Quantum chemical method/calculation

Quantum chemical calculations, 172 Quantum chemical method, calculations of the adsorption of water by, 172 Quantum mechanical calculations for the metal-solution interface (Kripsonsov), 174 and water adsorption, 76 Quartz crystal micro-balance, used for electronically conducting polymer formation, 578... 

Adsorption of toluene on zeolites Li-X, Na-X, K-X, Rb-X, and Cs-X has been investigated with quantum chemical methods. Calculations of geometries, Mulliken partial charges, and C chemical shift parameters of clusters representing the catalytically active site are presented. The polarisation of the toluene carbons is the first step in alkylation reactions catalysed by zeolites and, at an early stage, will influence the outcome of the reaction. We show the simultaneous influence of the Lewis acidic cation and the basicity of the zeolite is responsible for altering the electron distribution within the toluene and thus affecting the outcome of an alkylation reaction. 

Quantum chemical methods, exemplified by CASSCF and other MCSCF methods, have now evolved to an extent where it is possible to routinely treat accurately the excited electronic states of molecules containing a number of atoms. Mixed nuclear dynamics, such as swarm of trajectory based surface hopping or Ehrenfest dynamics, or the Gaussian wavepacket based multiple spawning method, use an approximate representation of the nuclear wavepacket based on classical trajectories. They are thus able to use the infoiination from quantum chemistry calculations required for the propagation of the nuclei in the form of forces. These methods seem able to reproduce, at least qualitatively, the dynamics of non-adiabatic systems. Test calculations have now been run using duect dynamics, and these show that even a small number of trajectories is able to produce useful mechanistic infomiation about the photochemistry of a system. In some cases it is even possible to extract some quantitative information. 

It is well known and accepted that the quality of the methods as well as of the underlying models has great effect on the results of scientific research, This is especially applicable to quantum chemical model calculations. If the method is adequate to the subject of investigation, and the model is well adapted, then a good modelling of macroscopic processes on a microscopic level can be expected. That is why it is of importance to... 

At the moment there exist no quantum chemical method which simultaneously satisfies all demands of chemists. Some special demands with respect to treatment of macromolecular systems are, the inclusion of as many as possible electrons of various atoms, the fast optimization of geometry of large molecules, and the high reliability of all data obtained. To overcome the point 4 of the disadvantages, it is necessary to include the interaction of the molecule with its surroundings by means of statistical thermodynamical calculations and to consider solvent influence. 

The chemical task in quantum chemistry consist of choosing a proven model (i. e. the reduction of the molecular system to as few as possible atoms while conserving its characteristic properties), and choosing a reliable quantum chemical method, and last but not least, the interpretation of the data calculated using suitable reaction theoretical concepts5 . The following part deals with quantum chemical methods often used and special qualities of their application. 

At present the chemist has a wide variety of quantum chemical methods available, and it is difficult to keep the numerous modifications of only a few basic statements in perspective, even for the insiders. All methods can be divided into two basic categories the ab initio calculations and the semiempirical calculations. The ab initio as well as the semiempirical treatments of chemical problems were developed proportional to the computers because... 

Table 2. Relative energies E (kJ mol-1) of the butyl cation dependent on the geometry and quantum chemical method used (data from 32) calculations with basis set 1-3 simple ab initio CEPA ab initio with electron correlation)...

The quantum chemical methods introduced in part 2.2 calculate only individual molecules at the temperature of 0 K. The energies obtained in these cases represent the energies of the molecules directly in the minimum of the potential energy, i.e. the zero point energy which is evident at 0 K and the thermic energy of an ensemble of... 

Figure4.7 Relativistic bond contractions A re for Au2 calculated in the years from 1989 to 2001 using different quantum chemical methods. Electron correlation effects Acte = te(corn) — /"e(HF) at the relativistic level are shown on the right hand side of each bar if available. From the left to the right in chronological order Hartree-Fock-Slater results from Ziegler et al. [147] AIMP coupled pair functional results from Stbmberg and Wahlgren [148] EC-ARPP results from Schwerdtfeger [5] EDA results from Haberlen and Rdsch [149] Dirac-Fock-Slater...

