Configuration interaction by perturbation

Configuration Interaction by Perturbation with Multiconfigurational Zero-Order Wave Function Selected by Iterative Process Configuration Interaction with Singles and Doubles Density Functional Theory Effective Core Potential Generalized Gradient Approximation Hartree-Fock... 

CIPSI Configuration Interaction by Perturbation with Multiconfigurational... 

This calculation is typically performed in some form of a restricted configuration interaction (Cl) expansion (CASSCF [complete active space self consistent field], MRCI [multireference configuration interaction]). The perturbation V is represented by the operators and The perturbed wave function F and energy E satisfy the equation... 

Although the minimal basis sets are very small, one can describe results that are exact within the one-electron space spanned by these basis functions. In particular, using the minimal basis sets, we can explore any number of different computational approaches and compare the results with the exact results for the same basis. In later chapters we will be using the same minimal basis STO-3G H2 and HeH models to illustrate configuration interaction calculations, perturbation theory calculations, etc. The results obtained there will be compared with the exact results for the same basis and the Hartree-Fock calculations of this chapter. 

Basis Sets Correlation Consistent Sets Complete Active Space Self-consistent Field (CASSCF) Second-order Perturbation Theory (CASPT2) Configuration Interaction Coupled-cluster Theory Density Functional Theory (DFT), Hartree-Fock (HF), and the Self-consistent Field G2 Theory Geometry Optimization 1 Gradient Theory Inter-molecular Interactions by Perturbation Theory Molecular Magnetic Properties NMR Chemical Shift Computation Ab Initio NMR Chemical Shift Computation Structural Applications Self-consistent Reaction Field Methods Spin Contamination. 

In practice, the different expansions for the correlation energy afforded by coupled cluster theory, configuration interaction and perturbation theory have to be truncated in order to render computations tractable. The different methods differ only in the way in which this truncation is carried out. However,... 

The amount of computation for MP2 is determined by the partial transformation of the two-electron integrals, what can be done in a time proportionally to m (m is the number of basis functions), which is comparable to computations involved in one step of CID (doubly-excited configuration interaction) calculation. To save some computer time and space, the core orbitals are frequently omitted from MP calculations. For more details on perturbation theory please see A. Szabo and N. Ostlund, Modem Quantum Chemistry, Macmillan, New York, 1985. 

There are three main methods for calculating electron correlation Configuration Interaction (Cl), Many Body Perturbation Theory (MBPT) and Coupled Cluster (CC). A word of caution before we describe these methods in more details. The Slater determinants are composed of spin-MOs, but since the Hamilton operator is independent of spin, the spin dependence can be factored out. Furthermore, to facilitate notation, it is often assumed that the HF determinant is of the RHF type. Finally, many of the expressions below involve double summations over identical sets of functions. To ensure only the unique terms are included, one of the summation indices must be restricted. Alternatively, both indices can be allowed to run over all values, and the overcounting corrected by a factor of 1/2. Various combinations of these assumptions result in final expressions which differ by factors of 1 /2, 1/4 etc. from those given here. In the present book the MOs are always spin-MOs, and conversion of a restricted summation to an unrestricted is always noted explicitly. 

The idea of coupling variational and perturbational methods is nowadays gaining wider and wider acceptance in the quantum chemistry community. The background philosophy is to realize the best blend of a well-defined theoretical plateau provided by the application of the variational principle coupled to the computational efficiency of the perturbation techniques. [29-34]. In that sense, the aim of these approaches is to improve a limited Configuration Interaction (Cl) wavefunction by a perturbation treatment. 

Cl methods [21] add a certain number of excited Slater determinants, usually selected by the excitation type (e.g. single, double, triple excitations), which were initially not present in the CASSCF wave function, and treat them in a non-perturbative way. Inclusion of additional configurations allows for more degrees of freedom in the total wave function, thus improving its overall description. These methods are extremely costly and therefore, are only applicable to small systems. Among this class of methods, DDCI (difference-dedicated configuration interaction) [22] and CISD (single- and double excitations) [21] are the most popular. 

The difference between the Hartree-Fock energy and the exact solution of the Schrodinger equation (Figure 60), the so-called correlation energy, can be calculated approximately within the Hartree-Fock theory by the configuration interaction method (Cl) or by a perturbation theoretical approach (Mpller-Plesset perturbation calculation wth order, MPn). Within a Cl calculation the wave function is composed of a linear combination of different Slater determinants. Excited-state Slater determinants are then generated by exciting electrons from the filled SCF orbitals to the virtual ones ... 

Recently, quantum chemical computational techniques, such as density functional theory (DFT), have been used to study the electrode interface. Other methods ab initio methods based on Hartree-Fock (HF) theory,65 such as Mollcr-PIcsset perturbation theory,66,67 have also been used. However, DFT is much more computationally efficient than HF methods and sufficiently accurate for many applications. Use of highly accurate configuration interaction (Cl) and coupled cluster (CC) methods is prohibited by their immense computational requirements.68 Advances in computing capabilities and the availability of commercial software packages have resulted in widespread application of DFT to catalysis. 

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