Molecular, generally geometry

A force field describes the restoring forces which occur in a molecule when the geometry of minima potential energy is disturbed. Force fields of the kind dealt with in this article describe the occurring forces with respect to a so-called strain-free molecular geometry or, more generally, with respect to a molecular reference geometry . 

This approach can be extended to 3D molecular geometry, defining generalized geometry matrices and corresponding 3D-double invariants. 

The natural attractiveness of the STO basis is countered by the numerical difficulties associated with the computation of the various molecular integrals for polyatomic molecules of general geometry. An enormous amount of work has been done over the past thirty years to try to solve these computational problems but despite this effort it is still true to say that the use of the STO basis is only practical for atoms and linear molecules. Even here we arc being slightly optimistic it is only atoms, diatomics and linear triatomics which are well within reach for the STO basis. 

The molecular integrals shall be tractable for polyatomic molecules of general geometry. 

The general geometry is illustrated in Fig. 2. We begin by considering the configuration where the molecular dipole is oriented perpendicular to the surface, i.e. y/ = 0. The potential is expanded in an infinite Legendre polynomial series as... 

In general, geometry optimization in the context of molecular potential energy functions has many possible caveats. Hence, a novice user especially should take the following precautions to generate as much confidence as possible in a minimization result. 

When constructing more general molecular wave functions there are several concepts that need to be defined. The concept of geometry is inhoduced to mean a (time-dependent) point in the generalized phase space for the total number of centers used to describe the END wave function. The notations R and P are used for the position and conjugate momenta vectors, such that... 

The primary reason for interest in extended Huckel today is because the method is general enough to use for all the elements in the periodic table. This is not an extremely accurate or sophisticated method however, it is still used for inorganic modeling due to the scarcity of full periodic table methods with reasonable CPU time requirements. Another current use is for computing band structures, which are extremely computation-intensive calculations. Because of this, extended Huckel is often the method of choice for band structure calculations. It is also a very convenient way to view orbital symmetry. It is known to be fairly poor at predicting molecular geometries. 

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