Multireference configuration interaction, MRCI

Since the time that Bowen s and co-workers article was published, the theory based on the BO approximation, except for one very recent multireference configuration interaction (MRCI) calculation by Chang et al. [127], has been unable to produce a value of the LiH adiabatic electron affinity that... 

Of the five group-13 elements, only B and A1 have experimentally well characterized electron affinities. Lists of recommended EAs [50,51] show errors ranging from 50% to 100% for Ga, In, and T1. Very few calculations have appeared for the latter atoms. These include the multireference configuration interaction (MRCI) ofAmau etal. using pseudopotentials [52], our relativistic coupled cluster work on T1 [45], and the multiconfiguration Dirac-Fock (MCDF) computation of Wijesundera [53]. 

When MCSCF wavefunctions are used as the reference, the most commonly used methods for recovering the electron correlation are multireference configuration interaction (MRCI) (15) and multireference perturbation theory (MRPT)... 

In the Table 2.1, the values of Ag shifts, Agtt = gtt- ge> calculated for a series of benchmark radicals [35], are compared with results of experiments [120-124] and various other computational methods multireference configuration interaction (MRCI) [125], one-component unrestricted KS (UKS) by Schreckenbach and Ziegler [111], by Malkin, Kaupp et al. [86,126], as well as two-component ROKS ZORA [112,127]. Our ROKS DKH data [35] were obtained with the BP GGA functional [128,129]. 

Because the contribution of the external orbitals to the correlation energy is neglected, this missing dynamic correlation can be essentially recovered in two ways multireference configuration interaction (MRCI) or multireference perturbation theory (MRPT) approaches [53]. 

Multireference configuration interaction (MRCI) calculations based on valence complete active space self-consistent field (CASSCF) wave functions with the quadruples corrections (-I-Q) [25-30] were used to determine the excitation energies of the N and P atoms using the AVQZ basis set. 

In the present paper, DFT, coupled cluster and multireference configuration interaction (MRCI) results will be presented for MF3, MCE" and MBrf, where M = B, AL Ga, all cations having 23 VEs. Results for BF3 from ref 4 will be included for comparison. 

Initially only state-averaged multiconfigurational self-consistent field (SA-MCSCF) wave functions could be treated but subsequently the algorithm was extended to treat general multireference configuration interaction (MRCI) wave functions. Here x(X) denotes the space fixed frame coordinates of the A electrons nuclei) and < >/ is one of A electronic... 

The most recent and high level computation satisfying both these requirements is the potential energy surfaces by Kurkal et al. [226], at the multireference configuration interaction (MRCI) level with a quadruple zeta basis set. 5000 points were calculated (up to bond length of 8.0 a.u.) and joined with cubic splines, and an ab initio quasi-diabatization method [373] was used to obtain diabatic surfaces. Wavepacket dynamics studies employing this surface has not been published however. 

The calculations were performed with several different levels of correlation treatment Hartree-Fock (HF), configuration interaction with single and double excitations (SDCI), Multiconfiguration self consistent field (CAS), and multireference configuration interaction (MRCI). Relativistic efferts were accounted for using either the Douglas-Kroll method or a relativistic effective core potential approach (RECP). 

The incremental scheme based on the wavefunction HF method was extended to the calculation of valence-band energies when the electron-correlation is taken into account. In [176,177] an effective Hamiltonian for the N — l)-electron system was set up in terms of local matrix elements derived from multireference configuration-interaction (MRCI) calcnlations for finite clnsters. This allowed correlation corrections to a HF band strnctnre to be expressed and rehable results obtained for the valence-band structure of covalent semicondnctors. A related method based on an efiective Hamiltonian in locahzed Wannier-type orbitals has also been proposed and applied to polymers [178,179]. Later, the incremental scheme was used to estimate the relative energies of valence-band states and also yield absolnte positions of snch states [180]. 

In this section we will introduce some wavefunction-based methods to calculate photoabsorption spectra. The Hartree-Fock method itself is a wavefunction-based approach to solve the static Schrodinger equation. For excited states one has to account for time-dependent phenomena as in the density-based approaches. Therefore, we will start with a short review of time-dependent Hartree-Fock. Several more advanced methods are available as well, e.g. configuration interaction (Cl), multireference configuration interaction (MRCI), multireference Moller-Plesset (MRMP), or complete active space self-consistent field (CASSCF), to name only a few. Also flavours of the coupled-cluster approach (equations-of-motion CC and linear-response CQ are used to calculate excited states. However, all these methods are applicable only to fairly small molecules due to their high computational costs. These approaches are therefore discussed only in a more phenomenological way here, and many post-Hartree-Fock methods are explicitly not included. 

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