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Molecular Physics
An International Journal at the Interface Between Chemistry and Physics
Volume 28, 1974 - Issue 6
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Original Articles

Non-adiabatic calculations for H2+, HD+ and D2+

David M. Bishop Department of Chemistry, University of Ottawa, Ottawa, K1N 6N5, Canada
Pages 1397-1408 | Received 08 Apr 1974, Published online: 22 Aug 2006

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Werner Kutzelnigg. (2007) Which masses are vibrating or rotating in a molecule?. Molecular Physics 105:19-22, pages 2627-2647.
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R.A. Kennedy, R.E. Moss & I.A. Sadler. (1988) Vibrational levels of HD+ near dissociation. Molecular Physics 64:2, pages 177-189.
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R.E. Moss & I.A. Sadler. (1987) Symmetry breaking effects in HD+ . Molecular Physics 61:4, pages 905-921.
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DavidM. Bishop, Janusz Pipin & JeremiahN. Silverman. (1986) Methods for introducing vibrational effects in the calculation of electric dipole polarizabilities and hyperpolarizabilities (with reference to H+ 2). Molecular Physics 59:2, pages 165-172.
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J. Czub & L. Wolniewicz. (1978) On the non-adiabatic potentials in diatomic molecules. Molecular Physics 36:5, pages 1301-1308.
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DavidM. Bishop & LapM. Cheung. (1978) Accurate expectation values for H2 + (and its isotopes) and H2 . Molecular Physics 36:2, pages 501-507.
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DavidM. Bishop & Geoffrey Hunter. (1975) Non-adiabatic potentials for H2 + . Molecular Physics 30:5, pages 1433-1439.
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Articles from other publishers (60)

Ziyong Chen & Jun Yang. (2021) Nucleus–electron correlation revising molecular bonding fingerprints from the exact wavefunction factorization. The Journal of Chemical Physics 155:10.
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Maximilian Beyer & Frédéric Merkt. (2016) Structure and dynamics of H2+ near the dissociation threshold: A combined experimental and computational investigation. Journal of Molecular Spectroscopy 330, pages 147-157.
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Néstor F. Aguirre, Pablo Villarreal, Gerardo Delgado-Barrio, Edwin Posada, Andrés Reyes, Malgorzata Biczysko, Alexander O. Mitrushchenkov & María Pilar de Lara-Castells. (2013) Including nuclear quantum effects into highly correlated electronic structure calculations of weakly bound systems. The Journal of Chemical Physics 138:18.
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Steven A. Alexander & Robert L. Coldwell. (2012) Vibrational energies of H 2 + using fully nonadiabatic wavefunctions . International Journal of Quantum Chemistry 112:23, pages 3703-3705.
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Hiroaki Nishizawa, Yutaka Imamura, Yasuhiro Ikabata & Hiromi Nakai. (2012) Development of the explicitly correlated Gaussian–nuclear orbital plus molecular orbital theory: Incorporation of electron–electron correlation. Chemical Physics Letters 533, pages 100-105.
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Hiroaki Nishizawa, Minoru Hoshino, Yutaka Imamura & Hiromi Nakai. (2012) Evaluation of electron repulsion integral of the explicitly correlated Gaussian-nuclear orbital plus molecular orbital theory. Chemical Physics Letters 521, pages 142-149.
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Minoru Hoshino, Hiroaki Nishizawa & Hiromi Nakai. (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.
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Takayoshi Ishimoto, Masanori Tachikawa & Umpei Nagashima. (2009) Review of multicomponent molecular orbital method for direct treatment of nuclear quantum effect. International Journal of Quantum Chemistry 109:12, pages 2677-2694.
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Yutaka Imamura, Yasuhiro Tsukamoto, Hiroyoshi Kiryu & Hiromi Nakai. (2009) Extension of Density Functional Theory to Nuclear Orbital plus Molecular Orbital Theory: Self-Consistent Field Calculations with the Colle–Salvetti Electron–Nucleus Correlation Functional. Bulletin of the Chemical Society of Japan 82:9, pages 1133-1139.
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Ralph Jaquet & Werner Kutzelnigg. (2008) Non-adiabatic theory in terms of a single potential energy surface. The vibration–rotation levels of and. Chemical Physics 346:1-3, pages 69-76.
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S. Stimson, M. Evans, C.-W. Hsu & C. Y. Ng. (2007) Rotationally resolved vacuum ultraviolet pulsed field ionization-photoelectron vibrational bands for HD+(XΣg+2,v+=–20). The Journal of Chemical Physics 126:16.
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Neji Khelifi, Brahim Oujia & Florent Xavier Gadea. (2007) Dynamic Couplings, Radiative and Nonradiative Lifetimes of the A1Σ+ and C1Σ+ States of the KH Molecule. Journal of Physical and Chemical Reference Data 36:1, pages 191-202.
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Hiromi Nakai & Minoru Hoshino. (2007) Non-Born-Oppenheimer Theory for Simultaneous Determination of Nuclear and Electronic Wave Functions: Nuclear Orbital plus Molecular Orbital (NOMO) Theory. Molecular Science 1:1, pages A0010-A0010.
