QCI methods

A disadvantage of all these limited Cl variants is that they are not size-consistent.The Quadratic Configuration Interaction (QCI) method was developed to correct this deficiency. The QCISD method adds terms to CISD to restore size consistency. QCISD also accounts for some correlation effects to infinite order. QCISD(T) adds triple substitutions to QCISD, providing even greater accuracy. Similarly, QCISD(TQ) adds both triples and quadruples from the full Cl expansion to QCISD. 

QCI methods 117 QCISD keywords 9,114 E4T option 186 quadratic Cl methods 114 quadrupole moment 21 quotation li... 

The CASSCF/CASPT2 calculations were performed with an active space including the five nd, the (n + l)s, the three (n+ l)p orbitals, and a second set of nd orbitals to account for the double shell effect. The importance of including a second 3d shell in the active space was detected in an early study of the electronic spectrum of the nickel atom [2]. This had already been suggested from MRCI results [1]. The results obtained by RT at about the same time indicated that such effects are effectively accounted for when a method is used that includes cluster corrections to all orders, like the QCI method used by them [3]. This result will hold true also for the less approximate coupled cluster method CCSD(T). 

In the 1980s, Pople and co-workers developed the non-variational quadratic configuration interaction (QCI) method, which is intermediate between CC and Cl methods. Similar to the CC methods, QCI also has the corresponding QCISD and QCISD(T) options. Both the CCSD(T) and QCISD(T) have been rated as the most reliable among the currently computationally affordable methods. 

Two approaches to electron correlation that are widely used today for the studies of organic radical cations are Coupled Cluster (CC) calculations or the similar, but not identical, Quadratic Configuration Interaction (QCI) method with single and double excitations, often followed by CCSD(T) or QCISD(T) single point calculations with a larger basis set. These methods suffer to a much lesser extent from... 

Accounting for relativistic effects in computational organotin studies becomes complicated, because Hartree-Fock (HF), density functional theory (DFT), and post-HF methods such as n-th order Mpller-Plesset perturbation (MPn), coupled cluster (CC), and quadratic configuration interaction (QCI) methods are non-relativistic. Relativistic effects can be incorporated in quantum chemical methods with Dirac-Hartree-Fock theory, which is based on the four-component Dirac equation. " Unformnately the four-component Flamiltonian in the all-electron relativistic Dirac-Fock method makes calculations time consuming, with calculations becoming 100 times more expensive. The four-component Dirac equation can be approximated by a two-component form, as seen in the Douglas-Kroll (DK) Hamiltonian or by the zero-order regular approximation To address the electron cor-... 

Whereas Cl methods are variational, giving upper bounds to the total energy, the other discriminating factor in choice of correlated method is whether a method scales correctly with size, or, equivalently, the number of electrons. This (size) extensive property, which can be quite significant numerically, is satisfied by many-body methods (e.g., MBPT, CC, and QCI methods) but not by Cl methods other than full Cl. Truncated Cl ap-... 

Pople and co-workers developed the nonvariational quadratic configuration-interaction (QCI) method, which is intermediate between the CC and Cl methods. The QCI method exists in the size-consistent forms QCISD, which is an approximation to CCSD, and QCISD(T), which is similar to CCSD + T(CCSD). QCISD(T) has given excellent results for correlation energies in many calculations and is available as an option in Gaussian [J. A. Pople, M. Head-Gordon, and K. Raghavachari, J. Chem. Phys., 87, 5968 (1987) 90, 4635 (1989) K. Raghavachari and G. W. Trucks, /. Chem. Phys., 91, 1062, 2457 (1989) J. Paldus et al., J. Chem. Phys., 90, 4356 (1989)]. 

To simplify the discussion of the Cl, CC and QCI methods, it is desireable to define single, double, triple, etc. substitution operators ... 

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