QCISD method

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. ... 

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). 

A disadvantage of all these limited Cl variants is that they are not size-consistent.The Quadratic Configuration Interaction (QCI) method was developed to correct this deficiency. The QCISD method adds terms to CISD to restore size consistency. QCISD also accounts for some correlation effects to infinite order. QCISD(T) adds triple substitutions to QCISD, providing even greater accuracy. Similarly, QCISD(TQ) adds both triples and quadruples from the full Cl expansion to QCISD. 

The QCISD method is also very closely related to coupled cluster theory, with singles and doubles (CCSD). In contrast to QCISD. 

Tables 6.6 - 6.8 present calculated [22] and experimental [3, 26, 35] heats of formation for a selection of small radicals, determined with the atomization approach. As these data show, all theoretical levels give good overall performance (MADs of 2.1 - 4.5 kJ/mol). Wl is the highest level of theory represented in these tables and indeed performs very well, with an MAD of 3.2 kJ/mol and an LD of +6.8 kJ/mol. The G2-RAD(QCISD) method gives the best statistical performance with an MAD of 2.1 kJ/mol and an LD of +5.6 kJ/mol. However, because of the modest number of comparisons, such differences are only of marginal significance. The G3-RAD approach also performs particularly well with an MAD of 2.5 kJ/mol and an LD of -5.5 kJ/mol. Overall, the G2-RAD(QCISD) method tends to slightly overestimate the heats of formation of the selected radicals (MD of +0.8 kJ/mol) while its G3-RAD counterpart tends to underestimate them (MD of -2.0 kJ/mol). Both of these modified Gn methods offer improved performance over the standard G2 and G3 procedures. However, the G3(MP2)-RAD approach performs less well (MAD of 4.5 kJ/mol) than G3(MP2) (MAD of 3.6 kJ/mol).

While it is well established that HO—ONO can be involved in such two-electron processes as alkene epoxidation and the oxidation of amines, sulfides and phosphines, the controversy remains concerning the mechanism of HO-ONO oxidation of saturated hydrocarbons. Rank and coworkers advanced the hypothesis that the reactive species in hydrocarbon oxidations by peroxynitrous acid, and in lipid peroxidation in the presence of air, is the discrete hydroxyl radical formed in the homolysis of HO—ONO. The HO—ONO oxidation of methane (equation 7) on the restricted surface with the B3LYP and QCISD methods gave about the same activation energy (31 3 kcalmol" ) irrespective of basis set size . ... 

FIGURE 1. The stationary points of reactions EH2 + H2 - EH4 E = Si369,371, Ge369, calculated with B3LYP, MP2, and QCISD methods. The symmetry group is given below each structure ... 

There are a few minor variations on the CC methods. The quadratic configuration interaction including singles and doubles (QCISD)" ° method is nearly equivalent to CCSD. Another variation on CCSD is to use the Brueckner orbitals. Brueckner orbitals are a set of MOs produced as a linear combination of the HF MOs such that all of the amplitudes of the singles configurations ( f) are zero. This method is called BD and differs from CCSD method only in fifth order." Inclusion of triples configurations in a perturbative way, BD(T), is frequently more stable (convergence of the wavefunction is often smoother) than in the CCSD(T) treatment. 

This inclnsion of electron correlation can be accomplished in several ways. One method has been to nse Mpller-Plesset (MP) pertnrbation theory. This theorized that the electron correlation was a perturbation of the wavefnnction, so the MP perturbation theory conld be applied to the HF wavefnnction to inclnde the electron correlation. As more perturbations are made to the system, more electron correlation is inclnded (these methods are denoted MP2, MP3, and MP4). Another method is to calculate the energy of the system when electrons are moved into vacant orbitals. These methods move electrons either one at a time (single), two at a time (double, such as the QCISD method), or three at a time (triple, such as the QCISDT method). These methods calculate energy values more accurately but at greater computational cost. 

Figure All. A comparison of the scaling and the approximate number of heavy atoms that can be handled by different theoretical treatments in the general order of increasing scaling and increasing accuracy. While the CISD and QCISD methods provide much more accuracy, the systems that can be examined are significantly smaller.

Use of this fact is also made in the Davidson correction for quadruples and in the Pople QCISD method.It has been demonstrated that QCISD amounts to an approximate CCSD method ° ° but, in most (but not alP ) cases, the additional terms that appear in the full CCSD equations appear to cancel for chemical reactions, since the results obtained by the two methods are often nearly the same.- ... 

Analytic computation of force constants (nuclear coordinate second derivatives), polarizabilities, hyperpolarizabilities, and dipole derivatives for the RHF, UHF, DFT, RMP2, UMP2, Cl-Singles, and CASSCF methods. Numerical computation of second derivatives for the MP3, MP4(SDQ), CID, CISD, CCD, and QCISD methods. Harmonic vibrational analysis and thermochemistry analysis using arbitrary isotopes, temperature, and pressure, and determination of IR and Raman intensities for vibrational transitions. 

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