# Charlotte Froese Fischer—Her Work and Her Impact

## Abstract

**:**

## 1. Foundations

## 2. Hartree-Fock Calculations

## 3. Extensions of HF

## 4. Some Illustrative Examples

## 5. Computer Programs for Atomic Structure

## 6. Extensions and Enhancements of MCHF—Non-Relativistic Treatment

#### 6.1. Non-Orthogonal Orbitals

- He: 1s${}^{2}$ and 1s2p—radially, the 1s function of the 1s2p state is close to being hydrogenic whereas the 1s function for the ground state resembles a screened hydrogenic function.
- Be: [1s${}^{2}$]2s${}^{2}$${}^{1}$S, 2s2p ${}^{3}$P${}^{\mathrm{o}}$ and ${}^{1}$P${}^{\mathrm{o}}$—the 2s functions differ somewhat from state to state, but the more significant feature is that the mean radii of the 2p functions in the two excited states differ by around a factor of two.
- Al-sequence: we have already noted in Table 1 that the optimal 3d function in the two lowest ${}^{2}$D states is very state dependent. A more appropriate CI expansion would have configurations of the form:$\text{}{}^{2}$D: 3s${}_{1}^{2}$3d; 3p${}_{1}^{2}$(${}^{1}$S)3d, 3p${}_{2}^{2}$(${}^{1}$D,${}^{3}$P)3d${}_{1}$, 3s${}_{2}$3p${}_{3}^{2}$where the same $nl$ orbital but with different subscripts need not be mutually orthogonal.
- The 3d orbital in open d-shells, for example in the iron group elements, can be very term-dependent even for an individual ion.

#### 6.2. Use of B-Splines

## 7. Inclusion of Relativity

#### 7.1. Breit-Pauli Calculations

- The radial functions were optimised in an $LS$ MCHF calculation.
- The angular and spin integrals of the relativistic operators were evaluated using the Racah algebra analysis given by Glass and Hibbert (1978) [46] and are input to the MCHF+BP code.
- Then the full Breit-Pauli Hamiltonian matrix was diagonalised to give the $LSJ$ wave functions. These wave functions take the form$$\Psi \left(J\right)\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}\sum _{i=1}^{M}{a}_{i}\phantom{\rule{0.166667em}{0ex}}{\Phi}_{i}\left({\alpha}_{i}{L}_{i}{S}_{i}J\right)$$

#### 7.2. Other Atomic Properties

#### 7.3. Further MCHF-Based Computer Packages

## 8. Fully Relativistic Codes

## 9. In Summary

^{th}birthday, her enthusiasm and commitment continue unabated.

