QCISD,

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. 

Higher order methods similarly ought to reproduce the exact solution to their corresponding problem. Methods including double excitations (see Appendix A) ought to reproduce the exact solution to the 2-electron problem, methods including triple excitations, like QCISD(T), ought to reproduce the exact solution to the three-electron problem, and so on. 

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

Methods based on Density Functional Theory also include some electron correlation effects (we ll consider them a bit later in this chapter). Of the traditional post-SCF methods, we ll be primarily using MP2, MP4, QCISD and QCISDfO in this work. 

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. 

Including triply excited configurations is often needed in order to obtain very accurate results with MP4, QCISD or CCSD (see Appendix A for some of the computational details). The following example illustrates this effect. 

The structure of ozone is a well-known pathological case for electronic structure theory. Prior to the QCI and coupled cluster methods, it proved very difficult to model accurately. The following table summarized the results of geometry optimizations of ozone, performed at the MP2, QCISD and QCISD(T) levels using the 6-31G(d) basis set ... 

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. ... 

Optimize the structure of acetyl radical using the 6-31G(d) basis set at the HF, MP2, B3LYP and QCISD levels of theory. We chose to perform an Opt Freq calculation at the Flartree-Fock level in order to produce initial force constants for the later optimizations (retrieved from the checkpoint file via OptsReadFC). Compare the predicted spin polarizations (listed as part of the population analysis output) for the carbon and oxygen atoms for the various methods to one another and to the experimental values of 0.7 for the C2 carbon atom and 0.2 for the oxygen atom. Note that for the MP2 and QCISD calculations you will need to include the keyword Density=Current in the job s route section, which specifies that the population analysis be performed using the electron density computed by the current theoretical method (the default is to use the Hartree-Fock density). 

The B3LYP and QCISD values are in good agreement with one another and with thi experimental observations. Both favor the resonance form with the radical centerec mainly on the C2 carbon. Therefore, we will use the B3LYP/6-31G(d) mode chemistry for the remainder of this study. 

Compute the isotropic hyperfine coupling constant for each of the atoms in HNCN with the HF, MP2, MP4(SDQ) and QCISD methods, using the D95(d,p) basis set Make sure that the population analysis for each job uses the proper electron density by including the Density=Current keyword in the route section. Also, include the 5D keyword in each job s route sectionfas was done in the original study). 

There is rather poor agreement between the QCISD values and all of the lower levels of theory this is a case where the successive MP orders converge rather slowly. Note that the QCISD values differ only a bit from Carmichael s QCISD(TQ) results. It turns out also that MP4(SDTQ) does not improve on the MP4(SDQ) values (accordingly, we chose the cheaper method for this exercise). ... 

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 ... 

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