Experimental frequencies CCSD methods

The CCSD results of Salek et al (2005) and the MCSCF results of Luo et al (1993) compute the frequency dependence as an intrinsic part of the correlated calculation. The work of Sim et alP (1993) and Reiss et al. (2005) takes the static value obtained at the MP2 level and scales it using the RPA method to get the frequency dependence. Luo et alP (1993) also report the result of an RHF/RPA calculation where the frequency dependence is the natural extension of the RHF method. The plotted points are at the four readily available laser frequencies that have been used in almost all experimental work. The most popular of these has been the YAG frequency corresponding to 1.17 eV or 1064 nm. At this frequency the spread of results ranges from about 1550 to 2600 au. If only the two fully frequency-dependent correlated calculations are considered the range is from about 1700 to 2600 au. Salek et al, using the CCSD method find that as the frequency is increased from zero to 1.17 eV, increases from 1736 to 2667 au and Luo et al, using MCSCF, from 1373 to 1898 au. 

For the vibrational frequencies, the CAS(2,2)CCSD method performs noticeably better than the CAS(2,2)CISD[+Q]. This can be seen by examining the standard deviations shown in Table 3.9. In Table 3.11 some selected spectroscopic constants calculated for FH in the ground eiectronic state (X S+) are shown. The results are compared with the experimental values taken from Huber and Herzberg [64], with the exception of the dissociation energy, Dg, which was taken from Lonardo and Douglas [74]. To calculate the spectroscopic constants we used the numerical differentiation formulas. As one can expect, the values of the spectroscopic constants... 

Table I. Mean absolute deviations of computed from experimentally observed vibrational frequencies for levels from Vi to Vi, Ave(Vi-V2), for the HF molecule obtained with CCSD and 4R-RMR CCSD methods and cc-pVXZ (X=D9T9Q) basis sets.

Table III. Average deviations of calculated from experimental frequencies in the vibrationally excited Rano n bands of the N2 molecule, as obtained with the CCSD, 4R- and 8R-RMR CCSD methods and cc-pVTZ basis set The last column gives the range of experimentally available rotational / values, /min /inax9 d the difference between the maximum and minimum deviations for this range of rotational sublevels is enclosed in parentheses.

If not otherwise stated the four-component Dirac method was used. The Hartree-Fock (HF) calculations are numerical and contain Breit and QED corrections (self-energy and vacuum polarization). For Au and Rg, the Fock-space coupled cluster (CC) results are taken from Kaldor and co-workers [4, 90], which contains the Breit term in the low-frequency limit. For Cu and Ag, Douglas-Kroll scalar relativistic CCSD(T) results are used from Sadlej and co-workers [6]. Experimental values are from Refs. [91, 92]. 

In Table 3 the computed and experimental harmonic frequencies are given. In general the B3LYP frequencies are within 4% of the experimental values. In all cases, except CrO and CuO, B3LYP overestimates the frequencies. The B3LYP results are of similar accuracy as the ab initio results of Bauschlicher and Maitre. The average absolute deviations from the experimental values are 3.2% in both studies. A noteworthy difference is seen for MnO, where B3LYP overestimates the vibration frequency by 34 cm-1 (4%) and the ab initio CCSD(T) method underestimates it by 46 cm-1 (5%). 

The structural parameters and vibrational frequencies of three selected examples, namely, H2O, O2F2, and B2H6, are summarized in Tables 5.6.1 to 5.6.3, respectively. Experimental results are also included for easy comparison. In each table, the structural parameters are optimized at ten theoretical levels, ranging from the fairly routine HF/6-31G(d) to the relatively sophisticated QCISD(T)/6-31G(d). In passing, it is noted that, in the last six correlation methods employed, CISD(FC), CCSD(FC),..., QCISD(T)(FC), FC denotes the frozen core approximation. In this approximation, only the correlation energy associated with the valence electrons is calculated. In other words, excitations out of the inner shell (core) orbitals of the molecule are not considered. The basis of this approximation is that the most significant chemical changes occur in the valence orbitals and the core orbitals remain essentially intact. On... 

Based on the optimized structure, the harmonic vibrational frequencies of Nf have been calculated at the CCSD(T)/6-311+G(2d) level, and these results are listed in Table 5.8.4, along with the experimental data. Comparing the experimental and calculated results, we can see that there is fairly good agreement between them, bearing in mind that the calculations are done on individual cations and experimental data are measured in the solid state. Such an agreement lends credence to the structure optimized by theoretical methods. 

Calculated interaction energies (corrected for the basis set superposition error and ZPE) are relatively large and amount to 9.8 kcal mol-1 by B3LYP and 8.9 kcal mol-1 by CCSD(T) methods. Harmonic vibration frequencies calculated for monomers and the complex are in reasonable agreement with experimental data241. Agreement is good for IR band shifts due to complexation and isotopic substitution. 

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