Using Semi-Empirical Methods

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. 

Semi-empirical methods are appropriate for a variety of modeling tasks, including the following  

For very large systems for which they are the only computationally practical quantum mechanical methods. 

As a first step for large systems. For example, you might run a semi-empirical optimization on a large system to obtain a starting structure for a subsequent Hartree-Fock or Density Functional Theory optimization. We used this approach in Exercise 3.6. 

For ground state molecular systems for which the semi-empirical method is well-parametrized and well-calibrated. In general, semi-empirical methods have been developed to focus on simple organic molecules. 

---

This quantity is found to be related to the local polarization energy and is complementary to the MEP at the same point in space, making it a potentially very useful descriptor. Reported studies on local ionization potentials have been based on HF ab-initio calculations. However, they could equally well use semi-empirical methods, especially because these are parameterized to give accurate Koopmans theorem ionization potentials. 

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. 

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... 

A variety of more advanced, all-electron methods of this type Me available, and are generally referred to as semi-empirical calculations. The acronyms used to name the individual methods are descriptive of the manner in which atomic overlap calculations are performed. Among the more widely used semi-empirical methods are those of complete neglect of differential overlap (CNDO/2) (12), modified intermediate neglect of differential overlap (MINDO/3) (13), and modified neglect of diatomic overlap (MNDO) (14). 

Spin-spin and spin-orbit constants for CO have been investigated using semi-empirical methods, for states which can be described by a single configuration.323... 

In volume 1 of this series, I compared the use of second-order many-body perturbation theory in its MP2 form with that of density functional theory and coupled cluster theory. I recorded how the number of hits in a literature search on the string MP2 rises from 3 in 1989 to 854 in 1998. The corresponding results for DFT, the most widely used semi-empirical method, are 7 in 1989 growing to 733 by 1998. By 1998, the number of hits recorded for CCSD stood as 244. 

Martin dt at. (70) have published a detailed study of phenylethylamine, utilizing EHT, CNDO, INDO, PCILO and AI. These authors used semi-empirical methods to generate a series of conformational energy surfaces and then used an AI procedure with a large basis set for a few selected points. EHT, CNDO and INDO all indicated a minimum for x at 90° EHT predicts a rotational barrier of 7 kcal/mol, while CNDO and INDO show a barrier of about 2 kcal/mol. PCILO gives a rotational barrier of about 2 kcal/mol, but it shows a very broad minimum for Xi, ranging from 45° to 135°. With respect to rotation about X2 these authors found the extended... 

The authors also use semi-empirical methods to estimate the equilibrium constants for mononuclear An(lV) hydroxide complexes. Two methods are suggested Model A assumes a linear correlation between the formation constants log,o (ML ) and the ion potential Z/riAn u, while Model B is based on an electrostatic approach described in detail in [2000NEC/KIM]. The model assumes a relationship between the consecutive equilibrium constants of the form ... 

Direct measurements of the hydration values AG, AH and AS are not feasible and they are usually calculated indirectly using semi-empirical methods (Born-Haber thermochemical cycles). These cycles lead to the general equations (Rosseinsky 1965, Morss 1976, Bratsch and Lagowski 1985b)... 

Marathon Oil developed a thermochemical process based on the oxidizing ability of i-butylanthraquinone [14] and further studied by Mark et al. [15] who employed computational chemistry using semi-empirical methods to determine the detailed chemical steps of the process occurring through Sg formation. 

---