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The efficient algorithm calculating the overlap and the kinetic integrals for the numerical atomic orbitals is implemented. The described algorithm exploits the properties of the prolate spheroidal coordinates. The overlap and the kinetic integrals in R^3 are reduced to the integrals over the rectangular domain in R^2, what substantially reduces the complexity of the problem. We prove that the integrand over the rectangular domain is continuous and does not have any slope singularities. For calculation of the integral over the rectangle any adaptive algorithm can be applied. The exemplary results were obtained by application of the adaptive Gauss quadrature.
The implemented algorithm is described in my paper: "Numerical calculation of overlap and kinetic integrals in prolate spheroidal coordinates", International Journal of Quantum Chemistry, Volume 108, Issue 2, Year 2008, Pages 249–256
http://onlinelibrary.wiley.com/doi/10.1002/qua.21485/full
Features
- Quantum chemistry
- Numerical methods
- Adaptive, numerical integration
- Overlap integral
- Kinetic integral
- C++
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