Pople diagram

The size of the basis set is, however, only one criterion for judging the level of an ab-initio calculation. The situation is best illustrated by what has become known as a Pople diagram [27], as shown in Figure 7-24. 

Figure 7-24. The Pople diagram . The vertical axis gives the size of the basis set and the horizontal axis the correlation treatment. The basis sets and methods given are chosen from the examples discussed in the text. Their positions on the axes (but not the order) are arbitrary.

Fig. 1. Pople diagram (8) illustrating the dependence of the accuracy of a computational method on the basis set and the treatment of correlation.

Karplus, M. 1990. Three-dimensional Pople diagram. Journal of Physical Chemistry 94 5435-5436. 

A useful tool for considering the quality of a quantum chemical calculation is the Pople diagram. Figure 5.1 shows a 3-dimensional version, suitable for use in the simulation of f-element complexes. The three axes of the Pople diagram represent the quantum chemical methodology, the chosen basis set, and the treatment of relativity, respectively. The main aim of this diagram is to ensure that a balanced calculation is performed, i.e., relevant... 

Figure 5.1 Three dimensional Pople diagram. The three axes correspond to quantum chemical methodology, basis set, and treatment of relativity...

Indazoles have been subjected to certain theoretical calculations. Kamiya (70BCJ3344) has used the semiempirical Pariser-Parr-Pople method with configuration interaction for calculation of the electronic spectrum, ionization energy, tt-electron distribution and total 7T-energy of indazole (36) and isoindazole (37). The tt-densities and bond orders are collected in Figure 5 the molecular diagrams for the lowest (77,77 ) singlet and (77,77 ) triplet states have also been calculated they show that the isomerization (36) -> (37) is easier in the excited state. 

Fig. 4.16 Phase diagram for aqueous solution of PEO iBio determined using SAXS and rheometry (Pople et al. 1997). The filled symbols mark the phase boundaries determined by SAXS, with the broken line as a guide to the eye, and the solid lines mark transitions determined using rheology (Deng et al. 1995 Pople et al. 1997). The error bars indicate uncertainties associated with the phase transitions determined from repeated heating and cooling ramps.

The next critical element in the development of CC theory was to incorporate the connected triple excitations, Tj,. Since even CCD puts in the dominant quadruple excitation effects, and CCSD some of the disconnected triple excitations effects, the only term left in fourth-order MBPT comes from T, and the triples will be much more important to CC theory than to Cl, since CIs unlinked diagrams have a very large role that can only be alleviated by putting in quadruple excitations (see Fig. 42.1). Triples had been explored in the ECPMET discussed above. Kvasnicka et al., Pople et al., Guest and Wilson, Urban et al., and ourselves had included triples in fourth-order MBPT = MP4 [59-64], but no attempt had been made to introduce them into general purpose CC methods. In 1984 we wrote a paper detailing the triple excitation equations in CC theory and reported results for CCSDT-1 [65], which meant the lead contribution of triples was included on top of CCSD. This also made it possible to treat triple excitations on-the-fly in the sense that we never required storage of the n N amplitudes. 

Figure 5.7 Application of the general spreadsheet to the calculation of the energy of the helium atom using the Pople, Hehre and Stewart sto-6g) basis set of Table 1.6 and the best Slater exponent, also reported elsewhere (8,9) from variation of the entry in cell oneel D l. For the Slater-rules exponent, 1.7, the helium energy is found to be —2.8461945 hartree with the Is orbital energy equal to —0.8918763 H. Note, the detail shown for the Vijkl term. On this spreadsheet all 1296 [6 integrals] are calculated, with the degeneracies over the primitives, colour-coded in the second diagram in the figure.

Fig. 5.4. The phase diagram of the Pariser-Parr-Pople model at half-filling, t = 2.5 eV.

The phase diagram of the undoped Pariser-Parr-Pople model... 

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