QCISD energies

Among the most widely used ab initio methods are those referred to as Gl" and 02." These methods incorporate large basis sets including d and / orbitals, called 6-311. The calculations also have extensive configuration interaction terms at the Moller-Plesset fourth order (MP4) and fiirther terms referred to as quadratic configuration interaction (QCISD). ° Finally, there are systematically applied correction terms calibrated by exact energies from small molecules. 

Quadratic Cl energies, optionally including triples and quadruples terms (QCISD, QCISDOl, and QCISDfTQI) and optimizations via analytic gradients for QCISD. 

We can compute all of the results except those in the first row by running just three jobs QCISD(T,E4T] calculations on HF and fluorine and a Hartree-Fock calculation on hydrogen (with only one electron, the electron correlation energy is zero). Note that the E4T option to the QCISDfT) keyword requests that the triples computation be included in the component MP4 calculation as well as in the QCISD calculation (they are not needed or computed by default). 

The experimental value for the H-F bond energy is 141.2 kcal-mol. The Hartree-Fock value is in error by over 40 kcal-mol" (we ve also included the HF/ STO-3G values to indicate just how bad very low level calculations can be). However, both the MP4 and QCISD(T) values are in excellent agreement with experiment. 

Compute the isomerization energy between acetaldehyde and ethylene oxide at STP with the QCISD(T)/6-31G(d) model chemistry, and compare the performance of the various model chemistries. Use HF/6-31G(d) to compute the thermal energy corrections. Remember to specify the scaling factor via the Freq=Recxllso option. (Note that we have already optimized the stmcture of acetaldehyde.)... 

MP4 and the two QCISD methods, the predicted isomerization energy v/ould continue to converge toward the experimental value as the basis set size increases. ... 

The short summary of these results is that none of these model chemistries is very accurate at modeling this process in toto. Some of them achieve good results on either the component dissociation energies or the final value of AH, but no method does well for all of them. Not even QCISD(T) at the very large 6-311+G(3df) basis set Ls adequate. A compound energy method is required to successfully address thus problem. We will see such a solution in the next chapter. ... 

Correct the base energy for residual correlation effects (to countera known deficiencies of truncating perturbation theory at fourth order) 1 computing the QCISD(T)/6-311G(d,p) energy. Subtract E from th energy to produce AE ... 

The quantity is essentially an apprortimation to an energy calculated directly at QCISD(T)/6-311+G(2df,p). Replacing this one very large calculation with four smaller ones is much fester. The components of a G1 calculation are summarized in steps 1 through 7 of the following table ... 

Make a plot of bond distance versus energy for the restricted and unrestricted method scans of methane for the HF, MP2, MP4, and QCISD(T) levels. 

For each system, plot the bond distance versus energy for each of the reported levels of theory. For CH, this will mean plotting the HF, MP2, MP3, and full MP4 (i.e., MP4(SDTQ)) energies at each point. For methane, include the HF, MP2, MP3, lull MP4, QCISD, and QCISD(T) levels. 

The importance of the triples contribution with QCISD theory is clearly illustrated in the enlargement. The QCISD curve is very near the MP4 curve. The authors of the paper from which this exercise is drawn emphasized the importance of the single and triples to the MP4 level, but nevertheless concluded that MP4(SDTQ) was not an adequate representation of the potential energy surface in the intermediate region... 

An infinite-order correction is similarly made to MP4 or QCISD(T) energies (approximate full Cl energies) ... 

To correct for electron correlation beyond QCISD(T) and basis set limitations, an empirical correction is added to the total energy. 

The energy is calculated at the MP4(SDQ)/6-31G(d,p) and QCISD(T)/6-31+G(dt) levels to estimate the effect from higher-order electron conelation. 

The free energy of activation at the QCISD(T)/6-31 H-- -G(d,p) level amounts to 21.1 kcal/mol. According to the authors, the large electron density redistribution arising upon cyclization makes it necessary to use extended basis sets and high-order electron correlation methods to describe the gas-phase thermodynamics, which indicates clearly the gas-phase preference of the azido species. However, the equilibrium is shifted toward the tetrazole as the polarity of a solvent is increased. For instance, SCRF calculations (e = 78.4) yield a relative free energy of solvation with respect to the cw-azido isomer of —2.4 kcal/mol for the tmns-zziAo compound and of —6.8 kcal/mol for the tetrazole isomer. At a much lower level, the... 

To obtain a satisfactory evaluation of relative energies, especially for the computation of activation barriers, higher levels of theory than those needed to obtain the underlying geometries are usually required. MP2 is the most economical and popular method of incorporation electron correlation. For a more accurate theoretical estimate, higher-level of correlation treatment such as QCISD(T) or CCSD(T) theory is desirable. 

---