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Froese Fischer, C. Reminiscences at the end of the century. Mol. Phys.
**2000**, 98, 1043–1050. [Google Scholar] [CrossRef] - Schrödinger, E. Quantisierung als eigenwertproblem. Ann. Phys.
**1926**, 79, 361–376. [Google Scholar] [CrossRef] - Hylleraas, E. A Über den Grundzustand des Heliumatoms. Z. Phys.
**1928**, 48, 469–494. [Google Scholar] [CrossRef] - Hartree, D.R. The Wave Mechanics of an Atom with a Non-Coulomb Central Field. Part I. Theory and methods. Proc. Camb. Philos. Soc.
**1927**, 24, 89–110. [Google Scholar] [CrossRef] - Hartree, D.R. The Wave Mechanics of an Atom with a Non-Coulomb Central Field. Part II. Some Results and Discussion. Proc. Camb. Philos. Soc.
**1928**, 24, 111–132. [Google Scholar] [CrossRef] - Fock, V.A. Näherungsmethode zur Lösung des quantenmechanischen Mehrkörperproblems. Z. Phys.
**1930**, 61, 126–148. [Google Scholar] [CrossRef] - Hartree, D.R. Approximate wave functions and atomic field for mercury. Phys. Rev.
**1934**, 46, 738–743. [Google Scholar] [CrossRef] - Hartree, D.R.; Hartree, W. Wave functions for negative ions of sodium and potassium. Proc. Camb. Philos. Soc.
**1938**, 34, 550–558. [Google Scholar] [CrossRef] - Hartree, D.R.; Hartree, W.; Swirles, B. Self-consistent field, including exchange and superposition of configurations, with some results for oxygen. Philos. Trans. R. Soc.
**1939**, A238, 229–247. [Google Scholar] [CrossRef][Green Version] - Hartree, D.R. The differential analyser. Nature
**1935**, 135, 940–943. [Google Scholar] [CrossRef] - Froese, C.; Hartree, D.R. Wave functions for the normal states of Ne
^{3+}and Ne^{4+}. Proc. Camb. Philos. Soc.**1957**, 53, 663–668. [Google Scholar] [CrossRef] - Hartree. D.R. The Calculation of Atomic Structures; John Wiley and Sons: New York, NY, USA, 1957; p. xiii+181. [Google Scholar]
- Froese, C. The self-consistent field with exchange for the ground state and first excited state of Fe
^{13+}. Mon. Not. R. Astron. Soc.**1957**, 117, 615–621. [Google Scholar] [CrossRef][Green Version] - Froese, C. The self-consistent field with exchange for some 10 and 12 electron systems. Proc. Camb. Philos. Soc.
**1957**, 53, 206–213. [Google Scholar] [CrossRef] - Froese, C. The limiting behaviour of atomic wave functions for large atomic number. Proc. R. Soc. Ser. A
**1957**, 239, 311–319. [Google Scholar] - Froese, C. The limiting behaviour of atomic wave functions for large atomic number. II. Proc. R. Soc. Ser. A
**1958**, 244, 390–397. [Google Scholar] - Froese, C. The limiting behavious of atomic wave functions for large atomic number. III. Proc. R. Soc. Ser. A
**1959**, 251, 534–535. [Google Scholar] - Froese, C. Numerical solution of the Hartree-Fock equations. Can. J. Phys.
**1963**, 41, 1895–1910. [Google Scholar] [CrossRef] - Slater, J.C. Note on Hartree’s method. Phys. Rev.
**1930**, 35, 210. [Google Scholar] [CrossRef] - Froese, C. Some multiplet strengths for transitions in Fe XVI and Fe XV. Astrophys. J.
**1964**, 140, A1489–A1494. [Google Scholar] [CrossRef] - Froese, C. Oscillator strengths for the 3s
^{2}3p^{2}P – 3s3p^{2}^{2}S transition in Al I. Astrophys. J.**1965**, 141, 1557–1559. [Google Scholar] [CrossRef] - Froese, C.; Underhill, A.B. gf-values for lines of the Si II spectrum. Astrophys. J.
**1966**, 146, 301–303. [Google Scholar] [CrossRef] - Froese Fischer, C. Superposition of configuration results for Si II. Astrophys. J.
**1968**, 151, 759–764. [Google Scholar] [CrossRef] - Froese Fischer, C. Lifetimes of low-lying
^{2}P^{o},^{2}D, and^{2}F^{o}states of the Al I isoelectronic sequence. Phys. Scr.**1981**, 23, 38–44. [Google Scholar] [CrossRef] - Hibbert, A.; Ojha, P.C.; Stafford, R.P. Allowed transitions in Si II. J. Phys. B At. Mol. Opt. Phys.
