Full configuration interaction limit

Estimation of the Full Configuration-interaction Limit Selected Potential Energy Surfaces. 

In the frame of characterizing the metal-insulator transition, the polarizability of linear ehains of equally spaced lithium atoms (Li , = 2, 4, 6, and 8) has been computed ab initio in the full configuration interaction limit.The perpendicular (to the chain direction) components of the per atom polarizability tensor, whieh depends little on the number of atoms, increases with the interatomic distance and tends monotonically towards the isolated atom polarizability value. On the other hand, the parallel component of the per atom polarizability displays a much different behavior (i) for short distanees, it inereases similarly to its perpendicular counterpart, (ii) then, it increases very quickly and this is magnified with larger number of Li atoms, and (iii) finally, for even larger distances, it decreases and tends to the isolated atom response. 

The ideal calculation would use an infinite basis set and encompass complete incorporation of electron correlation (full configuration interaction). Since this is not feasible in practice, a number of compound methods have been introduced which attempt to approach this limit through additivity and/or extrapolation procedures. Such methods (e.g. G3 [14], CBS-Q [15] and Wl [16]) make it possible to approximate results with a more complete incorporation of electron correlation and a larger basis set than might be accessible from direct calculations. Table 6.1 presents the principal features of a selection of these methods. 

Configuration Interaction. Provides an account of Electron Correlation by way of explicit promotion (excitation) of electrons from occupied molecular orbitals into unoccupied molecular orbitals. Full configuration interaction (all possible promotions) is not a practical method and limited schemes, for example, CIS, CID and CISD Models, need to be employed. 

Having discussed ways to reduce the scope of the MCSCF problem, it is appropriate to consider the other limiting case. What if we carry out a CASSCF calculation for all electrons including all orbitals in the complete active space Such a calculation is called full configuration interaction or full CF. Witliin the choice of basis set, it is the best possible calculation that can be done, because it considers the contribution of every possible CSF. Thus, a full CI with an infinite basis set is an exact solution of the (non-relativistic, Bom-Oppenheimer, time-independent) Schrodinger equation. 

Nondynamical electron correlation effects are generally important for reaction path calculations, when chemical bonds are broken and new bonds are formed. The multiconfiguration self-consistent field (MCSCF) method provides the appropriate description of these effects [25], In the last decade, the complete active space self-consistent field (CASSCF) method [26] has become the most widely employed MCSCF method. In the CASSCF method, a full configuration interaction (Cl) calculation is performed within a limited orbital space, the so-called active space. Thus all near degeneracy (nondynamical electron correlation) effects and orbital relaxation effects within the active space are treated at the variational level. A full-valence active space CASSCF calculation is expected to yield a qualitatively reliable description of excited-state PE surfaces. For larger systems, however, a full-valence active space CASSCF calculation quickly becomes intractable. 

Truncated Cl Wavefunctions.—Between the limits of a minimal and a full configuration interaction one is faced with the problem of choosing how many configurations and more importantly, which configurations are to be included. A computational problem arises because of the very slow convergence, generally... 

Equations (6.123) are similar to the Roothaan-Hall equations used to obtain the Hartree-Fock energy. A full configuration interaction treatment is feasible only for the simplest molecular systems, and therefore much effort has been expended on establishing the best ways to achieve the optimum limited configuration interaction. One... 

The exponential operator T creates excitations from 4>o according to T = l + 72 + 73 + , where the subscript indicates the excitation level (single, double, triple, etc.). This excitation level can be truncated. If excitations up to Tn (where N is the number of electrons) were included, vPcc would become equivalent to the full configuration interaction wave function. One does not normally approach this limit, but higher excitations are included at lower levels of coupled-cluster calculations, so that convergence towards the full Cl limit is faster than for MP calculations. 

Olsen J, J0rgensen P and Simons J 1990 Passing the one-billion limit in full configuration-interaction (Fci) calculations Chem. Phys. Lett. 169 463-72... 

This second approach leads to what Pople and his co-workers term a theoretical model chemistry. In practical applications, the complete basis set limit for full configuration interaction cannot be achieved with finite computing resources, except for the very smallest systems. Compromises have to be made in order to achieve a wide range of applicability. Geometry optimization may, for example, be carried out with some lower level theory and/or basis set of moderate size followed by more accurate calculations using higher level theory and/or an extended ... 

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