Quadratically convergent SCF

These options to the IRC keyword increase the maximum number of points on each side of the path to 15 and the step size between points to 0.3 amu bohr (30 units of 0.1 amu bohr), where the defaults are 6 steps and 0.1 amu bohr, respectively. The SCF=QC keyword requests the quadratic convergence SCF procedure, a somewhat slower but significantly more reliable SCF procedure. 

Density Matrix-Based Quadratically Convergent SCF (D-QCSCF)... 

Bacskay G B 1981 A quadratically convergent Hartree-Fock (QC-SCF) method. Applications to the closed-shell case Chem. Phys. 61 385... 

MC-SCF calculations on polyatomic molecules are still rather rare, although there have been many such calculations on triatomic and diatomic molecules. Levy45 has described the results of such calculations using a minimal STO basis set for CH4, C2H4, and CjjHa. A quadratically convergent method was described and the results of localizing the orbitals were investigated. 

In order to test the general validity of the previous results, first we have applied algorithm MC-A to a set of diatomic systems, shown in Table VII. In all the cases, we have used SCF MO s as starting point. The "split valence" basis set of Dunning and Hay /51 / was used for each atom and the interatomic distances were taken from the work of Snyder and Basch /52/ or, if not quoted there, as the experimental reported value. Almost quadratic convergence is obtained in all cases. The number of MO iterations needed in each global iteration varies with the number of orbitals present, as expected. Furthermore, we have also verified the invariance of the final result from the starting point. 

Quadratically Convergent" or "Second-Order" SCF. As mentioned in Section 3.6,... 

Show by comparing the difference between the SCF total energies at successive iterations and the converged SCF total energy that the convergence of the above SCF approach is quadratic or second order. 

The same considerations apply to the closed-shell restricted, open-shell restricted and open-shell unrestricted SCF procedures. Likewise, both standard iteration procedures such as DIIS and quadratically convergent schemes can be utilized with any approach to handling the two-electron integrals. Only conventional procedures are currently available for MCSCF methods, although the same considerations apply in principle. 

Quiney (2000)]. The quadratically convergent NR algorithm for relativistic MCDF SCF calculations has been discussed in detail in previous work [Vilkas et al. (1998a)] and is not discussed further. To remove the arbitrariness of the MC SCF spinors and density weighting, the canonical SCF spinors are transformed into natural spinors for subsequent pertur-... 

Quadratically Convergent or Second-Order SCF. As mentioned in Section 3.6, the variational procedure can be formulated in terms of an exponential transformation of the MOs, with the (independent) variational parameters contained in an X matrix. Note that the X variables are preferred over the MO coefficients in eq. (3.48) for optimization, since the latter are not independent (the MOs must be orthonormal). The exponential may be written as a series expansion, and the energy expanded in terms of the X variables describing the occupied-virtual mixing of the orbitals. 

Second-order convergence requires that the error in the (n + l)th iteration is the square of the error in the nth iteration. In the first iteration above the error is 0.001274 thus in the next iteration the error should be (0.001274) = 0,0000016 if we used a second-order procedure. Since the second iteration s error is 0.000204, the convergency of the above SCF procedure is linear rather than quadratic. 

In the classical MC SCF method, when minimizing the energy with respect to the parameters, we use only linear terms in the expansion of the energy with respect to these parameters. In the unitary formulation, on the other hand, we use both linear and quadratic terms. This implies much better convergence of the unitary method. 

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