General functions Hessian computation

Computationally the super-CI method is more complicated to work with than the Newton-Raphson approach. The major reason is that the matrix d is more complicated than the Hessian matrix c. Some of the matrix elements of d will contain up to fourth order density matrix elements for a general MCSCF wave function. In the CASSCF case only third order term remain, since rotations between the active orbitals can be excluded. Besides, if an unfolded procedure is used, where the Cl problem is solved to convergence in each iteration, the highest order terms cancel out. In this case up to third order density matrix elements will be present in the matrix elements of d in the general case. Thus super-CI does not represent any simplification compared to the Newton-Raphson method. 

In principle, any electronic structure method that can produce a gradient and Hessian can be used in quasi-classical dynamics. However, density functional theory (DFT)-based methods are, in general (at the time of writing), limited to ground-state surfaces. CASSCF-based dynamics calculations can be used for excited-state computations, and we will focus our discussion on this method. In this case, the size of the molecule that can be studied is limited by the size of the active space (Section 2.2.1) at present, no more than 10 active elec-... 

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