We should mention the recent progress in Au(I) and Au(III) catalyzed organic reactions [24, 297]. A number of groups of theoretical chemists are currently investigating the reaction mechanisms using quantum chemical methods [298-301]. Li and Mia published DFT calculations on AU5H5X hydrometal pentagons with Dsh planar pentacoordinate nonmetal centers (X = Si, Ge, P, S) [302]. The introduction of the nonmetal centers X introduces p aromaticity to MHX complexes. 

Methods Based on Quantum Chemical Semiempirical Calculations... 

This theory appears not to involve adjustable parameters (other than the nuclear radius parameters that were taken from the literature). In particular, it was criticized that the calibration approach involved a slope that is too high by about a factor of two. However, in actual calculations with the linear response approach, it was found that the slope of the correlation line between theory and experiment (dependent on the quantum chemical method) is close to 0.5. Thus, it also requires a scaling factor of about 2 in order to reach quantitative agreement with experiment. The standard deviations between the calibration and linear response approaches are comparable thus indicating that the major error in both approaches still stems from errors in the description of the bonding that is responsible for the actual valence shell electron distribution. 

The usefulness of quantum-chemical methods varies considerably depending on what sort of force field parameter is to be calculated (for a detailed discussion, see [46]). There are relatively few molecular properties which quantum chemistry can provide in such a way that they can be used directly and profitably in the construction of a force field. Quantum chemistry does very well for molecular bond lengths and bond angles. Even semiempirical methods can do a good job for standard organic molecules. However, in many cases, these are known with sufficient accuracy a C-C single bond is 1.53 A except under exotic circumstances. Similarly, vibrational force constants can often be transferred from similar molecules and need not be recalculated. 

Hpp describes the primary system by a quantum-chemical method. The choice is dictated by the system size and the purpose of the calculation. Two approaches of using a finite computer budget are found If an expensive ab-initio or density functional method is used the number of configurations that can be afforded is limited. Hence, the computationally intensive Hamiltonians are mostly used in geometry optimization (molecular mechanics) problems (see, e. g., [66]). The second approach is to use cheaper and less accurate semi-empirical methods. This is the only choice when many conformations are to be evaluated, i. e., when molecular dynamics or Monte Carlo calculations with meaningful statistical sampling are to be performed. The drawback of semi-empirical methods is that they may be inaccurate to the extent that they produce qualitatively incorrect results, so that their applicability to a given problem has to be established first [67]. 

The computational prediction of vibrational spectra is among the important areas of application for modem quantum chemical methods because it allows the interpretation of experimental spectra and can be very instrumental for the identification of unknown species. A vibrational spectrum consists of two characteristics, the frequency of the incident light at which the absorption occurs and how much of the radiation is absorbed. The first quantity can be obtained computationally by calculating the harmonic vibrational frequencies of a molecule. As outlined in Chapter 8 density functional methods do a rather good job in that area. To complete the picture, one must also consider the second quantity, i. e., accurate computational predictions of the corresponding intensities have to be provided. 

Bases stacked rather than hydrogen bonded have also been studied with quantum chemical methods [182, 244-247]. The nature of excited states in these systems has been debated and theoretical calculations are called to decide on the degree of excited state localization or delocalization, as well as the presence and energy of charge transfer states. The experimentally observed hypochromism of DNA compared to its individual bases has been known for decades [248], Accurate quantum chemical calculations are limited in these systems because of their increased size. Many of the reported studies have used TDDFT to calculate excited states of bases stacked with other bases [182, 244, 246, 247], However, one has to be cautious when us-... 

The applications of quantum chemical calculations to biological systems has been made possible by huge advances in computer facilities and the creation of better computer programs, capable of handling large systems. This book describes some of the quantum chemical methods used for such calculations, together with some widely used computer programs. 

Chapter 1 gives a short description of ab initio methods, Hartree-Fock and post-Hartree-Fock, focusing on the Gaussian computer programs. Chapter 2 describes semi-empirical calculations and their applications to biological systems. Chapter 3 addresses itself to electrostatic properties of molecules, as determined by quantum-chemical methods. The density functional method is discussed in chapter 4. Chapter 5 compares theoretically obtained parameters to experimental data. 

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