Full matrix diagonalization

J (interdimer) = -1.7 cm" —essentially the same as before, and not equivalent to a square. It would perhaps be worthwhile to use a rectangular, D2, model and full matrix diagonalization to attempt finer delineation of the interactions. 

Spectra are simulated based on full matrix diagonalization with the Sophe partitioning scheme. Further, the superhyperfine interactions may Ije treated with up to 3rd order perturbation theory. This methodology imposes no limitations on the spin systems to be simulated ... 

A diva It MM3 wilh Ihe cumrnand mm3. Answer questions file etheiie.mm3, parameter file Enter (default) line number 1, option 2. The defaull parameter sel is Ihe MM3 parameler sel don t ehange il. The line number starts Ihe system reading on the first line of your input file, and option 2 is the block diagonal followed by full matrix minimi7 ation mentioned at the end of the section on the Hessian matrix. You will see intermediate atomic coordinates as the system minimises the geometry, followed by a final steiic eireigy, Kird with 0, output Enter, cooidinates Enter,... 

I won t give you the results in full, but on matrix diagonalization we find a deseription of the first excited singlet state as... 

The main disadvantage of the full matrix analysis is that it requires volume integrals of all spectral peaks, including the diagonal. 

Kluzik (7J3) compared diagonal versus full matrix approximations to J(X) and concluded that ... 

The state estimations that use a time-varying full matrix Q lead to a better performance than the constant diagonal matrix, as it is shown in Figure 1. Although the linearized approach performance has not been as good as the Monte Carlo approach performance, it can be improved whether the parameter covariance matrix Cp is available from parameter estimation [5]. Besides, the CEKF has presented the best performance for the state estimation for all the tuning techniques. 

Fig. 1. Graphical example of ihe bracketing theorem. The vertical asymptotes are the eigenvalues of the matrix M. The horizontal asymptote is the diagonal element B of the full matrix. The intersections of the branches of the function L(A) with the straight line R(A) are the eigenvalues of the full matrix. These intersections satisfy the bracketing theorem relations...

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