Empirical Calculations

Let us start a survey of computational methods by beginning with 

Empirical parameters are also involved in the EPCE-F2ef method of Sinanoglu and Pamuk as well as the method suggested by dementi 

The correlation energies given by this approach are, however, only semiquantitativs and their combination with near Hartree-Fock data cannot be expected to provide highly accurate predictions. 

The EPC --F20r method of Sinanoglu and Pamuk is based on the Many-Electron Theory (MET) of Sinanoglu which will be noted in Section 4.G. In its simplest form, MET predicts the correlation energy to be a sum of the pair correlation energies (eqn, (4,47)) which in the LCAO approximation becomes  

The last symbol in the designation of the method means that in con- 

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Z-matriccs arc commonly used as input to quantum mechanical ab initio and serai-empirical) calculations as they properly describe the spatial arrangement of the atoms of a molecule. Note that there is no explicit information on the connectivity present in the Z-matrix, as there is, c.g., in a connection table, but quantum mechanics derives the bonding and non-bonding intramolecular interactions from the molecular electronic wavefunction, starting from atomic wavefiinctions and a crude 3D structure. In contrast to that, most of the molecular mechanics packages require the initial molecular geometry as 3D Cartesian coordinates plus the connection table, as they have to assign appropriate force constants and potentials to each atom and each bond in order to relax and optimi-/e the molecular structure. Furthermore, Cartesian coordinates are preferable to internal coordinates if the spatial situations of ensembles of different molecules have to be compared. Of course, both representations are interconvertible. 

Molecular dipole moments are often used as descriptors in QPSR models. They are calculated reliably by most quantum mechanical techniques, not least because they are part of the parameterization data for semi-empirical MO techniques. Higher multipole moments are especially easily available from semi-empirical calculations using the natural atomic orbital-point charge (NAO-PC) technique [40], but can also be calculated rehably using ab-initio or DFT methods. They have been used for some QSPR models. 

A good source of information regarding the scientifre background of ab-initio and semi-empirical calculations are the manuals that accompany commercial software. Some of the documentation is available for evaluation on the Internet,... 

Because of the LCAO-MO approximation, ah iniiio and semi-empirical calculation s produce occupied and unoccupied (viriual) orbitals. The Aufban or building up" principle determines the... 

Model Builder lo get a reasonable starting geometry, with the possibility of refilling the geometry by sem i-empirical calculations before submitting it to ah initio computation. 

Choose the atoms of interest for the sem i-empirical calculation, then use the Bctend to sp option on the. Select menu to establish the appropriate atomic boundaries for the c uantnm mechanics calculation. TTyperChem substitutes pararmeteri/ed pseudo-fluorine atom s for th e portion s of the molecule n ot included directly in the calculation (see the second part of this book, Theory and Methods). 

After you select a method for a semi-empirical calculation (using the Semi-empirical item on the Setup menu l, choose Optionsm the dialog box to set conditions for the calculation. You sec the Semi-empirical Options dialog box. Th e I ollowmg section s explain th esc option s. 

For example, semi-empirical calculation s on a substrate m oleculc provide a set o f ch arges th at you can use in a m olecu lar m ech an ics calculation of the interaction of that substrate with another molecule. Fo include the effects of po lari,ration, repeated sem i-empiri-cal calculations can provide a set of charges that respond to the en viron rn en t. 

What is the enthalpy of isomerization of propene (CLiH ) to cyclopropane at 298 K by a semi empirical calculation ... 

The simplest empirical calculations use a group additivity method. These calculations can be performed very quickly on small desktop computers. They are most accurate for a small organic molecule with common functional groups. The prediction is only as good as the aspects of molecular structure being par-... 

For large molecules, the choice between semiempirical calculations and empirical calculations should be based on a test case. 

The introduction of a methyl substituent into the empirical calculations may be performed according to two main different models the pseudoheteroatomic model and the hyperconjugated model (161-166). Both approximations have been used in rr-electron methods (HMO, w, PPP). On the other hand, in the all-valence-electrons... 

There are two types of Cl calculations implemented in Hyper-Chem — singly excited Cl and microstate CL The singly excited Cl which is available for both ab initio and semi-empirical calculations may be used to generate UV spectra and the microstate Cl available only for the semi-empirical methods in HyperChem is used to improve the wave function and energies including the electronic correlation. Only single point calculations can be performed in HyperChem using CL... 

This equation is important in interpreting the results of calculations. In ab initio and semi-empirical calculations, atomic orbitals are functions of the x, y, and z coordinates of the electron that closely resemble the valence orbitals of the isolated atoms. 

Even with the minimal basis set of atomic orbitals used in most semi-empirical calculations, the number of molecular orbitals resulting from an SCFcalculation exceeds the number of occupied molecular orbitals by a factor of about two. The number of virtual orbitals in an ab initio calculation depends on the basis set used in this calculation. 

To limit a semi-empirical calculation to part of a molecule, select the atoms of interest. Then choose Bttend to sp3 on the Select menu to terminate correctly the selected group of atoms. Only the selected atoms move, but the frozen atoms influence the calculation. This is now possible with all the semi-empirical methods in HyperChem. 

You can perform quantum mechanical calculations on a part of a molecular system, such as a solute, while using molecular mechanics for the rest of the system, such as the solvent surrounding the solute. This boundary technique is available in HyperChem for all quantum mechanical methods. It is somewhat less complete with ab initio calculations than with semi-empirical calculations, however. With ab initio calculations the boundary must occur between molecules rather than inside a molecule. 

You can use the information obtained from semi-empirical calculations to investigate many thermodynamic and kinetic aspects of chemical processes. Energies and geometries of molecules have clear relation ships to chemical ph en om ena. 0ther quan tities, like atomic charges and Frontier Orbitals, are less defined but provide useful qualitative results. 

The geometries obtained from optimizations with semi-empirical calculations describe the shapes of molecules. The calculations have varying degrees of accuracy and take more time than molecular mechanics methods. The accuracy of the results depends on the molecule. 

Caution For ionic reactions in solution, solvent effects can play a significant role. These, of course, are neglected in calculations on a single molecule. You can obtain an indication of solvent effects from semi-empirical calculations by carefully adding water molecules to the solute molecule. 

HyperChem should not be viewed as a black box that computes only what its designers thought correct. It has an open architecture that makes it possible to customize it many ways. As far as is possible, the parameters of molecular mechanics and semi-empirical calculations are in the user s hands. As the techniques of software engineering advance and our expertise in building new... 

Amolecular system in HyperChem consists of N nuclei A (having positive charges, -t-Z ) and M electrons i (each with negative charge, q = -1). The nuclei are described by a vector, R, with 3N Cartesian X, Y, and Z components. The electrons are described by a vector, r, with 3M Cartesian x, y, and z components. The electrons are explicitly considered only in semi-empirical calculations. 

HyperChem s semi-empirical calculations solve (approximately) the Schrodinger equation for this electronic Hamiltonian leading to an electronic wave function I eiecW for the electrons ... 

HyperChem quantum mechanical calculations are ab initio and semi-empirical. Ab initio calculations use parameters (contracted basis functions) associated with shells, such as an s shell, sp shell, etc., or atomic numbers (atoms). Semi-empirical calculations use parameters associated with specific atomic numbers. The concept of atom types is not used in the conventional quantum mechanics methods. Semi-empirical quantum mechanics methods use a rigorous quantum mechanical formulation combined with the use of empirical parameters obtained from comparison with experiment. If parameters are available for the atoms of a given molecule, the ab initio and semi-empirical calculations have an a priori aspect when compared with a molecular mechanics calculation, letting... 

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