Diagonalizing the Born–Oppenheimer Hamiltonian via Moyal perturbation theory, nonadiabatic corrections, and translational degrees of freedom

Littlejohn, Robert; Rawlinson, Jonathan; Subotnik, Joseph

doi:10.1063/5.0192465

Title: Diagonalizing the Born–Oppenheimer Hamiltonian via Moyal perturbation theory, nonadiabatic corrections, and translational degrees of freedom

Journal Article · 18 March 2024 · Journal of Chemical Physics

DOI: https://doi.org/10.1063/5.0192465 · OSTI ID:2510487

^[1];

^[2];

^[3]

University of California, Berkeley, CA (United States)
University of Manchester (United Kingdom)
University of Pennsylvania, Philadelphia, PA (United States)

This article describes a method for calculating higher order or nonadiabatic corrections in Born–Oppenheimer theory and its interaction with the translational degrees of freedom. The method uses the Wigner–Weyl correspondence to map nuclear operators into functions on the classical phase space and the Moyal star product to represent operator multiplication on those functions. These are explained in the body of the paper. The result is a power series in κ², where κ = (m/M)1/4 is the usual Born–Oppenheimer parameter. The lowest order term is the usual Born–Oppenheimer approximation, while higher order terms are nonadiabatic corrections. These are needed in calculations of electronic currents, momenta, and densities. The separation of nuclear and electronic degrees of freedom takes place in the context of the exact symmetries (for an isolated molecule) of translations and rotations, and these, especially translations, are explicitly incorporated into our discussion. This article presents an independent derivation of the Moyal expansion in molecular Born–Oppenheimer theory. Here, we show how electronic currents and momenta can be calculated within the framework of Moyal perturbation theory; we derive the transformation laws of the electronic Hamiltonian, the electronic eigenstates, and the derivative couplings under translations; we discuss in detail the rectilinear motion of the molecular center of mass in the Born–Oppenheimer representation; and we show how the elimination of the translational components of the derivative couplings leads to a unitary transformation that has the effect of exactly separating the translational degrees of freedom.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: University of Pennsylvania, Philadelphia, PA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0019397

OSTI ID:: 2510487

Journal Information:: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 11 Vol. 160; ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

References (102)

