Computational methods Semi-empirical

Results of a recent literature study indicate that frequencies computed using semi-empirical PM3, AMI, and MNDO methods compare well to values obtained at iht ab initio level using medium size basis sets. Of these three methods, PM3 showed the closest correspondence to experimental values, which is generally about 10 percent too high in value from stretches (Seeger, D.M. Korze-niewski, C. Kowalchyk, W., J. Phys.Chem. 95 68-71, 1991). 

For small molecules, the accuracy of solutions to the Schrodinger equation competes with the accuracy of experimental results. However, these accurate ab initio calculations require enormous computation and are only suitable for the molecular systems with small or medium size. Ab initio calculations for very large molecules are beyond the realm of current computers, so HyperChem also supports semi-empirical quantum mechanics methods. Semi-empirical approximate solutions are appropriate and allow extensive chemical exploration. The inaccuracy of the approximations made in semi-empirical methods is offset to a degree by recourse to experimental data in defining the parameters of the method. Indeed, semi-empirical methods can sometimes be more accurate than some poorer ab initio methods, which require much longer computation times. 

The quantum mechanical treatment is always limited to a small subsystem due to the high computational cost. Semi-empirical (SE) methods can treat much larger systems than ab initio or DFT approaches, however, they are still not able to include a part... 

An alternative to the use of principal components or factor analysis is the BCUT method of Pearlman [Pearlman and Smith 1998]. In this method, three square matrices are constructed for each molecule. Each matrix is of a size equal to the number of atoms in the molecule and has as its elements various atomic and interatomic parameters. One matrix is intended to represent atomic charge properties, another represents atomic polarisabilities and the third hydrogen-bonding capabilities. These quantities can be computed with semi-empirical... 

This description of quantum mechanical methods for computing (hyper)polarizabilities demonstrates why, nowada, the determination of hyperpolarizabilities of systems containing hundreds of atoms can, at best, be achieved by adopting, for obvious computational reasons, semi-empirical schemes. In this study, the evaluation of the static and dynamic polarizabilities and first hyperpolaiizabilities was carried out at die Time-Dependent Hartree-Fock (TDOT) [39] level with the AMI [50] Hamiltonian. The dipole moments were also evaluated using the AMI scheme. The reliability of the semi-empirical AMI calculations was addressed in two ways. For small and medium-size push-pull polyenes, the TDHF/AMl approach was compared to Hartree-Fock and post Hartree-Fock [51] calculations of die static and dynamic longitudinal first hyperpolarizability. Except near resonance, the TDHF/AMl scheme was shown to perform appreciably better than the ab initio TDHF scheme. Then, the static electronic first hyperpolaiizabilities of the MNA molecule and dimer have been calculated [15] with various ab initio schemes and compared to the AMI results. In particular, the inclusion of electron correlation at the MP2 level leads to an increase of Paaa by about 50% with respect to the CPHF approach, similar to the effect calculated by Sim et al. [52] for the longitudinal p tensor component of p-nitroaniline. The use of AMI Hamiltonian predicts a p aa value that is smaller than the correlated MP2/6-31G result but larger than any of the CPHF ones, which results fi-om the implicit treatment of correlation effects, characteristic of die semi-empirical methods. This comparison confirms that a part of die electron... 

A Hessian computed by semi-empirical MO methods. Some empirical adjustment of the second derivatives is usually necessary, since the semi-empirical methods tend to overestimate some terms and underestimate others. 

For TT-electron systems, this was the Hiickel method proposed by Erich Hiickel. For all valence electron systems, the extended Hiickel method was proposed by Roald Hoffmann. Semi-empirical calculations are much faster than their ab initio coxmter-parts. Their results, however, can be very wrong if the molecule being computed is not similar enough to the molecules in the database used to parametrize the method. Semi-empirical calculations have been most successful in the description of organic chemistry, where only a few elements are used extensively and molecules are of moderate size. However, semi-empirical methods were also appHed to solids and nanostructures but with different parameterization. As with empirical methods, we can distinguish if ... 

