Quantum chemical methods, computational applicability

The maintenance of a connection to experiment is essential in that reliability is only measurable against experimental results. However, in practice, the computational cost of the most reliable conventional quantum chemical methods has tended to preclude their application to the large, low-symmetry molecules which form liquid crystals. There have however, been several recent steps forward in this area and here we will review some of these newest developments in predictive computer simulation of intramolecular properties of liquid crystals. In the next section we begin with a brief overview of important molecular properties which are the focus of much current computational effort and highlight some specific examples of cases where the molecular electronic origin of macroscopic properties is well established. 

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. 

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. 

Quantum chemical methods are well established, accepted and of high potential for investigation of inorganic reaction mechanisms, especially if they can be applied as a fruitful interplay between theory and experiment. In the case of solvent exchange reactions their major deficiency is the limited possibility of including solvent effects. We demonstrated that with recent DFT-and ab initio methods, reaction mechanisms can be successfully explored. To obtain an idea about solvent effects, implicit solvent models can be used in the calculations, when their limitations are kept in mind. In future, more powerful computers will be available and will allow more sophisticated calculations to be performed. This will enable scientists to treat solvent molecules explicitly by ab initio molecular dynamics (e.g., Car-Parrinello simulations). The application of such methods will in turn complement the quantum chemical toolbox for the exploration of solvent and ligand exchange reactions. 

During the last decade, density-functional theory (DFT)-based approaches [1, 2] have advanced to prominent first-principles quantum chemical methods. As computationally affordable tools apt to treat fairly extended systems at the correlated level, they are also of special interest for applications in medicinal chemistry (as demonstrated in the chapters by Rovira, Raber et al. and Cavalli et al. in this book). Several excellent text books [3-5] and reviews [6] are available as introduction to the basic theory and to the various flavors of its practical realization (in terms of different approximations for the exchange-correlation functional). The actual performance of these different approximations for diverse chemical [7] and biological systems [8] has been evaluated in a number of contributions. 

For applications of quantum chemical methods on transition metal compounds see the articles which appeared in the special issue on Computational Transition Metal Chemistry in Chem. Rev. 100 (2000). 

In summary, computational quantum mechanics has reached such a state that its use in chemical kinetics is possible. However, since these methods still are at various stages of development, their routine and direct use without carefully evaluating the reasonableness of predictions must be avoided. Since ab initio methods presently are far too expensive from the computational point of view, and still require the application of empirical corrections, semiempirical quantum chemical methods represent the most accessible option in chemical reaction engineering today. One productive approach is to use semiempirical methods to build systematically the necessary thermochemical and kinetic-parameter data bases for mechanism development. Following this, the mechanism would be subjected to sensitivity and reaction path analyses for the determination of the rank-order of importance of reactions. Important reactions and species can then be studied with greatest scrutiny using rigorous ab initio calculations, as well as by experiments. 

An EU COST project under action D23 Metachem Metalaboratories for Complex Computational Applications in Chemistry . Project number D23/0001/01 European Metalaboratory for multireference quantum chemical methods (01/02/200118/07/2005). Participants P. Carsky, J. Pittner (J. Heyrovsky Institute, Prague, Czech Republic), 1. Hubac (Comenius University, Slovakia), S. Wilson (Rutherford Appleton Laboratory, UK), W. Wenzel (Universitat Dortmund Germany), L. Meissner (Nicholas Copernicus University Poland), V. Staemmler (Ruhr Universitat Bochum Germany), C. Tsipis (Aristotle University of Thessaloniki, Greece), A. Mavridis (National and Kapodistrian University of Athens, Greece). 

The enormous progress in accessible computational power over the past decade has allowed for increased application of high-level ab initio quantum-chemical methods to questions of structure and reactivity, and this trend has been reflected in studies on pyrans and derivatives. As is the case with many computational studies, there has been substantial effort directed toward the comparison of data obtained by various computational methods with empirical data. Table 1 provides a compilation of studies involving the applications of theoretical methods to pyrans and related molecules. 

