Basis sets spectroscopic constants

The CPF approach gives quantitative reement with the experimental spectroscopic constants (24-25) for the ground state of Cu2 when large one-particle basis sets are used, provided that relativistic effects are included and the 3d electrons are correlated. In addition, CPF calculations have given (26) a potential surface for Cus that confirms the Jahn-Teller stabilization energy and pseudorotational barrier deduced (27-28) from the Cus fluorescence spectra (29). The CPF method has been used (9) to study clusters of up to six aluminum atoms. 

Many of these points are well illustrated by Cu2, which has become a benchmark for theoretical calculations owing to its relative simplicity and the availability of accurate experimental data. The theoretical spectroscopic constants are quite poor unless the 3d electrons are correlated, even though both Cu atoms nominally have a 3d °4s occupation. In fact, quantitative agreement with experiment is achieved only if both the 3d and 4s electrons are correlated, both higher excitations and relativistic effects are included, and large one-particle basis sets, including several sets of polarization functions, are used (24,25). This level of treatment is difficult to apply even to Cua, let alone larger Cu clusters. 

The low-lying excited states of the hydrogen molecule conhned in the harmonic potential were studied using the configuration interaction method and large basis sets. Axially symmetric harmonic oscillator potentials were used. The effect of the confinement on the geometry and spectroscopic constants was analyzed. Detailed analysis of the effect of confinement on the composition of the wavefunction was performed. 

Table I. CCSD(T) spectroscopic constants calculated for the 11 state of YC using the new ECP-based cc-pVnZ-PP (V/tZ-PP) and all-electron cc- pVQZ (-NR and -DK) basis sets for Y and cc-pV/fZ for C...

Table II. CCSD(T) spectroscopic constants calculated for the X state of HgH using the new ECP-based cc-pVwZ-PP (VifZ-PP) and aug-cc-pViiZ (AV/fZ-PP) basis sets for Hg. The cc-pViiZ and aug-cc-pVwZ basis sets were...

In Table 5.3 we list MRCI+Q spectroscopic constants for N2 obtained with one of our largest basis sets. Of the remaining errors compared to experiment, we can estimate that about 0.001 A of the error in the bond length arises from relativistic effects [71]. These would also increase the frequency slightly. Explicit calculations... 

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. 

This Report deals with the calculation of spectroscopic constants both for diatomic and for polyatomic molecules, while concentrating on the former. The spectroscopic constants included are restricted to those measured in high-resolution gas-phase work. We cover the whole range of complexity in computation since this is determined not by the method used in computing the expectation value, but by the quality of the wavefunction used. Generally the wavefunctions used are of the ab initio type, but their quality will depend on the size and type of basis set employed as well as the method. 

We shall compare the potential curves obtained with the two different methods. Second order perturbation theory (CASPT2) has been used to estimate the remaining correlation effects in the FCI calculation with the smaller number of orbitals. This approach will be described in detail below. The spectroscopic constants are presented in Table 5-2. As can be seen, the two results are almost identical. The results are obviously far from experiment because of the small basis set used but that is not relevant to the present discussion. With the smaller number of orbitals we can now perform much more advanced calculations using larger basis sets and approach the experimental values. As an illustration, such a result is also given in the table. 

Table 5-2. Spectroscopic constants for the N2 molecule obtained with different methods and the DZ basis set...

Table 6-8. Spectroscopic constants of the ground state of Pb2 (Og), with various basis sets at the DC-CASPT2 level. BSSE is estimated by counterpoise correction (CPC)...

Table 6-9. Spectroscopic constants of low-lying states of Pb2 molecule (0g(I), Og(III) and 1U(I)), at the DC-CASPT2 level. The size of basis set for Pb is [25s2 lp 14d9f]/(10s9p5d3f)...

Another problem of a rigorous comparison of ab initio results with experiment is encountered with any observable which Is determined by a polynomial fit to calculated points. Some molecular properties (mainly spectroscopic constants) depend on the fitting procedure rather strongly and if an inappropriate fit is used the discrepancies with experiment which are found may be erroneously assigned to basis set or correlation effects. 

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