Dynamic correlation effects

However, if this is not the case, the perturbations are large and perturbation theory is no longer appropriate. In other words, perturbation methods based on single-determinant wavefunctions cannot be used to recover non-dynamic correlation effects in cases where more than one configuration is needed to obtain a reasonable approximation to the true many-electron wavefunction. This represents a serious impediment to the calculation of well-correlated wavefunctions for excited states which is only possible by means of cumbersome and computationally expensive multi-reference Cl methods. 

We can thus conclude that the complementarity of the Cl and CC approaches in their ability to account, respectively, for the nondynamic and dynamic correlation effects, is worthy of a further pursuit in view of their relative affordability and due to the fact that both types of wave functions are simply related via the exponential Ansatz and yield the same exact result in their respective FCI and FCC limit. 

The second step of the calculation involves the treatment of dynamic correlation effects, which can be approached by many-body perturbation theory (62) or configuration interaction (63). Multireference coupled-cluster techniques have been developed (64—66) but they are computationally far more demanding and still not established as standard methods. At this point, we will only focus on configuration interaction approaches. What is done in these approaches is to regard the entire zeroth-order wavefunc-tion Tj) or its constituent parts double excitations relative to these reference functions. This produces a set of excited CSFs ( Q) that are used as expansion space for the configuration interaction (Cl) procedure. The resulting wavefunction may be written as... 

In summary, it can be said that multireference Cl methods provide a balanced description of static and dynamic correlation effects. This comes at the cost of a considerably increased computational demand compared to single-reference methods. Nevertheless, a multireference approach is inevitable for systems with a genuine multiconfigurational character such as symmetric transition metal compounds. 

The RAS concept combines the features of the CAS wave functions with those of more advanced Cl wave functions, where dynamical correlation effects are included. It is thus able to give a more accurate treatment of correlation effects in molecules. The fact that orbital optimization is included makes this method especially attractive for studies of energy surfaces, when there is a need to compute the energy gradient and Hessian with respect to the nuclear coordinates. 

One should be aware of the fact that the MCSCF results will not by themselves yield very accurate excitation energies. Dynamical correlation effects are often different for different excited states, and if they are not accounted for, errors... 

However, for larger molecules this approach might not be possible. The treatment of the differential dynamical correlation effects is for such cases not an easy task, which still awaits a satisfactory solution. 

These results and also the results for the excitation energies will of course be modified by dynamical correlation effects, which will be accounted for by means of MR-CI calculations based on the CASSCF orbitals for each state. The transition moments will be computed using the CASSI method, where the two A are allowed to interact. The final results can be expected to be accurate to within 0.1 eV for the excitation energies and 10% for the transition moments. The study of the CCCN system is not yet finished. Hopefully some result can be presented in the lectures. 

If the aim of the calculation is to describe dynamical correlation effects, there is seldom any point to using a basis that is smaller than double zeta in the valence shell and lacks polarization functions. Such a basis recovers so little of the correlation energy, and such an unrepresentative fraction (because of the poor treatment of angular correlation), that the results can be hopelessly unreliable. In this sense we should regard a DZP basis (or equivalent) as a minimal, in the sense of minimum acceptable, basis set for correlated calculations. 

---