Palabras clave
teoría de perturbaciones de muchos cuerpos
efectos cuánticos nucleares
química muónica
programa LOWDIN
Cómo citar
Descargas
Societal impact
Resumen
Se presenta una teoría alternativa de perturbaciones de muchos cuerpos de segundo orden (MBPT(2)) para el método de orbitales moleculares para cualquier partícula (Any-Particle Molecular Orbital, APMO). En dicho marco, la función de onda de referencia se construyó como un producto de determinantes de Slater para especies ligeras (por ejemplo, electrones) y productos de Hartree de orbitales localizados para especies pesadas (por ejemplo, muones y núcleos). Se analizó el impacto de esta aproximación de producto de Hartree (Hartree Product Approximation, HPA) en las energías APMO/MBPT(2) en la molécula de hidrogeno y en dímeros unidos por enlaces de hidrogeno. Se observó que el efecto de la HPA en las energías de primer orden es despreciable. En cambio, la HPA introduce cambios en los términos de correlación núcleo-electrón, lo que conduce a reducciones del orden de 10−2 u.a. en las energías de segundo orden. Las energías APMO/MBPT(2)/HPA están más cercanas a las energías de interacción de configuración completa (full-CI) que las energías APMO/MBPT(2) convencionales. La aplicación a sistemas que contienen múltiples núcleos de hidrógeno reveló que la HPA reduce el escalado formal de la transformación de integrales núcleo-electrón y núcleo-núcleo, pasando de quintico a cuártico y cúbico, respectivamente. Estas reducciones permiten realizar cálculos APMO/MBPT(2) en sistemas mucho más grandes. La aplicación del método APMO/MBPT(2) a átomos de helio y litio muónicos, así como al dímero de helio muónico, muestra que la correlación muón-electrón es del orden de apenas 1×10−6 u.a. Este trabajo constituye una contribución metodológica y computacional que ofrece una aproximación pragmática y de bajo costo para estudios exploratorios de efectos cuánticos nucleares en sistemas de tamaño medio. La principal ventaja reside en la reducción de la complejidad computacional, lo que permite explorar sistemas más grandes y superficies de energía potencial.
Referencias
Aguirre, N. F., Villarreal, P., Delgado-Barrio, G., Posada, E., Reyes, A., Biczysko, M., Mitrushchenkov, A., & de Lara-Castells, M. (2013). Including nuclear quantum effects into highly correlated electronic structure calculations of weakly bound systems. The Journal of Chemical Physics, 138(18), 184113. https://doi.org/10.1063/1.4803546
Auer, B., & Hammes-Schiffer, S. (2010). Localized Hartree product treatment of multiple protons in the nuclear-electronic orbital framework. The Journal of Chemical Physics, 132(8), 084110. https://doi.org/10.1063/1.3323015
Born, M., & Oppenheimer, J. R. (1927). Zur Quantentheorie der Molekeln. Annalen der Physik, 84(20), 457–484. https://doi.org/10.1002/andp.19273892002
Cafiero, M., Bubin, S., & Adamowicz, L. (2003). Non-Born–Oppenheimer calculations of atoms and molecules. Physical Chemistry Chemical Physics, 5(7), 1491–1501. https://doi.org/10.1039/B211422M
Charry, J., Varella, M. T. d. N., & Reyes, A. (2018). Binding matter with antimatter: The covalent positron bond. Angewandte Chemie International Edition, 130(29), 8997–9002. https://doi.org/10.1002/anie.201804538
Charry Martinez, J. A., Barborini, M., & Tkatchenko, A. (2022). Correlated wave functions for electron-positron interactions in atoms and molecules. Journal of Chemical Theory and Computation, 18(4), 2267–2280. https://doi.org/10.1021/acs.jctc.1c01211
