Performance of Semi-empirical Methods

80 heats of formation for species with N and/or O (kcal/mol) 11.69 46 dipole moments 0.54D 

Some typical errors in heat of formation for the MNDO, AMI and PM3 methods are given in Table 3.1. The exact numbers of course depend on which, and how many, compounds have been selected for comparison, thus the numbers should only be taken as a guideline for the accuracy expected. Some typical errors in bond distances are given in Table 3.2. 

Angles are typically predicted with an accuracy of a few degrees, the average errors for MNDO, AMI and PM3 are 4.3°, 3.3° and 3.9°. Ionization potentials are typically 

Considering that the parameters for the MNDO/d method for all first row elements (which are present in most of the training set of compounds) are identical to MNDO, the improvement by addition of d-functions is quite impressive. It should also be noted that MNDO/d only contains 15 parameters, compared to 18 for PM3, and that some of the 15 parameters are taken from atomic data (analogously to the MNDO/AMl parameterization), and not used in the molecular data fitting as in PM3. 

The Huckel methods perform the parameterization on the Fock matrix elements (eqs. (3.50) and (3.51)), and not at the integral level as do NDDO/INDO/CNDO. This means that Huckel methods are non-iterative, they only require a single diagonalization of the Fock (Huckel) matrix. The Extended Huckel Theory (EHT) or Method (EHM), developed primarily by Hoffmann again only considers the valence electrons. It makes use of Koopmans theorem (eq. (3.46)) and assigns the diagonal elements in the F 

The K constant is usually taken as 1.75 this value reproduces the rotational barrier in ethane. 

A//f(molecule) = Feiec(niolecule)- eiec(atoms)- A//f(atoms) (3.97) 

Some typical errors in bond distances are given in Table 3.2.  

ELECTRONIC STRUCTURE METHODS INDEPENDENT-PARTICLE MODELS 

Angles are typically predicted with an accuracy of a few degrees. The average errors for MNDO, AMI and PM3 are 4.3°, 3.3° and 3.9°, respectively. Ionization potentials are typically accurate to 0.5-1. OeV. Average errors for MNDO, AMI and PM3 are 0.78, 0.61 and 0.57 eV, respectively. Average errors tor dipole moments are 0.45, 0.35 and 0.38 debye, respectively. 

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Performance of Semi-empirical Methods 90 5.8 Basis Set Superposition Errors 172... 

Hpp describes the primary system by a quantum-chemical method. The choice is dictated by the system size and the purpose of the calculation. Two approaches of using a finite computer budget are found If an expensive ab-initio or density functional method is used the number of configurations that can be afforded is limited. Hence, the computationally intensive Hamiltonians are mostly used in geometry optimization (molecular mechanics) problems (see, e. g., [66]). The second approach is to use cheaper and less accurate semi-empirical methods. This is the only choice when many conformations are to be evaluated, i. e., when molecular dynamics or Monte Carlo calculations with meaningful statistical sampling are to be performed. The drawback of semi-empirical methods is that they may be inaccurate to the extent that they produce qualitatively incorrect results, so that their applicability to a given problem has to be established first [67]. 

Such work could be used to test the validity of a quantum approach to preferred conformations of Lewis adducts. We therefore decided to perform such a test by means of semi-empirical methods in the hope of providing chemists with an inexpensive, rapid, reliable tool for the study of large series of compounds. 

Acetylacetone (AcAc) infrared spectra were calculated with Hyper-Chem software. Calculations were carried out by the use of semi-empirical methods PM3 and ZINDO/1 and ah initio method with 6-3IG basis set [16]. Results of calculation have been compared with instrumental measurement performed IR-Fourier spectrometer FSM-1201. Liquid adhesive components were preliminary stirred in ratio 1 1 and 1 2 for the purpose of interaction investigation. Stirring was carried out with magnetic mixer. Silver powder was preliminary crumbled up in agate mortar. Then acetylacetone was added. Obtained mixture was taken for sample after silver powder precipitation. 

In addition to the basis-set problem, it should be noted that band structure results (as well as results derived from these, e.g., transport data) ate usually obtained by considering tubes of infinite length. The infinite-tube results, however, are quite different from those obtained for tubes of finite length. [5, 6, 7] Taking into account that realistic calculations have to be performed for tubes of finite length and that ab initio methods are not easily applicable to systems consisting of a moderate number of atoms ( 1000 atoms are necessary for simulations of finite tubes), it can be seen that a practical calculation would require use of semi-empirical methods such as the TB. 

I hcre arc two types of Cl calculations im piemen ted in Hyper-Ch ern sin gly exciled Cl an d in icroslate Cl. I hc sin gly excited C which is available for both ah initio and sem i-etn pirical calculations may be used to generate CV spectra and the microstate Cl available only for the semi-empirical methods in HyperChern is used to improve the wave function and energies including the electron ic correlation. On ly sin gle point calculation s can he perform cd in HyperChetn using Cl. 

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