Use of semi-empirical methods

The MINDO/3 procedure was applied to calculate HOMO-LUMO properties of simple and conjugated enamines240, partial optimization of the molecular geometry of 

Type N planar N pyramidal N pyram. 90° twist, F inside  

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Our studies on the three enzymes have involved the use of semi-empirical methods, using published and also SRP parameter sets. For both LADH and MADH (Figures 5-3a and b) hybrid QM/MM models were employed [8, 9, 88-90], In LADH the PES surface was calculated at the AMI level [20] but scaled by data from the HF/3-21G surface [91]. The results of the CVT calculation with the SCT correction show quite modest yet contributory degrees of tunnelling, an RTE... 

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. 

These methods, TD-DFT in particular, are reported to provide good correlations between calculated and experimental absorption maxima and oscillator strengths over a wide range of chemical types of dye, at least comparable to the predictions provided by the use of semi-empirical methods. However, in view of their higher level of sophistication and enhanced theoretical rigour, the methods offer... 

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. 

HyperChem computes the Hessian using numerical second derivative of the total energy with respect to the nuclear positions based on the analytically calculated first derivatives in ab initio methods and any of the semi-empirical methods, except the Extended Hiickel. Vibration calculations in HyperChem using an ab initio method may take much longer than calculations using the 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. 

The first step in reducing the computational problem is to consider only the valence electrons explicitly, the core electrons are accounted for by reducing the nuclear charge or introducing functions to model the combined repulsion due to the nuclei and core electrons. Furthermore, only a minimum basis set (the minimum number of functions necessary for accommodating the electrons in the neutral atom) is used for the valence electrons. Hydrogen thus has one basis function, and all atoms in the second and third rows of the periodic table have four basis functions (one s- and one set of p-orbitals, pj, , Pj, and Pj). The large majority of semi-empirical methods to date use only s- and p-functions, and the basis functions are taken to be Slater type orbitals (see Chapter 5), i.e. exponential functions. 

The central assumption of semi-empirical methods is the Zero Differential Overlap (ZDO) approximation, which neglects all products of basis functions depending on the same electron coordinates when located on different atoms. Denoting an atomic orbital on centre A as /ja (it is customary to denote basis functions with /j, u, A and cr in semi-empirical theory, while we are using Xn, xs for ab initio methods), the ZDO... 

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]. 

The use of Eq. (5-10) to evaluate the reaction rate is characterised by the calculation of Hessians for a large number of points along the MEP which are required to locate the free energy maximum and also to evaluate the curvature required for evaluation of the transmission coefficient. In view of the associated computational expense, high-level electronic structure calculations are not feasible and alternative strategies, one of which is to use a semi-empirical method, are usually employed [81]. 

Whatever scheme is chosen, a method is needed to rapidly evaluate the appropriate QM energy. If this could be done with confidence using a semi-empirical method the solution of many previously inaccessible problems could well become possible. This has provided the catalyst for the present renaissance in the development of such... 

Semi-empirical methods, such as those implemented in the MOPAC [9] program, simplify the equations considerably by neglecting many terms, but then compensate for this by parameterising some of them so that the calculations reproduce experimental information on, for example, the heat of formation. Once the various approximations are made, the molecular properties to which the parameters are fitted, and the molecules used in the fitting, define a model Hamiltonian, of which the most commonly used are the AMI and the PM3 Hamiltonians found in MOPAC. A major advantage of semi-empirical methods is... 

The Gaussian programs are the product of Gaussian, Inc., Pittsburgh, Pennsylvania. They perform quantum chemical calculations, using either semi-empirical methods such as AMI, MINDO/3, PM3, or ab initio calculations which have been discussed previously. 

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. 

Now any decision to break from these simple symmetry ideas must not be taken lightly since, as we shall see, this step automatically excludes the use of a whole class of semi-empirical methods for the evaluation of molecular integrals. 

Larsson and co-workers have used relation (18) to calculate Tjb for organic molecules in which two centers are bridged by saturated groups [65,66], and for mixed valence systems [67]. The stationary states /i and /2 are determined by a CNDO/S method, with extensive configuration interaction and use of semi-empirical parameters. The nuclear configuration Q where relation (18) is valid is adjusted so as to satisfy the delocalization property expressed by (17). These... 

As with the solution of other many-body electronic structure problems, determination of the unperturbed eigenvalues is numerically challenging and involves compromises in the following areas (1) approximations to the hamiltonian to simplify the problem (e.g., use of semi-empirical molecular orbital methods) (2) use of incomplete basis sets (3) neglect of highly excited states (4) neglect of screening effects due to other molecules in the condensed phase. 

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