Direct MP2 method

The efforts to extend the direct SCF methodology to post-SCF calculations began with the paper by Taylor.Soon afterward, practical implementations of the direct MP2 method were published, almost simultaneously, by Pople s and Almlof s groups. The latter report also considered the direct MP3 method and presented an example of an MP2 calculation with 318 basis functions. The direct post-SCF methods are discussed later in this review. 

The table indicates how resource usage varies by problem size. For example, it indicates that for direct MP2 energy calculations, CPU requirements scale roughly as the fourth power of the number of basis functions if the number of electrons stays the same. Using the table with timings from previous jobs (using the same method and executed on the same computer system) should enable you to estimate how long a potential job will run. 

However, the values in Tables 26-30 are directly calculated BDEs, according to equation 1. Taking only those molecules for which there are reliable experimental information (Table 26), and excluding the problematic (S 2) cases (CCH-, COOH-, NCO-, CN-, NC-, CHCH2- and N3 ) and the decomposed radical (CH3CO2 ), the average MP2 error for CH3—Y is 2.0 kcalmol-1 (21 cases) and for MP4 is 3.8 kcal mol-1 (19 cases). It thus seems that the particular choice of basis set and level of calculation used here gives the best cancellation of errors for the MP2 method. 

Quantum chemical calculations predict the primary ethylcation, C H/" to have /(-hydrido-bridgcd structure 5 which is 6-8 kcal/mol more stable than the Kekule line-bond structure for the primary cation 4. The ethylcation is not stable enough to be observable directly in superacid media. The NMR chemical shifts were calculated for both isomers 4 and 5 using the GIAO-MP2 method for CCSD optimized structures.23... 

A promising recent development in the study of nitrenium ions has been the introduction of time-resolved vibrational spectroscopy for their characterization. These methods are based on pulsed laser photolysis. However, they employ either time resolved IR (TRIR) or time-resolved resonance Raman (TRRR) spectroscopy as the mode of detection. While these detection techniques are inherently less sensitive than UV-vis absorption, they provide more detailed and readily interpretable spectral information. In fact, it is possible to directly calculate these spectra using relatively fast and inexpensive DFT and MP2 methods. Thus, spectra derived from experiment can be used to validate (or falsify) various computational treatments of nitrenium ion stmctures and reactivity. In contrast, UV-vis spectra do not lend themselves to detailed structural analysis and, moreover, calculating these spectra from first principles is still expensive and highly approximate. 

Direct MP2, CCSD methods, 142 Even-tempered basis set, 155 G2nVIP21 G2(MP2SVP > G20 165 ... 

One test of the ability of these methods to accurately follow changes in the properties is to look at the proton affinity. The calculated value (Table 3) for the linear HNN structure at the QCISD(T)/PP//MP2/PV level is 122.9 kcalmol" The ZPE difference between N2 (3.1 kcalmol" ) and linear HNJ (9.8 kcalmoF ) from the MP2 frequencies is 6.7 kcal moF (Table 11). This gives an adjusted QCISD(T) result of 116.2 kcalmoF to be compared with the experimental value of 118.2 kcalmoF The direct MP2... 

The selection of functional directly controls the accuracy of the DFT methods. A study of ORR by hybrid density functional (HDFT) method and MP2 method has been reported by Albu et al. [29, 30]. They evaluated a large number of HDFT methods toward calculation of potential-dependent activation energies for uncatalyzed and Pt-catalyzed oxygen reduction and hydroperoxyl oxidation reactions. In the HDFT methods, the one-parameter hybrid Fock-Kohn-Sham operator is written as... 

In the next sections we briefly discuss the basic ideas of Cl, MCSCF and CC post-HF methods for molecules as they are directly extended to the crystalline solids in the framework of the molecular cluster model. In more detail, the local correlation and MP2 methods are considered both for the molecules and the periodic systems. 

Another Unear-scaUng MP2 algorithm was proposed in [129] that is based on the atomic-orbitals Laplace-transform (LT) MP2 method [137]. In this method, the energy denominators (5.32) in (5.30) are ehminated by Laplace-transformation, which paves the way to express the MP2 energy directly in the basis. The price to pay is the additional Laplace integration, which is carried out by quadrature over a few (8-10) points. For each of the quadrature points an integral transformation has to... 

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