Direct CI method

P.E.M. Siegbahn The Direct-CI Method., in G.H.F. Diercksen and S. Wilson (ed.) Methods in Computational Molecular Physics., D. Reidel Publising Company, Dordrecht, p. 189 (1983). 

In this paper, the main features of the two-step method are presented and PNC calculations are discussed, both those without accounting for correlation effects (PbF and HgF) and those in which electron correlations are taken into account by a combined method of the second-order perturbation theory (PT2) and configuration interaction (Cl), or PT2/CI [100] (for BaF and YbF), by the relativistic coupled cluster (RCC) method [101, 102] (for TIF, PbO, and HI+), and by the spin-orbit direct-CI method [103, 104, 105] (for PbO). In the ab initio calculations discussed here, the best accuracy of any current method has been attained for the hyperfine constants and P,T-odd parameters regarding the molecules containing heavy atoms. 

To check the influence of correlation energy on the analysis performed, single reference configuration interaction calculations [hereafter referred to as Single plus Double Configuration Interaction (SDCI)] have been carried out on the compound Fe CO)i 7i -CH2O), by using the direct-CI method [3]. 58 electrons have been frozen because of the dimensions... 

Multi-Reference Configuration Interaction (MRCI) calculations were subsequently performed on the saddle point, the reagents, and the products, in order to improve the determination of the barrier height and the exoergicity. These calculations, which include single and double excitations from the active orbitals, have been performed by using the direct-CI method [10]. Davidson s correction [11] was also added to account for the effect of unlinked clusters this will be denoted MRCI-I-Q in Table 1. 

The super-CI method thus leads to the stationary point by a direct annihilation of the single excitations (4 54). 

In order to be able to write out all the terms of the direct Cl equations explicitly, the Hamiltonian operator is needed in a form where the integrals appear. This is done using the language of second quantization, which has been reviewed in the mathematical lectures. Since, in the MR-CI method, we will generally work with spin-adapted configurations a particularly useful form of the Hamiltonian is obtained in terms of the generators of the unitary group. The Hamiltonian in terms of these operators is written,... 

In fact, the distinction between two-step and direct dynamics is rather fuzzy. The basic issue is what kind and amount of preliminary work is needed before starting a dynamical calculation. Direct ab initio dynamics [90,97-101] requires a minimum of preparation some tests to choose basis sets and other options may suffice. For large systems, however, fully ab initio calculations are impractical, and one has to resort to QM/MM or PCM approaches but then, a host of empirical parameters are introduced, which may need some readjustement to avoid artefacts and to improve the accuracy before starting the dynamical calculations. The same holds for the semiempirical methods in order to represent at best the excited states, one has to re-parameterize the hamiltonian. In particular, our FOMO-SCF-CI method [56-58] differs considerably from the normal SCF or SCF+CIS procedures, so that the standard parameters need to be modified. However, the parameter sets are fairly transferable, and their optimization can be limited to the atoms belonging to the chromophore. In the two-step strategies one fits the ab... 

Rotational barriers have been probed for a number of bisalkyne complexes (Table VII). Cationic [CpM(RC=CR)2(CO)]+ complexes exhibit relatively high barriers (16-21 kcal/mol). Both standard variable-temperature NMR techniques (94) and two-dimensional methods (162) have been used to elucidate isomer interconversion schemes with two unsymmetrical alkynes in the coordination sphere. The plane of symmetry present when two symmetrical alkynes bind to a CpMX fragment is not retained in all isomers with RC=CH ligands. The availability of distal and proximal alkyne termini locations relative to the adjacent cis ligand leads to two cis isomers (R and R near one another) and one trans isomer (Fig. 25). Rotation of only one alkyne ligand converts cis to trans and vice versa, but direct cis to cis conversion is not possible unless both alkynes rotate simultaneously. 

The CPU scaling of the GST method with the size of the basis set exjjansion has been investigated in an application to CI-1-CH4. A scaling better than N, close to A"lnA in fact, was observed as illustrated in Fig. 6. This is cilso the scaling normally found in wavepacket Ccilculations and decidedly better than the api)roximately scaling observed in direct diagonalization methods. Note also that the GST method has only smcill requirements on primary memory. 

DIRECT MCSCF AND MCSCF-CI METHODS matrix U can be written in the form... 

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