UMP2 methods

PUMP2 Projected (—>) UMP2 method, whereby higher spin contaminants are removed from the UMP2 wavefunction. 

In Gaussian, open shell calculations are requested by prepending the method keyword with a U (for unrestricted) similarly, closed shell calculations use an initial R (for example, RHF versus UHF, RMP2 versus UMP2 and so on). ... 

Perturbative approximation methods are usually based on the Mpller-Plesset (MP) perturbation theory for correcting the HF wavefunction. Energetic corrections may be calculated to second (MP2), third (MP3), or higher order. As usual, the open- versus closed-shell character of the wavefunction can be specified by an appropriate prefix, such as ROMP2 or UMP2 for restricted open-shell or unrestricted MP2, respectively. 

The main feature of the CBS (complete basis set) methods (e.g. CBS-Q [15] and CBS-QB3 [20]) is extrapolation to the complete basis set limit at the UMP2 level. Additional calculations [UMP4 and UQ-CISD(T) or UCCSD(T)] are performed to estimate higher-order effects. A scaled ZPVE, together with a size-consistent empirical correction and a spin-contamination correction, are added to yield the total CBS energy of the molecule. 

It is often assumed that there will be substantial cancellation of errors associated with the calculation of stabilization energies via reactions such as (6.2). However, this is not always the case. In particular, it has recently been shown [21, 34] that stabilization energies calculated for the cyanomethyl and cyanovinyl radicals show large variation with level of theory. For these situations, methods such as UMP2 perform very poorly because errors associated with spin contamination in the reactant and product radicals are very different and do not cancel. 

For example, the UMP2 level of theory performs poorly, the RB3LYP approach predicts higher (by ca. 5-6 kJ/mol) barriers than its UB3LYP counterpart, and the G3(MP2)-RAD level of theory gives a higher barrier than the CBS-RAD method. One noticeable difference is the absence of a significant basis-set effect in the DFT calculations on the intramolecular addition. 

Figure 3. The shapes of the potential energy curves of the OH radical from the 2-RDM methods with DQG and DQGT2 conditions as well as the approximate wavefunction methods UMP2 and UCCSD are compared with the shape of the FCl curve. The potential energy curves of the approximate methods are shifted by a constant to make them agree with the FCl curve at equilibrium or 1.00 A. The 2-RDM method with the DQGT2 conditions yields a potential curve that within the graph is indistinguishable in its contour from the FCl curve.

Barone and coworkers250 also determined EPR hyperfine splittings nN of the radical 40 at the UMP2/DZ + P level of theory using the Fermi contact operator and a finite field method with an increment size of 0.001 a.u. Expectation values of aN, < aN >, at higher temperatures T were calculated by assuming a Boltzmann population of vibrational levels according to equation 23 ... 

Bond distances for phenoxyl radical, calculated by using CASSCF,(25, 34) UHF, UMP2, and various density functional methods.(2 ) Carbon atom numbering starts with Ci bonded to the oxygen and proceeds around the ring. Except for the first column of CASSCF calculations. 

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