**1992**, 25, 4153–4162. [Google Scholar] [CrossRef] - Shull, J.M.; Snow, T.P.; York, D.G. Observationally determined Silicon II oscillator strengths. Astrophys. J.
**1981**, 246, 549–553. [Google Scholar] [CrossRef] - Tong, M.; Froese Fischer, C.; Sturesson, L. Systematic transition probability studies for neutral nitrogen. J. Phys. B At. Mol. Opt. Phys.
**1994**, 27, 4819–4828. [Google Scholar] [CrossRef] - Kramida, A.; Ralchenko, Y.; Reader, J.; NIST ASD Team. NIST Atomic Spectra Database (ver. 5.3); National Institute of Standards and Technology: Gaithersburg, MD, USA, 2018. Available online: http://physics.nist.gov/asd (accessed on 26 July 2019).
- Froese Fischer, C. A Multiconfiguration Hartree-Fock program. Comput. Phys. Commun.
**1969**, 1, 151–166. [Google Scholar] [CrossRef] - Froese Fischer, C. A Multiconfiguration Hartree-Fock program with improved stability. Comput. Phys. Commun.
**1972**, 4, 107–116. [Google Scholar] [CrossRef] - Froese Fischer, C. A general multi-configuration Hartree-Fock program. Comput. Phys. Commun.
**1978**, 14, 145–153. [Google Scholar] [CrossRef] - Hibbert, A. A general program for calculating angular momentum integrals in atomic structure. Comput. Phys. Commun.
**1970**, 1, 359–377. [Google Scholar] [CrossRef] - Hibbert, A. A new version of a general program to calculate angular momentum integrals. Comput. Phys. Commun.
**1971**, 2, 180–190. [Google Scholar] [CrossRef] - Hibbert, A. Adaptation of a program to calculate angular momentum integrals: Inclusion of the one-electron part of the Hamiltonian. Comput. Phys. Commun.
**1974**, 7, 318–326. [Google Scholar] [CrossRef] - Robinson, D.J.R.; Hibbert, A. Quartet transitions in neutral nitrogen. J. Phys. B At. Mol. Opt. Phys.
**1997**, 30, 4813–4825. [Google Scholar] [CrossRef] - Hibbert, A.; Dufton, P.L.; Keenan, F.P. Oscillator strengths for transitions in N I and the interstellar abundance of nitrogen. Mon. Not. R. Astron. Soc.
**1985**, 213, 721–734. [Google Scholar] [CrossRef][Green Version] - Hibbert, A.; Froese Fischer, C.; Godefroid, M.R. Non-orthogonal orbitals in MCHF or configuration interaction wave functions. Comput. Phys. Commun.
**1988**, 51, 285–293. [Google Scholar] [CrossRef] - Olsen, J.; Godefroid, M.R.; Jönsson, P.; Malmqvist, P.Å.; Froese Fischer, C. Transition probability calculations for atoms using nonorthogonal orbitals. Phys. Rev. E
**1995**, 52, 4499–4508. [Google Scholar] [CrossRef] - Carlsson, J.; Jönsson, P.; Sturesson, L.; Froese Fischer, C. Lifetimes and transition probabilities of the boron atom calculated with the active space multiconfiguration Hartree-Fock method. Phys. Rev. A
**1994**, 49, 3426–3431. [Google Scholar] [CrossRef] [PubMed][Green Version] - O’Brian, T.R.; Lawler, J. Radiative lifetimes in B I using ultraviolet and vacuum-ultraviolet laser-induced fluorescence. Astron. Astrophys.
**1992**, 255, 420–426. [Google Scholar] - Brage, T.; Froese Fischer, C. Spline-Galerkin calculations for Rydberg series calculations of calcium. Phys. Scr.
**1994**, 49, 651–660. [Google Scholar] [CrossRef] - Bachau, H.; Cormier, E.; Decleva, P.; Hansen, J.E.; Martin, F. Application of B-splines in atomic and molecular physics. Rep. Prog. Phys.
**2001**, 64, 1815–1942. [Google Scholar] [CrossRef] - Burke, P.G.; Hibbert, A.; Robb, W.D. Electron scattering by complex atoms. J. Phys. B At. Mol. Phys.
**1971**, 4, 153–161. [Google Scholar] [CrossRef] - Berrington, K.A.; Burke, P.G.; Le Dourneuf, M.; Robb, W.D.; Taylor, K.T.; Lan, V.K. A new version of the general program to calculate atomic continuum processes using the R-matrix method. Comput. Phys. Commun.
