Navegar

Colección

Datos Estadísticas

Artículo

El editor permite incluir el artículo en su versión final en nuestro repositorio
Consulte el artículo en la página del editor
Consulte la política de Acceso Abierto del editor

Abstract:

In this paper we propose a functional of the many-body cumulant of the second-order reduced density matrix within the spin-free formalism of quantum chemistry which quantifies the idea of electron correlation and allows one to detect spin entanglement. Its properties are rigorously stated and discussed for spin-adapted pure states. Numerical determinations are performed for both equilibrium conformations and dissociation processes in molecular systems. © 2010 American Institute of Physics.

Registro:

Documento: Artículo
Título:On the measure of electron correlation and entanglement in quantum chemistry based on the cumulant of the second-order reduced density matrix
Autor:Alcoba, D.R.; Bochicchio, R.C.; Lain, L.; Torre, A.
Filiación:Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires 1428, Argentina
Instituto de Física de Buenos Aires, Consejo Nacional de Investigaciones Científicas y Técnicas, Ciudad Universitaria, Buenos Aires 1428, Argentina
Departamento de Química Física, Facultad de Ciencia y Tecnología, Universidad Del País Vasco, Apdo. 644, Bilbao E-48080, Spain
Palabras clave:Cumulants; Dissociation process; Equilibrium conformation; Many-body; Molecular systems; Pure state; Second-order reduced density; Spin entanglement; Dissociation; Electron correlations; Electron density measurement; Quantum entanglement
Año:2010
Volumen:133
Número:14
DOI: http://dx.doi.org/10.1063/1.3503766
Título revista:Journal of Chemical Physics
Título revista abreviado:J Chem Phys
ISSN:00219606
CODEN:JCPSA
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_00219606_v133_n14_p_Alcoba.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00219606_v133_n14_p_Alcoba

Referencias:

