Basis function monomial

These functions, which one might call the monomial equivalent of the hy-drogenic pol3momial functions, were introduced as approximation functions for AOs very early by J. C. Slater and have become universally known as Slater-Type Orbitals (STOs). From what we have said, this notation is slightly unfortunate since they are not orbitals but basis functions and, indeed, they are sometimes referred to as Slater-Type Functions (STFs). This may be a convenient place to remind ourselves of the usage of the term orbital in quantum chemistry. Strictly speaking ... 

The use of the Cartesian Monomials for the 6 d and 10 / basis functions is not always appropriate it is often preferable to work explicitly in terms of the cubic harmonic (5) d functions or (7) / functions. 

Now to the problem in hand the use of symmetry-adapted linear combinations of the basis functions in the SCF procedure. The method is now obvious, it is simply one more additional step in the chain of transformations from the raw basis to the actual working basis. Deferring the actual technique of calculation of the elements of the transformation between the raw basis and the symmetry-adapted basis until later in this chapter, we assume that the matrix U effects this transformation. The matrix is actually unitary or, more commonly in the real case, orthogonal so that, unlike the monomial/harmonic transformation above, it does not disturb the orthogonality properties of the basis and it is, of course, square. 

In MLS methods, although it is more common to use monomial functions, it is also possible to use other functions as basis. For example, in problems with singular solutions, singular functions can be used. 

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