**1978**, 14, 367–412. [Google Scholar] [CrossRef] - Zatsarinny, O.; Froese Fischer, C. The use of B-splines and non-orthogonal orbitals in R-matrix calculations: Application to Li Photoionization. J. Phys. B At. Mol. Opt. Phys.
**2000**, 33, 313–341. [Google Scholar] [CrossRef] - Glass, R.; Hibbert, A. Relativistic effects in many-electron atoms. Comput. Phys. Commun.
**1978**, 16, 19–34. [Google Scholar] [CrossRef] - Froese Fischer, C. Multiconfiguration Hartree-Fock Breit-Pauli results for
^{2}P_{1/2}-^{2}P_{3/2}transitions in the boron sequence. J. Phys. B At. Mol. Opt. Phys.**1983**, 16, 157–165. [Google Scholar] [CrossRef] - Huang, K.-N.; Kim, Y.-K.; Cheng, K.T.; Desclaux, J.P. Correlation and relativistic effects in spin-orbit splitting. Phys. Rev. Lett.
**1982**, 48, 1245–1248. [Google Scholar] [CrossRef] - Froese Fischer, C.; Saha, H.P. Multiconfiguration Hartree-Fock results with Breit-Pauli corrections for transitions in the carbon sequence. Phys. Scr.
**1985**, 32, 181–194. [Google Scholar] [CrossRef] - Godefroid, M.; Froese Fischer, C. MCHF-BP fine structure splittings and transition rates for the ground configuration in the nitrogen sequence. J. Phys. B At. Mol. Opt. Phys.
**1984**, 17, 681–692. [Google Scholar] [CrossRef] - Froese Fischer, C.; Saha, H.P. Multiconfiguration Hartree-Fock results with Breit-Pauli corrections for forbidden transitions in the 2p
^{4}configuration. Phys. Rev. A**1983**, 28, 3169–3178. [Google Scholar] [CrossRef] - Froese Fischer, C.; Saha, H.P. MCHF+BP results for electric dipole transitions in the oxygen isoelectronic sequence. J. Phys. B At. Mol. Opt. Phys.
**1984**, 17, 943–952. [Google Scholar] [CrossRef] - Froese Fischer, C. Allowed transitions and intercombination lines in C III and C II. Phys. Scr.
**1994**, 49, 323–330. [Google Scholar] [CrossRef] - Fleming, J.; Hibbert, A.; Stafford, R.P. The 1909Å Intercombination Line in C III. Phys. Scr.
**1994**, 49, 316–322. [Google Scholar] [CrossRef] - Jönsson, P.; Froese Fischer, C. Multiconfiguration Dirac-Fock calculations of the 2s
^{2}^{1}S_{0}– 2s2p^{3}P_{1}intercombination transition in C III. Phys. Rev. A**1998**, 57, 4967–4970. [Google Scholar] [CrossRef] - Kwong, V.H.S.; Fang, Z.; Gibbons, T.T.; Parkinson, W.H.; Smith, P.L. Measurement of the transition probability of the C III 190.9 nanometer intersystem line. Astrophys. J.
**1993**, 411, 431–437. [Google Scholar] [CrossRef] - Doerfert, J.; Träbert, E.; Wolf, A.; Schwalm, D.; Uwira, O. Precision measurement of the electric dipole intercombination rate in C
^{2+}. Phys. Rev. Lett.**1997**, 78, 4355–4358. [Google Scholar] [CrossRef] - Froese Fischer, C.; Gaigalas, G. Note on the 2s
^{2}^{1}S_{0}– 2s2p^{3}P_{1}intercombination line of B II and C III. Phys. Scr.**1997**, 56, 436–438. [Google Scholar] [CrossRef] - Froese Fischer, C.; Tachiev, G. Breit–Pauli energy levels, lifetimes, and transition probabilities for the beryllium-like to neon-like sequences. Atom. Data Nucl. Data Tables
**2004**, 87, 1–184. [Google Scholar] [CrossRef] - Froese Fischer, C.; Tachiev, G.; Irimia, A. Relativistic energy levels, lifetimes, and transition probabilities for the sodium-like to argon-like sequences. Atom. Data Nucl. Data Tables
**2006**, 92, 607–812. [Google Scholar] [CrossRef] - Jönsson, P.; Froese Fischer, C.; Godefroid, M.R. Accurate calculations of transition probabilities, isotope shifts and hyperfine structures for some allowed 2s
^{2}2p^{n}–2s2p^{n+1}transitions in B I, C II and C I. J. Phys. B At. Mol. Opt. Phys.**1996**, 29, 2393–2412. [Google Scholar] [CrossRef] - Froese Fischer, C.; Saha, H.P. Photoionization of magnesium. Can. J. Phys.
