Finite element method for two-dimensional vibrational wave functions: Theory and application to van der Waals molecules
| Autor: | George C. Schatz, Timothy J. Dudley, Rajeev R. Pandey, Mark R. Hoffmann, Philip E. Staffin |
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| Rok vydání: | 2001 |
| Předmět: |
Power series
Physics Mathematical analysis Trigonometric integral General Physics and Astronomy Basis function Order of integration (calculus) Matrix (mathematics) symbols.namesake Zero differential overlap Computational chemistry Slater integrals symbols Physical and Theoretical Chemistry van der Waals force |
| Zdroj: | The Journal of Chemical Physics. 114:6166-6179 |
| ISSN: | 1089-7690 0021-9606 |
| Popis: | A variational formulation finite element method is developed for calculation of vibrational wave functions in a domain spanned by close-coupled, or Jacobi, coordinates R and γ. C1 tensor-product basis functions, which allow straightforward separation of kinetic and overlap integrals into products of one-dimensional integrals, are used. Furthermore, representation of the potential energy surface in terms of the same tensor-product basis functions used to represent the wave functions allows the potential energy integrals to also be written as a sum of products of one-dimensional integrals. Factorization of the integrals, together with expression of one-dimensional integrals in analytic or rapidly convergent power series form, reduces the computational effort of calculation of all matrix elements to a small, and arguably insignificant, level. It is shown that the theoretical error in eigenvalue, i.e., O(h6) for bicubic Hermite functions, is achieved for a number of rare gas van der Waals triatomics for which... |
| Databáze: | OpenAIRE |
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