DOI: 10.1063/1.1353585. On the density matrix based approach to time-dependent density functional response theory

On the density matrix based approach to time-dependent density functional response theory

10.1063/1.1353585

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

The formulation of time-dependent Kohn–Sham (TDKS) response theory based on the noninteracting one-particle density matrix is reanalyzed in detail. A transparent derivation starting from a von-Neumann-type equation of motion for the TDKS one-particle density matrix is presented. The resulting scheme has a simple structure and leads to compact expressions for frequency-dependent response properties. A systematic treatment of excited states is inferred from a pole analysis of the frequency-dependent density matrix response. A variational principle for excitation energies is established. Excited state properties are straightforward by analytical derivative techniques. The theory provides a particularly suitable starting point for linear scaling implementations. Magneto-optic properties such as rotatory strengths and the rotatory dispersion are accessible from the TDKS current-density response. The formalism is gauge-invariant. Various new sum rules within the adiabatic approximation (AA) are derived. It is shown that there is no “assignment problem” for excited states in the density matrix based formulation; the common density based approach is included as a special case. Merits and limitations of the AA are discussed.

Bibliography

Furche, F. (2001). On the density matrix based approach to time-dependent density functional response theory. The Journal of Chemical Physics, 114(14), 5982â5992.

Authors 1

Filipp Furche (first)

References 51 Referenced 390

10.1016/0009-2614(96)00440-X / Chem. Phys. Lett. (1996)
10.1063/1.471140 / J. Chem. Phys. (1996)
10.1063/1.477483 / J. Chem. Phys. (1998)
10.1063/1.477922 / J. Chem. Phys. (1999)
10.1016/S0010-4655(99)00187-3 / Comput. Phys. Commun. (1999)
10.1039/a910321j / Phys. Chem. Chem. Phys. (2000)
10.1063/1.482020 / J. Chem. Phys. (2000)
10.1063/1.481315 / J. Chem. Phys. (2000)
10.1016/S0009-2614(96)01343-7 / Chem. Phys. Lett. (1997)
10.1021/ja9730167 / J. Am. Chem. Soc. (1998)
10.1021/ja991960s / J. Am. Chem. Soc. (2000)
10.1016/S0009-2614(99)01428-1 / Chem. Phys. Lett. (2000)
10.1007/BFb0016643 / Top. Curr. Chem. (1996)
10.1103/PhysRevLett.76.1212 / Phys. Rev. Lett. (1996)
10.1103/PhysRevA.21.1561 / Phys. Rev. A (1980)
{'key': '2024020620224147000_r16'}
10.1016/S0065-3276(08)60600-0 / Adv. Quantum Chem. (1990)
10.1103/PhysRevLett.52.997 / Phys. Rev. Lett. (1984)
10.1103/PhysRevA.38.1149 / Phys. Rev. A (1988)
{'key': '2024020620224147000_r20'}
10.1063/1.448223 / J. Chem. Phys. (1985)
{'key': '2024020620224147000_r22'}
10.1063/1.451255 / J. Chem. Phys. (1986)
10.1002/jcc.540120409 / J. Comput. Chem. (1991)
10.1103/PhysRevLett.78.3097 / Phys. Rev. Lett. (1997)
10.1063/1.477762 / J. Chem. Phys. (1998)
10.1103/PhysRevLett.76.3168 / Phys. Rev. Lett. (1996)
10.1063/1.476741 / J. Chem. Phys. (1998)
10.1063/1.1318745 / J. Chem. Phys. (2000)
10.1103/PhysRevLett.80.1280 / Phys. Rev. Lett. (1998)
10.1007/BF01342393 / Z. Phys. (1929)
10.1016/S0009-2614(99)01346-9 / Chem. Phys. Lett. (2000)
10.1016/S0009-2614(97)00402-8 / Chem. Phys. Lett. (1997)
10.1063/1.465370 / J. Chem. Phys. (1993)
10.1002/(SICI)1097-461X(1998)68:1<1::AID-QUA1>3.0.CO;2-Z / Int. J. Quantum Chem. (1998)
10.1103/RevModPhys.36.844 / Rev. Mod. Phys. (1964)
10.1063/1.468366 / J. Chem. Phys. (1994)
10.1016/S0009-2614(99)01149-5 / Chem. Phys. Lett. (1999)
{'key': '2024020620224147000_r39', 'first-page': '545', 'volume': '44', 'year': '1980', 'journal-title': 'Adv. Chem. Phys.'} / Adv. Chem. Phys. (1980)
10.1016/0009-2614(93)85608-Q / Chem. Phys. Lett. (1993)
10.1016/S0065-3276(08)60381-0 / Adv. Quantum Chem. (1964)
10.1103/PhysRevA.59.3359 / Phys. Rev. A (1999)
10.1103/PhysRevLett.83.4361 / Phys. Rev. Lett. (1999)
10.1103/PhysRevA.57.2556 / Phys. Rev. A (1998)
10.1063/1.1318750 / J. Chem. Phys. (2000)
10.1103/PhysRevLett.82.378 / Phys. Rev. Lett. (1999)
10.1103/PhysRevLett.79.1905 / Phys. Rev. Lett. (1997)
10.1103/PhysRevA.55.2630 / Phys. Rev. A (1997)
{'key': '2024020620224147000_r49'}
10.1063/1.1701562 / J. Chem. Phys. (1967)
10.1063/1.471637 / J. Chem. Phys. (1996)

Dates

Type	When
Created	23 years, 1 month ago (July 26, 2002, 10:16 a.m.)
Deposited	1 year, 6 months ago (Feb. 6, 2024, 7:10 p.m.)
Indexed	3 weeks, 3 days ago (Aug. 7, 2025, 4:47 p.m.)
Issued	24 years, 4 months ago (April 8, 2001)
Published	24 years, 4 months ago (April 8, 2001)
Published Print	24 years, 4 months ago (April 8, 2001)

Funders 0

None

BibTeX

@article{Furche_2001, title={On the density matrix based approach to time-dependent density functional response theory}, volume={114}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.1353585}, DOI={10.1063/1.1353585}, number={14}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Furche, Filipp}, year={2001}, month=apr, pages={5982–5992} }

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  "short-title": [],
  "issued": {
    "date-parts": [
      [
        2001,
        4,
        8
      ]
    ]
  },
  "references-count": 51,
  "journal-issue": {
    "issue": "14",
    "published-print": {
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        [
          2001,
          4,
          8
        ]
      ]
    }
  },
  "URL": "http://dx.doi.org/10.1063/1.1353585",
  "relation": {},
  "ISSN": [
    "0021-9606",
    "1089-7690"
  ],
  "subject": [],
  "published-other": {
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      [
        2001,
        4,
        8
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    ]
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  "published": {
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        2001,
        4,
        8
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  }
}