  • Fulde, P., (1993) Electron Correlations in Molecules and Solids, , (Springer, Berlin) (and references therein)
  • Löwdin, P.O., (1955) Phys. Rev., 97, p. 1474. , PHRVAO 0031-899X,. 10.1103/PhysRev.97.1474
  • Davidson, E.R., (1976) Reduced Density Matrices in Quantum Chemistry, , (Academic, New York) (and references therein)
  • Bader, R.F.W., (1994) Atoms in Molecules: A Quantum Theory, , (Clarendon, Oxford) (see also references therein)
  • Popelier, P.L.A., (1999) Atoms in Molecules: An Introduction, , (Pearson, London)
  • Lobayan, R.M., Bochicchio, R.C., Lain, L., Torre, A., Electron-density topology in molecular systems: Paired and unpaired densities (2005) Journal of Chemical Physics, 123 (14), pp. 1-9. , DOI 10.1063/1.2049227, 144116
  • Lobayan, R.M., Bochicchio, R.C., Lain, L., Torre, A., Laplacian field of the effectively unpaired electron density: Determination of many-body effects on electron distributions (2007) Journal of Physical Chemistry A, 111 (16), pp. 3166-3172. , DOI 10.1021/jp0681101
  • Lobayan, R.M., Bochicchio, R.C., Torre, A., Lain, L., (2009) J. Chem. Theory Comput., 5, p. 2030. , JCTCCE 1549-9618,. 10.1021/ct900281q
  • Lobayan, R.M., Alcoba, D.R., Bochicchio, R.C., Torre, A., Lain, L., (2010) J. Phys. Chem. A, 114, p. 1200. , JPCAFH 1089-5639,. 10.1021/jp909935j
  • McWeeny, R., (1969) Methods of Molecular Quantum Mechanics, , (Academic, London) (see also references therein)
  • Szabo, A., Ostlund, N.S., (1982) Modern Quantum Chemistry: Introduction to Advanced Electronic Structure, , (Macmillan, New York)
  • Bochicchio, R.C., (1991) J. Mol. Struct.: THEOCHEM, 228, p. 209. , THEODJ 0166-1280, () (and references therein). 10.1016/0166-1280(91) 90058-R
  • Fradera, X., Austen, M.A., Bader, R.F.W., (1999) J. Phys. Chem. A, 103, p. 304. , JPCAFH 1089-5639,. 10.1021/jp983362q
  • Bochicchio, R.C., Lain, L., Torre, A., On the definition of bond orders at correlated level (2003) Chemical Physics Letters, 374 (5-6), pp. 567-571. , DOI 10.1016/S0009-2614(03)00751-6, PII S0009261403007516
  • Alcoba, D.R., Bochicchio, R.C., Lain, L., Torre, A., Covalent bond indices and ionicities from similarity measures (2007) Chemical Physics Letters, 442 (1-3), pp. 157-163. , DOI 10.1016/j.cplett.2007.05.068, PII S0009261407006549
  • Takatsuka, K., Fueno, T., Yamaguchi, K., (1978) Theor. Chim. Acta, 48, p. 175. , TCHAAM 0040-5744,. 10.1007/BF00549017
  • Takatsuka, K., Fueno, T., (1978) J. Chem. Phys., 69, p. 661. , JCPSA6 0021-9606,. 10.1063/1.436631
  • Bochicchio, R.C., (1998) J. Mol. Struct.: THEOCHEM, 429, p. 229. , THEODJ 0166-1280,. 10.1016/S0166-1280(97)00357-6
  • Bochicchio, R.C., Lain, L., Torre, A., Atomic valence in molecular systems (2003) Chemical Physics Letters, 375 (1-2), pp. 45-53. , DOI 10.1016/S0009-2614(03)00805-4, PII S0009261403008054
  • Luzanov, A.V., Prezhdo, O.V., High-order entropy measures and spin-free quantum entanglement for molecular problems (2007) Molecular Physics, 105 (19-22), pp. 2879-2891. , DOI 10.1080/00268970701725039, PII 788615950, A Special Issue in Honour of Professor Peter Pulay
  • Luzanov, A.V., Zhikol, O.A., Collectivity, shell openness indices, and complexity measures of multiconfigurational states: Computations within full CI scheme (2005) International Journal of Quantum Chemistry, 104 (2 SPEC. ISS.), pp. 167-180. , DOI 10.1002/qua.20511
  • Juhasz, T., Mazziotti, D.A., The cumulant two-particle reduced density matrix as a measure of electron correlation and entanglement (2006) Journal of Chemical Physics, 125 (17), p. 174105. , DOI 10.1063/1.2378768
  • Kais, S., (2007) Reduced-Density-Matrix Mechanics with Applications to Many-Electron Atoms and Molecules, 134. , in, Advances in Chemical Physics Vol., edited by D. A. Mazziotti (Wiley-Intersience, Hoboken) (and references therein). 10.1002/9780470106600. ch18
  • Kutzelnigg, W., Mukherjee, D., Irreducible Brillouin conditions and contracted Schrödinger equations for n-electron systems. II. Spin-free formulation (2002) Journal of Chemical Physics, 116 (12), pp. 4787-4801. , DOI 10.1063/1.1448827
  • Kutzelnigg, W., Mukherjee, D., (1999) J. Chem. Phys., 110, p. 2800. , JCPSA6 0021-9606,. 10.1063/1.478189
  • Diósi, L., (2007) A Short Course in Quantum Information Theory. An Approach from Theoretical Physics, , (Springer, Berlin)
  • Ghirardi, G., Marinatto, L., Weber, T., Entanglement and properties of composite quantum systems: A conceptual and mathematical analysis (2002) Journal of Statistical Physics, 108 (1-2), pp. 49-122. , DOI 10.1023/A:1015439502289
  • Ghirardi, G.C., Marinatto, L., Identical particles and entanglement (2005) Optics and Spectroscopy (English translation of Optika i Spektroskopiya), 99 (3), pp. 386-390. , DOI 10.1134/1.2055932
  • McWeeny, R., (2007) Faraday Discuss., 135, p. 13. , FDISE6 0301-7249,. 10.1039/b615518a
  • Lain, L., Torre, A., Alcoba, D.R., Bochicchio, R.C., (2009) Chem. Phys. Lett., 476, p. 101. , CHPLBC 0009-2614,. 10.1016/j.cplett.2009.05.071
  • Alcoba, D.R., Bochicchio, R.C., Lain, L., Torre, A., On the definition of the effectively unpaired electron density matrix: A similarity measure approach (2006) Chemical Physics Letters, 429 (1-3), pp. 286-288. , DOI 10.1016/j.cplett.2006.07.068, PII S0009261406010906
  • Valdemoro, C., (2007) Reduced-Density-Matrix Mechanics with Applications to Many-Electron Atoms and Molecules, 134. , in, Advances in Chemical Physics Vol., edited by D. A. Mazziotti (Wiley-Intersience, Hoboken) (and references therein). 10.1002/9780470106600.ch7
  • Mazziotti, D.A., (1998) Phys. Rev. A, 57, p. 4219. , PLRAAN 1050-2947,. 10.1103/PhysRevA.57.4219
  • Mazziotti, D.A., (1998) Chem. Phys. Lett., 289, p. 419. , CHPLBC 0009-2614,. 10.1016/S0009-2614(98)00470-9
  • Alcoba, D.R., Bochicchio, R.C., Lain, L., Torre, A., (2008) Phys. Chem. Chem. Phys., 10, p. 5144. , PPCPFQ 1463-9076,. 10.1039/b806268d
  • McWeeny, R., Mizuno, Y., (1961) Proc. R. Soc. London, 259, p. 554. , PRSLAZ 0370-1662
  • Lain, L., Torre, A., Bochicchio, R., (2002) J. Chem. Phys., 117, p. 5497. , JCPSA6 0021-9606,. 10.1063/1.1499955
  • Torre, A., Lain, L., (1998) J. Mol. Struct.: THEOCHEM, 426, p. 25. , THEODJ 0166-1280, () (and references therein). 10.1016/S0166-1280(97) 00304-7
  • Kutzelnigg, W., (2007) Reduced-Density-Matrix Mechanics with Applications to Many-Electron Atoms and Molecules, 134. , in, Advances in Chemical Physics Vol., edited by D. A. Mazziotti (Wiley-Intersience, Hoboken) (and references therein). 10.1002/9780470106600. ch11
  • Harriman, J., (2007) Reduced-Density-Matrix Mechanics with Applications to Many-Electron Atoms and Molecules, 134. , in, Advances in Chemical Physics Vol., edited by D. A. Mazziotti (Wiley-Intersience, Hoboken)
  • Alcoba, D.R., Lain, L., Torre, A., Bochicchio, R.C., (2009) Chem. Phys. Lett., 470, p. 136. , CHPLBC 0009-2614,. 10.1016/j.cplett.2009.01.034
  • Lain, L., Torre, A., Bochicchio, R.C., Ponec, R., On the density matrix of effectively unpaired electrons (2001) Chemical Physics Letters, 346 (3-4), pp. 283-287. , DOI 10.1016/S0009-2614(01)00974-5, PII S0009261401009745
  • Staroverov, V.N., Davidson, E.R., Diradical character of the cope rearrangement transition state (2000) Journal of the American Chemical Society, 122 (1), pp. 186-187. , DOI 10.1021/ja993375x
  • Staroverov, V.N., Davidson, E.R., (2000) Chem. Phys. Lett., 330, p. 161. , CHPLBC 0009-2614,. 10.1016/S0009-2614(00)01088-5
  • Torre, A., Alcoba, D.R., Lain, L., Bochicchio, R.C., (2010) J. Phys. Chem. A, 114, p. 2344. , JPCAFH 1089-5639,. 10.1021/jp9090848
  • Head-Gordon, M., Characterizing unpaired electrons from the one-particle density matrix (2003) Chemical Physics Letters, 372 (3-4), pp. 508-511. , DOI 10.1016/S0009-2614(03)00422-6, PII S0009261403004226
  • Bochicchio, R.C., Torre, A., Lain, L., (2003) Chem. Phys. Lett., 380, p. 486. , CHPLBC 0009-2614,. 10.1016/j.cplett.2003.09.035
  • Rosina, M., (1968) Reduced Density Matrices with Applications to Physical and Chemical Systems, 11. , in, Queen's Papers on Pure and Applied Mathematics Vol., edited by J. Coleman and R. M. Erdahl (Queen's University, Kingston, Ontario)
  • Bru, D., (2002) J. Math. Phys., 43, p. 4237. , JMAPAQ 0022-2488,. 10.1063/1.1494474
  • Valdemoro, C., (1992) Phys. Rev. A, 45, p. 4462. , PLRAAN 1050-2947,. 10.1103/PhysRevA.45.4462
  • (1979) Handbook of Chemistry and Physics, , 59th ed., edited by R. C. Weast (CRC, Cleveland, OH)
  • Crawford, T.D., Sherrill, C.D., Valeev, E.F., Fermann, J.T., King, R.A., Leininger, M.L., Brown, S.T., Allen, W.D., Software news and update PSI3: An open-source Ab Initio electronic structure package (2007) Journal of Computational Chemistry, 28 (9), pp. 1610-1616. , DOI 10.1002/jcc.20573