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Stephen Wilson. 2007. Topics in the Theory Of Chemical and Physical Systems. Topics in the Theory Of Chemical and Physical Systems 35 61 .
Hiromi Nakai. (2007) Nuclear orbital plus molecular orbital theory: Simultaneous determination of nuclear and electronic wave functions without Born–Oppenheimer approximation. International Journal of Quantum Chemistry 107:14, pages 2849-2869.
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Neji Khelifi, Brahim Oujia & Florent Xavier Gadea. (2006) Dynamic study: Radiative and nonradiative lifetimes for vibrational levels of the A 1∑+ and C 1∑+ states of the alkali hydride KH. Journal of Russian Laser Research 27:6, pages 575-600.
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D. L. Nascimento & A. L. A. Fonseca. (2003) Relativistic method to get analytic solutions for many-body problems: Application to theH+2 molecule. International Journal of Quantum Chemistry 95:3, pages 274-280.
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Hiromi Nakai. (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, pages 511-517.
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Inbal Tuvi & Y. B. Band. (1999) Modified Born-Oppenheimer basis for nonadiabatic coupling: Application to the vibronic spectrum of HD+. The Journal of Chemical Physics 111:13, pages 5808-5823.
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Inbal Tuvi & Y. B. Band. (1999) Nonadiabatic coupling using a corrected Born-Oppenheimer basis: The vibronic spectrum of . Physical Review A 59:4, pages 2680-2683.
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Jerzy Cioslowski. 1999. Pauling's Legacy - Modem Modelling of the Chemical Bond. Pauling's Legacy - Modem Modelling of the Chemical Bond 1 20 .
S Stimson, Y.-J Chen, M Evans, C.-L Liao, C.Y Ng, C.-W Hsu & P Heimann. (1998) Rotational-resolved pulsed field ionization photoelectron bands for H2+(X 2Σg+, v+=0, 2, 9 and 11). Chemical Physics Letters 289:5-6, pages 507-515.
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Y. Shigeta, H. Takahashi, S. Yamanaka, M. Mitani, H. Nagao & K. Yamaguchi. (1998) Density functional theory without the Born-Oppenheimer approximation and its application. International Journal of Quantum Chemistry 70:4-5, pages 659-669.
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Y. Shigeta, Y. Ozaki, K. Kodama, H. Nagao, H. Kawabe & K. Nishikawa. (1998) Nonadiabatic molecular theory and its application. II. Water molecule. International Journal of Quantum Chemistry 69:5, pages 629-637.
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Jose Ramón Álvarez-Collado, Alfredo Aguado & Miguel Paniagua. (1995) The vibrational structure of H+4 and D+4. The Journal of Chemical Physics 102:14, pages 5725-5732.
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Gerd Blanke & Heinz Kleindienst. (1994) NonadiabaticNO expansions for the ground state wave function of H2+. International Journal of Quantum Chemistry 51:1, pages 3-11.
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Heinz Kleindienst & Rainer Emrich. 1991. Numerical Treatment of Eigenvalue Problems Vol. 5 / Numerische Behandlung von Eigenwertaufgaben Band 5. Numerical Treatment of Eigenvalue Problems Vol. 5 / Numerische Behandlung von Eigenwertaufgaben Band 5 131 142 .
A Carrington, I R McNab & C A Montgomerie. (1989) Spectroscopy of the hydrogen molecular ion. Journal of Physics B: Atomic, Molecular and Optical Physics 22:22, pages 3551-3586.
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Heinz Kleindienst & Andreas Müller. (1989) Nonadiabatic lower bound calculations on HD+, DT+ and HT+. Chemical Physics Letters 157:5, pages 426-429.
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Andrew Komornicki & David A. Dixon. (1987) Structure, vibrational spectrum, and energetics of the CH+5 ion. A theoretical investigation. The Journal of Chemical Physics 86:10, pages 5625-5634.
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Jeremiah N. Silverman & David M. Bishop. (1986) Physical origins of high-order nonadiabatic molecular electric polarizabilities: Application to a twentieth-order perturbation study of . Physical Review A 34:6, pages 5142-5145.
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Jeremiah N. Silverman & David M. Bishop. (1986) High-order non-born-oppenheimer electric polarizabilities for excited states of H+2 via the perturbational-variational rayleigh-ritz formalism. Chemical Physics Letters 132:1, pages 37-43.
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R. S. Bhattacharjee, R. P. Saxena, P. K. Srivastava & K. V. Sane. (1986) Vibrational-rotational (v-J) levels of HD+, evaluated in the adiabatic approximation for the electronic ground state (1sσg). Proceedings / Indian Academy of Sciences 97:2, pages 191-207.
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Heinz Kleindienst & Dirk Hoppe. (1986) A nonadiabatic lower bound calculation of H 2 + and D 2 +. Theoretica Chimica Acta 70:3, pages 221-225.
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Jeremiah N. Silverman, David M. Bishop & Janusz Pipin. (1986) Twentieth-Order Perturbation Study of the Nondiabatic Electric Polarizabilities for via the Perturbational-Variational Rayleigh-Ritz Formalism . Physical Review Letters 56:13, pages 1358-1361.
