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We are submitting a revised version of our manuscript titled "Real |
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space electrostatics for multipoles. I. Development of methods" by |
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Madan Lamichhane, Kathie Newman, and myself. |
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We would like to thank the reviewers for providing valuable comments |
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on two lengthy manuscripts. We have made some significant |
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modifications to the paper in response to reviewer comments. These |
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are: |
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* At the suggestion of reviewer 1, we have changed the titles of the |
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two manuscripts to make them more reflective of their content. |
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* Reviewer 2 commented on some confusing notation, so we have modified |
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our notation to make it more consistent. In this (and the following |
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paper) we now use bold-face to denote vector quantities, sans-serif |
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fonts for tensors and matrices, hats for unit vectors, and standard |
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equation fonts for indices. |
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* Reviewer 1 had some questions on our figures and specifically on the |
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different scales being used for dipolar and quadrupolar arrays. We |
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have remade figures 2-5 as figures 2 and 3 in the new manuscript |
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showing the radial dependence of the dipolar and quadrupolar |
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lattices on similar distance scales, and for identical values of the |
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damping coefficient. We think this simplifies the manuscript |
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considerably and helps to clarify the role of the damping |
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coefficient. |
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* Because the crystalline arrays only sample a small number of |
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relative orientations of closely-packed multipoles, some of the |
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questions reviewer 1 had about the damping coefficient are best |
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answered in the second paper in our discussion of liquid structural |
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and dynamical properties. Evaluation of the peformance of the |
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methods as a function of the damping parameter has been moved to the |
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second paper, and a discussion of the orientational sampling has |
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been included on page 22 of this manuscript. |
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* Reviewer 2 mentioned the enhanded damped coulomb potential of Zahn |
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et al. We certainly recognize that the DSF potential was |
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essentially correct in that paper, so we have clarified our |
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discussion of the earlier real-space approaches in the introduction. |
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* Reviewer 1 made a number of comments about the inclusion of the TSF |
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method, when the SP and GSF methods do a much better job at |
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reproducing energy constants. We have added a discussion of why TSF |
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was included on page 23 of the manuscript. The basic reason is that |
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the structure of the orientational / radial contributions would not |
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have been made clear without the Taylor-series approach, and the |
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performance of TSF relative to other methods (hard cutoff, reaction |
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field) is actually quite good. It is only in comparison with GSF |
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and SP that it does not look quite as good. TSF also generates |
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electrostatic kernels with multiple vanishing derivatives, and this |
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property has proven useful in computing dielectric properties in the |
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past. |
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* All of the typographical errors mentioned by both reviewers have |
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been fixed. |
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* A reference to the supplemental material has been added as reference 38. |
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We hope that we have answered all reviewer concerns with these |
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changes, and that the manuscript is now acceptable for publication in |
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this form. If you have any questions or comments, I can be reached via |
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email at: gezelter@nd.edu, or by phone at (574) 631-7595. |
