Stretched geometries

We can also see from Table 1 that very accurated values of NPE are yielded by CAS-SDCI (1.0 mHa), ec-CCSD(CAS-SDCI) (1.3 mHa), (SC)2CAS-SDCI (1.6 mHa) and ec-CCSD((SC) CAS-SDCI) (1.6 mHa as well). It is not the case of standard CCSD which failure at stretched geometries yields 18.6 mHa NPE error. 

The variational 2-RDM method has been applied to a variety of atoms and molecules at both equilibrium and stretched geometries. We will summarize calculations on a variety of molecules (i) the nitrogen molecule [31], (ii) carbon monoxide with and without an electric field [37], (iii) a set of inorganic molecules [34], (iv) the hydroxide radical [35], and (v) a hydrogen chain [28]. 

In both the HF molecule and BH molecules, the HF/L-CTSD and HF/L-CTD theories give energies comparable to CCSD at the equilibrium geometry. However, as the bond is stretched, they both display significantly increased errors, typical of a single-reference theory. At stretched geometries, the errors of the HF/L-CTSD method are worse than those of CCSD and comparable to those of the linearized CCSD theory. 

The essential role of the size-consistency in molecular applications is strikingly conspicuous already in the SR case. Indeed, the SR CCSD method is manifestly size-extensive, yet it fails when breaking genuine chemical bonds, as the well-known examples illustrate [82,83]. This breakdown is of course most prominent when multiple bonds are involved, as the example of the CCSD PEC for N2, shown in Fig. 1, clearly illustrates [83]. Note that even when we employ the UHF reference, we will not generate a smooth PEC in view of the presence of the triplet instability (see, e.g., [84, 85] and references therein), whose onset occurs at an intermediately stretched geometry [86]. 

Table 7.4 Average errors in correlation energies (kcal mol ) compared to full CI for various methods applied to HB, H2O, and HF at both equilibrium and bond-stretched geometries...

Level of theory Equilibrium geometry Equilibrium and stretched geometries... 

A full Cl wavefunction is invariant to orbital rotations and even to the choice of the reference function. By contrast, the simple CISD method is quite sensitive to the choice of reference and orbitals. This explains the poor performance of CISD when the bonds are stretched in H2O (cf. Table 2) the SCF wave-function becomes an inadequate reference at stretched geometries, and CISD is unable to overcome this inadequacy. Such difficulties can occur even at equilibrium geometries if multiple low-lying electronic states are present. For... 

The above outlined almost-linear (AL) versions of the RMR CCSD method have been applied to several model systems involving four and eight hydrogen atoms, as well as to a double zeta (DZ) model of the water molecule at both the equilibrium and stretched geometries. 

Atom Equilibrium geometry Stretched geometry Bent geometry External field ... 

Table 4 gives the deviation of CCSD-I-T(CCSD) and CCSD(T) energies from the corresponding FCl results for the same cases used before to evaluate the accuracy of the other CC methods. The comparison with CCSDT emphasizes the excellent performance of the CCSD(T) approach. The agreement with CCSDT is in all cases similar to that achieved in the iterative CCSDT-1 calculations. The results for CCSD -I- T(CCSD) obtained for the stretched geometries illustrate the overestimation of the pure fourth-order correction, as the calculated energies are considerably lower than the corresponding CCSDT values. 

Table IIS.1.1 The weights of the even-order excitation levels for m ground-state water molecules, calculated in the cc-pVDZ basis at the reference geometry and at the stretched geometry 2R f...

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