Single-reference methods theory

One area in which Cl methods appear to be thoroughly superior to perturbation theory is in the treatment of multireference problems problems with substantial nondynamical correlation effects. Even UHF-based single reference perturbation theory methods may not cope with some such situations, and multireference perturbation theory, despite many efforts over the years, still appears to be far from developing a general flexible approach that is competitive with MRCI. Transition-metal chemistry, in particular, is a graveyard for UHF-based MP methods. 

A final point of some importance concerns the use of single-reference methods. Density fiinctional theory is often the method of choice in computational transition metal chemistry, simply because it is often the only affordable method that yields a qualitatively accurate description of the PESs. However, it is in some respects a single-reference, method in that it constructs a wavefunc-tion from a single Slater determinant and cannot therefore describe systems that inherently require a representation in terms of multiple determinants, such as low-spin open-shell systems. This makes it inappropriate for treating some regions on PESs, although experience shows that DFT is somewhat less sensitive to this effect than other single-determinant systems. 

Because of its size-extensivity and faster convergence with respect to excitation level Coupled cluster theory has replaced Cl theory as the dominant approach in ab initio correlation calculations. Like MBPT the theory is still mainly applied in cases where the exact wave function is dominated by a single determinant, but multireference methods have been formulated and begin to enter mainstream quantum chemistry. Generalization of the algorithms to the relativistic no-pair level can again be achieved via the spinorbital formulation of the methods. I will first discuss the single reference method and then consider the Fock space method [40] that uses multi-reference wavefiinctions for ionized or excited states. 

A review of single-reference methods for large-molecule excited-state calculations noted that LR-TDDFT can treat systems with up to 200 to 300 first-row atoms and stated that LR-TDDFT is the most prominent method for the calculation of excited states of medium-sized and large molecules [A. Dreuw and M. Head-Gordon, Chem. Rev., 105, 4009 (2005)]. For more on TDDFT, see C. Ullrich, Time-Dependent Density-Functional Theory, Oxford, 2012. 

The Cn-kij A) terms are easy to determine. The zero-body term, Cq a)i equals 1 the one-body term, C mA)-> equals Ti the two-body term, C2(mA), equals T2 + if rriA > 2 the three-body term, Cz rnA) equals riT2 + if rriA = 2 and Ts + T1T2 + if rriA > 3, etc. The coefficients, Eq. (27), define the generalized moments of CC equations (for a discussion of the relationship between the method of moments of Krylov [99] and the single-reference CC theory, see Ref. [100]). They are readily available for the basic CC approximations, such as CCSD (the rriA = 2 case). As pointed out in our original work [11,30], the generalized moments represent the most fundamental quantities... 

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