Configuration interaction, full

Each cell in the chart defines a model chemistry. The columns correspond to differcni theoretical methods and the rows to different basis sets. The level of correlation increases as you move to the right across any row, with the Hartree-Fock method jI the extreme left (including no correlation), and the Full Configuration Interaction method at the right (which fuUy accounts for electron correlation). In general, computational cost and accuracy increase as you move to the right as well. The relative costs of different model chemistries for various job types is discussed in... 

Nobes, Pople, Radotn, Handy and Knowles have studied the convergence of the Moller-Plesset orders in some detail. They computed the energies of hydrogen cyanide, cyanide anion and cyano radical through order 24 as well as at the full Configuration Interaction level. Here are some of their results ... 

A CASSCF calculation is a combination of an SCF computation with a full Configuration Interaction calculation involving a subset of the orbitals. The orbitals involved in the Cl are known as the active space. In this way, the CASSCF method optimizes the orbitals appropriately for the excited state. In contrast, the Cl-Singles method uses SCF orbitals for the excited state. Since Hartree-Fock orbitals are biased toward the ground state, a CASSCF description of the excited state electronic configuration is often an improvement. 

Under these conditions, the 3-RDM of the three lower states of the Beryllium atom and the two lower ones of the Water molecule were determined [48] by taking as initial data the 2-RDM obtained in a Full Configuration Interaction. In Table 4 some of these results are given and as can be seen they are very satisfactory. 

The difference between the energy obtained with a single determinant (HF method) and that obtained by using the combination of all the possible determinants (full configuration interaction, full Cl method) is called the correlation energy. It so happens that correlation energy is usually very important in transition metal compounds, and because of this, its introduction is often mandatory in computational transition metal chemistry. 

For small basis sets and molecules, it is possible to calculate the full set of energies in the coupled-cluster hierarchy, from the Hartree-Fock to the full configuration-interaction (FCI) energy [18]. Although such... 

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. 

The most commonly used model space in quantum chemistry is the so-called full configuration interaction (FCI) space. It is the antisymmetric and spin-adapted N-fold tensorial power, of the 2A -dimensional spin-orbital one-electron space V. The... 

Figure 1. The shape of the potential curve for nitrogen in a correlation-consistent polarized double-zeta basis set is presented for the variational 2-RDM method as well as (a) single-reference coupled cluster, (b) multireference second-order perturbation theory (MRPT) and single-double configuration interaction (MRCl), and full configuration interaction (FCl) wavefunction methods. The symbol 2-RDM indicates that the potential curve was shifted by the difference between the 2-RDM and CCSD(T) energies at equilibrium.

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)". 

For Three Molecules in Valence Double-Zeta Basis Sets, a Comparison of Energies in Hartrees (H) from the 2-RDM Method with the T2 Condition (DQGT2) with the Energies from Second-Order Many-Body Perturbation Theory (MP2), Coupled-Cluster Method with Single-Double Excitations and a Perturbative Triples Correction (CCSD(T)), and Full Configuration Interaction (FCI)... 

Finally, in order to illustrate the role of the 1-MZ purification procedure in improving the approximated 2-RDMs obtained by application of the independent pair model within the framework of the SRH theory, all the different spin-blocks of these matrices were purified. The energy of both the initial (non-purified) and updated (purified) RDMs was calculated. These energies and those corresponding to a full configuration interaction (full Cl) calculation are reported in Table 111. As can be appreciated from this table, the nonpurified energies of all the test systems lie below the full Cl ones while the purified ones lie above and very close to the full Cl ones. 

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