2R-CISD

CISD gives about the same NPE as for the ground state, while 2R-CISD deteriorates in the nondegenerate region, so that the corresponding NPE is almost three-times as large as for the ground state. 

A similar situation to that just described for the 2R CISD will clearly arise in the general case, the number of quadruples involved being proportional to the dimension of the model space. Nonetheless, these quadruples will represent a very small subset of all possible quadruples, their number being essentially a multiple of the number of doubles by the factor (M — 1), M being the number of reference configurations. Moreover, these quadruples will be used only once to correct the absolute term of CCSD equations. 

We first consider the standard double-zeta (DZ) model of the HE molecule. Relying on the minimal 2-electron/2-active-orbital space, we employ both the 2R space spanned by IOq) = laaaP) and WE>i) = la (xa P), and the 4R space spanned by IOo>, lOi), = iaaa p), and lOa) = la ocap). In Table IV, we list the FCI energies for the five geometries (namely for R=Re=l.l33 bohr, 1.5/ , 2Rg, 2,5Rg, and 3Re), and the energy differences relative to the FCI as obtained with the CCSD, 2R-CISD, 2R-CISD+EN(2), CCSD-[2R], and with 4R-CISD, 4R-CISD+EN(2), and CCSD-[4R] methods. 

The CCSD error increases from 1.6 millihartree (mhartree) at Rg to 11.6 mhartree at 3Rg, an increase of about 10 mhartree. The 2R-CISD error increases by about the same amount. The 4R-CISD method performs better, and its errors are within the 5.7—7.5 mhartree range. With the second-order EN perturbation corrections to a small MR CISD wave function, we also get good results. For 2R-CISD+EN(2), the deviations are less than 1 mhartree, and for 4R-... 

Although the 8R CISD results are reasonably good, they are far from being satisfactory, since the deviations from the FCI increase from 13 mhartree at Rg to 38 mhartree at 3Rg. However, when we compute the energy 5, combining effectively CCSD with 8R CISD, or even 4R CISD, we get much improved results The CCSD-[8R] errors are within 5—18 mhartree, and the CCSD-[4R] ones are within 5—17 mhartree. Yet, using the smallest 2R CISD, the CCSD-[2R] PEC still shows a hump. 

It is interesting to compare the MR-CISD+EN(2) results with the CCSD-[MR] ones for M= 2, 4, and 8. Qualitatively, they are very similar. In both cases the smallest 2R space is not large enough to eliminate the CCSD hump, even though CCSD-[2R] yields a better result than 2R-CISD+EN(2). With 4R and 8R spaces, the MR-CISD+EN(2) absolute errors are smaller for R g [Re,l,5Re than CCSD-[MR] ones, but for R > l.SRg, the 4R-CISD+EN(2) error increases much faster than the corresponding CCSD-[4R] error. Indeed, over the interval Rgmore than 2.5 mhartree over the entire range of intemuclear separations. 

Table II. The SR, 2R, 4R and (2/2)R CISD ground state energies together with various Davidson-type corrections relative to the FCI energy (in mH) for the DZP H4 model with 0 < a < 0.5. The nonparallelism errors (NPE) are givenin the last two rows. See the text for details. 

Table 11 The CISD monomer correlation energy (in mEh) for one to eight noninteracting water molecules, calculated in the cc-pVDZ basis with and without the Davidson correction applied. The weight of the Hartree-Fock configuration in the CISD wave function IVhf is also listed. The calculations have been carried out for the C2 water molecule with R = / ref and R = IR ct where Rra = 1.84345ao- The HOH bond angle is fixed at 110.565°. At Rnt and 2R,et, the Hartree-Fock energies are —76.0240 and —75.5877 Eh, respectively, and the t CI correlation energies are —217.8 and —364.0 mEh, respectively...

---