Coupled cluster CC method

The problem of a many-body correlation of motion of anything is extremely difficult and so far unresolved (e.g., weather forecasting). The problem of electron correlation also seemed to be hopelessly difficult. It still remains so, however, it turns out that we can exploit a certain observation made by Sinanoglu. This author noticed that the major portion of the correlation is taken into account through the in- 

The importance of a given double excitation depends on the energy connected with the electron relocation and the arrangement of points A,B,C,D. Yet this simplistic reasoning suggests single citations do not carry any correlation (this is confirmed by the Brillouin theorem) and this is why their role is very small. Moreover, it also suggests that double citations should be very important. 

The general idea of the coupled cluster method relies on the more and more accurate description of the many-electron i stem, begiiming with the picture of the independent electrons, next of independent pairs, nect of independent pair-pair sets, etc. 

---

In the coupled-cluster (CC) method [61J, one expresses the wavefunctlon In a somewhat different manner ... 

Perturbation methods add all types of corrections (S, D, T, Q etc.) to the reference wave function to a given order (2, 3, 4 etc.). The idea in Coupled Cluster (CC) methods is to include all corrections of a given type to infinite order. The (intermediate normalized) coupled cluster wave function is written as... 

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. 

Recent years have witnessed a considerable activity towards extending the standard single-reference coupled-cluster (CC) methods (1-9) to potential energy surfaces (PESs) involving bond breaking without invoking a multireference description (see, e.g., refs 9-31). Undoubtedly, it would be very useful if we could routinely calculate large portions of molecular PESs with the ease-... 

In the last few years, the improvements in computer hardware and software have allowed the simulation of molecules and materials with an increasing number of atoms. However, the most accurate electronic structure methods based on N-particle wavefunctions, for example, the configuration interaction (Cl) method or the coupled-cluster (CC) method, are computationally too expensive to be applied to large systems. There is a great need for treatments of electron correlation that scale favorably with the number of electrons. 

The coupled cluster (CC) method is actually related to both the perturbation (Section 5.4.2) and the Cl approaches (Section 5.4.3). Like perturbation theory, CC theory is connected to the linked cluster theorem (linked diagram theorem) [101], which proves that MP calculations are size-consistent (see below). Like standard Cl it expresses the correlated wavefunction as a sum of the HF ground state determinant and determinants representing the promotion of electrons from this into virtual MOs. As with the Mpller-Plesset equations, the derivation of the CC equations is complicated. The basic idea is to express the correlated wave-function Tasa sum of determinants by allowing a series of operators 7), 73,... to act on the HF wavefunction ... 

The coupled-cluster (CC) method [41, 118-120] expresses the wave function of a molecule in the ground state by... 

The coupled-cluster (CC) method has been recognized in recent years as a very powerful method for the calculation of correlation effects.1-14 It became an attractive alternative to more common configuration interac-... 

For nondegenerate systems, single reference coupled cluster (CC) methods have proven to be quite successful in their description of the electron correlation problem (1-3). This is primarily due to their (size) extensivity and ability to efficiently incorporate higher-order correlation effects—CC models including triple excitation effects are generally within 1-2 kcal mol 1 of full Cl (3). 

---