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Complete TDA and RPA Calculations on the Electronic Transitions of Fullerene‐C 60 in the CNDO/S and INDO/S Approximations *
Author(s) -
Hara Toshiki,
Narita Susumu,
Kumei Sukeyuki,
Shibuya Taiichi
Publication year - 2001
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.6000
Subject(s) - cndo/2 , excited state , degenerate energy levels , wave function , projection (relational algebra) , quantum mechanics , configuration interaction , atomic orbital , singlet state , slater determinant , diagonalizable matrix , random phase approximation , linear subspace , chemistry , eigenvalues and eigenvectors , mathematical physics , mathematics , physics , molecule , pure mathematics , symmetric matrix , electron , algorithm
Complete single‐excitation mixing calculations on the electronic transitions of the icosahedral C 60 molecule have been carried out with the Tamm–Dancoff approximation (TDA) and random‐phase approximation (RPA) schemes in the CNDO/S and INDO/S approximations. The complete space of 14,400 (1p–1h) pairs is partitioned into subspaces classified according to the irreducible representations of the Ih group. For this purpose, matrix representations of the group generators are obtained on a fixed set of basis functions and are used to construct the projection operators. Degenerate molecular orbitals in each energy level are symmetry‐adapted to these projection operators. Degenerate (1p–1h) pairs or singly excited configuration wave functions are similarly symmetrized. In addition, the Clebsch–Gordan coefficients are obtained and listed in an Appendix. The TDA and RPA equations are then solved for each irreducible representation separately. Both schemes with the projection operators and with the Clebsch–Gordan coefficients gave the same results as expected, indicating that the calculations were correctly done. The transition energies from the ground state 1 1 A g to low‐lying singlet and triplet excited states and the oscillator strengths for the allowed transitions (n 1 T 1u –1 1 A g ) are given in tables. A proper way to normalize is discussed for the eigenvectors of the RPA‐type matrix equation. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001