State-specific coupled cluster theory

III. A STATE-SPECIFIC COUPLED CLUSTER THEORY WITH A DECONTRACTED REFERENCE FUNCTION... 

In the decontracted description of the state specific coupled cluster theory, we shall posit the following Ansatz for the exact function ... 

Keywords Many-body theory Brillouin-Wigner theory State-specific multireference correlation problem Many-body perturbation theory Coupled cluster theory Configuration interaction Collaborative virtual enviroments... 

Multireference State-Specific Coupled Cluster Theory with a Complete Active Space Reference... 

Keywords State-specific coupled-cluster theory Electron correlation Configuration interaction Many-body perturbation theory Single and double excitation... 

Multireference State-Specific Coupled Cluster Theory... 

The current volume presents the compilation of splendid contributions distributed over 21 chapters. The very first chapter contributed by Istvan Hargittai presents the historical account of development of structural chemistry. It also depicts some historical memories of scientists presented in the form of their pictures. This historical description covers a vast period of time. Intruder states pose serious problem in the multireference formulation based on Rayleigh-Schrodinger expansion. Ivan Hubac and Stephen Wilson discuss the ciurent development and future prospects of Many-Body Brillouin-Wigner theories to avoid the problem of intruder states in the next chapter. The third chapter written by Vladimir Ivanov and collaborators reveals the development of multireference state-specific coupled cluster theory. The next chapter from Maria Barysz discusses the development and application of relativistic effects in chemical problems while the fifth chapter contributed by Manthos Papadopoulos and coworkers describes electronic, vibrational and relativistic contributions to the linear and nonlinear optical properties of molecules. 

Mahapatra, U. S. Datta, B. Mukheijee, D. A size-consistent state-specific multireference coupled cluster theory Formal developments and molecular applications, J. Chem. Phys. 1999,110, 6171-6188. 

Evangelista, F. A. AUen, W. D. Schaefer m, H. F. Coupling term derivation and general implementation of state-specific multireference coupled cluster theories, J. Chem. Phys. 2007,127, 024102-024117. 

The exponential ansatz given in Eq. [31] is one of the central equations of coupled cluster theory. The exponentiated cluster operator, T, when applied to the reference determinant, produces a new wavefunction containing cluster functions, each of which correlates the motion of electrons within specific orbitals. If T includes contributions from all possible orbital groupings for the N-electron system (that is, T, T2, . , T ), then the exact wavefunction within the given one-electron basis may be obtained from the reference function. The cluster operators, T , are frequently referred to as excitation operators, since the determinants they produce from fl>o resemble excited states in Hartree-Fock theory. Truncation of the cluster operator at specific substi-tution/excitation levels leads to a hierarchy of coupled cluster techniques (e.g., T = Ti + f 2 CCSD T T + T2 + —> CCSDT, etc., where S, D, and... 

F. A. Evangelista, J. Gauss, Insights into the orbital invariance problem in state-specific multireference couple cluster theory, J. Chem. Phys. 133 (2010) 044101. 

Although the approach described above is presented in its most general form, using a multiple coupled-cluster Ansatz for the SS-MRCC formalism, suitable approxi-mants to it such as the state-specific multi-reference perturbation theory (SS-MRPT) or state-specific multi-reference CEPA (SS-MRCEPA) can be generated by straightforward approximations. Since the new closed component of the wave operator for IMS appear first at the quadratic power, it is evident that the expressions we have derived in this and the earlier papers for the CAS will remain valid if the quadratic powers of are ignored in the approximants to SS-MRCC for IMS. This implies that all the SS-MRPT... 

So far most of the computations have been performed for few-electron atoms or for medium atoms modeled by one-electron potentials. However, there are methods, like the state specific CESE and MEMPT approach (13), which can be applied to leurger systems. Also combination of complex-rotation technique with the many body perturbation theory (30) or coupled cluster method (31), which are addressed to large systems, seems to be promissing in this context. 

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