Electronic Structure Calculations with the Exact Pseudopotential and Interpolating Wavelet Basis
Round 1
Reviewer 1 Report
Referee Report on "Electronic Structure Calculations with the Exact Pseudopotential and Interpolating Wavelet Basis," by Tommi Höynälänmaa and Tapio T. Rantala
The authors presented a calculation for some small atoms such as hydrogen and helium by using a method to include the exact pseudopotential (EPP) for orbitals with an interpolating wave basis set. They compared the present results with other Hartree-Fock energies. The present method may have a potential to be extended to calculate energies for more complex atoms. The present paper might be considered for publication in Atoms after the authors have addressed the following issues.
(1) In Table 1, I suggest to the authors that they should also compare their results with other accurate non-relativistic values. (see for example, G.W.F. Drake, in “Atomic, Molecular, and Optical Physics Handbook”. (Edited by G.W.F. Drake) (AIP press, New York, 1996), pp. 154– 171.)
(2) Usually, the correlation energy of an atomic system, E_corr, is defined as the difference between the exact energy (from a high-precision calculation or from an accurate experimental measurement), E_exact, and the Hartree-Fock energy, E_HF, i.e., E_corr = E_exact - E_HF. From Table 1, the energy of the excited He(1s2s ^1S) state shows E_EPP = -2.153148, compared with the accurate non-relativistic energy of −2.145974046054419 (see the reference in issue (1), above). A comment, or discussion, should be given as to why the present energy lies at a position LOWER than that of the accurate energy. If we could include correlation into the present calculation, the final energy would be even lower than the present E_EPP.
Author Response
Please see the attachment.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Referee Report
The manuscript by T. Höynälänmaa and T.T. Rantala is devoted to the development of numerical method of solving the Schrödinger equation for atoms using interpolating wavelet basis and exact pseudopotential. The method is tested by calculating the eigenenergies of hydrogen atom 1s, 2s and 2p orbitals and He atom configurations 1s2, and 1s2s. The high accuracy of calculations is demonstrated by comparison with other methods. The paper is clearly written with sufficient number of references. I recommend the paper for publication with two small corrections.
1. Please, repeat explanation of the abbreviation EPP in the text (not only in the abstract).
2. Please, define functions Ï•# before equation (10).
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
It is fine to accept the revised version of this paper.
