Semi-empirical methods AMI and

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). 

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 ... 

Pericas and coworkers173 studied the endo selective reactions of 1-alkoxy-l,3-butadienes and 1-alkoxy-l,3-octadienes with maleic anhydride. They found that the trans-2-phenyl-cyclohexan-l-ol and 3-exo-(neopentyloxy)isobornan-l-ol based chiral dienes induced the highest facial selectivities. The relative transition state energies for the formation of the different diastereomers were calculated using semi-empirical methods (AMI). 

In the decade between 1985 and 1995, molecular orbital calculations using semi-empirical methods for 1,2,3-triazoles and benzotriazoles have received increasing interest. In particular, the semi-empirical methods AMI, PM3, and MNDO, have been widely used in theoretical calculations for... 

The reliability of semi-empirical methods (AMI, PM3, and MNDO) for the treatment of tautomeric equilibria has been tested for a series of five-membered nitrogen heterocycles, including 1,2,3-triazole and benzotriazole. The known tendency of MNDO to overestimate the stability of heterocycles with two or more adjacent pyridine-like lone pairs is also present in AMI and to a somewhat lesser extent in PM3. Tautomers with a different number of adjacent pyridine-like nitrogens cannot be adequately treated by these semi-empirical methods. Both AMI and PM3 represent major improvements over MNDO in the case of lactam-lactim tautomerism. The stability of N-oxides as compared to N-hydroxy tautomers is overestimated by PM3 method. All three methods give reliable ionization potentials and dipole moments (90ZN(A)1328). 

Bishop and Gu have calculated the static polarizability and y-hyperpolariz-ability of finite T -symmetry clusters from CH4 to C281H172 in which fragments of the diamond structure are capped by hydrogens. Semi-empirical, MNDO, AMI and PM3 hamiltonians and ab initio methods using STO-3g, 3-21G and 6-31G basis sets have been used. The results are claimed to be consistent with the little experimental evidence available on diamond. 

A valuable review of the MOPAC program and the semi-empirical methods MNDO, MINDO/3, AMI, and PM3. Of particular use are theoretical discussions of these semi-empirical methods and many tables validating the accuracy of the MOPAC program and its associated Hamiltonians. 

Example Researchers have used MNDO and AMI semi-empirical methods to calculate possible reaction pathways for the interaction of glycine and cocaine. In choosing possible interaction sites,... 

In large systems there can be many orbitals in a small energy range, and the size of the Cl matrix can be very sensitive to the value of the maximum excitation if you use Biergy Criterion. Since calculation time depends heavily on the size of the Cl matrix, you can end up with very long calculations, especially if you use the ab initio methods or the MNDO, AMI, or PM3 semi-empirical methods. This could exhaust the memory of your system. Again, inspecting the results of an RHF (no Cl) calculation will help you avoid these pitfalls. 

The researchers established that the potential energy surface is dependent on the basis set (the description of individual atomic orbitals). Using an ab initio method (6-3IG ), they found eight Cg stationary points for the conformational potential energy surface, including four minima. They also found four minima of Cg symmetry. Both the AMI and PM3 semi-empirical methods found three minima. Only one of these minima corresponded to the 6-3IG conformational potential energy surface. 

In order to conserve the total energy in molecular dynamics calculations using semi-empirical methods, the gradient needs to be very accurate. Although the gradient is calculated analytically, it is a function of wavefunction, so its accuracy depends on that of the wavefunction. Tests for CH4 show that the convergence limit needs to be at most le-6 for CNDO and INDO and le-7 for MINDO/3, MNDO, AMI, and PM3 for accurate energy conservation. ZINDO/S is not suitable for molecular dynamics calculations. 

The following data (Table 1) for molecules, including hydrocarbons, strained ring systems, molecules with heteroatoms, radicals, and ions comes from a review by Stewart.For most organic molecules, AMI reports heats of formation accurate to within a few kilocalories per mol. For some molecules (particularly inorganic compounds with several halogens, such asperchloryl fluoride, even the best semi-empirical method fails completely. 

The quality of the vibrational frequencies varies widely with the semi-empirical method that is used. Generally, AMI, and PM3 are in closer agreement with experiment than methods based on CNDO orINDO. 

Many problems with MNDO involve cases where the NDO approximation electron-electron repulsion is most important. AMI is an improvement over MNDO, even though it uses the same basic approximation. It is generally the most accurate semi-empirical method in HyperChem and is the method of choice for most problems. Altering part of the theoretical framework (the function describing repulsion between atomic cores) and assigning new parameters improves the performance of AMI. It deals with hydrogen bonds properly, produces accurate predictions of activation barriers for many reactions, and predicts heats of formation of molecules with an error that is about 40 percent smaller than with MNDO. 

This difference is shown in the next illustration which presents the qualitative form of a potential curve for a diatomic molecule for both a molecular mechanics method (like AMBER) or a semi-empirical method (like AMI). At large internuclear distances, the differences between the two methods are obvious. With AMI, the molecule properly dissociates into atoms, while the AMBERpoten-tial continues to rise. However, in explorations of the potential curve only around the minimum, results from the two methods might be rather similar. Indeed, it is quite possible that AMBER will give more accurate structural results than AMI. This is due to the closer link between experimental data and computed results of molecular mechanics calculations. 

Semi-empirical methods, such as AMI, MINDO/3 and PM3, implemented in programs like MOPAC, AMPAC, HyperChem, and Gaussian, use parameters derived from experimental data to simplify the computation. They solve an approximate form of the Schrodinger equation that depends on having appropriate parameters available for the type of chemical system under investigation. Different semi-emipirical methods are largely characterized by their differing parameter sets. 

Semi-empirical methods are characterized by their use of parameters derived from experimental data in order to simplify the approximation to the Schrbdinger equation. As such, they are relatively inexpensive and can be practically applied to very, very large molecules. There are a variety of semi-empirical methods. Among the best known are AMI, PM3 and MNDO. Gaussian includes a variety of semi-empirical models, and they are also the central focus or present in many other programs including AMPAC, MOPAC, HyperChem and Spartan. 

Despite these inconsistencies, the semi-empirical methods produce bond angles, bond lengths and heats of formation that are in reasonable agreement with experimental results. A new version, PM5, will soon be available and is four times more accurate than AMI or PM3. The advantage of PM5 over the other semi-empirical methods is that d-orbitals are being introduced [5]. 

The basis set is 6-31G(d,p), and electron correlation at the MP2 level is included. A similar structure is obtained with the AMI and PM3 semi-empirical methods. Density functional theory at the B3LYP/6-31G(dp,p) level also produced the same structure for this ion-pair. The only observed differences between the semi-empiri-cal and the ab initio structures were slightly shorter hydrogen bonds (PM3 and AMI) between FI, F2, and F5 and the G2-F1 (H18) on the imidazolium ring. 

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