**1987**, 65, 772–776. [Google Scholar] [CrossRef] - Froese Fischer, C.; Idrees, M. Autoionization rates for core excited
^{5}P states of Na^{−}. Phys. Scr.**1989**, 39, 70–72. [Google Scholar] [CrossRef] - Froese Fischer, C. The MCHF atomic-structure package. Comput. Phys. Commun.
**1991**, 64, 369–398. [Google Scholar] [CrossRef] - Froese Fischer, C. MCHF atomic-structure package: Support; libraries and utilities. Comput. Phys. Commun.
**1991**, 64, 399–405. [Google Scholar] [CrossRef] - Froese Fischer, C.; Liu, B. A program to generate configuration-state lists. Comput. Phys. Commun.
**1991**, 64, 405–416. [Google Scholar] [CrossRef] - Hibbert, A.; Froese Fischer, C. A general program for computing angular integrals of the non-relativistic Hamiltonian with non-orthogonal orbitals. Comput. Phys. Commun.
**1991**, 64, 417–430. [Google Scholar] [CrossRef] - Froese Fischer, C. A general multi-configuration Hartree-Fock program. Comput. Phys. Commun.
**1991**, 64, 431–454. [Google Scholar] [CrossRef] - Hibbert, A.; Glass, R.; Froese Fischer, C. A general program for computing angular integrals of the Breit-Pauli Hamiltonian. Comput. Phys. Commun.
**1991**, 64, 455–472. [Google Scholar] [CrossRef] - Froese Fischer, C. A configuration interaction program. Comput. Phys. Commun.
**1991**, 64, 473–485. [Google Scholar] [CrossRef] - Froese Fischer, C.; Godefroid, M.R.; Hibbert, A. A program for performing angular integrations for transition operators. Comput. Phys. Commun.
**1991**, 64, 486–500. [Google Scholar] [CrossRef] - Froese Fischer, C.; Godefroid, M.R. Programs for computing LS and LSJ transitions from MCHF wave functions. Comput. Phys. Commun.
**1991**, 64, 501–519. [Google Scholar] [CrossRef] - Desclaux, J.P. A multiconfiguration relativistic Dirac-Fock program. Comput. Phys. Commun.
**1975**, 9, 31–45. [Google Scholar] [CrossRef] - Dyall, K.G.; Grant, I.P.; Johnson, C.T.; Parpia, F.A.; Plummer, E.P. GRASP: A general-purpose relativistic atomic structure program. Comput. Phys. Commun.
**1987**, 55, 425–456. [Google Scholar] [CrossRef] - Parpia, F.A.; Froese Fischer, C.; Grant, I.P. GRASP92: A package for large-scale relativistic atomic structure calculations. Comput. Phys. Commun.
**1996**, 94, 249–271. [Google Scholar] [CrossRef] - Froese Fischer, C.; Gaigalas, G.; Ralchenko, Y. Some corrections to GRASP92. Comput. Phys. Commun.
**2006**, 175, 738–744. [Google Scholar] [CrossRef] - Jönsson, P.; He, X.; Froese Fischer, C.; Grant, I.P. The GRASP2K relativistic atomic structure package. Comput. Phys. Commun.
**2007**, 177, 597–622. [Google Scholar] [CrossRef] - Jönsson, P.; Parpia, F.A.; Froese Fischer, C. HFS92: A program for relativistic atomic hyperfine structure calculations. Comput. Phys. Commun.
**1996**, 96, 301–310. [Google Scholar] [CrossRef] - Jönsson, P.; Froese Fischer, C. SMS92: A program for relativistic isotope calculations. Comput. Phys. Commun.
**1997**, 100, 81–92. [Google Scholar] [CrossRef] - Gaigalas, G.; Rudzikas, Z.; Froese Fischer, C. An efficient approach for spin-angular integrations in atomic structure calculations. J. Phys. B At. Mol. Opt. Phys.
**1997**, 30, 3747–3771. [Google Scholar] [CrossRef] - Davidson, E.R. The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices. J. Comput. Phys.
**1975**, 17, 87–94. [Google Scholar] [CrossRef] - Stathopoulos, A.; Froese Fischer, C. A Davidson program for finding a few selected extreme eigenpairs of a large, sparse, real, symmetric matrix. Comput. Phys. Commun.
**1994**, 79, 268–290. [Google Scholar] [CrossRef] - Froese Fischer, C. The Hartree-Fock Method for Atoms; Wiley Interscience: New York, NY, USA, 1977; p. xi+320. [Google Scholar]
- Froese Fischer, C.; Brage, T.; Jönsson, P. Computational Atomic Structure—An MCHF Approach; Institute of Physics Publishing: Bristol, UK, 1997; p. xi+279. [Google Scholar]

