Quantum mechanical techniques, molecular modelling

Molecular dipole moments are often used as descriptors in QPSR models. They are calculated reliably by most quantum mechanical techniques, not least because they are part of the parameterization data for semi-empirical MO techniques. Higher multipole moments are especially easily available from semi-empirical calculations using the natural atomic orbital-point charge (NAO-PC) technique [40], but can also be calculated rehably using ab-initio or DFT methods. They have been used for some QSPR models. 

The progression of sections leads the reader from the principles of quantum mechanics and several model problems which illustrate these principles and relate to chemical phenomena, through atomic and molecular orbitals, N-electron configurations, states, and term symbols, vibrational and rotational energy levels, photon-induced transitions among various levels, and eventually to computational techniques for treating chemical bonding and reactivity. 

Theorehcal methods such as quantum mechanics or molecular mechanics can produce 3D molecular models of high quality and predict a number of molecular properhes with high precision. Unfortunately, these techniques also require at least some reasonable 3D geometry of the molecule as starhng point. 

Design of molecular materials with specific properties often requires interdisciplinary research involving various experimental and theoretical techniques. Molecular modeling by ab initio methods based on quantum-mechanics is now commonly used in such studies. However, theoretical investigations are still dominated by traditional, static approaches in which the stationary points on the respective potential... 

An alternative simulation procedure is to replace the explicit solvent molecules with a continuous medium having the bulk dielectric constant. - " Once the solvent has been simplified, it is much easier to employ quantum mechanical techniques for the ENP relaxation of electronic and molecular structure in solution thus this approach is complementary to simulation insofar as it typically focuses on the response of the solute to the solvent. Since the properties of the continuum solvent must represent an average over solvent configurations, such approaches are most accurately described as quantum statistical models. 

In summary, quantum mechanics attempts to model the position or distribution of the electrons or bonds, while mtv lecular mechanics attempts to model the positions of the nuclei or atoms. Quantum mechanics calculations are used commonly to generate or verify molecular mechanics parameters. Larger. structures can be studied hy use of molecular mechanics, and with. simulation techniques such as molecular dynamics, the behavior of drugs in solution or even in pas.sage through bilayer membranes can he studied. 

Molecular dynamic simulation methods, in addition to being essential for interpreting NMR data at the atomic level, also augment experimental studies in a number of other ways [101] modeling techniques can (i) yield structural information where experimental data has not yet been acquired, (ii) expand on experimental data through simulations that yield dynamic trajectories whose analysis provides unique information on lesion mobility, and (iii) provide thermodynamic insights by ensemble analysis using statistical mechanical methods. Furthermore, reaction mechanisms can now be determined with some confidence by combined quantum mechanical and molecular mechanical methods [104, 105],... 

Our aim in this chapter will be to establish the basic elements of those quantum mechanical methods that are most widely used in molecular modelling. We shall assume some familiarity with the elementary concepts of quantum mechanics as found in most general physical chemistry textbooks, but little else other than some basic mathematics (see Section 1.10). There are also many excellent introductory texts to quantum mechanics. In Chapter 3 we then build upon this chapter and consider more advanced concepts. Quantum mechanics does, of course, predate the first computers by many years, and it is a tribute to the pioneers in the field that so many of the methods in common use today are based upon their efforts. The early applications were restricted to atomic, diatomic or highly symmetrical systems which could be solved by hand. The development of quantum mechanical techniques that are more generally applicable and that can be implemented on a computer (thereby eliminating the need for much laborious hand calculation) means that quantum mechanics can now be used to perform calculations on molecular systems of real, practical interest. Quantum mechanics explicitly represents the electrons in a calculation, and so it is possible to derive properties that depend upon the electronic distribution and, in particular, to investigate chemical reactions in which bonds are broken and formed. These qualities, which differentiate quantum mechanics from the empirical force field methods described in Qiapter 4, will be emphasised in our discussion of typical applications. 

Grigorenko, B. L., Nemukhin, A. V, Topol, 1. A., Burt, S. K. [2002], Modeling of Biomolecular Systems with the Quantum Mechanical and Molecular Mechanical Method Based on the Effective Fragment Potential Technique Proposal of Flexible Fragments,/ Phys. Chem. A, 106,10663-10672. 

The atomistic methods usually employ atoms, molecules or their group and can be classified into three main categories, namely the quantum mechanics (QM), molecular dynamics (MD) and Monte Carlo (MC). Other atomistic modeling techniques such as tight bonding molecular dynamics (TBMD), local density (LD), dissipative particle dynamics (DPD), lattice Boltzmann (LB), Brownian dynamics (BD), time-dependent Ginzbuig-Lanau method, Morse potential function model, and modified Morse potential fimction model were also applied afterwards. 

In dye chemistiy, the relationship between the molecular structure of a dye and its technical performance, including colour and fastness properties, is now well-established. As discussed at length in Chapter 2, computational methods have emerged as indispensible tools in the development of our fundamental understanding of the properties of coloured molecules and in the design of new products. Molecular modelling techniques, which include a range of methods based on quantum mechanics and molecular mechanics, allow the molecular and physical properties of a particular dye to be predicted by calculation with some confidence, and without the need to resort to synthesis. The same principles apply to the molecular structures of... 

Taking advantage of molecular modeling and quantum mechanical techniques to obtain relevant structural parameters and molecular properties such as conformational behavior, ionization potentials, and dipole moments, several researchers have proposed alternative predictive models of lipophilicity. Using parameters derived from the 3D molecular structure should in principle introduce the (missing) third dimension in log P calculations. 

In QM/MM models of solutions, solute and solvent molecules are described exphcifly. However, while the solute and (if required) a few solvent molecules are described using Quantum Mechanics techniques, their environment is described classically using a force-field from Molecular Mechanics. Since (by construction) there are no covalent bonds between the QM and MM subsystems, the total Hamiltonian is simply written ... 

Combined Quantum Mechanical and Molecular Mechanical Potentials Combined Quantum Mechanics and Molecular Mechanics Approaches to Chemical and Biochemical Reactivity Diradicals Hybrid Methods Hybrid Quantum Mechanical/Molecular Mechanical (QM/MM) Methods Quantum Mechanical/Molecular Mechanical (QM/MM) Coupled Potentials Quantum Mechanics/Molecular Mechanics (QM/MM) Self-consistent Reaction Field Methods Self-consistent Reaction Field Methods Cavities Solvation Modeling Transition States in Organic Chemistry Ab Initio Transition Structure Optimization Techniques. 

The molecular electronic polarizability is one of the most important descriptors used in QSPR models. Paradoxically, although it is an electronic property, it is often easier to calculate the polarizability by an additive method (see Section 7.1) than quantum mechanically. Ah-initio and DFT methods need very large basis sets before they give accurate polarizabilities. Accurate molecular polarizabilities are available from semi-empirical MO calculations very easily using a modified version of a simple variational technique proposed by Rivail and co-workers [41]. The molecular electronic polarizability correlates quite strongly with the molecular volume, although there are many cases where both descriptors are useful in QSPR models. 

Molecular modeling has evolved as a synthesis of techniques from a number of disciplines—organic chemistry, medicinal chemistry, physical chemistry, chemical physics, computer science, mathematics, and statistics. With the development of quantum mechanics (1,2) ia the early 1900s, the laws of physics necessary to relate molecular electronic stmcture to observable properties were defined. In a confluence of related developments, engineering and the national defense both played roles ia the development of computing machinery itself ia the United States (3). This evolution had a direct impact on computing ia chemistry, as the newly developed devices could be appHed to problems ia chemistry, permitting solutions to problems previously considered intractable. 

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