Pople-Hehre method

Tools developed in the previous section will be utilized to analyze some of the different integral evaluation schemes. The mathematics, however, stops at this point, or as Boys states after having the analytic expressions for the simplest ERI ... we can easily derive the formulae for the general class. .. . From this point onwards the principal matter is to make the most efficient use of the tools as possible. The methods covered will involve most of those available in the standard quantum chemistry packages today. The Pople-Hehre method is included for historical reasons as it constituted the first efficient integral code. The early versions of GAUSSIAN owe much of their success to this integral evaluation scheme. 

The Pople-Hehre method was developed primarily to compute integrals for L shell basis sets, and is a method in which the integral classes to (pp pp) are com-... 

As demonstrated by the Pople-Hehre method it is possible to achieve considerable reduction in the computational expense of contracted ERIs if large parts of the integral manipulation are performed after the contraction step. The McMurchie-Davidson and the Obara-Saika methods utilization of the transfer equation (17) to minimize the operation count has been shown. This idea can, however, be employed to the extent that all manipulations are performed on fully or partially contracted integrals. Recently a number of methods have been presented along those lines.The method of Gill and Pople will be used as an example of the approach because it is currently one of the most commonly used integral methods. Note the concept of early contraction, however, applies to any of the methods presented in the chapter. 

It is straightforward and instructive to repeat the Pople, Hehre and Stewart calculations using the spreadsheet method. 

Hehre, W.J. Stewart, R.F. Pople, J.A. Self-consistent molecular-orbital methods. I. Use of Gaussian expressions of Slater-Type Atomic Orbitals 7 Chem. 51 2657-2664, 1969. 

Pietro, W.I. Francl, M.M. Hehre, W.I. Defrees, D.I. Pople, I.A. Binkley, I.S. Self-consistent molecular orbital methods. 24. Supplemented small split-valence basis sets for second-row elements J. Am. Chem. Soc. 104 5039-5048, 1982. 

Self Consistent Molecular-Orbital Methods I. Use of Gaussian Expansions of Slater-Type Atomic Orbitals W. J. Hehre, R. F. Stewart and J. A. Pople The Journal of Chemical Physics 51 (1969) 2657-2665... 

A. Szabo and N. S. Ostlund Modem Quantum Chemistry, McGraw-Hill, 1982 R. McWeeny, Methods of Molecular Quantum Mechanics, Academic Press, 1992 W. J. Hehre, L. Radom, J. A. Pople and P. v. R. Schleyer Ah Initio Molecular Orbital Theory, Wiley, 1986 J. Simons, J. Phys. Chem., 95 (1991), 1017 J. Simons and J. Nichols, Quantum Mechanics in Chemistry, Oxford University Press, 1997. 

Hehre, W. J., Ditchfield, R., Pople, J. A., 1972, Self-Consistent Molecular Orbital Methods. XII. Further Extensions of Gaussian-Type Basis Sets for Use in Molecular Orbital Studies of Organic Molecules J. Chem. Phys., 56, 2257. 

MP2 methods at the 6-31G level using the GAUSSIAN90 program, See W. J. Hehre, L. Radom, P. v. R. Schleyer and J. A. Pople, Ab initio Molecular Orbital Theory, Wiley, New York, 1986. 

Erancl MM, Pietro WJ, Hehre WJ, Binkley JS, Gordon MS, DePrees DJ, Pople JA (1982) Self-consistent molecular-orbital methods. 23. A polarization-type basis set for 2 row elements. J Chem Phys 77 3654-3665... 

W. J. Hehre, R. Ditchfield, and J. A. Pople, Self-consistent molecular orbital methods. Xll. Further extensions of Gaussian-type basis sets for use in molecular orbital studies of organic molecules. J. Chem. Phys. 56, 2257-2261 (1972). 

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