CI Coefficients for ${}^{2}$D States of Si II | |||
---|---|---|---|

Configurations | 3s3p${}^{2}$ | 3s${}^{2}$3d | 3s${}^{2}$3d (orthog) |

3s3p${}^{2}$ | 0.7908 | −0.5629 | −0.5263 |

3s${}^{2}$3d | 0.5994 | 0.8016 | 0.8251 |

3p${}^{2}$(${}^{1}$S)3d | 0.1146 | 0.1921 | 0.1977 |

3p${}^{2}$(${}^{1}$D)3d | 0.0118 | ||

3p${}^{2}$(${}^{3}$P)3d | −0.0603 | −0.0563 | |

3s3d${}^{2}$ | 0.0467 | ||

$gf$-values from the 3s${}^{2}$3p ${}^{2}$P${}^{\mathrm{o}}$ ground state | |||

Froese Fischer (1968) [23] | 0.103 | 6.22 | |

Froese Fischer (1981) [24] | 0.006 | 6.83 | |

Hibbert et al. (1992) [25] | 0.011 | 6.69 |

**Table 2.**Oscillator strengths for the 2s${}^{2}$2p${}^{3}$${}^{4}$S${}^{\mathrm{o}}$− 2s2p${}^{4}$${}^{4}$P transition in N I [27].

Model Number | Configuration Complexes ${}^{\u2020}$ | $\mathsf{\Delta}\mathit{E}$ | ${\mathit{f}}_{\mathit{l}}$ | ${\mathit{f}}_{\mathit{v}}$ |
---|---|---|---|---|

1 | {2}${}^{3}$ {2,3,...,6}${}^{2}$ | 87,271 | 0.3513 | 0.3628 |

2 | {2}${}^{2}$ {2,3}${}^{1}$ {2,3,...,6}${}^{2}$ | 88,524 | 0.0533 | 0.0563 |

3 | {2}${}^{1}$ {2,3}${}^{2}$ {2,3,...,6}${}^{2}$ | 88,375 | 0.0667 | 0.0693 |

3+ | {2}${}^{1}$ {2,3}${}^{2}$ {2,3,...,7}${}^{2}$ | 88,356 | 0.0658 | 0.0687 |

Within model 3 | {2}${}^{1}$ {2,3}${}^{2}$ {2,3}${}^{2}$ | 89,760 | 0.3163 | 0.4062 |

{2}${}^{1}$ {2,3}${}^{2}$ {2,3,...,4}${}^{2}$ | 89,324 | 0.1108 | 0.1171 | |

{2}${}^{1}$ {2,3}${}^{2}$ {2,3,...,5}${}^{2}$ | 88,446 | 0.0701 | 0.0717 | |

{2}${}^{1}$ {2,3}${}^{2}$ {2,3,...,6}${}^{2}$ | 88,375 | 0.0667 | 0.0693 | |

{2}${}^{1}$ {2,3}${}^{2}$ {2,3,...,7}${}^{2}$ | 88,356 | 0.0658 | 0.0687 | |

Exp. [28] Average over J | 88,132 |

**Table 3.**Oscillator strengths for the 2s${}^{2}$2p ${}^{2}$P${}^{\mathrm{o}}$− 2s2p${}^{2}$${}^{2}$D transition in B I [38].

