CCSDT method

Table X shows the total energies as a function of bond length Tnn using several CT methods, as well as those using the HF, FCl, CASSCF, MRMP, CCSD, and CCSDT methods. Figure 9 plots the energy differences from the FCl results.

CCSD augmented by a non-iterative triple excitations Different approximate CCSDT methods that are obtained by truncating the T3 equation. Different n values define different... 

Every term in the coupled cluster amplitude equations that is nonlinear in T may be factored into linear components. As a result, each step of the iterative solution of the CCSD equations scales at worst as ca. 0(X ) (where X is the number of molecular orbitals). The full CCSDT method in which all Tycon-taining terms are included requires an iterative 0(X ) algorithm, whereas the CCSD(T) method, which is designed to approximate CCSDT, requires a noniterative O(X ) algorithm. The inclusion of all T4 clusters in the CCSDTQ method scales as... 

As usual in degenerate time-independent diagrammatic methods,512 27 37 38 excited determinants are represented by external space operators rather than by pair creation-annihilation operators. Diagrammati-cally, an external line is a ray, whereas an internal line is a line segment. The four possible types of rays and line segments that arise in a CCSDT method are shown in Fig. 5. The indexing convention we will use for the rest of the chapter is that u, v, and w will denote external holes i and j internal holes /3, y, and e external particles (i.e., electrons) and a and b internal particles. 

In the single reference CC world, the full CCSDT model (23-26) has seen modest use because it requires a substantial effort over CCSD to code, and because the resource requirements—CPU time, memory, disk—are significantly greater. As a result, a number of approximations to the full CCSDT method have been proposed and have proven quite effective at incorporating important effects of triple excitations while at the same time minimizing the above concerns (27-31). In the same spirit, we examine the FSCCSDT equations with an eye to approximating or ignoring the most expensive terms to evaluate. In this sense, the simplest possible approximation would be to evaluate the triple... 

A difficulty with this local approach to dynamical correlation is that, in Moller-Plesset theory, for example, the zero-order Fock operator is no longer diagonal in the space of the Slater determinants, making the application of such theories slightly more complicated than theories based on canonical orbitals. Currently, the development of local correlation methods is an active area of research [57-63]. The diatomics-inmolecules (DIM) method and the triatomics-in-molecules (TRIM) method, for instance, recover typically 95% and 99.7%, respectively, of the full MP2 correlation energy [63]. By means of a linear scaling local variant of the CCSDT method,... 

A few years ago we extended EOM-CCSD to the full EOM-CCSDT method and made some fairly large basis set ( 90 function) calculations, based upon the full triple excitation. CCSDT ground state, and the inclusion of all triple excitations in h [149]. At the same time others [150] reported a study of Hg. These authors also looked at simple potential energy curves with EOM-CCSDT and its active orbital modification, EOM-CCSDT [151,152]. Now, by virtue of their automated procedures, [153] EOM-CC can be taken to any level. Hirata has similarly done EOM-CCSDTQ [154], and Kallay EOM-CCSDTQP. 

As one would expect, if we describe ionization potentials with IP-EOM-CCSD, we will have similar behavior. We should do quite well for most principal ionizations where the eigenstate is dominated by single excitations, meaning linear combinations of i lO) determinants, with i a.y Q) playing most of the correlation and relaxation role but when the latter shake-up is dominant, then we would logically need i ayb k )Q in our space to do as well for the shake-up eigenvalues. The latter requires IP-EOM-CCSDT [156], and the complementary EA-EOM-CCSDT method [157] and higher [166]... 

The general conclusion reached on the basis of the EOM EE calculations is that the most reliable variant of the EOM-CC approach with approximate inclusion of the connected triples is that referred to in the Uteratme as CCSDT-3. At the ground state level this approach differs from the fiiU CCSDT method only in the construction of the target amplitudes, where all the terms containing T- contributions to the target amplitude are removed, yet we retain all possible Tj and T2 terms. This procedure eliminates any terms that would require more than an n procedure. It also bypasses any need to store the rr amplitudes as ffiey can be dealt with on-the-fly . 

The CCD, CCSD, CCSD(T), and CCSDT methods are size consistent but not variational. Analytic gradients are available for these methods. Often, the frozen-core (FC) approximation is used in CC calculations. Here, excitations of inner-shell electrons are omitted. 

The computational cost of the CCD and CCSD (singles and doubles) methods scales as N, where is a number of molecular orbitals (occupied and virtual ), whereas the analogous cost of the CCSDT (singles, doubles, triples) method requires scaling. This means that, if we increase the orbital basis twice, the increase in the computational cost of the CCSDT method will be four times larger than that of the CCSD scheme. This is a lot, and because of this widespread popularity, it has been gained for the CCSD(T) method, which only partly uses the triple excitations. 

In particular, the standard CCSD method is obtained by setting rriA = 2 in Eq. (9). In the CCSDT method, ttia is set at 3 in the CCSDTQ approach, rriA = 4, etc. The cluster operator or the cluster amplitudes define it are obtained by solving the system of nonlinear, energy-independent, algebraic (polynomial) equations, which can be given the following symbolic form ... 

Interest in the F - - H2 reaction was largely due to Lee s benchmark molecular beam studies [105] and early chemiluminescence and chemical laser work [98]. This work led to the early QCT studies of Muckerman [88], Blais and Truhlar [13], and Polanyi and Schreiber [97], using the PES but with serious flaws. A series of surface by Truhlar and his coworkers [17,84,122,135] led to gradual improvement, and then Stark and Werner developed surfaces (SW PES) [121] from multireference configuration interaction calculations that resolved many of the earlier issues, even some problems remain. Very recently, Zhang and his coworkers developed several versions of the PES for the F-I-H2 reaction using icMRCI [100] and CCSDT method [40,102], whose ultimate version has been proved to be of spectroscopy accuracy. 

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