Dunning, J., Thom H. (1989). Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen. The Journal of Chemical Physics, 90(2), 1007–1023. https://doi.org/10.1063/1.456153
Flores-Moreno, R., Posada, E., Moncada, F., Romero, J., Charry, J., Díaz-Tinoco, M., González, S. A., Aguirre, N. F., & Reyes, A. (2014). LOWDIN: The any particle molecular orbital code. International Journal of Quantum Chemistry, 114(1), 50–56. https://doi.org/10.1002/qua.24531
Fowler, D., & Brorsen, K. R. (2022). (T) correction for multicomponent coupled-cluster theory for a single quantum proton. Journal of Chemical Theory and Computation, 18(12), 7298–7305. https://doi.org/10.1021/acs.jctc.2c00701
González, S. A., Aguirre, N. F., & Reyes, A. (2008). Theoretical investigation of isotope effects: The any-particle molecular orbital code. International Journal of Quantum Chemistry, 108(10), 1742–1749. https://doi.org/10.1002/qua.21728
González, S. A., & Reyes, A. (2010). Nuclear quantum effects on the He2H+ complex with the nuclear molecular orbital approach. International Journal of Quantum Chemistry, 110(4), 689–696. https://doi.org/10.1002/qua.22055
Hehre, W. J., Ditchfield, R., & Pople, J. A. (1972). Self—Consistent Molecular Orbital Methods. XII. Further Extensions of Gaussian—Type Basis Sets for Use in Molecular Orbital Studies of Organic Molecules. The Journal of Chemical Physics, 56(6), 2257–2261. https://doi.org/10.1063/1.1677527
Hehre, W. J., Stewart, R. F., & Pople, J. A. (1969). Self-Consistent Molecular-Orbital Methods. I. Use of Gaussian Expansions of Slater-Type Atomic Orbitals. The Journal of Chemical Physics, 51(6), 2657–2664. https://doi.org/10.1063/1.1672392
Hoshino, M., & Nakai, H. (2006). Elimination of translational and rotational motions in nuclear orbital plus molecular orbital theory: Application of Møller-Plesset perturbation theory. The Journal of Chemical Physics, 124(19), 194110. https://doi.org/10.1063/1.2193513
Hoshino, M., Tsukamoto, Y., & Nakai, H. (2007). Development of analytic energy gradient method in nuclear orbital plus molecular orbital theory. International Journal of Quantum Chemistry, 107(14), 2575–2585. https://doi.org/10.1002/qua.21456
Hoshino, M., Nishizawa, H., & Nakai, H. (2011). Rigorous non-born-oppenheimer theory: Combination of explicitly correlated Gaussian method and nuclear orbital plus molecular orbital theory. The Journal of Chemical Physics, 135(2), 024111. https://doi.org/10.1063/1.3609344
Ishii, Y., Kuwahata, K., Shimazaki, T., & Tachikawa, M. (2025). Theoretical analysis of H/D isotope effect in K3H(SO4)2 and its influence on phase transition temperature. Physical Chemistry Chemical Physics, 28. https://doi.org/10.1039/D5CP02885J
Ishimoto, T., Ishihara, Y., Teramae, H., Baba, M., & Nagashima, U. (2008). H/D isotope effect of methyl internal rotation for acetaldehyde in ground state as calculated from a multicomponent molecular orbital method. The Journal of Chemical Physics, 128(18), 184309. https://doi.org/10.1063/1.2913164
Ishimoto, T., Tachikawa, M., & Nagashima, U. (2006). Electron-electron and electron-nucleus correlation effects on exponent values of Gaussian-type functions for quantum protons and deuterons. The Journal of Chemical Physics, 125(4), 044103. https://doi.org/10.1063/1.2222378
Ishimoto, T., Tachikawa, M., & Nagashima, U. (2008). Simultaneous analytical optimization of variational parameters in Gaussian-type functions with full configuration interaction of multicomponent molecular orbital method by elimination of translational and rotational motions: Application to isotopomers of the hydrogen molecule. The Journal of Chemical Physics, 128(16), 164118. https://doi.org/10.1063/1.2902973
