Semi-empirical methods for calculations

MNDO, AMI, and PM3 notoriously underestimate azine heats of formation thus, correction terms have been suggested <1997JMT(393)9> (see Table 9). PM3 appears to be the most accurate semi-empirical method for calculation of nitrogen heterocycle heats of formation. 

A semi-empirical method for calculating the additive portion of the interaction third virial coefficient from a knowledge of the reduced third virial coefficient of a pure substance was proposed by Rowlinson, Sumner, and Sutton. Their equation can be written in the form... 

E. E. Hodgkin and W. G. Richards, J. Chem. Soc., Chem. Commun., 1342 (1980). A Semi-Empirical Method for Calculating Molecular Similarity. 

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 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... 

Also in the M.O. method semi-empirical methods of calculation are of practical importance (comp. p. 27i)3 rf. Thus Carter puts for the resonance energy R ... 

Van Ingen, J.L. (1956). A suggested semi-empirical method for the calculation of the boundary layer transition region. Inst. Of Technology, Dept, of Aeronautics and Engg.Rept. VTH-74-... 

The valence-bond approach plays a very important role in the qualitative discussion of chemical bonding. It provides the basis for the two most important semi-empirical methods of calculating potential energy surfaces (LEPS and DIM methods, see below), and is also the starting point for the semi-theoretical atoms-in-molecules method. This latter method attempts to use experimental atomic energies to correct for the known atomic errors in a molecular calculation. Despite its success as a qualitative theory the valence-bond method has been used only rarely in quantitative applications. The reason for this lies in the so-called non-orthogonality problem, which refers to the difficulty of calculating the Hamiltonian matrix elements between valence-bond structures. 

Access to clusters of principally all elements in the periodic table as outlined above has to some extent fulfilled the wish expressed by J Friedel in 1976 [47] Access to free clusters is a dream for a theoretician , although there are still a number of unknown values of different properties for these clusters. Furthermore, although one today has access to fast computers and a number of ab intio as well as semi-empirical methods for solution of the Schrodinger and Dirac equations [141-144], calculations for clusters of more than ten to twenty atoms are still unfeasible in many cases. The general goal for many of the calculations has been to determine the geometry for the ground state for series of clusters as exemplified for niobium in Fig. 17 [145-147]. 

An attempt at an ab initio calculation of the pNA hyperpolarizability by Sim et a/.38 using double zeta quality basis sets with diffuse polarizing functions within the finite field/HF/MP2 regime gave values which are even lower than those obtained by the semi-empirical methods. These calculations are at zero frequency but have been corrected to 1064 nm using the usual two state model. Bartlett and Sekino90,91 have discussed the relationship between hyperpolarizabilities calculated by ab initio methods and by SOS formalisms. They conclude that only the most powerful recent methods for correlated calculations can be expected to produce accuracy of about 10% for gas phase hyperpolarizabilities, while ab initio calculations interpreted in terms of the SOS expansion give very poor results when the equivalent number of states is small. 

A modified mechanism has been proposed for formation of the M—92 and M—106 ions in the mass spectra of carotenoids (see Scheme 1). Further resonance-enhanced laser Raman spectra of retinal derivatives have been reported.A comparison between various semi-empirical methods for the calculation of -carotene MO s has appeared. A better correlation between the u.v. spectrum and theoretical predictions is claimed by Suzuki et... 

Fig. 1. Comparison of four semi-empirical methods for the calculation of the global hardness of some homonuclear diatomics (C2,02,F2,P2.S2,Cl2,Br2,l2) versus the experimentally determined (I — A) value (from Kef. [8]).

AMI Austin Mcxiel 1, a semi-empirical method for the quantum calculation of molecular electronic structure in computational chemistry based on NDDO." ... 

The recently proposed semi empirical method for simulation of photochemical processes and calculation of quantum yields of reactions has been modified. The specific form of double minimum potential energy surfaces of the molecules involved in the conversion has been considered in a more correct manner. It has been shown that the number of molecular models parameters can be reduced by two-thirds compared with the approach used previously. The quantum yields of photochemical transformations of six dienes into their cyclic isomers have been calculated. Substantially better quantitative agreement of the calculated values with the experimental data has been achieved for all the reactions. It has been shown that the model parameters have good transferability in a series of related molecules. 

Methods to calculate the pressure distribution in the contact zone are presented by Johannesson (4) and Johannesson and Kassfeldt (7). In (4) a semi-empirical method for the calculation of the pressure distribution in an 0-ring seal contact for arbitrary sealed pressures is presented, cind in (7) an approximate analytical method, for calculation of the pressure distribution in an arbitrary elastomeric seal contact, is suggested. In both these papers measurements verifying the calculated pressure distributions are also presented. 

In 2000, Allis and Spencer carried out theoretical studies of new classes of molecules that are based on charged aromatic electron donors and acceptors linked through polyhedral cluster bridges. These compounds displayed large calculated nonlinear optical responses a do50-carborane derivative which exhibits an extraordinary hyperpolarizability is shown in Figure 13.7 (left side). The p value calculated with semi-empirical methods for this tropylium- and cyclopentadienyl-substi-tuted p-carborane is 998 x 10 ° cm esu. ... 

The reaction pathways of TMC during cationic ROP have been explored by Holder and Liu applying Austin Model 1 (a semi-empirical method for the quantum calculation) (AMI) semiempirical calculations. They established a species evolution diagram, and the propagation chain ends on the ether oxygen atom have been identified as the species that ultimately lead to decarboxylation (Scheme 31). 

The hydrophile-lipophile balance (HLB) of a surfactant typically ranges from 1 to 20 and is an indication of the relative affinity of a surfactant molecule for the oil or aqueous phase. A widely used semi-empirical method of calculating the HLB value is ... 

The first point to remark is that methods that are to be incorporated in MD, and thus require frequent updates, must be both accurate and efficient. It is likely that only semi-empirical and density functional (DFT) methods are suitable for embedding. Semi-empirical methods include MO (molecular orbital) [90] and valence-bond methods [89], both being dependent on suitable parametrizations that can be validated by high-level ab initio QM. The quality of DFT has improved recently by refinements of the exchange density functional to such an extent that its accuracy rivals that of the best ab initio calculations [91]. DFT is quite suitable for embedding into a classical environment [92]. Therefore DFT is expected to have the best potential for future incorporation in embedded QM/MD. 

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. 

Covers theory and applications of ah initio quantum mechanics calculations. The discussions are useful for understanding the differences between ah initio and semi-empirical methods. Although both sections are valuable, the discussion of the applications oi ah initio theory fills a void. It includes comparisons between experiment and many types and levels of calculation. The material is helpful in determining strategies for, and the validity of. ah initio calculations. 

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. 

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