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ALAN CARRINGTON & RICHARD A. KENNEDY. 1984. Ions and Light. Ions and Light 393 442 .
J. G. Ribeiro Tostes & A. F. R. de Toledo Piza. (1983) Nonadiabatic generator-coordinate calculation of . Physical Review A 28:2, pages 538-543.
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R. D. Poshusta. (2004) Nonadiabatic singer polymal wave functions for three‐particle systems. International Journal of Quantum Chemistry 24:1, pages 65-77.
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C. R. Vidal & W. C. Stwalley. (1982) The A  1Σ+– X  1Σ+ system of the isotopic lithium hydrides: The molecular constants, potential energy curves, and their adiabatic corrections . The Journal of Chemical Physics 77:2, pages 883-898.
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J. E. Pollard, D. J. Trevor, J. E. Reutt, Y. T. Lee & D. A. Shirley. (1982) Rotationally resolved photoelectron spectroscopy of n -H2, p -H2, HD, and D2 . The Journal of Chemical Physics 77:1, pages 34-46.
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Alan Carrington, Juliet Buttenshaw & Richard A. Kennedy. (1982) Vibration-rotation spectroscopy of the HD+ ion. Journal of Molecular Structure 80, pages 47-69.
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P.G. Fournier & B. Lassier-Govers. (1982) Calculs des niveaux d'énergie liés et quasi-liés des ions moléculaires muoniques Heμ+ et Neμ+. Journal de Physique Lettres 43:13, pages 483-491.
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R McWeeny & B T Pickup. (1980) Quantum theory of molecular electronic structure. Reports on Progress in Physics 43:9, pages 1065-1144.
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Craig W. Brown. (1980) Shortcomings of the Hellmann-Feynman Theorem. Physical Review Letters 44:16, pages 1054-1057.
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David M. Bishop & Lap M. Cheung. 1980. 1 42 .
Heinz Kleindienst & Wolfgang M�ller. (1980) Variance minimization. A variational principle for accurate lower and upper bounds of the eigenvalues of a selfadjoint operator, bounded below. Theoretica Chimica Acta 56:3, pages 183-189.
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Hans A. Schuessler. 1979. Progress in Atomic Spectroscopy. Progress in Atomic Spectroscopy 999 1029 .
David M. Bishop & Lap M. Cheung. (1978) Rigorous theoretical investigation of the ground state of . Physical Review A 18:5, pages 1846-1852.
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L Wolniewicz & J.D Poll. (1978) Ab initio nonadiabatic vibrational energies of the hydrogen molecule ion. Journal of Molecular Spectroscopy 72:2, pages 264-274.
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R.I. Price. (1978) Rotational predissociation of HeH+: The effect of nuclear motion on ro-vibrational energies and widths. Chemical Physics 31:2, pages 309-317.
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David M. Bishop & Lap M. Cheung. (1977) Calculation of transition frequencies for and its isotopes to spectroscopic accuracy . Physical Review A 16:2, pages 640-645.
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Ch. Jungen & O. Atabek. (1977) Rovibronic interactions in the photoabsorption spectrum of molecular hydrogen and deuterium: An application of multichannel quantum defect methods. The Journal of Chemical Physics 66:12, pages 5584-5609.
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David M. Bishop. (1976) Adiabatic relativistic rotation-vibration energy levels for HD+, HT+, and DT+. Atomic Data and Nuclear Data Tables 18:6, pages 521-524.
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E.A. Colbourn & P.R. Bunker. (1976) Accurate theoretical vibration-rotation energies and transition moments for HD+, HT+, and DT+. Journal of Molecular Spectroscopy 63:2, pages 155-163.
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David M. Bishop. (1976) Accurate Calculation of the Infrared Spectra of H , H , and D . Physical Review Letters 37:8, pages 484-485.
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William H. Wing, George A. Ruff, Willis E. Lamb & Joseph J. Spezeski. (1976) Observation of the Infrared Spectrum of the Hydrogen Molecular Ion H . Physical Review Letters 36:25, pages 1488-1491.
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David M. Bishop. (1976) Use of an effective Schrödinger equation for calculating the vibrational energy spacings of H2+ and D2+. Journal of Molecular Spectroscopy 61:3, pages 474-476.
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Wm. B. Peatman. (1976) Threshold electron photoionization study of H2: Vibration–rotation states of H+2( X  2Σ+ g ) . The Journal of Chemical Physics 64:10, pages 4093-4099.
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David M. Bishop & Shing‐kuo Shih. (1976) An effective Schrödinger equation for the rovibronic energies of H 2 and D 2 . The Journal of Chemical Physics 64:1, pages 162-169.
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David M. Bishop, Shing-Kuo Shih, Charles L. Beckel, Fun-Min Wu & James M. Peek. (1975) Theoretical study of H+2 spectroscopic properties. IV. Adiabatic effects for the 2 p π u and 3 d σ g electronic states . The Journal of Chemical Physics 63:11, pages 4836-4841.
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