dorsal/arxiv
View SchemaClassical kinetic energy, quantum fluctuation terms and kinetic-energy functionals
| Authors | I. P. Hamilton, Ricardo A. Mosna, L. Delle Site |
|---|---|
| Categories | |
| ArXiv ID | physics/0609148 |
| URL | https://arxiv.org/abs/physics/0609148 |
| DOI | 10.1007/s00214-007-0279-5 |
| Journal | Theor Chem Acc 118, 407-415 (2007) |
Abstract
We employ a recently formulated dequantization procedure to obtain an exact expression for the kinetic energy which is applicable to all kinetic-energy functionals. We express the kinetic energy of an N-electron system as the sum of an N-electron classical kinetic energy and an N-electron purely quantum kinetic energy arising from the quantum fluctuations that turn the classical momentum into the quantum momentum. This leads to an interesting analogy with Nelson's stochastic approach to quantum mechanics, which we use to conceptually clarify the physical nature of part of the kinetic-energy functional in terms of statistical fluctuations and in direct correspondence with Fisher Information Theory. We show that the N-electron purely quantum kinetic energy can be written as the sum of the (one-electron) Weizsacker term and an (N-1)-electron kinetic correlation term. We further show that the Weizsacker term results from local fluctuations while the kinetic correlation term results from the nonlocal fluctuations. For one-electron orbitals (where kinetic correlation is neglected) we obtain an exact (albeit impractical) expression for the noninteracting kinetic energy as the sum of the classical kinetic energy and the Weizsacker term. The classical kinetic energy is seen to be explicitly dependent on the electron phase and this has implications for the development of accurate orbital-free kinetic-energy functionals. Also, there is a direct connection between the classical kinetic energy and the angular momentum and, across a row of the periodic table, the classical kinetic energy component of the noninteracting kinetic energy generally increases as Z increases.
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"abstract": "We employ a recently formulated dequantization procedure to obtain an exact\nexpression for the kinetic energy which is applicable to all kinetic-energy\nfunctionals. We express the kinetic energy of an N-electron system as the sum\nof an N-electron classical kinetic energy and an N-electron purely quantum\nkinetic energy arising from the quantum fluctuations that turn the classical\nmomentum into the quantum momentum. This leads to an interesting analogy with\nNelson\u0027s stochastic approach to quantum mechanics, which we use to conceptually\nclarify the physical nature of part of the kinetic-energy functional in terms\nof statistical fluctuations and in direct correspondence with Fisher\nInformation Theory. We show that the N-electron purely quantum kinetic energy\ncan be written as the sum of the (one-electron) Weizsacker term and an\n(N-1)-electron kinetic correlation term. We further show that the Weizsacker\nterm results from local fluctuations while the kinetic correlation term results\nfrom the nonlocal fluctuations. For one-electron orbitals (where kinetic\ncorrelation is neglected) we obtain an exact (albeit impractical) expression\nfor the noninteracting kinetic energy as the sum of the classical kinetic\nenergy and the Weizsacker term. The classical kinetic energy is seen to be\nexplicitly dependent on the electron phase and this has implications for the\ndevelopment of accurate orbital-free kinetic-energy functionals. Also, there is\na direct connection between the classical kinetic energy and the angular\nmomentum and, across a row of the periodic table, the classical kinetic energy\ncomponent of the noninteracting kinetic energy generally increases as Z\nincreases.",
"arxiv_id": "physics/0609148",
"authors": [
"I. P. Hamilton",
"Ricardo A. Mosna",
"L. Delle Site"
],
"categories": [
"physics.chem-ph",
"math-ph",
"math.MP",
"quant-ph"
],
"doi": "10.1007/s00214-007-0279-5",
"journal_ref": "Theor Chem Acc 118, 407-415 (2007)",
"title": "Classical kinetic energy, quantum fluctuation terms and kinetic-energy functionals",
"url": "https://arxiv.org/abs/physics/0609148"
},
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