Quantum chemical methods aim to treat the fundamental quantum mechanics of electronic structure, and so can be used to model chemical reactions. Such quantum chemical methods are more flexible and more generally applicable than molecular mechanics methods, and so are often preferable and can be easier to apply. The major problem with electronic structure calculations on enzymes is presented by the very large computational resources required, which significantly limits the size of the system that can be treated. To overcome this problem, small models of enzyme active sites can be studied in isolation (and perhaps with an approximate model of solvation). Alternatively, a quantum chemical treatment of the enzyme active site can be combined with a molecular mechanics description of the protein and solvent environment the QM/MM approach. Both will be described below. 

The cluster approach opens the way for a direct application of quantum-chemical methods to the problems of chemisorption and catalysis. Quantum chemistry has a rich experience in describing the local chemical interactions in molecular systems. Its methods are continuously refined and improved, and the computational techniques have become more and more accurate and predictive. 

Two methods are mainly responsible for the breakthrough in the application of quantum chemical methods to heavy atom molecules. One method consists of pseudopotentials, which are also called effective core potentials (ECPs). Although ECPs have been known for a long time, their application was not widespread in the theoretical community which focused more on all-electron methods. Two reviews which appeared in 1996 showed that well-defined ECPs with standard valence basis sets give results whose accuracy is hardly hampered by the replacement of the core electrons with parameterized mathematical functions" . ECPs not only significantly reduce the computer time of the calculations compared with all-electron methods, they also make it possible to treat relativistic effects in an approximate way which turned out to be sufficiently accurate for most chemical studies. Thus, ECPs are a very powerful and effective method to handle both theoretical problems which are posed by heavy atoms, i.e. the large number of electrons and relativistic effects. 

Quantum chemical methods are valuable tools for studying atmospheric nucle-ation phenomena. Molecular geometries and binding energies computed using electronic structure methods can be used to determine potential parameters for classical molecular dynamic simulations, which in turn provide information on the dynamics and qualitative energetics of nucleation processes. Quantum chemistry calculations can also be used to obtain accurate and reliable information on the fundamental chemical and physical properties of molecular systems relevant to nucleation. Successful atmospheric applications include investigations on the hydration of sulfuric acid and the role of ammonia, sulfur trioxide and/or ions... 

Unfortunately, quantitatively reliable quantum chemical calculations of nucleation rates for atmospherically relevant systems would require the application of both high-level electronic structure methods and complicated anharmonic thermochemical analysis to large cluster structures. Such computations are therefore computationally too expensive for currently available computer systems, and will likely remain so for the foreseeable future. Instead, a synthesis of different approaches will probably be necessary. In the future, successful nucleation studies are likely to contain combinations of the best features of both classical (Monte Carlo and molecular dynamics) and quantum chemical methods, with the ultimate objective being a chemically accurate, complete configurational sampling. 

The periodic approach is not the only one available for atomistic simulations of these materials and we should first mention that much progress has been made in the application of molecular quantum chemical methods using cluster representations of the local structure of oxide materials [1, 2], More recently, this has given way to mixed quantum mechanics/molecular mechanics (QM/MM) calculations. In QM/MM simulations the important region, the active site for catalysis, is represented at a quantum chemical level while the influence of its environment, the extended solid, is represented using the computationally less-demanding atomistic force field approach. This allows complex structures such as metal particles supported on oxides to be tackled [3]. 

Application of quantum chemical methods to polymeric systems is complicated. The computer hardware capabilities to deal with real polymers are, at this point, inadequate. In general, the CPU requirements grow with the fourth to sixth power of the number of functions used and the system Hamiltonian does not normally contain information about the solvent. The major limitation is the length of time that can be simulated. Important dynamic polymer properties are associated with relaxation times that are many orders of magni-... 

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