Semiempirical methods parameters

The Huckel method and is one of the earliest and simplest semiempirical methods. A Huckel calculation models only the 7t valence electrons in a planar conjugated hydrocarbon. A parameter is used to describe the interaction between bonded atoms. There are no second atom affects. Huckel calculations do reflect orbital symmetry and qualitatively predict orbital coefficients. Huckel calculations can give crude quantitative information or qualitative insight into conjugated compounds, but are seldom used today. The primary use of Huckel calculations now is as a class exercise because it is a calculation that can be done by hand. 

The most commonly used semiempirical for describing PES s is the diatomics-in-molecules (DIM) method. This method uses a Hamiltonian with parameters for describing atomic and diatomic fragments within a molecule. The functional form, which is covered in detail by Tully, allows it to be parameterized from either ah initio calculations or spectroscopic results. The parameters must be fitted carefully in order for the method to give a reasonable description of the entire PES. Most cases where DIM yielded completely unreasonable results can be attributed to a poor fitting of parameters. Other semiempirical methods for describing the PES, which are discussed in the reviews below, are LEPS, hyperbolic map functions, the method of Agmon and Levine, and the mole-cules-in-molecules (MIM) method. 

There is one semiempirical program, called HyperNMR, that computes NMR chemical shifts. This program goes one step further than other semiempiricals by defining different parameters for the various hybridizations, such as sp carbon vs. sp carbon. This method is called the typed neglect of differential overlap method (TNDO/1 and TNDO/2). As with any semiempirical method, the results are better for species with functional groups similar to those in the set of molecules used to parameterize the method. 

From this equation it is seen that parameters have been introduced into the QM-MM method, with K, L, M, and corresponding to the pseudo s orbital on the classical atom. These parameters can be optimized to reproduce experimental or high level theoretical data. Field et al. [9] perfonned extensive investigations of the values of these extra parameters and suggested that the parameters K, L, and M (i = 1,. . . , 4) can be set to zero and that should take a value of 5.0. These are generally the values used in most current QM-MM implementations that employ semiempirical methods in the quantum region. 

The semiempirical methods represent a real alternative for this research. Aside from the limitation to the treatment of only special groups of electrons (e.g. n- or valence electrons), the neglect of numerous integrals above all leads to a drastic reduction of computer time in comparison with ab initio calculations. In an attempt to compensate for the inaccuracies by the neglects, parametrization of the methods is used. Meaning that values of special integrals are estimated or calibrated semiempirically with the help of experimental results. The usefulness of a set of parameters can be estimated by the theoretical reproduction of special properties of reference molecules obtained experimentally. Each of the numerous semiempirical methods has its own set of parameters because there is not an universial set to calculate all properties of molecules with exact precision. The parametrization of a method is always conformed to a special problem. This explains the multiplicity of semiempirical methods. 

The usefulness of quantum-chemical methods varies considerably depending on what sort of force field parameter is to be calculated (for a detailed discussion, see [46]). There are relatively few molecular properties which quantum chemistry can provide in such a way that they can be used directly and profitably in the construction of a force field. Quantum chemistry does very well for molecular bond lengths and bond angles. Even semiempirical methods can do a good job for standard organic molecules. However, in many cases, these are known with sufficient accuracy a C-C single bond is 1.53 A except under exotic circumstances. Similarly, vibrational force constants can often be transferred from similar molecules and need not be recalculated. 

Stewart J (1989) Optimization of parameters for semiempirical methods. 1 method. J Comput Chem 10(2) 209-220... 

A useful compromise between speed and accuracy is provided by semiempirical methods. In this context, semiempirical methods can be used as fitting tools rather than predictive methods [76], Optimization of the semiempirical parameters to reproduce experimental or high-level ah initio results, for a specific reaction, can yield an accurate potential for the problem of interest at relatively low cost [77]. This approach has been shown to be successful in a QM/MM framework also [78] and is a powerful tool in the accurate study of enzyme reactions [57, 79] (see also Section 6.5.2). 

