotrypsin (21) and caboxypeptIdase (22). 

Several methods considered in this article, such as the quantum-chemical approaches developed by Clark et al. [51,113,114] or the ALOGPS program [99], provide an estimation of the accuracy of model predictions. Other approaches to estimate accuracy of model predictions were reviewed elsewhere [99,141],... 

Another major point in which the theoretical methods differ is the quantum chemical approach to solve the operator equation of the Hamilton operator itself. The most important schemes are Hartree-Fock self consistent field (HF-SCF), density functional theory (DFT) and multi-body second order perturbation theory (MP2). Different combinations have been established, so for instance GIAO-SCF, GlAO-DI I, (,IA()-MI>2, or DF I-IGLO. Most precise measurements on small systems were done with coupled cluster methods, as for instance GIAO-CCSDT-n. ... 

We now report how theoretical methods can be used to provide information on the adsorption, diffusion, and reactivity of hydrocarbons within acidic zeolite catalysts. In Section A, dealing with adsorption, the physical chemistry of molecules adsorbed in zeolites is reviewed. Furthermore, in this section the results of hydrocarbon diffusion as these data are obtained from the use of the same theoretical methods are described. In Section B we summarize the capability of the quantum-chemical approaches. In this section, the contribution of the theoretical approaches to the understanding of physical chemistry of zeolite catalysis is reported. Finally, in Section C, using this information, we study the kinetics of a reaction catalyzed by acidic zeolite. This last section also illustrates the gaps that persist in the theoretical approaches to allow the investigation of a full catalytic cycle. 

Atypical example is an above cited work in which the modeling ofthe structure of the methane molecule is used not to validate the quantum chemical approach but to test how many basis set functions are sufficient to get a correct result (Janoschek et al. 1967). To this point also compare Nye ... 

Takahito Nakajima received his Ph.D. in chemistry in 1997 working under the direction of Hiroshi Nakatsuji at Kyoto University. He then joined the Department of Applied Chemistry at the University of Tokyo in 1999. He is an Associate Professor at the Department of Applied Chemistry, the University of Tokyo. He is also a researcher of PRESTO, Japan Science and Technology Corporation (JST). His current research interests include the developments of the relativistic molecular theory and the quantum chemical approach towards large-scale calculations. 

The reaction mechanisms and regioselectivities of sEH, LEH, and HheC were analyzed in detail. The computational results support the proposed mechanisms and are able to explain the experimentally observed regioselectivities of these enzymes. The quantum chemical approach also allowed us to identify and quantify the importance of individual functional groups for the reaction mechanism and the regioselectivity of epoxide opening. 

The results confirm the high potentiality of large pore zeolites in the Diels-Alder cycloaddition reactions which can be performed with high regio and stereoselectivity at low temperature and pressure, and the validation of the quantum chemical approach to interpret both catalytic activity and selectivity for these reactions. 

Why is the quantum chemical approach particularly challenging for clusters The basic answer is that, by its very definition, a cluster consists of... 

The quantum chemical approach is exemplified by the work of Portmann et al who performed ab initio computations on complexes of alkali metal ions with a large number of organic ligands. From their results the authors fitted the interactions Eint between the cations and the atoms H, C, N, O, and S to functions V(r), using the relation ... 

Peculiarities of the inclusion technique of zinc active component into HZSM-5 zeolite and some experimental data lead to conclusion that the reaction occurred on ZnZd sites. The same cluster model and level of the quantum chemical approach... 

Isomer effects cannot be predicted. This means the same activity coefficients are obtained, for example, for o-/m-/p-xylene or phenanthrene/anthracene with the different solvents. But at least in the case of VLE or SLE calculation this is not a great problem, since the required standard fugacities, that is, vapor pressure, melting point, and heat of fusion are of much greater importance than small differences of the activity coefficients. Similar problems are also observed for other predictive models, for example, the quantum chemical approach. 

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