Band Hessian

The ground state force field, vibrational normal modes and frequencies have been obtained with MCSCF analytic gradient and hessian calculations [176]. Frequencies computed with the DZ basis set are compared with experimental ones in Table 16. The T - So transition moments were obtained using distorted benzene geometries with atomic displacements along the normal modes, and with the derivatives in Eq. 97 obtained by numerical differentiation. The normal modes active for phosphorescence in benzene are depicted in Fig. 12. The final formula for the radiative lifetime of the k spin sublevel produced by radiation in all (i/f) bands is (ZFS representation x,y,z is used [49]) ... 

The preconditioner M is a band matrix obtained from the Hessian. 

If the structure of the Hessian is provided, it is exploited to calculate the same Hessian. In this case, the product Gp is performed by using the Hessian. Moreover, the first time that the Hessian is calculated, the rows and columns are sorted using the Reverse CuthiU-McKee Ordering method to make the selection of the preconditioner M easier. It is selected according to the number of coefficients within a band so as to use an object from the BzzFactor-izedSymmetricBand class. 

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