Internally contracted MRCI

We used the aug-cc-pv(5 -I- d)z basis for P [20] and the aug-cc-pv5z basis set for F and Cl [21], and in all calculations, we restricted the angular momentum on the basis of spdf. This was primarily because the locally written codes that performed the subsequent Hirshfeld analysis are limited to basis functions with these symmetries. We characterized the molecules using the SCF, CASSCF, the internally contracted mrci and the RCCSD(t) methods as implemented in MOLPRO [22], and in all cases, we only... 

When a CASSCF wave function is used for a MRCISD calculation, the number of CSFs produced may be too many to deal with, so various methods are used to reduce the amount of computation needed. One widely used procedure is internally contracted MRCI (icMRCI) [H.-J. Werner and P. J. Knowles, J. Chem. Phys., 89,5803 (1988)]. Here, the optimized MCSCF function is treated as a single reference function (with fixed coefficients) from which one generates doubly excited functions. Each excited function is a linear combination of many ordinary CSFs, with the coefficients within a given excited function being held fixed at the values for the MCSCF function. Thus, far fewer coefficients need to be calculated than in a conventional (uncontracted) MRCI calculation. (Singly excited functions are also included, but for technical reasons, these are not contracted but are treated as in uncontracted MRCI.) Experience has shown that the contracted MRCI wave function is almost as accurate as the uncontracted one. 

ACPF = averaged CPF ANO = atomic natural orbital CCSD(T) = singles and doubles coupled-cluster approach with a perturbational estimate of the triples excitation Cl = configuration interaction CPF = coupled pair functional CPP = core polarization potential CVCI = core-valence Cl FCI = full configuration interaction ICACPF = internally contracted ACPF ICMRCI = internally contracted MRCI MCPF = modified CPF MRCI = multi-reference configuration interaction NHF = numeric Hartree-Fock SDCI = singles plus doubles Cl. 

The ansatz of Ten-no was taken up by Shiozaki et al. and applied to CASPT2 and internally contracted MRCI. The use of this development for obtaining converged ground and excited state potential energy surfaces is illustrated by Fig. 7. 

Werner and co-workers [2, 21, 34] used internally-contracted multi-reference configuration-interaction (IC-MRCI) calculations, based on state-averaged (three-state) multi-configuration, self-consistent-field (MCSCF) calculations with large atomic orbital basis sets, to determine the three electronically adiabatic C1(F)+H2 PESs in the reactant arrangement L4, 2A, and lA. These all correlate with X( P) + H2. These three adiabatic electronic states are the IC-MRCI approximations to the three lowest eigenfunctions of Hgi, namely... 

The main restriction of the methods discussed in the main part of this chapter is the assumption of a single dominant configuration. This requirement is not met for systems with strong non-dynamical correlation effects such as biradicals (e.g. in bond-breaking situations) or transition metal compounds. In this case the reference function must be a multireference expansion. The fixed-amplitude approximation lends itself very well to a multireference extension of the formalism, as demonstrated first by Ten-no who devised an F12-based internally contracted geminal correction to the multireference MP2 (MRMP2) method. A closely related approach was considered by Torheyden and Valeev, who proposed a generalized perturbative correction to arbitrary wavefunctions and which they applied to a MRCI wavefunction. A spin-free formulation was reported recently.The approach was also used by Booth et al. to get a basis set limit estimate for their full Cl quantum Monte Carlo method, which can also be seen as an approach to tackle systems with multireference character. 

Equations (8) and (9) define a minimal MRCI approach, with the dimension being only 3Ap. It is both internally and externally contracted and further augmented with secondary functions. For this reason, the approach can be designated as ixc-MRCISD+s. By replacing the summation over the compound index q (i.e., )t 6 C A U fl, (7 6 A i,j, a,b E. A ) in... 

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