Triple-excitation energy component

Table V CPU times on the CRAY-1 and the IBM 360/195 computer required to execute the inner loop in evaluation of triple excitation energy component.

The innermost loop in the program written to evaluate the triple-excitation energy component described in the previous subsection has the form... 

Rendell et al. compared three previously reported algorithms to the fourth-order triple excitation energy component in MBPT." The authors investigated the implementation of these algorithms on current Intel distributed-memory parallel computers. The algorithms had been developed for shared-... 

A third class of compound methods are the extrapolation-based procedures due to Martin [5], which attempt to approximate infinite-basis-set URCCSD(T) calculations. In the Wl method [16] calculations are performed at the URCCSD and URCCSD(T) levels of theory with basis sets of systematically increasing size. Separate extrapolations are then performed to determine the SCF, URCCSD valence-correlation, and triple-excitation components of the total atomization energy at... 

In this section, we propose to illustrate how the availability of the CRAY has assisted progress in the area of molecular electronic structure. We shall concentrate on two recent advances, namely, the evaluation of the components of the correlation energy which may be associated with higher order excitations, in particular triple-excitations with respect to a single-determinantal, Hartree-Fock reference function, and the construction of the large basis sets which are ultimately going to be necessary to perform calculations of chemical accuracy, that is one millihartree. 

Table VI CPU times on the CRAY-1 computer required to evaluate the double-excitation/ tD/ triple-excitation/ and quadruple-excitation/ t / components of the correlation energy.

Table VII Fourth-order linked-diagram triple-excitation and quadruple excitation components of the electron correlation energy in a number of atoms and small molecules...

The triple-excitation fourth-order energy, in contrast to the quadruple-excitation component, arises from connected wave function diagrams. The algorithm required to evaluate this energy component is considerably less tractable than that for the quadruple-excitation energy, depending on 7, where n is the number of basis functions. The triple-excitation diagrams can be written in terms of the intermediates. 

Again a number of calculations of the triple-excitation component of the correlation energy have been reported.138 139 141... 

We shall provide an overview of the applications that have been made over the period being review which demonstrate the many-body Brillouin-Wigner approach for each of these methods. By using Brillouin-Wigner methods, any problems associated with intruder states can be avoided. A posteriori corrections can be introduced to remove terms which scale in a non linear fashion with particle number. We shall not, for example, consider in any detail hybrid methods such as the widely used ccsd(t) which employs ccsd theory together with a perturbative estimate of the triple excitation component of the correlation energy. 

EOMCCSD excitation energy and is the n-body component of by the simplified form of it which represents the Mpller-Plesset-like denominator for triple excitations, + e + — e, — — fjt)]. The differences between... 

Efficient computer code for evaluating the numerical values of the energies associated with various coupled cluster approximations is available in a number of quantum chemistry packages. Coupled cluster calculations are more computationally demanding than those based on low order perturbation theory. However, they can support higher accuracy, particularly in cases where there is some quasi-degeneracy. Actually, the so-called gold standard adopted in recent years as a best compromise between computational demands and accuracy, is the hybrid ccsd(t) method which combines use of a coupled cluster expansion with perturbation theory for the triple excitation component. 

We begin our discussion with the results for i c-H = Re- For transitions to states that have a predominantly biexcited nature (the first-excited E state and the lowest two A states) and for the second 11 state that has a significant biexcited component, the errors in the vertical excitation energies at the equilibrium value of Rc-h, obtained with the noniterative MMCC(2,3) approach, are 0.01-0.10 eV (98). This should be compared to the 0.33-. 92 eV errors in the EOMCCSD results, the 0.2-0.3 eV errors obtained with various perturbative triples approaches, and the 0.50-0.88 eV errors in the results obtained with the CISDt approach (see refs 40, 41, 97, 98, and references therein). For other states studied in refs 40, 41, 97, 98 and elsewhere (31,32,35,36) (the third and fourth E" states and the lowest state), the errors in the MMCC(2,3) results, relative to full Cl, are 0.00-0.01 eV (98). The MMCC(2,3) results at Rq-h = Re are as good as or even better than the results provided by the EOMCCSDt method. 

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