Electronic strucmre methods are characterized by their various mathematical approximations to its solution, since exact solutions to the Schrddinger equation are not computationally practical. There are three classes of electronic structure methods semi-empirical methods, density functional theory (DFT) methods, and... 

The molecular descriptors obtained by computation of molecular mechanics and quantum chemical methods are used to describe the molecular structures of A -(3-Oxo-3,4-dihydro-2//-benzo[l,4]oxazine-6-carbonyl) guanidines. The three-dimensional structures of the molecules are optimized with the software Hyperchem. Prior to the semi-empirical quantum chemical computation, all structures of the compounds are submitted to MM+ computation of molecular mechanics for energy optimization. The structural descriptors are obtained via the computation of semi-empirical method PM3. The computations are carried out at restricted Hartree-Fock level without configuration interaction. 

Elementary rate constants can be estimated also using semi-empirical methods, which are not as accurate as quantum mechanical approaches, being able at the same time to reduce the computational costs of model development. One of such computationally inexpensive semi-empirical approaches appHcable to small molecules, is the bond-order conservation (BOG) or unity bond index—quadratic exponential potential (UBI—QEP) technique of Shustorovich and Sellers. This method ensures thermodynamic consistency... 

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. 

A textbook describing the theory associated with calculation s of Ih e electronic structure of molecti lar system s. While the book focuses on ab ini/rci calculation s, much of the in formation is also relevant to semi-empirical methods. The sections on the Hartree-fock an d Con figuration ItUeracTion s tn elh ods, in particular, apply to HyperChem. fhe self-paced exercisesare useful for the beginning computational chemist. 

Schaeffer H F III (Editor) 1977. Applications of Electronic Structure Theory. New York, Plenum Press. Schaeffer H F III (Editor) 1977. Methods of Electronic Structure Theory. New York, Plenum Press. Stei. art J J P 1990. MOP AC A Semi-Empirical Molecular Orbital Program. Journal of Computer-Aided Molecular Design 4 1-45. 

I 1 er M C 1991. Semi-empirical Molecular Orbital Methods. In Lipkowitz K B and D B Boyd (Editors). Reviews in Computational Chemistry Volume 2. New York, VCH Publishers, pp 313-366. 

Stewart J J P 1989a. Optimisation of Parameters for Semi-empirical Methods 1. Method. Journal of Computational Chemistry 10 209-220. 

In this section, the conceptual framework of molecular orbital theory is developed. Applications are presented and problems are given and solved within qualitative and semi-empirical models of electronic structure. Ab Initio approaches to these same matters, whose solutions require the use of digital computers, are treated later in Section 6. Semi-empirical methods, most of which also require access to a computer, are treated in this section and in Appendix F. 

Each of these tools has advantages and limitations. Ab initio methods involve intensive computation and therefore tend to be limited, for practical reasons of computer time, to smaller atoms, molecules, radicals, and ions. Their CPU time needs usually vary with basis set size (M) as at least M correlated methods require time proportional to at least M because they involve transformation of the atomic-orbital-based two-electron integrals to the molecular orbital basis. As computers continue to advance in power and memory size, and as theoretical methods and algorithms continue to improve, ab initio techniques will be applied to larger and more complex species. When dealing with systems in which qualitatively new electronic environments and/or new bonding types arise, or excited electronic states that are unusual, ab initio methods are essential. Semi-empirical or empirical methods would be of little use on systems whose electronic properties have not been included in the data base used to construct the parameters of such models. 

Nearly every technical difficulty known is routinely encountered in transition metal calculations. Calculations on open-shell compounds encounter problems due to spin contamination and experience more problems with SCF convergence. For the heavier transition metals, relativistic effects are significant. Many transition metals compounds require correlation even to obtain results that are qualitatively correct. Compounds with low-lying excited states are difficult to converge and require additional work to ensure that the desired states are being computed. Metals also present additional problems in parameterizing semi-empirical and molecular mechanics methods. 

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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