Ishimoto, T., Tachikawa, M., & Nagashima, U. (2009). Review of multicomponent molecular orbital method for direct treatment of nuclear quantum effect. International Journal of Quantum Chemistry, 109(12), 2677–2694. https://doi.org/10.1002/qua.22069
Kaneko, M., Udagawa, T., & Tachikawa, M. (2010). Geometric isotope effect on low barrier hydrogen-bonding systems of acetic acid dimer, formic acid dimer, and their anionic clusters by using the multi-component molecular orbital method. Journal of Computer Chemistry, Japan, 9(1), 21–28. https://doi.org/10.2477/jccj.H2113
Kikuta, Y., Ishimoto, T., & Nagashima, U. (2008). Geometrical and kinetic isotope effects on R–H (D)···R type intramolecular hydrogen bonds (R= CH2, NH, and O) using a multi-component molecular orbital method. Bulletin of the Chemical Society of Japan, 81(7), 820–825. https://doi.org/10.1246/bcsj.81.820
Kita, Y., & Tachikawa, M. (2009). Nuclear quantum effects on molecular magnetic properties. Journal of Molecular Structure: THEOCHEM, 912(1-3), 2–4. https://doi.org/10.1016/j.theochem.2009.04.032
Kreibich, T., & Gross, E. K. U. (2001). Multicomponent density-functional theory for electrons and nuclei. Physical Review Letters, 86(14), 2984–2987. https://doi.org/10.1103/PhysRevLett.86.2984
Moncada, F., Cruz, D., & Reyes, A. (2012). Muonic alchemy: Transmuting elements with the inclusion of negative muons. Chemical Physics Letters, 539-540, 209–213. https://doi.org/10.1016/j.cplett.2012.03.073
Moncada, F., Cruz, D., & Reyes, A. (2013a). Electronic properties of atoms and molecules containing one and two negative muons. Chemical Physics Letters, 570, 16–21. https://doi.org/10.1016/j.cplett.2013.03.047
Moncada, F., Cruz, D., & Reyes, A. (2013b). Electronic properties of atoms and molecules containing one and two negative muons. Chemical Physics Letters, 570, 16–21. https://doi.org/10.1016/j.cplett.2013.03.047
Moncada, F., González, S. A., & Reyes, A. (2010). First principles investigation of hydrogen isotope effects in [XSO4–H–SO4X]− (X = H, K) complexes. Molecular Physics, 108(12), 1545–1552. https://doi.org/10.1080/00268971003716616
Moncada, F., Uribe, L. S., Romero, J., & Reyes, A. (2013a). Hydrogen isotope effects on covalent and noncovalent interactions: The case of protonated rare gas clusters. International Journal of Quantum Chemistry, 113(22), 1556–1561. https://doi.org/10.1002/qua.24479
Moncada, F., Uribe, L. S., Romero, J., & Reyes, A. (2013b). Hydrogen isotope effects on covalent and noncovalent interactions: The case of protonated rare gas clusters. International Journal of Quantum Chemistry, 113(10), 1556–1561. https://doi.org/10.1002/qua.24357
Moreno, D. V., González, S. A., & Reyes, A. (2010). Secondary hydrogen isotope effects on the structure and stability of cation-π complexes (Cation = Li+, Na+, K+ and π = Acetylene, Ethylene, Benzene). The Journal of Physical Chemistry A, 114(36), 9231–9236. https://doi.org/10.1021/jp1038237
Moreno, D. V., González, S. A., & Reyes, A. (2011). Turning symmetric an asymmetric hydrogen bond with the inclusion of nuclear quantum effects: The case of the [CN···H···NC]−-complex. The Journal of Chemical Physics, 134(2), 024115. https://doi.org/10.1063/1.3523961
Nakai, H. (2002). Simultaneous determination of nuclear and electronic wave functions without Born–Oppenheimer approximation: Ab initio NO+ MO/HF theory. International Journal of Quantum Chemistry, 86(6), 511–517. https://doi.org/10.1002/qua.10026
