Diagonal Curvature in Second Order Jahn Teller Theory Can Be Negative: An Analytic Proof with First-Principles Confirmation in NH3
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866917344517816320 |
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| author | Li, Zhian Mi, Hanxiang Cheng, Xiyue Kohler, Jurgen Deng, Shuiquan |
| author_facet | Li, Zhian Mi, Hanxiang Cheng, Xiyue Kohler, Jurgen Deng, Shuiquan |
| contents | We demonstrate that the diagonal curvature in second-order Jahn-Teller theory (SOJTT) can be negative, invalidating its foundational positivity assumption. Using a frozen-phonon many-body expansion, we show no quantum-mechanical principle enforces its positivity; recasting into the Kohn-Sham framework further reveals that phonon-induced eigen-energy changes arise solely from electron-nuclear, Hartree, and exchange-correlation terms, with kinetic-energy contributions canceling identically. First principles calculations on NH3 place the D3h reference configuration at an A2" saddle point; Schwarz-inequality upper-bound analysis confines the HOMO-LUMO mixing contribution to < 0.2% of the total energy drop,while 99.8% originates from the diagonal electron-nuclear term driving N (2s-2pz) electron redistribution. These findings overturn a core SOJTT tenet and establish that spontaneous structural symmetry breaking demands prior verification of a saddle point, not assumed positivity of the diagonal curvature. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_14291 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Diagonal Curvature in Second Order Jahn Teller Theory Can Be Negative: An Analytic Proof with First-Principles Confirmation in NH3 Li, Zhian Mi, Hanxiang Cheng, Xiyue Kohler, Jurgen Deng, Shuiquan Materials Science We demonstrate that the diagonal curvature in second-order Jahn-Teller theory (SOJTT) can be negative, invalidating its foundational positivity assumption. Using a frozen-phonon many-body expansion, we show no quantum-mechanical principle enforces its positivity; recasting into the Kohn-Sham framework further reveals that phonon-induced eigen-energy changes arise solely from electron-nuclear, Hartree, and exchange-correlation terms, with kinetic-energy contributions canceling identically. First principles calculations on NH3 place the D3h reference configuration at an A2" saddle point; Schwarz-inequality upper-bound analysis confines the HOMO-LUMO mixing contribution to < 0.2% of the total energy drop,while 99.8% originates from the diagonal electron-nuclear term driving N (2s-2pz) electron redistribution. These findings overturn a core SOJTT tenet and establish that spontaneous structural symmetry breaking demands prior verification of a saddle point, not assumed positivity of the diagonal curvature. |
| title | Diagonal Curvature in Second Order Jahn Teller Theory Can Be Negative: An Analytic Proof with First-Principles Confirmation in NH3 |
| topic | Materials Science |
| url | https://arxiv.org/abs/2603.14291 |