Basis sets dissociation curves

Figure 11.1 shows the bond dissociation curve at the HF level with the STO-3G, 3-21G, 6-31G(d,p), cc-pVDZ and cc-pVQZ basis sets. The total energy drops considerably upon going from the STO-3G to the 3-21G and again to the 6-3IG(d,p) basis. This is primarily due to the improved description of the oxygen Is-orbital. The two different... 

We will now look at how different types of wave functions behave when the O-H bond is stretched. The basis set used in all cases is the aug-cc-pVTZ, and the reference curve is taken as the [8, 8J-CASSCF result, which is slightly larger than a full-valence Cl. As mentioned in Section 4.6, this allows a correct dissociation, and since all the valence electrons are correlated, it will generate a curve close to the full Cl limit. The bond dissociation energy calculated at this level is 122.1 kcaPmol, which is comparable to the experimental value of 125.9 kcal/mol. 

Table 1. shows the total energies obtained using the RHF method for 1. LCAO minimal basis set STO-IG for the sake of comparison with FSGO, 2. FSGO in its symmetric and broken symmetry solutions and, 3. LCAO minimal basis set STO-3G in order to allow a safer comparison with the quality of the subminimal basis used in the FSGO technique. The dissociation curves are given in Figure 1. 

For sake of comparison, in all studied cases, we run calculations for those geometries and basis sets with a FCI (or near FCI) available. The methods we deal with are CCSD, CAS-SDCI, (SC)2CAS-SDCI and ec-CCSD corrected from both CAS-SDCI and (SC) CAS-SDCI. The performance of the methods is examined from two aspects the total energy and the quality of the potential energy surface (PES), being this quality measured by the so-called non-parallelity error (NPE). For a given set of calculations in a dissociative curve, the NPE is defined as the difference between the maximal and minimal deviation from the exact FCI PES. 

The BOVB method has been successfully tested for its ability to reproduce dissociation energies and/or dissociation energy curves, close to the results (or estimated ones) of full Cl or to other highly accurate calculations performed with the same basis sets. A variety of two-electron and odd-electron bonds, including difficult test cases as F2, FH, and F2 (38,42), and the H3M-C1 series (M = C, Si, Ge, Sn, Pb) (39,43,44) were investigated. 

By nature, the BOVB method describes properly the dissociation process. As a test case, the dissociation curve of the FH molecule was calculated at the highest BOVB level (extended SD-BOVB), and compared with a reference full Cl dissociation curve calculated by Bauschlicher et al. [33] with the same basis set. The two curves, that were compared in Ref. 12, were found to be practically indistinguishable within an error margin of 0.8 kcal/mol, showing the ability of the BOVB method to describe the bonding interaction equally well at any interatomic distance from equilibrium all the way to infinite separation [12]. 

Schaefer250 has gone beyond the Hartree-Fock approximation and computed the ground-state PE curve, using first-order wavefunctions.251 A contracted STO basis set has been used, with 128 configurations included. The molecule now dissociates to two oxygen atoms, and De was computed to be 4.72 eV (expt. 5.21 eV). Spectroscopic constants were usually in better agreement with experiment than a previous minimal-basis full Cl calculation. The value of Re obtained was close to the experimental value. 

The HF calculations predict a 3II ground state, which is the same as found for CaO, but as noted above, Cl might well reverse this ordering, and it is clear that very extensive calculations are needed before this question is definitely settled. A very recent paper reporting PE curves for BeO, MgO, and CaO, using DZ + P basis sets, has also appeared,310 and the authors also discuss the dissociation behaviour of the ground state. Calculation of the spin-orbit matrix elements shows that 3I1 and 12+ states are not significantly mixed. 

Relativistic Methods 204 8.1 Connection Between the Dirac and Schrodinger Equations 207 8.2 Many-particle Systems 210 8.3 Four-component Calculations 213 11.4.1 Ab Initio Methods 272 11.4.2 DFT Methods 273 11.5 Bond Dissociation Curve 274 11.5.1 Basis Set Effect at the HF Level 274 11.5.2 Performance of Different Types of Wave Function 276... 

The ground state of NH3O has a long NO bond (1.689 A) and the potential energy curves for the dissociation to NH3(/1i) and OQD) were obtained. Population analyses were presented, and NH3O was predicted to be ca. 126 kJ mol less stable than NH2OH, a result rather similar to that obtained by Trindle with a smaller basis set. 

Calculated DFT properties listed in Table 1 were obtained from the fit of the ground-state potential energy curves to 12 points calculated around the energy minimum [32]. Dissociation energy has been corrected for basis set superposition error by a standard counterpoise technique. The local approximation to the exchange and correlation gives the best fit to bond distances, theoretical values differ by no more than 0.03 A (4%) from the experimental ones (see Table 1). Vibrational frequencies are also predicted to lie within 1 % off the experiment. One should remember, however, that other advanced quantum chemical methods give equally satisfactory results for these, basicaly one-electron quantities and that inclusion of nonlocal effects does not improve the DFT predictions. The dipole moment, fi, is much more sensitive... 

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