Configuration interaction quadratic

The MPn method treats the correlation part of the Hamiltonian as a perturbation on the Hartree-Fock part, and truncates the perturbation expansion at some order, typically n = 4. MP4 theory incorporates the effect of single, double, triple and quadruple substitutions. The method is size-consistent but not variational. It is commonly believed that the series MPl, MP2, MP3,. .. converges very slowly. 

Quadratic Configuration Interaction. A general technique for determining electron correlation energies 

John A. Pople, Martin Head-Gordon and Krishnan Raghavachari Journal of Chemical Physics 87 (1987) 5968-5975 

Suppose we have an HF determinantal wavefunction fi o constructed from singly occupied spin orbitals , (that is, a UHF wavefunction). Other 

Various types of antisymmetric wavefunction can be obtained by applying different functions of the T operators to fi o. and the unknown coefficients together with the energy can be determined from the projection equations 

Suppose we have an HF determinantal wavefunction I o constructed from singly occupied spin orbitals 2. . fyn (that is, a UHF wavefunction). Other determinantal wavefunctions are derived from P0 by substitution of occupied spin orbitals by virtual spin orbitals. If we use indices A, B,. .. for the occupied spin orbitals and X, Y. for the virtual spin orbitals, then we define complete single, double, triple,. .. substitution operators 

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Among the most widely used ab initio methods are those referred to as Gl" and 02." These methods incorporate large basis sets including d and / orbitals, called 6-311. The calculations also have extensive configuration interaction terms at the Moller-Plesset fourth order (MP4) and fiirther terms referred to as quadratic configuration interaction (QCISD). ° Finally, there are systematically applied correction terms calibrated by exact energies from small molecules. 

Coupled Cluster and Quadratic Configuration Interaction 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. 

Curtiss, L. A. Raghavachari, K. Pople, J. A. Gaussian-2 theory use of higher level correlation methods, quadratic configuration interaction geometries, and second-order Mpller Plesset zero-point energies. J. Chem. Phys. 1995, 103, 4192-4120. 

Scott, A. P., Radom, L., 1996, Harmonic Vibrational Frequencies An Evaluation of Hartree-Fock, Moller-Plesset, Quadratic Configuration Interaction, Density Functional Theory, and Semiempirical Scale Factors , J. Phys. Chem., 100, 16502. 

There is also a hierarchy of electron correlation procedures. The Hartree-Fock (HF) approximation neglects correlation of electrons with antiparallel spins. Increasing levels of accuracy of electron correlation treatment are achieved by Mpller-Plesset perturbation theory truncated at the second (MP2), third (MP3), or fourth (MP4) order. Further inclusion of electron correlation is achieved by methods such as quadratic configuration interaction with single, double, and (perturbatively calculated) triple excitations [QCISD(T)], and by the analogous coupled cluster theory [CCSD(T)] [8],... 

Scott AP, Radom L(1996) Harmonic vibrational frequencies An evaluation of Hartree-Fock, Moller-Plesset, quadratic configuration interaction, density functional theory, and semiempirical scale factors. J Phys Chem 100 16502-16513... 

QCISD Quadratic configuration interaction including singles and doubles... 

The concomitant advances in theoretical methodologies and algorithms have also played a vital role in increasing computational capabilities for theoretical thermochemistry. These advances include (1) new methods for accurate treatment of electron correlation in molecules and atoms such as coupled cluster and quadratic configuration interaction methods, (2) new basis sets such as the correlation consistent basis sets, and (3) development of model chemistry ... 

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