Multireference coupled clusters

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... 

One way of achieving size-consistency for a dissociation process is to use an MCSCF wave function as the reference. Unfortunately, as noted above, there are as yet no general multireference perturbation theory or multireference coupled-cluster treatments that can be applied to such an MCSCF reference function. For rather few electrons, as we shall see, the MRCI approach performs acceptably. 

For molecules that require a multireference description, use of a single reference post-HF method can often fail since the dynamic correlation space is insufficient. Multireference post-HF methods are quite taxing in terms of computational resources and comprise a very active area of theoretical development." A method that has shown some recent promise is multireference coupled cluster (MRCC) theory, and the implementation proposed by Mukheijee and coworkers" (often labeled as MkCC or MkMRCC) has garnered much interest." ... 

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. 

Finally, Pittner and coworkers " examined the PESs of singlet and triplet TMEs using two multireference coupled cluster methods (two-determinant CCSD and multireference Brillouin-Wigner CCSD) with the cc-pVDZ basis set. With both methods, the singlet is always below the triplet for all values of t. The smallest singlet-triplet gap, 1.3 kcal moE, occurs at an angle r = 45° and Ihis is reduced when a near-cc-pVTZ basis set is used. 

Pittner, J. Nachtigall, R Carsky, R Hubac, I. State-specific BriUouin-Wigner multireference coupled cluster study of the singlet-triplet separation in the tetramethyleneethane diradical, 7. Phys. Chem. A 2001,105,1354-1356. 

Simsa, D. Demel, O. Bhaskaran-Nair, K. Hubac, I. Mach, R Pittner, J. Multireference coupled cluster study of the oxyallyl diradical, Chem. Phys. 2012,401, 203-207. 

L. Meissner and R. J. Bartlett, J. Chem. Phys., 94, 6670 (1991). Transformation of the Hamiltonian in Excitation Energy Calculations Comparison Between Fock-Space Multireference Coupled-Cluster and Equation-of-Motion Coupled-Cluster Methods. 

C. M. L. Rittby and R. J. Bartlett, Theor. Chim. Acta, 80, 469 (1991). Multireference Coupled Cluster Theory in Fock Space. 

P. Piecuch, N. Oliphant, and L. Adamowicz, /. Chem. Phys., 99, 1875 (1993). A State-Selective Multireference Coupled-Cluster Theory Employing the Single-Reference Formalism. 

Keywords many-electron correlation problem, post-Hartree-Fock methods, coupled cluster approaches, configuration interaction, externally corrected coupled cluster methods, reduced multireference coupled cluster method... 

Multireference coupled cluster methods, which started development more recently, are generally divided into two types. Hilbert space CC methods use multiple reference functions to obtain a description of a few states, including the reference state (for a review see (4)). Fock space methods (for a review see (5)), on the other hand, provide direct state-to-state energy differences, relative to some common reference state. The Fock space approach is particularly well-suited to the calculation of ionization potentials (IPs), electron affinities (EAs), and excitation energies (EEs). For principal IPs and EAs, FSCC is equivalent (6, 7) to the EOM-IP and EOM-EA CC methods (1, 2, 7, 8). In this paper, we will focus primarily on the IP problem. 

U. Kaldor, Intruder states and incomplete model spaces in multireference coupled-cluster theory The 2p states of Be, Phys. Rev. A 38 (1988) 6013. 

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

Molecular Applications of Multireference Coupled-Cluster Methods Using an Incomplete Model Space. Direa Calculation of Excitation Energies. (FS-MRCCSD.)... 

Multireference Coupled-Cluster Theory for C)eneral Single Determinant Reference Functions. 

A Fock space multireference coupled cluster method was described by Rittby and Bartlett <91TCA469>, applied to the calculation of ionization potentials and excitation energies of 1,2,4,5-tetrazines, and compared with conventional ab initio calculations and experimental results. 

U. Kaldor, Atomic and molecular applications of the multireference coupled-cluster method, in U. Kaldor (Ed.), Many-body methods in quantum chemistry, lecture notes in chemistry, Vol. 52, Springer, Berlin, 1989, pp. 199-213, J. Chem. Phys., 87 (1987) 467. 

Multireference coupled cluster method based on the Brillouin-Wigner perturbation theory... 

---