Orthogonalization Methods

Foret et al.98 collected fractions of model proteins and variants of human hemoglobins after fractionation by CIEF, and then analyzed them by matrix-assisted laser desorption-time-of-flight-mass spectrometry (MALDI-TOF-MS). As the authors point out, MS is an orthogonal method to CIEF because it separates according to molecular mass. 

If a secondary method is required during early phase development, a level 3 method is developed and validated to support phase 2b or early phase 3 clinical studies. This method should be capable of separating all components of interest identified up to this stage of pharmaceutical development. In cases where the initial primary method is still viable, the level 1-level 2 method may be maintained. As in early development, the use of an orthogonal method to evaluate DS generated via new synthetic schemes and to evaluate new formulations remains an important means of assuring that the primary method is sufficient for characterizing DS and DP. 

The level 3 method is used until synthetic routes and formulations have been finalized and forced degradation and preliminary stability studies have been conducted i.e., until the components that need to be separated in the final DS and in the final DP have been clearly determined. At this juncture, the focus shifts to the development of fast, robust and transferable final methods to be used for primary stability studies and post-approval analyses. Freqnently, separate methods are developed for DS and DP since the goals of each method are different (see Section I). Orthogonal methods continue to be of importance to troubleshoot any questions that may arise during the subsequent life cycle of the drug. 

In other words, it is used to verify that the specificity of the levels 1-3 method is maintained throughout development. In cases where the orthogonal method shows the primary method to be deficient, the orthogonal method is validated and is used as a secondary method in conjunction with the primary method. Additional new methods may also need to be developed to address specific issues encountered in stress studies, such as when mass balance is not observed. 

Pellett et al. presented a procedure to develop orthogonal methods for nine routine RPLC methods from six pharmaceutical laboratories. During this study, several drug products... 

Usually on the first iteration of an SCF calculation W is computed by the Schmidt orthogonalization method but thereafter W is chosen to be the C matrix from the previous iteration. This produces an F matrix which is nearly diagonal so the Jacobi method becomes quite efficient after the first iteration. Further, in the Jacobi method, F is diagonalized by an iterative sequence of simple plane-rotation transformations... 

Firstly, the function (70) is invariant under a linear transformation of the m doubly occupied orbitals amongst themselves. A proof of this statement seems hardly necessary as, in the case m = N, equation (70) is equivalent to a Slater determinant, and this property of a determinant is well-known. The m orbitals m may therefore be orthogonalized amongst themselves by a linear transformation, without altering the total wavefunction. This, of course, may be done in several ways, by transforming to MOs for example, but perhaps the most convenient method is to employ the Lowdin symmetric orthogonalization method 73... 

Lowdin s symmetric orthogonalization method is an often employed technique for the generation of orthonormal molecular basis sets. Since within most LCAO MO methods, density matrices are determined by AO basis set coefficients, and idempotency of density matrices is a property easily controlled on an orthonormal basis, Lowdin s transforma-... 

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