Citas:

---------- APA ----------
Alcoba, D.R., Bochicchio, R.C., Lain, L. & Torre, A. (2010) . On the measure of electron correlation and entanglement in quantum chemistry based on the cumulant of the second-order reduced density matrix. Journal of Chemical Physics, 133(14).
http://dx.doi.org/10.1063/1.3503766
---------- CHICAGO ----------
Alcoba, D.R., Bochicchio, R.C., Lain, L., Torre, A. "On the measure of electron correlation and entanglement in quantum chemistry based on the cumulant of the second-order reduced density matrix" . Journal of Chemical Physics 133, no. 14 (2010).
http://dx.doi.org/10.1063/1.3503766
---------- MLA ----------
Alcoba, D.R., Bochicchio, R.C., Lain, L., Torre, A. "On the measure of electron correlation and entanglement in quantum chemistry based on the cumulant of the second-order reduced density matrix" . Journal of Chemical Physics, vol. 133, no. 14, 2010.
http://dx.doi.org/10.1063/1.3503766
---------- VANCOUVER ----------
Alcoba, D.R., Bochicchio, R.C., Lain, L., Torre, A. On the measure of electron correlation and entanglement in quantum chemistry based on the cumulant of the second-order reduced density matrix. J Chem Phys. 2010;133(14).
http://dx.doi.org/10.1063/1.3503766