Active Set: max n | $\mathsf{\Delta}\mathit{E}$(cm${}^{-1}$) | ${\mathit{gf}}_{\mathit{l}}$ | ${\mathit{gf}}_{\mathit{v}}$ |
---|---|---|---|

3 | 53,197 | 0.6876 | 0.8156 |

4 | 48,720 | 0.2456 | 0.2606 |

5 | 48,440 | 0.2625 | 0.2695 |

6 | 48,125 | 0.2891 | 0.2866 |

7 | 48,051 | 0.2928 | 0.2900 |

7 ${}^{E}$ | 47,847 | 0.2916 | 0.2912 |

Other results | |||

Method | ${\mathit{gf}}_{\mathit{l}}$ | ${\mathit{gf}}_{\mathit{v}}$ | |

MCHF [39] | 0.243 | 0.274 | |

Expt: LIF [40] | 0.283 ± 0.020 |

Label | Exp [28] | MCHF+BS | MCHF |
---|---|---|---|

4s4p | 25,654 | 25,472 | 24,689 |

4s5p | 12,574 | 12,684 | 12,160 |

4s6p | 7627 | 7638 | 7060 |

3d4p | 5372 | 5269 | 4609 |

4s7p | 3881 | 3799 | 3247 |

4s8p | 2826 | 2786 | 2405 |

4s9p | 2122 | 2102 | 1853 |

⋯ | |||

4s22p | 271 | 271 |

Method | B | N${}^{2+}$ | Ne${}^{5+}$ | Si${}^{9+}$ | Fe${}^{21+}$ |
---|---|---|---|---|---|

MCHF+BP [47] | 15.0 | 170.0 | 1292 | 6961 | 119,175 |

MCDHF ${}^{\mathrm{a}}$ | 15.7 | 172.4 | 1298 | 6968 | 118,177 |

Exp ${}^{\mathrm{b}}$ | 15.3 | 174.5 | 1307 | 6990 | 118,255 |

**Table 6.**MCHF+BP transition rates of the 2s${}^{2}$${}^{1}$S${}_{0}$− 2s2p ${}^{3}$P${}_{1}^{\mathrm{o}}$ line in C III [53].

Degree of Correlation | Active Space | $\mathsf{\Delta}\mathit{E}$ (cm${}^{-1}$) | ${}^{1}$P${}_{1}^{\mathbf{o}}$−${}^{3}$P${}_{1}^{\mathbf{o}}$ | ${}^{3}$P${}_{2}^{\mathbf{o}}$−${}^{3}$P${}_{0}^{\mathbf{o}}$ | A (s${}^{-1}$) |
---|---|---|---|---|---|

Val ${}^{a}$ | n = 3 | 52,746 | 51,592 | 76.79 | 89.3 |

n = 6 | 52,733 | 50,684 | 77.08 | 95.6 | |

+CP ${}^{b}$ | n = 3 | 52,640 | 50,567 | 78.06 | 97.6 |

n = 6 | 52,520 | 50,098 | 80.18 | 105.7 | |

+CC ${}^{c}$ | n = 3 | 52,362 | 50,948 | 77.33 | 91.9 |

n = 6 | 52,343 | 50,230 | 79.53 | 103.1 | |

CIV3 [54] | 52,369 | 50,325 | 78.9 | 103.8 | |

MCDHF [55] | n = 8 | 52,384 | 50,098 | 79.86 | 102.72 |

Experiment | [28] | 52,391 | 49,961 | 80.05 | |

[56] | 121 ± 7 | ||||

[57] | 102.94 ± 0.14 |

Authors | Short Title | Type of Paper |
---|---|---|

Froese Fischer [64] | The MCHF atomic structure package | Methods |

Froese Fischer [65] | MCHF support libraries and utilities | Package |

Froese Fischer, Liu [66] | Configuration-state lists | Package |

Hibbert, Froese Fischer [67] | Angular integrals with non-orthogonal orbitals | Package |

Froese Fischer [68] | General MCHF program | Package |

Hibbert, Glass, Froese Fischer [69] | Angular integrals for Breit-Pauli Hamiltonian | Package |

Froese Fischer [70] | General CI program | Package |

Froese Fischer, Godefroid, Hibbert [71] | Angular integrals for transition operators | Package |

Froese Fischer, Godefroid [72] | Programs for $LS$ and $LSJ$ transitions | Package |

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Hibbert, A. Charlotte Froese Fischer—Her Work and Her Impact. *Atoms* **2019**, *7*, 107.
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Hibbert A. Charlotte Froese Fischer—Her Work and Her Impact. *Atoms*. 2019; 7(4):107.
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Hibbert, Alan. 2019. "Charlotte Froese Fischer—Her Work and Her Impact" *Atoms* 7, no. 4: 107.
https://doi.org/10.3390/atoms7040107