Multireference configuration interaction MRCI methods

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]. 

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. 

MRCI (multireference configuration interaction) a correlated ah initio method multiconfigurational self-consistent field (MCSCF) a correlated ah initio method... 

Equilibrium Bond Distance and the Harmonic Frequency for N2 from the 2-RDM Method with 2-Positivity (DQG) Conditions Compared with Their Values from Coupled-Cluster Singles-Doubles with Perturbative Triples (CCD(T)), Multireference Second-Order Perturbation Theory (MRPT), Multireference Configuration Interaction with Single-Double Excitations (MRCI), and Full Configuration Interaction (FCI)". 

The MCSCF provides a good first-order description covering the static electron correlation due to degeneracy problems. Dynamic electron correlation should be addressed with the MCSCF wave function as a reference. The multireference configuration interaction, or MRCI, generates excited determinants from all (or selected) determinants included in the MCSCF. The complete active space perturbation theory, second order (CASPT2) is a more economical approach. Both methods can be applied to compute excited states. 

Figure 1 A family tree of quantum chemistry DFT, density functional theory QMC, quantum Monte Carlo RRV, Rayleigh-Ritz variational theory X-a, X-alpha method KS, Kohn-Sham approach LDA, BP, B3LYP, density functional approximations VQMC, variational QMC DQMC, diffusion QMC FNQMC, fixed-node QMC PIQMC, path integral QMC EQMC, exact QMC HF, Hartree-Fock EC, explicitly correlated functions P, perturbational MP2, MP4, Maller-Plesset perturbational Cl, configuration interaction MRCI, multireference Cl FCI, full Cl CC, CCSD(T), coupled-cluster approaches. Other acronyms are defined in the text.

The configuration interaction (Cl) method and, especially, its multireference variants (MRCI) have proven themselves useful for the study of both ground and excited states potential energy surfaces. Most of the developed Cl algorithms rely heavily on the existence of well-defined relationships among configurations... 

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