σ-SCF: A direct energy-targeting method to mean-field excited states
The mean-field solutions of electronic excited states are much less accessible than ground state (e.g., Hartree-Fock) solutions. Energy-based optimization methods for excited states, like ∆-SCF (selfconsistent field), tend to fall into the lowest solution consistent with a given symmetry—a problem...
| Main Authors: | , , , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
American Institute of Physics (AIP)
2018
|
| Online Access: | http://hdl.handle.net/1721.1/119440 https://orcid.org/0000-0002-3714-2753 https://orcid.org/0000-0001-8659-6535 https://orcid.org/0000-0002-5338-8876 https://orcid.org/0000-0001-7111-0176 |
| _version_ | 1811075619583164416 |
|---|---|
| author | Ye, Hongzhou Welborn, Matthew Gregory Ricke, Nathan Darrell Van Voorhis, Troy |
| author2 | Massachusetts Institute of Technology. Department of Chemistry |
| author_facet | Massachusetts Institute of Technology. Department of Chemistry Ye, Hongzhou Welborn, Matthew Gregory Ricke, Nathan Darrell Van Voorhis, Troy |
| author_sort | Ye, Hongzhou |
| collection | MIT |
| description | The mean-field solutions of electronic excited states are much less accessible than ground state (e.g., Hartree-Fock) solutions. Energy-based optimization methods for excited states, like ∆-SCF (selfconsistent
field), tend to fall into the lowest solution consistent with a given symmetry—a problem known as “variational collapse.” In this work, we combine the ideas of direct energy-targeting and variance-based optimization in order to describe excited states at the mean-field level. The resulting method, σ-SCF, has several advantages. First, it allows one to target any desired excited state by specifying a single parameter: a guess of the energy of that state. It can therefore, in principle, find all excited states. Second, it avoids variational collapse by using a variance-based, unconstrained local minimization. As a consequence, all states—ground or excited—are treated on an equal footing. Third, it provides an alternate approach to locate ∆-SCF solutions that are otherwise hardly accessible
by the usual non-aufbau configuration initial guess. We present results for this new method for small
atoms (He, Be) and molecules (H2, HF). We find that σ-SCF is very effective at locating excited states, including individual, high energy excitations within a dense manifold of excited states. Like all single determinant methods, σ-SCF shows prominent spin-symmetry breaking for open shell states
and our results suggest that this method could be further improved with spin projection |
| first_indexed | 2024-09-23T10:09:19Z |
| format | Article |
| id | mit-1721.1/119440 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T10:09:19Z |
| publishDate | 2018 |
| publisher | American Institute of Physics (AIP) |
| record_format | dspace |
| spelling | mit-1721.1/1194402022-09-26T16:05:58Z σ-SCF: A direct energy-targeting method to mean-field excited states Ye, Hongzhou Welborn, Matthew Gregory Ricke, Nathan Darrell Van Voorhis, Troy Massachusetts Institute of Technology. Department of Chemistry Voorhis, Troy Van Ye, Hongzhou Welborn, Matthew Gregory Ricke, Nathan Darrell Van Voorhis, Troy The mean-field solutions of electronic excited states are much less accessible than ground state (e.g., Hartree-Fock) solutions. Energy-based optimization methods for excited states, like ∆-SCF (selfconsistent field), tend to fall into the lowest solution consistent with a given symmetry—a problem known as “variational collapse.” In this work, we combine the ideas of direct energy-targeting and variance-based optimization in order to describe excited states at the mean-field level. The resulting method, σ-SCF, has several advantages. First, it allows one to target any desired excited state by specifying a single parameter: a guess of the energy of that state. It can therefore, in principle, find all excited states. Second, it avoids variational collapse by using a variance-based, unconstrained local minimization. As a consequence, all states—ground or excited—are treated on an equal footing. Third, it provides an alternate approach to locate ∆-SCF solutions that are otherwise hardly accessible by the usual non-aufbau configuration initial guess. We present results for this new method for small atoms (He, Be) and molecules (H2, HF). We find that σ-SCF is very effective at locating excited states, including individual, high energy excitations within a dense manifold of excited states. Like all single determinant methods, σ-SCF shows prominent spin-symmetry breaking for open shell states and our results suggest that this method could be further improved with spin projection National Science Foundation (U.S.) (CHE-1464804) David & Lucile Packard Foundation 2018-12-04T21:20:49Z 2018-12-04T21:20:49Z 2017-12 2017-08 Article http://purl.org/eprint/type/JournalArticle 0021-9606 1089-7690 http://hdl.handle.net/1721.1/119440 Ye, Hong-Zhou, Matthew Welborn, Nathan D. Ricke, and Troy Van Voorhis. “σ-SCF: A Direct Energy-Targeting Method to Mean-Field Excited States.” The Journal of Chemical Physics 147, no. 21 (December 7, 2017): 214104. © 2018 AIP Publishing LLC https://orcid.org/0000-0002-3714-2753 https://orcid.org/0000-0001-8659-6535 https://orcid.org/0000-0002-5338-8876 https://orcid.org/0000-0001-7111-0176 en_US https://doi.org/10.1063/1.5001262 The Journal of Chemical Physics Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Institute of Physics (AIP) Prof. Van Voorhis via Erja Kajosalo |
| spellingShingle | Ye, Hongzhou Welborn, Matthew Gregory Ricke, Nathan Darrell Van Voorhis, Troy σ-SCF: A direct energy-targeting method to mean-field excited states |
| title | σ-SCF: A direct energy-targeting method to mean-field excited states |
| title_full | σ-SCF: A direct energy-targeting method to mean-field excited states |
| title_fullStr | σ-SCF: A direct energy-targeting method to mean-field excited states |
| title_full_unstemmed | σ-SCF: A direct energy-targeting method to mean-field excited states |
| title_short | σ-SCF: A direct energy-targeting method to mean-field excited states |
| title_sort | σ scf a direct energy targeting method to mean field excited states |
| url | http://hdl.handle.net/1721.1/119440 https://orcid.org/0000-0002-3714-2753 https://orcid.org/0000-0001-8659-6535 https://orcid.org/0000-0002-5338-8876 https://orcid.org/0000-0001-7111-0176 |
| work_keys_str_mv | AT yehongzhou sscfadirectenergytargetingmethodtomeanfieldexcitedstates AT welbornmatthewgregory sscfadirectenergytargetingmethodtomeanfieldexcitedstates AT rickenathandarrell sscfadirectenergytargetingmethodtomeanfieldexcitedstates AT vanvoorhistroy sscfadirectenergytargetingmethodtomeanfieldexcitedstates |