Nakai, H. (2007). Nuclear orbital plus molecular orbital theory: Simultaneous determination of nuclear and electronic wave functions without Born–Oppenheimer approximation. International Journal of Quantum Chemistry, 107(15), 2849–2869. https://doi.org/10.1002/qua.21457
Nakai, H., Ikabata, Y., Tsukamoto, Y., Imamura, Y., Miyamoto, K., & Hoshino, M. (2007). Isotope effect in dihydrogen-bonded systems: Application of the analytical energy gradient method in the nuclear orbital plus molecular orbital theory. Molecular Physics, 105(20-22), 2649–2657. https://doi.org/10.1080/00268970701648713
Nakai, H., & Sodeyama, K. (2003). Many-body effects in nonadiabatic molecular theory for simultaneous determination of nuclear and electronic wave functions: Ab initio NOMO-MBPT and CC methods. The Journal of Chemical Physics, 118(3), 1119. https://doi.org/10.1063/1.1528951
Nakai, H., Hoshino, M., Miyamoto, K., & Hyodo, S. (2005). Elimination of translational and rotational motions in nuclear orbital plus molecular orbital theory. The Journal of Chemical Physics, 122(16), 164101. https://doi.org/10.1063/1.1884601
Pavošević, F., Culpitt, T., & Hammes-Schiffer, S. (2019). Multicomponent coupled cluster singles and doubles theory within the nuclear-electronic orbital framework. Journal of Chemical Theory and Computation, 15(1), 338–347. https://doi.org/10.1021/acs.jctc.8b00975
Pedraza-González, L., Romero, J., Alí-Torres, J., & Reyes, A. (2016). Prediction of proton affinities of organic molecules using the any-particle molecular-orbital second-order proton propagator approach. Physical Chemistry Chemical Physics, 18(39), 27185–27189. https://doi.org/10.1039/C6CP13455F
Peng, Q., Zhang, X., Hung, L., Carter, E. A., & Lu, G. (2008). Quantum simulation of materials at micron scales and beyond. Physical Review B, 78(5), 054118. https://doi.org/10.1103/PhysRevB.78.054118
Posada, E., Moncada, F., & Reyes, A. (2014). Negative muon chemistry: The quantum muon effect and the finite nuclear mass effect. The Journal of Physical Chemistry A, 118(40), 9491–9499. https://doi.org/10.1021/jp505852b
Reyes, A., Pak, M. V., & Hammes-Schiffer, S. (2005). Investigation of isotope effects with the nuclear-electronic orbital approach. The Journal of Chemical Physics, 123(6), 064104. https://doi.org/10.1063/1.1990116
Reyes, A., Moncada, F., & Charry, J. (2019). The any particle molecular orbital approach: A short review of the theory and applications. International Journal of Quantum Chemistry, 119(2), e25705. https://doi.org/10.1002/qua.25705
Romero, J., Posada, E., Flores-Moreno, R., & Reyes, A. (2012). A generalized any particle propagator theory: Assessment of nuclear quantum effects on electron propagator calculations. The Journal of Chemical Physics, 137(7), 074105. https://doi.org/10.1063/1.4742869
Stanke, M., Kedziorski, A., & Adamowicz, L. (2026). High-accuracy non-Born-Oppenheimer calculations with all-electron explicitly correlated Gaussians of finite-nuclear-mass effects in the spectrum of the ten lowest 1D Rydberg states of beryllium. Physical Review A, 113(1), 012814. https://doi.org/10.1103/PhysRevA.113.012814
Swalina, C., Pak, M. V., & Hammes-Schiffer, S. (2005). Alternative formulation of many-body perturbation theory for electron-proton correlation. Chemical Physics Letters, 404(4-6), 394–399. https://doi.org/10.1016/j.cplett.2005.01.114
Szabo, A., & Ostlund, N. S. (1996). Modern quantum chemistry: Introduction to Advanced Electronic Structure Theory. Dover Publications.
