Semi-empirical quantum

The influence of selenium on the geometry of a number of aryl-substituted selenopyrans 12 was determined using quantum semi-empirical PM3 and DFT calculations. These results were compared with experimentally determined X-ray structures <2002J(P2)1909> (see Section 7.11.3.1). 

How the solute M is described, either classical (force field) or quantum (semi-empirical or ab initio). 

Thiel W 1996 Perspectives on semiempirical molecular orbital theory New Methods in Computationai Quantum Meohanios (Adv. Chem. Phys. XCiti) ed I Prigogine I and S A Rice (New York Wiley) pp 703-57 Earlier texts dealing with semi-empirical methods include ... 

Molecular orbitals were one of the first molecular features that could be visualized with simple graphical hardware. The reason for this early representation is found in the complex theory of quantum chemistry. Basically, a structure is more attractive and easier to understand when orbitals are displayed, rather than numerical orbital coefficients. The molecular orbitals, calculated by semi-empirical or ab initio quantum mechanical methods, are represented by isosurfaces, corresponding to the electron density surfeces Figure 2-125a). 

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 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. 

The MEP at the molecular surface has been used for many QSAR and QSPR applications. Quantum mechanically calculated MEPs are more detailed and accurate at the important areas of the surface than those derived from net atomic charges and are therefore usually preferable [Ij. However, any of the techniques based on MEPs calculated from net atomic charges can be used for full quantum mechanical calculations, and vice versa. The best-known descriptors based on the statistics of the MEP at the molecular surface are those introduced by Murray and Politzer [44]. These were originally formulated for DFT calculations using an isodensity surface. They have also been used very extensively with semi-empirical MO techniques and solvent-accessible surfaces [1, 2]. The charged polar surface area (CPSA) descriptors proposed by Stanton and Jurs [45] are also based on charges derived from semi-empirical MO calculations. 

The quantum mechanical techniques discussed so far are typically appUed to moderate-sized molecules (up to about 100 atoms for ab-initio or DFT and up to 500 for semi-empirical MO techniques). However, what about very large systems, such as enzymes or DNA, for which we need to treat tens of thousand of atoms. There are two possible solutions to this problem, depending on the application. 

The problem with most quantum mechanical methods is that they scale badly. This means that, for instance, a calculation for twice as large a molecule does not require twice as much computer time and resources (this would be linear scaling), but rather 2" times as much, where n varies between about 3 for DFT calculations to 4 for Hartree-Fock and very large numbers for ab-initio techniques with explicit treatment of electron correlation. Thus, the size of the molecules that we can treat with conventional methods is limited. Linear scaling methods have been developed for ab-initio, DFT and semi-empirical methods, but only the latter are currently able to treat complete enzymes. There are two different approaches available. 

For many applications, especially studies on enzyme reaction mechanisms, we do not need to treat the entire system quantum mechanically. It is often sufficient to treat the center of interest (e.g., the active site and the reacting molecules) quantum mechanically. The rest of the molecule can be treated using classical molecular mechanics (MM see Section 7.2). The quantum mechanical technique can be ab-initio, DFT or semi-empirical. Many such techniques have been proposed and have been reviewed and classified by Thiel and co-workers [50] Two effects of the MM environment must be incorporated into the quantum mechanical system. 

Breindl et. al. published a model based on semi-empirical quantum mechanical descriptors and back-propagation neural networks [14]. The training data set consisted of 1085 compounds, and 36 descriptors were derived from AMI and PM3 calculations describing electronic and spatial effects. The best results with a standard deviation of 0.41 were obtained with the AMl-based descriptors and a net architecture 16-25-1, corresponding to 451 adjustable parameters and a ratio of 2.17 to the number of input data. For a test data set a standard deviation of 0.53 was reported, which is quite close to the training model. 

A descriptor for the 3D arrangement of atoms in a molceulc can be derived in a similar manner. The Cartesian coordinates of the atoms in a molecule can be calculated by semi-empirical quantum mechanical or molecular mechanics (force field) methods, For larger data sets, fast 3D structure generators are available that combine data- and rule-driven methods to calculate Cartesian coordinates from the connection table of a molecule (e.g., CORINA [10]). 

Covers theory and applications of ah initio quantum mechanics calculations. The discussions are useful for understanding the differences between ah initio and semi-empirical methods. Although both sections are valuable, the discussion of the applications oi ah initio theory fills a void. It includes comparisons between experiment and many types and levels of calculation. The material is helpful in determining strategies for, and the validity of. ah initio calculations. 

Containsnine reviews in computational chemistry by various experts. This book is particularly useful for beginning computational chemists. Six chapters address issues relevant to HyperChem. including semi-empirical quantum mechanics... 

For small molecules, the accuracy of solutions to the Schrtidinger equation competes with the accuracy of experimental results. However, these accurate a i initw calculations require enormous com putation an d are on ly suitable for the molecular system s with small or medium size. Ah initio calculations for very large molecules are beyond the realm of current computers, so HyperChern also supports sern i-em p irical quantum meclian ics m eth ods. Sem i-em pirical approximate solutions are appropriate and allow extensive cliem ical exploration, Th e in accuracy of the approxirn ation s made in semi-empirical methods is offset to a degree by recourse to experimental data in defining the parameters of the method. 

Programs for Semi-empirical Quantum Mechanical Calculations... 

J. Sadlej, Semi-Empirical Method, of Quantum Chemistry Ellis Harwood, Chichester (1985). 

Apractical introduction to molecular mechanics and semi-empirical quantum mechanics calculations, with extensive examples from the MMP2 (not in HyperChem), MINDO/3, and MNDO methods. One of the more accessible books for new computational chemists. 

Provides a survey of quantum mechanics, semi-empirical computational methods, and the application of molecular orbital theory to organic chemistry. The concepts explored in this book should be easy for most readers to understand. 

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