Independently Optimized Orbital Sets in GRASP—The Case of Hyperfine Structure in Li I
, Per Jönsson 2,*,†, Michel Godefroid 3, Gediminas Gaigalas 4, Jacek Bieroń 5, José Pires Marques 6, Paul Indelicato 7 and Chongyang Chen 1Round 1
Reviewer 1 Report
The MCDHF method is a superb method to calculate complex atomic structure parameters. One of its greatest advantages is that it can well describe the electron correlation effect by using the activity-space method based on the multi-reference configurations. However, most of the atomic parameters, such as transition probabilities and level lifetimes, are oscillatory convergent when the active space is extended layer-by-layer. In this paper, the authors combined the correlation orbitals obtained from different optimizations together, and orthogonalized them. Then, they performed the CI calculations to obtain the atomic state wavefunctions. This method, at the very least, is very successful in calculating the hyperfine structure constants of the 2s, 2p_1/2, 2p_3/2 states of Li atoms. I think this optimization method can be used for other multi-electron atom calculations as well and it is a very important progress in the calculations using the MCDHF method. I recommend publishing this article on Atoms.
There are a small number of errors and the authors should examine them in detail, such as Line 220 on page 8, " In Figure 4 we display, in blue triangles, ... ". There are no blue triangles in this figure and it should be "blue crosses"
Author Response
Please see the attachment.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
In this paper, the authors presented a procedure for orbital basis set construction by merging separately optimized orbital sets that target different important correlation effects, such as energy minimization and correlation effects important for calculations of atomic properties. The paper is well written and would be a great addition to the special issue of GRASP in Atoms. The authors introduce the theory and methods in sufficient detail, as well as the challenges that motivated their work.
Several possible revisions follow:
In the discussion in Section 4.1 comparing the layer-by-layer method used in this work and the fully variational calculation performed with the MCDFGME code, is there a good reason why the MCDFGME calculations were done up to nmax=5, while the other calculations were done up to nmx=13? Would it be possible to include more data points to see the convergence via MCDFGME?
In the discussion at the end of Section 4.2 mentioning a great improvement in efficiency and accuracy, it may be of interest to include a concrete comparison or reference to one.
I advise the authors to carefully proofread the paper. I spotted several typos and grammatical errors, including very long sentences that could be better understood if broken into smaller sentences.
On line 139: polarisation -> polarization.
It is not clear what the acronyms OL and EOL mean. They could be omitted as they only show up one other time in Figure 4.
Perhaps re-evaluate the usage of "e.g" in some sentences - it may not be necessary in some cases.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