Tachikawa, M. (2002). Multi-component molecular orbital theory for electrons and nuclei including many-body effect with full configuration interaction treatment: Isotope effects on hydrogen molecules. Chemical Physics Letters, 360(5-6), 494–500. https://doi.org/10.1016/S0009-2614(02)00881-3
Tachikawa, M. (2008). Multi-component first-principles calculation on isotope effect in hydrogen-bonded dieletric materials K3H(SO4)2 and K3D(SO4)2. Integrated Ferroelectrics, 100(1), 72–78. https://doi.org/10.1080/10584580802540549
Tachikawa, M., Ishimoto, T., Tokiwa, H., Kasatani, H., & Deguchi, K. (2002). First-principle calculation on isotope effect in KH2PO4 and KD2PO4 of hydrogen-bonded dielectric materials. Approach with dynamic extended molecular orbital method. Ferroelectrics, 268(1), 3–9. https://doi.org/10.1080/00150190211440
Tachikawa, M., Mori, K., Nakai, H., & Iguchi, K. (1998). An extension of ab initio molecular orbital theory to nuclear motion. Chemical Physics Letters, 290(4-5), 437–442. https://doi.org/10.1016/S0009-2614(98)00519-5
Tachikawa, M., & Osamura, Y. (2000). Simultaneous optimization of exponents, centers of Gaussian-type basis functions, and geometry with full-configuration interaction wave function: Application to the ground and excited states of hydrogen molecule. The Journal of Chemical Physics, 113(11), 4942–4947. https://doi.org/10.1063/1.1290432
Tanaka, H., Kuwahata, K., Tachikawa, M., & Udagawa, T. (2025). Nuclear quantum and H/D isotope effects on hydrogen-bond symmetrization in lithium hydroxide crystals at high pressure. The Journal of Chemical Physics, 163. https://doi.org/10.1063/5.0276067
Udagawa, T., Ishimoto, T., Tokiwa, H., Tachikawa, M., & Nagashima, U. (2006). Geometric isotope effect of various intermolecular and intramolecular C-H···O hydrogen bonds, using the multicomponent molecular orbital method. The Journal of Physical Chemistry A, 110(23), 7279–7285. https://doi.org/10.1021/jp0605953
Udagawa, T., & Tachikawa, M. (2006). H/D isotope effect on porphine and porphycene molecules with multicomponent hybrid density functional theory. The Journal of Chemical Physics, 125(24), 244105. https://doi.org/10.1063/1.2403855
Udagawa, T., & Tachikawa, M. (2009). Multi-component molecular orbital theory. Nova Science Publishers.
Webb, S. P., Iordanov, T., & Hammes-Schiffer, S. (2002). Multiconfigurational nuclear-electronic orbital approach: Incorporation of nuclear quantum effects in electronic structure calculations. The Journal of Chemical Physics, 117(9), 4106–4115. https://doi.org/10.1063/1.1494985
Yamamoto, S., & Nagashima, U. (2005). Four-index integral transformation exploiting symmetry. Computer Physics Communications, 166(1), 58–65. https://doi.org/10.1016/j.cpc.2004.10.003
Yodsin, N., Udagawa, T., Daengngern, R., Jungsutthiwong, S., & Tachikawa, M. (2025). Unraveling H2 dissociation in CO2 hydrogenation on frustrated Lewis pair-functionalized UiO–67: DFT and nuclear quantum effects. International Journal of Hydrogen Energy, 195, 152499. https://doi.org/10.1016/j.ijhydene.2025.152499
Esta obra está bajo una licencia internacional Creative Commons Atribución-NoComercial-SinDerivadas 4.0.
Derechos de autor 2026 Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales