Quantum mechanics semiempirical methods

In addition, the SM2/AM1 model together with the SCRF method [101-103] was used to assess solvent effects on relative N- and O- acidity of2- and 4-[(2,4, 6-trinitrophenyl)amino] benzioic acids. The authors stated that SCRF appears superior to SM2/AM1 but that the poorer performance of the latter might be due to limitations of the underlying quantum mechanical - semiempirical - method rather than to the approximate treatment of the solvent [104],... 

The MOPAC program (Molecular Orbital PACkag) (26) Is one of the popular quantum mechanical semiempirical methods. The AM1 (Austin Model 1), developed by Michael Dewar (26), is a generalization of the modified neglect of differential diatomic overlap (MNDO) approximation. Often, AM1 is implemented in the MOPAC, and MOPAC(AMt) has been widely used to minimize molecular conformations, to calculate electronic configuration, and to predict such properties as electron distribution and partial charges. 

As is evident from these examples, computational quantum mechanics, semiempirical and ab initio methods alike, represent important new tools for the estimation of rate parameters from first principles. Our ability to estimate activation energies is particularly significant because until the advent of these techniques, no fundamentally based methods were available for the determination of this important rate parameter. It must be recognized, however, that these theoretical approaches still are at their early stages of development that is to say, computational quantum chemical methods should only be used with considerable care and in conjunction with conventional methods of estimation discussed earlier in this article, as well with experiments. 

Quantum-mechanical studies on the tautomerism of heterocyclic compounds involve, in general, two aspects. The first deals with the prediction of physicochemical properties of defined tautomeric forms (e.g., ultraviolet spectra, dipole moments, ionization potentials, etc.). This seems to be easy to handle. Using any semiempirical or nonempirical quantum-mechanical computational method, depending on approximations involved in the method, we are able to calculate properties that, more or less, agree with experimental values. Calculations of this type do not contribute to a direct estimation of the relative stability of the tautomers, however they are particularly important for cases in which a tautomeric form of a compound is so rare that it is not possible to measure it directly. 

This book starts with seven chapters devoted to methods for the computation of molecular structure molecular mechanics, semiempirical methods, wave function-based quantum chemistry, density-functional theory methods, hybrid methods, an assessment of the accuracy and applicability of these methods, and finally 3D structure generation and conformational analysis. 

Electronic structure methods or quantum mechanics (QM) methods use the laws of quantum mechanics rather than classical physics as the basis for their computations. QM states that the energy and related properties of a molecule may be obtained by solving the Schrddinger equation H- r = Eiji. For any but the smallest systems, however, exact solutions to the Schrddinger equation are not computationally practical. QM methods are characterized by various mathematical approximations to its solution. There are three classes of QM methods semiempirical, ab initio, and density functional theory (DFT). 

Quantum chemistry is an enormous field of study that consists of three main approaches ah initio (19,20), density functional theory (DFT) (21,22), and semiempirical quantum mechanical (SQM) methods (23-25).The main strength of quantum chemistry lies in its ability to describe chemical structures, energetics, and reactions quantitatively. 

As far as large, complex, and flexible molecular systems are considered, an effective computational treatment is represented by the use of a hybrid QM/MM methodology that allows us to combine two or more computational methods for different portions of the system in such a way that only the chemical and physical interesting region is modeled at the highest level of accuracy. As an example, the well-known ONIOM [72-74] scheme allows the combination of a variety of quantum mechanical, semiempirical, and molecular mechanics methods, providing an accurate and well-defined Hamiltonian. 

The most severe limitation of ah initio methods is the limited size of the molecule that can be modeled on even the largest computers. Semiempirical calculations can be used for large organic molecules, but are also too computation-intensive for most biomolecular systems. If a molecule is so big that a semiempirical treatment cannot be used elfectively, it is still possible to model its behavior avoiding quantum mechanics totally by using molecular mechanics. 

Thermodynamic properties such as heats of reaction and heats of formation can be computed mote rehably by ab initio theory than by semiempirical MO methods (55). However, the Hterature of the method appropriate to the study should be carefully checked before a technique is selected. Finally, the role of computer graphics in evaluating quantum mechanical properties should not be overlooked. As seen in Figures 2—6, significant information can be conveyed with stick models or various surfaces with charge properties mapped onto them. Additionally, information about orbitals, such as the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), which ate important sites of reactivity in electrophilic and nucleophilic reactions, can be plotted readily. Figure 7 shows representations of the HOMO and LUMO, respectively, for the antiulcer dmg Zantac. 

The final application considered in this chapter is chosen to illustrate the application of a QM-MM study of an enzyme reaction that employs an ab initio Hamiltonian in the quantum region [67]. Because of the computational intensity of such calculations there are currently very few examples in the literahire of QM-MM shidies that use a quanhim mechanical technique that is more sopliisticated than a semiempirical method. MuUiolland et al. [67] recently reported a study of part of the reaction catalyzed by citrate synthase (CS) in wliich the quanhim region is treated by Hartree-Fock and MP2 methods [10,51],... 

The choices of quantum mechanical method typically include the semi-empirical methods AMI, PM3, and MNDO/d [1-A. These three methods (and some of their variations) are those most commonly used in the current literature. Of these semi-empirical methods, only MNDO/d includes the effects of d-orbitals. Some of the problems associated with these semiempirical methods include ... 

In addition to the obvious structural information, vibrational spectra can also be obtained from both semi-empirical and ab initio calculations. Computer-generated IR and Raman spectra from ab initio calculations have already proved useful in the analysis of chloroaluminate ionic liquids [19]. Other useful information derived from quantum mechanical calculations include and chemical shifts, quadru-pole coupling constants, thermochemical properties, electron densities, bond energies, ionization potentials and electron affinities. As semiempirical and ab initio methods are improved over time, it is likely that investigators will come to consider theoretical calculations to be a routine procedure. 

Since the quantum chemical calculations used to parameterize equations 6 and 7 are relatively crude semiempirical methods, these equations should not be used to prove or disprove differences in mechanisms of decomposition within a family of initiators. The assumption made in the present study has been that the mechanism of decomposition of initiators does not change within a particular family of initiators (reactions 1-4). It is generally accepted that trow5-symmetric bisalkyl diazenes (1) decompose entirely by a concerted, synchronous mechanism and that trans-phenyl, alkyl diazenes (2) decompose by a stepwise mechanism, with an intermediate phenyldiazenyl radical (37). For R groups with equal or larger pi-... 

Equation (4-5) can be directly utilized in statistical mechanical Monte Carlo and molecular dynamics simulations by choosing an appropriate QM model, balancing computational efficiency and accuracy, and MM force fields for biomacromolecules and the solvent water. Our group has extensively explored various QM/MM methods using different quantum models, ranging from semiempirical methods to ab initio molecular orbital and valence bond theories to density functional theory, applied to a wide range of applications in chemistry and biology. Some of these studies have been discussed before and they are not emphasized in this article. We focus on developments that have not been often discussed. 

Quantum mechanical and selected semiclassical and semiempirical methods for the calculation of electron impact ionization cross sections are described and their successes and limitations noted. Experimental methods for the measurement of absolute and relative ionization cross sections are also described in some detail. Four theoretical methods, one quantum mechanical and three semiclassical, have been used to calculate cross sections for the total ionization of the inert gases and small molecules and the results compared with experimental measurements reported in the literature. Two of the theoretical methods, one quantum mechanical and one semiclassical, have been applied to the calculation of orientation-dependent electron impact ionization cross sections and the results compared with recent experiments. 

Due to the complexity of a full quantum mechanical treatment of electron impact ionization, or even a partial wave approximation, for all but relatively simple systems, a large number of semiempirical and semiclassical formulae have been developed. These often make basic assumptions which can limit their range of validity to fairly small classes of atomic or molecular systems. The more successful approaches apply to broad classes of systems and can be very useful for generating cross sections in the absence of good experimental results. The success of such calculations to reproduce experimentally determined cross sections can also give insight into the validity of the approximations and assumptions on which the methods are based. 

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. 

Many other approaches for finding a correct structural model are possible. A short description of ab-initio, density functional, and semiempirical methods are included here. This information has been summarized from the paperback book Chemistry with Computation An Introduction to Spartan. The Spartan program is described in the Computer Software section below.65 Another description of computational chemistry including more mathematical treatments of quantum mechanical, molecular mechanical, and statistical mechanical methods is found in the Oxford Chemistry Primers volume Computational Chemistry,52... 

MOPAC is a general-purpose semiempirical molecular orbital program for the study of chemical structures and reactions. It is available in desktop PC running Windows, Macintosh OS, and Unix-based workstation versions. It uses semiempirical quantum mechanical methods that are based on Hartree-Fock (HF) theory with some parameterized functions and empirically determined parameters replacing some sections of the complete HF treatment. The approximations in... 

In a very extensive test of the SM5 method (a type of GBM), Hawkins et al. found the average absolute deviation in AGsoivation to be 0.38 kcal/mole for 260 molecular solutes in water and in 90 organic solvents 131 for ions in water, it was 3.8 kcal/mole, for experimental AGsolvation between -58 and -110 kcal/mole. Semiempirical quantum-mechanical procedures were used. 

---