Summary
The second-quantization magnetic dipole operator that arises when London atomic orbitals are used as basis functions is derived. In atomic units, the magnetic dipole operator is defined as the negative of the first derivative of the electronic Hamiltonian containing the interaction with the external magnetic field. It is shown that for finite basis sets, the gauge origin dependence of the resulting magnetic dipole operator is analogous to that of the exact operator, and that the derived operator converges to the exact operator in the limit of a complete basis set. It is also demonstrated that the length expression for the rotatory strength in linear response calculations gives gauge-origin-independent results. Sample calculations ontrans-cyclooctene and its fragments are presented. Compared to conventional orbitals, the basis set convergence of the rotatory strengths calculated in the length form using London atomic orbitals is favourable. The rotatory strength calculated fortrans-cyclooctene agrees nicely with the corresponding experimental circular dichroism spectrum, but the spectra for the fragment molecules show little resemblance with that oftrans-cyclooctene.
Similar content being viewed by others
References
Hansen AaE, Bouman TD (1980) Adv Chem Phys 44:545
London F (1937) J Phys Radium 8:397
Hameka HF (1958) Mol Phys 1:203
Hameka HF (1959) Z Naturforsch 14a:599
Mc Weeny R (1958) Mol Phys 1:311
Seamans L, Linderberg J (1972) Mol Phys 24:1393
Dalgaard E (1978) Proc R Soc Lond A 361:487
Ditchfield R (1972) J Chem Phys 56:5688
Wolinski K, Hinton JF, Pulay P (1990) J Am Chem Soc 112:8251
Gauss J (1992) Chem Phys Lett 191:614
Ruud K, Helgaker T, Kobayashi R, Jørgensen P, aiBak KL, Jensen HJAa (1994) J Chem Phys 100:8178
Ruud K, Helgaker T, Bak KL, Jørgensen P, Jensen HJAa (1993) J Chem Phys 99:3847
Ruud K, Skaane H, Helgaker T, Bak KL, Jørgensen P (1994) J Am Chem Soc
Bak KL, Jørgensen P, Helgaker T, Ruud K, Jensen HJAa (1993) J Chem Phys 98:8873
Bak KL, Jørgensen P, Helgaker T, Ruud K Jensen HJAa (1994) J Chem Phys 100:6620
McLachlan AD, Ball MA (1964) Rev Mod Phys 36:844
Linderberg J, Öhrn Y (1973) Propagators in quantum chemistry. Academic Press, New York
Olsen J, Jørgensen P (1985) J Chem Phys 82:3235
Olsen J, Bak KL, Helgaker T, Ruud K, Jørgensen P, Theoret Chem Acta submitted
Mason MG, Schnepp O (1973) J Chem Phys 59:1092
Levi CC, Hoffmann R (1972) J Am Chem Soc 94:3446
Hansen AaE, Bouman TD (1985) J Am Chem Soc 107:4828
Helgaker T, Jørgensen P (1991) J Chem Phys 95:2595
Yeager DL, Jørgensen P (1979) Chem Phys Lett 65:77
Koch H, Helgaker T, Jørgensen P (1990) J Chem Phys 93:3345.
Helgaker T, Bak KL, Jensen HJAa, Jørgensen P, Kobayashi R, Koch H, Mikkelsen K, Olsen J, Ruud K, Taylor PR, Vahtras O, ABACUS, a second-order MCSCF molecular property program
Jensen HJAa, Ågren H, SIRIUS, a program for calculation for MCSCF wave functions
Rauk A, Barriel JM, Ziegler T (1977) Prog Theoret Org Chem 2:467
Liskow DH, Segal GA (1978) J Am Chem Soc 100:2945
The dihedral angle H-C1-C2-H in Ref [22], Table 1 is misprinted as 188.9. The correct value is −188.9
Dunning THJr (1989) J Chem Phys 90:1007
Kendall RA, Dunning THJr, Harrison RJ (1992) J Chem Phys 96:6796
Woon DE, Dunning THJr (1993) J Chem Phys 98:1358
Author information
Authors and Affiliations
Additional information
Dedicated to Prof. Jan Linderberg
Rights and permissions
About this article
Cite this article
Bak, K.L., Hansen, A.E., Ruud, K. et al. Ab initio calculation of electronic circular dichroism fortrans-cyclooctene using London atomic orbitals. Theoret. Chim. Acta 90, 441–458 (1995). https://doi.org/10.1007/BF01113546
Received:
Revised:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01113546