Coupled cluster (CC) method is a technique used for description of the many-body systems. The method was initially developed by Fritz Coester and Hermann Kümmel in 1950's for studying nuclear physics phenomena but it became more frequently used after Jiři Čížek and Josef Paldus reformulated the method for studying electronic correlation in atoms and molecules in 1960's. It is now one of the most prevalent methods in quantum chemistry that include electronic correlation. The n-body problem is the problem of finding, given the initial positions, masses, and velocities of n bodies, their subsequent motions as determined by classical mechanics, i. ... Events and trends Technology United States tests the first fusion bomb. ... Nuclear physics is the branch of physics concerned with the nucleus of the atom. ... Electronic correlation refers to the interaction between electrons in a quantum system whose electronic structure is being considered. ... Properties For alternative meanings see atom (disambiguation). ... In science, a molecule is the smallest particle of a pure chemical substance that still retains its chemical composition and properties. ... Events and trends The 1960s was a turbulent decade of change around the world. ... Linus Pauling, as a pioneer of the valence bond theory, is one of the first quantum chemists. ...

Background

The method is based on exponential ansatz: Ansatz is a term (from German) often used by physicists. ...

,

where is the wave function, is the reference function (e.g. Hartree-Fock function), and is the cluster operator: In computational physics and computational chemistry, the Hartree-Fock (HF) or self-consistent field (SCF) calculation scheme is a self-consistent iterative variational procedure to calculate the Slater determinant (or the molecular orbitals which it is made of) for which the expectation value of the electronic molecular Hamiltonian is minimum. ...

,

where in the formalism of second quantization: Second quantization refers to quantizing fields by expressing them as operator-valued distributions The most elementary, or semiclassical treatments of quantum mechanics fix the number of particles and treat the field classically, including it as a parameter in the Hamiltonian or Lagrangian or whatever. ...

In the above formulae and denote the creation and annihilation operators and i,j stand for occupied and a,b for unoccupied orbitals. T₁ and T₂ are called the one-particle excitation operator, and the two-particle excitation operator, because they effectively convert the reference function into a linear combination of singly- and doubly-excited Slater determinants. Solving for the coefficients and , in order to satisfy the definition of the cluster operator, constitutes a coupled cluster calculation. This article needs to be cleaned up to conform to a higher standard of quality. ... A Slater determinant (named after the physicist John C. Slater) is an expression in quantum mechanics for the wavefunction of a many-fermion system, which by construction satisfies the Pauli principle. ...

The indices on the cluster operator need not represent orbitals. In vibronic coupling, the indices can represent vibrational and electronic quantum states. For rovibrational considerations, the indicies can represent rotational and vibrational indices. In this context, the exponential operator is related to Van Vleck transformations. In theoretical chemistry, the vibronic coupling terms (which are neglected within the Born-Oppenheimer approximation) are proportional to the interaction between electronic and nuclear motions of molecules. ...

Coupled cluster with doubles (CCD)

In the simplest version one considers only operator (double excitations). This method is called coupled cluster with doubles (CCD in short).

Coupled cluster with singles and doubles (CCSD)

you have 2 believe in urself

Description of the theory

The method gives exact non-relativistic solution of the Schrödinger equation of the n-body problem if one includes up to the cluster operator. However, the computational effort of solving the equations grows steeply with the order of the cluster operator and in practical applications the method is limited to the first few orders. Albert Einsteins theory of relativity is a set of two theories in physics: special relativity and general relativity. ... In physics, the Schrödinger equation, proposed by the Austrian physicist Erwin Schrödinger in 1925, describes the time-dependence of quantum mechanical systems. ...

Most frequently, one solves the CC equation using the operator , which produces all Slater determinants which differ from the reference determinant by one or two spin-orbitals. This approach, called coupled-cluster singles and doubles (CCSD), has the effect of describing coupled two-body electron correlation effects and orbital relaxation effects. Because the operator is exponentiated in coupled-cluster theory, higher-order "disconnected" electron correlations are also accounted for in an approximate way. It is also fairly common (although also more computationally expensive) to include an approximate, non-iterative correction accounting for three-body electron correlations in a method designated CCSD(T). For ground electronic states near their equilibrium geometries, CCSD(T) is often called a "gold standard" of quantum chemistry because it provides results very close to those of full configuration interaction (full CI), which solves the non-relativistic electronic Schrödinger equation exactly within the given one-particle basis set. Full configuration interaction (or full CI) is a linear variational approach which provides numerically exact solutions (within the given one-particle basis set) to the electronic Schrödinger equation. ... In physics, the Schrödinger equation, proposed by the Austrian physicist Erwin Schrödinger in 1925, describes the time-dependence of quantum mechanical systems. ...

One possible improvement to the standard coupled-cluster approach is to add terms linear in the interelectronic distances through methods such as CCSD-R12. This improves the treatment of dynamical electron correlation by satisfying the Kato cusp condition and accelerates convergence with respect to the orbital basis set. Unfortunately, R12 methods invoke the resolution of the identity which requires a relatively large basis set in order to be valid.

The coupled cluster method described above is also known as the single-reference (SR) coupled cluster method because the exponential Ansatz involves only one reference function . The standard generalizations of the SR-CC method are the multi-reference (MR) approaches: state-universal coupled cluster (a.k.a. Hilbert space coupled cluster), valence-universal coupled cluster (a.k.a. Fock space coupled cluster) and state-selective coupled cluster (a.k.a. state-specific coupled cluster). State-universal coupled cluster (SUCC) method is one of several multi-reference (MR) generalizations of single-reference coupled cluster method. ... Aka can refer to the following meanings: Aka is an initialism for Also Known As. ... In mathematics, a Hilbert space is an inner product space that is complete with respect to the norm defined by the inner product. ... The Fock space is an algebraic system (Hilbert space) used in quantum mechanics to describe quantum states with a variable or unknown number of particles. ...

The coupled cluster equations are usually derived using diagrammatic technique and result in nonlinear equations which can be solved in an iterative way. ELLIOT GREER IS THE BIGGEST GAY BOY EVER!!!

External resources

• A theoretical review and introduction to coupled cluster theory