Integral evaluation method

The use of Slater-type orbitals as basis functions is currently feasible only for atoms, diatomics and, with effort, linear polyatomic molecules. However, research into more powerful methods continues and the physical attractiveness of these functions is such that the development of effective integral evaluation methods would be a major breakthrough in quantum chemistry. 

Ak N mm complementary deformation energy, used in the /-integral evaluation method of Merkle and Corten... 

Figure 4.21. Determination of the parameters of a type 2 kinetic model (Fig. 4.12) using integral data evaluation methods. In (b), the Walker diagram shows a corre> sponding integral evaluation method for various kinetic equations. (Adapted from Wilderer, 1976.)...

The program can use conventional, in-core, or direct integral evaluation. The default ah initio algorithm checks the disk space and memory available. It then uses an in-core method if sufficient memory is available. If memory is not available for in core evaluation, the program uses a conventional method if... 

One of the major selling points of Q-Chem is its use of a continuous fast multipole method (CFMM) for linear scaling DFT calculations. Our tests comparing Gaussian FMM and Q-Chem CFMM indicated some calculations where Gaussian used less CPU time by as much as 6% and other cases where Q-Chem ran faster by as much as 43%. Q-Chem also required more memory to run. Both direct and semidirect integral evaluation routines are available in Q-Chem. 

The most significant treatment of excited states within the CNDO approach is that of Del Bene and Jaffe, who made three modifications to the original CNDO parameterization scheme. Two of the modifications were just minor tinkering with the integral evaluation, and need not concern us. The key point in their method was the treatment of the p parameters. Think of a pair of bonded carbon atoms in a large molecule. Some of the p-type basis functions on Ca will be aligned to those on Cb in a type interaction was reduced. They wrote... 

In standard quantum-mechanical molecular structure calculations, we normally work with a set of nuclear-centred atomic orbitals Xi< Xi CTOs are a good choice for the if only because of the ease of integral evaluation. Procedures such as HF-LCAO then express the molecular electronic wavefunction in terms of these basis functions and at first sight the resulting HF-LCAO orbitals are delocalized over regions of molecules. It is often thought desirable to have a simple ab initio method that can correlate with chemical concepts such as bonds, lone pairs and inner shells. A theorem due to Fock (1930) enables one to transform the HF-LCAOs into localized orbitals that often have the desired spatial properties. 

To some other experts the meaning of the term ab initio is rather clear cut. Their response is that "ab initio" simply means that all atomic/molecular integrals are computed analytically, without recourse to empirical parametrization. They insist that it does not mean that the method is exact nor that the basis set contraction coefficients were obtained without recourse to parametrization. Yet others point out that even the integrals need not be evaluated exactly for a method to be called ab initio, given that, for instance, Gaussian employs several asymptotic and other cutoffs to approximate integral evaluation. 

The solubility of naphthalene in supercritical carbon dioxide fluids has been evaluated by means of the integral equation method (Tanaka and Nakanishi, 1994). 

Cools, N., De Pauw, E. and Deckers, J. 2003. Towards an integration of conventional land evaluation methods and farmers soil suitability assessment a case study in northwestern Syria. Agriculture, Ecosystems and Environment 95(1) 327-342. 

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