One might add that the failure of CNDO/2 is probably mainly due to the method of parametrization. If a semiempirical method is to be used to estimate heats of formation and molecular geometries, the parameters in it should be chosen accordingly rather than to mimic the results of an approximation known to give unsatisfactory estimates of energies. Recent studies suggest that CNDO/2 may in fact prove useful if properly parametrized. u>... 

As indicated above, early attempts to use semiempirical methods had proved unsatisfactory, due to the wrong choice of parameters. A similar situation had existed in the Pople 14> treatment of conjugated molecules using the Huckel o, ir approximation the parameters in this were chosen to fit spectroscopic data and with these the method gave poor estimates of ground state properties. Subsequent work in our laboratories has shown JS) that this approach can lead to estimates of heats of atomization and molecular geometries that are in almost perfect agreement with experiment if the parameters are chosen to reproduce these quantities. 

The valence state ionization potential —the resonance integrals and the one-center electron repulsion integrals can be considered as basic parameters of the semiempirical method and can be adjusted to give optimal agreement. The core charges Z, indicate the number of 71 electrons the center M contributes to the n system, and the two-center electron repulsion integrals are obtained from an empirical relationship such as the Mataga-Nishimoto formula ... 

I. Selection of parameters and the basis of configuration interaction in closed shell and restricted open shell semiempirical methods. J. Phys. Chem. 77, 107 (1973). 

Semiempirical methods are widely used, based on zero differential overlap (ZDO) approximations which assume that the products of two different basis functions for the same electron, related to different atoms, are equal to zero [21]. The use of semiempirical methods, like MNDO, ZINDO, etc., reduces the calculations to about integrals. This approach, however, causes certain errors that should be compensated by assigning empirical parameters to the integrals. The limited sets of parameters available, in particular for transition metals, make the semiempirical methods of limited use. Moreover, for TM systems the self-consistent field (SCF) procedures are hardly convergent because atoms with partly filled d shells have many... 

In summary, computational quantum mechanics has reached such a state that its use in chemical kinetics is possible. However, since these methods still are at various stages of development, their routine and direct use without carefully evaluating the reasonableness of predictions must be avoided. Since ab initio methods presently are far too expensive from the computational point of view, and still require the application of empirical corrections, semiempirical quantum chemical methods represent the most accessible option in chemical reaction engineering today. One productive approach is to use semiempirical methods to build systematically the necessary thermochemical and kinetic-parameter data bases for mechanism development. Following this, the mechanism would be subjected to sensitivity and reaction path analyses for the determination of the rank-order of importance of reactions. Important reactions and species can then be studied with greatest scrutiny using rigorous ab initio calculations, as well as by experiments. 

Stewart, J. J. P., Optimization of Parameters for Semiempirical Methods I. Method , J. Comput. Chemistry, 10, 209 (1989a). 

The reactivities of isomeric thienothiophenes calculated in n -electron approximation by the PPP method, and those calculated considering all valence electrons, show reasonable agreement. It should be noted, however, that the choice of parameters in PPP calculations is somewhat arbitrary, especially for heavy atoms (e.g., sulfur). This may lead to a discrepancy between theoretical (in 7r-electron approximation) and experimental estimation of reactivities. For example, Clark applied the semiempirical method PPP SCF MO to calculate the reactivities of different positions in thienothiophenes 1—3, thiophene, and naphthalene from the localization energy values and found the following order of decreasing reactivity for electrophilic substitution thieno[3,4-b]-thiophene (3) > thieno[2,3-Z>]thiophene (I) > thieno [3,2-b]thiophene... 

Dipole moments of PMA are calculated with the RIS scheme with two states per bond. When the dipole moment of the ester group lateral to the chain is placed in the orientation deduced by semiempirical methods, calculated values of the dipole moment are in excellent agreement with experimental results without any kind of adjustement of the energy parameters obtained by Flory and co-workers (A 0751. 

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