Semi-empirical algorithms

This method is valid only in the static field limit (zero frequency), which is a weakness. However, recent advances of a derived procedure (Coupled Perturbed Hartree-Fock) permit the frequency dependence of hyperpolarizabilities to be computed. The FF method mainly uses MNDO (modified neglect of diatomic differential overlap) semi-empirical algorithm and the associated parametrizations of AM-1 and PM-3, which are readily available in the popular MOPAC software package. ... 

Semi-Empirical Algorithms for Secondary Structure Prediction. 183... 

Semi-Empirical Algorithms for Seccmdary Structure Prediction... 

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. 

This method is available for all semi-empirical methods except Extended Hiickel, and for ab initio calculations. This algorithm may be used if the structure is far from a minimum. 

The algorithms of the mixed classical-quantum model used in HyperChem are different for semi-empirical and ab mi/io methods. The semi-empirical methods in HyperChem treat boundary atoms (atoms that are used to terminate a subset quantum mechanical region inside a single molecule) as specially parameterized pseudofluorine atoms. However, HyperChem will not carry on mixed model calculations, using ab initio quantum mechanical methods, if there are any boundary atoms in the molecular system. Thus, if you would like to compute a wavefunction for only a portion of a molecular system using ab initio methods, you must select single or multiple isolated molecules as your selected quantum mechanical region, without any boundary atoms. 

Semi-empirical methods could thus treat the receptor portion of a single protein molecule as a quantum mechanical region but ab mdio methods cannot. However, both semi-empirical and ab initio methods could treat solvents as a perturbation on a quantum mechanical solute. In the future, HyperChem may have an algorithm for correctly treating the boundary between a classical region and an ab mdio quantum mechanical region in the same molecule. For the time being it does not. 

Pseudo-Newton-Raphson methods have traditionally been the preferred algorithms with ab initio wave function. The interpolation methods tend to have a somewhat poor convergence characteristic, requiring many function and gradient evaluations, and have consequently primarily been used in connection with semi-empirical and force field methods. 

Such considerations have allowed the development of highly efficient potential energy surface walking algorithms (see, for example, J. Nichols, H. L. Taylor, P. Schmidt, and J. Simons, J. Chem. Phys. 92, 340 (1990) and references therein) designed to trace out streambeds and to locate and characterize, via the local harmonic frequencies, minima and transition states. These algorithms form essential components of most modern ab initio, semi-empirical, and empirical computational chemistry software packages. 

The basis of molecular modeling is that all important molecular properties, i. e., stabilities, reactivities and electronic properties, are related to the molecular structure (Fig. 1.1). Therefore, if it is possible to develop algorithms that are able to calculate a structure with a given stoichiometry and connectivity, it must be possible to compute the molecular properties based on the calculated structure, and vice versa. There are many different approaches and related computer programs, including ab-initio calculations, various semi-empirical molecular orbital (MO) methods, ligand field calculations, molecular mechanics, purely geometrical approaches, and neural networks, that can calculate structures and one or more additional molecular properties. 

We have also examined here the use of approximate solutions of the coupled perturbed Hartree-Fock equations for estimating the Hessian matrix. This Hessian appears to be more accurate than any updated Hessian we have been able to generate during the normal course of an optimization (usually the structure has optimized to within the specified tolerance before the Hessian is very accurate). For semi-empirical methods the use of this approximation in a Newton-like algorithm for minima appears optimal as demonstrated in Table 17. In ab-initio methods searching for minima, the BFGS procedure we describe is the best compromise. 

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