Multireference coupled cluster expansions

Single state coupled cluster expansions and multireference coupled cluster expansions based on the generalized Brillouin-Wigner pertm bation theory have been described elsewhere [19]. The generalized Brillouin-Wigner perturbation theory can also be applied to the configuration interaction problem. 

The second step of the calculation involves the treatment of dynamic correlation effects, which can be approached by many-body perturbation theory (62) or configuration interaction (63). Multireference coupled-cluster techniques have been developed (64—66) but they are computationally far more demanding and still not established as standard methods. At this point, we will only focus on configuration interaction approaches. What is done in these approaches is to regard the entire zeroth-order wavefunc-tion Tj) or its constituent parts double excitations relative to these reference functions. This produces a set of excited CSFs ( Q) that are used as expansion space for the configuration interaction (Cl) procedure. The resulting wavefunction may be written as... 

In section 6.1 we briefly describe the single reference Brillouin-Wigner coupled cluster expansions. The multireference case is considered in more detail in section 6.2. 

MULTIREFERENCE BRILLOUIN-WIGNER COUPLED CLUSTER EXPANSIONS... 

GENERALIZED BRILLOUIN-WIGNER COUPLED CLUSTER EXPANSIONS GENERALIZED MULTIREFERENCE BRILLOUIN-WIGNER COUPLED CLUSTER EXPANSIONS... 

MULTIREFERENCE BRILLOUIN-WICNER COUPLED CLUSTER EXPANSION... 

In addition to the encouraging numerical results, the canonical transformation theory has a number of appealing formal features. It is based on a unitary exponential and is therefore a Hermitian theory it is size-consistent and it has a cost comparable to that of single-reference coupled-cluster theory. Cumulants are used in two places in the theory to close the commutator expansion of the unitary exponential, and to decouple the complexity of the multireference wave-function from the treatment of dynamic correlation. 

So far, we have specified the wave operator H in the BW form (15). If we adopt an exponential ansatz for the wave operator Cl, we can speak about the single-root multireference Brillouin-Wigner coupled-cluster (MR BWCC) theory. The simplest way how to accomplish the idea of an exponential expansion is to exploit the so-called state universal or Hilbert space exponential ansatz of Jeziorski and Monkhorst [23]... 

Coupled Cluster (cc) expansions Approximations based on CC expansions [3, 91,92] include ccd, ccsd, ccsdt, etc., and their multireference variants mr-CCD, MR-ccsD, MR-ccsDT, etc. The CCSD approximation is also known as the coupled pair approximation (cpa) [59] or the coupled pair many electron theory (CPMET) [20,21,93]. 

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. 

The simplest way to realize an exponential expansion is to employ the exponential ansdtz of Jeziorski and Monkhorst [87] which exploits a complete model space. This is the approach that we followed in Section 4.2.2.2 in developing a multi-root multireference Brillouin-Wigner coupled cluster theory. The Jeziorski and Monkhorst exponential ansatz may be written... 

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