Zur Quantentheorie der Molekeln Born, M.; Oppenheimer, R. Annalen der Physik, Vol. 389, Issue 20 https://doi.org/10.1002/andp.19273892002	journal	January 1927
Vibrational optical activity: From discovery and development to future challenges Nafie, Laurence A. Chirality, Vol. 32, Issue 5 https://doi.org/10.1002/chir.23191	journal	February 2020
Some difficulties in considering rotation motion within the Born–Oppenheimer approximation for polyatomic molecules Sutcliffe, Brian International Journal of Quantum Chemistry, Vol. 112, Issue 17 https://doi.org/10.1002/qua.24021	journal	March 2012
Dipole length versus dipole velocity in the calculation of infrared intensities with Born–Oppenheimer wave functions Mead, C. Alden; Moscowitz, Albert International Journal of Quantum Chemistry, Vol. 1, Issue 3 https://doi.org/10.1002/qua.560010304	journal	May 1967
Coordinates which diagonalize the kinetic energy of relative motion Hirschfelder, Joseph O. International Journal of Quantum Chemistry, Vol. 3, Issue S3A https://doi.org/10.1002/qua.560030706	journal	June 2009
Moyal Quantum Mechanics: The Semiclassical Heisenberg Dynamics Osborn, T. A.; Molzahn, F. H. Annals of Physics, Vol. 241, Issue 1 https://doi.org/10.1006/aphy.1995.1057	journal	July 1995
Quantenmechanik und Gruppentheorie Weyl, H. Zeitschrift für Physik, Vol. 46, Issue 1-2 https://doi.org/10.1007/bf02055756	journal	November 1927
Geometry of the transport equation in multicomponent WKB approximations Emmrich, C.; Weinstein, A. Communications in Mathematical Physics, Vol. 176, Issue 3 https://doi.org/10.1007/bf02099256	journal	March 1996
A criterion for the confluence of two seams of conical intersection in triatomic molecules Yarkony, David R. Theoretical Chemistry Accounts: Theory, Computation, and Modeling (Theoretica Chimica Acta), Vol. 98, Issue 4 https://doi.org/10.1007/s002140050293	journal	January 1998
Tertiary and general-order collisions (II) Delves, L. M. Nuclear Physics, Vol. 20 https://doi.org/10.1016/0029-5582(60)90174-7	journal	October 1960
Velocity-dependent property surfaces and the theory of vibrational circular dichroism Buckingham, A. D.; Fowler, P. W.; Galwas, P. A. Chemical Physics, Vol. 112, Issue 1 https://doi.org/10.1016/0301-0104(87)85017-6	journal	February 1987
Wigner's function and other distribution functions in mock phase spaces Balazs, N. L.; Jennings, B. K. Physics Reports, Vol. 104, Issue 6 https://doi.org/10.1016/0370-1573(84)90151-0	journal	February 1984
The semiclassical evolution of wave packets Littlejohn, R. Physics Reports, Vol. 138, Issue 4-5 https://doi.org/10.1016/0370-1573(86)90103-1	journal	May 1986
Phase-space representations of wave equations with applications to the eikonal approximation for short-wavelength waves McDonald, Steven W. Physics Reports, Vol. 158, Issue 6 https://doi.org/10.1016/0370-1573(88)90012-9	journal	February 1988
The exact wavefunction of interacting N degrees of freedom as a product of N single-degree-of-freedom wavefunctions Cederbaum, Lorenz S. Chemical Physics, Vol. 457 https://doi.org/10.1016/j.chemphys.2015.05.021	journal	August 2015
Numerical analysis of the exact factorization of molecular time-dependent Schrödinger wavefunctions Lorin, Emmanuel Communications in Nonlinear Science and Numerical Simulation, Vol. 95 https://doi.org/10.1016/j.cnsns.2020.105627	journal	April 2021
Electron flux in molecules induced by nuclear motion Okuyama, Michihiro; Takatsuka, Kazuo Chemical Physics Letters, Vol. 476, Issue 1-3 https://doi.org/10.1016/j.cplett.2009.05.077	journal	July 2009
Concerted quantum effects of electronic and nuclear fluxes in molecules Barth, Ingo; Hege, Hans-Christian; Ikeda, Hiroshi Chemical Physics Letters, Vol. 481, Issue 1-3 https://doi.org/10.1016/j.cplett.2009.09.011	journal	October 2009
Molecular orbital calculations of infrared intensities beyond the born-oppenheimer approximation using the dipole momentum operator Freedman, Teresa B.; Nafie, Laurence A. Chemical Physics Letters, Vol. 126, Issue 5 https://doi.org/10.1016/s0009-2614(86)80132-4	journal	May 1986
On the principles of elementary quantum mechanics Groenewold, H. J. Physica, Vol. 12, Issue 7 https://doi.org/10.1016/s0031-8914(46)80059-4	journal	October 1946
Quantum mechanics as a statistical theory Moyal, J. E. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 45, Issue 1 https://doi.org/10.1017/s0305004100000487	journal	January 1949
Electronic Flux Density beyond the Born–Oppenheimer Approximation Schild, Axel; Agostini, Federica; Gross, E. K. U. The Journal of Physical Chemistry A, Vol. 120, Issue 19 https://doi.org/10.1021/acs.jpca.5b12657	journal	February 2016
On the Dynamics through a Conical Intersection Curchod, Basile F. E.; Agostini, Federica The Journal of Physical Chemistry Letters, Vol. 8, Issue 4 https://doi.org/10.1021/acs.jpclett.7b00043	journal	January 2017
Nuclear Velocity Perturbation Theory of Vibrational Circular Dichroism Scherrer, A.; Vuilleumier, R.; Sebastiani, D. Journal of Chemical Theory and Computation, Vol. 9, Issue 12 https://doi.org/10.1021/ct400700c	journal	November 2013
Theory of vibrational circular dichroism Stephens, Philip J. The Journal of Physical Chemistry, Vol. 89, Issue 5 https://doi.org/10.1021/j100251a006	journal	February 1985
Conical Intersections: The New Conventional Wisdom Yarkony, David R. The Journal of Physical Chemistry A, Vol. 105, Issue 26 https://doi.org/10.1021/jp003731u	journal	July 2001
Coupled-Channels Quantum Theory of Electronic Flux Density in Electronically Adiabatic Processes: Fundamentals Diestler, D. J. The Journal of Physical Chemistry A, Vol. 116, Issue 11 https://doi.org/10.1021/jp207843z	journal	November 2011
Quasi-Classical Theory of Electronic Flux Density in Electronically Adiabatic Molecular Processes Diestler, D. J. The Journal of Physical Chemistry A, Vol. 116, Issue 46 https://doi.org/10.1021/jp304747a	journal	July 2012
Computation of the Electronic Flux Density in the Born–Oppenheimer Approximation Diestler, D. J.; Kenfack, A.; Manz, J. The Journal of Physical Chemistry A, Vol. 117, Issue 36 https://doi.org/10.1021/jp4002302	journal	March 2013
Beyond the Born–Oppenheimer Approximation: A Treatment of Electronic Flux Density in Electronically Adiabatic Molecular Processes Diestler, D. J. The Journal of Physical Chemistry A, Vol. 117, Issue 22 https://doi.org/10.1021/jp4022079	journal	May 2013
Energies and Derivative Couplings in the Vicinity of a Conical Intersection Using Degenerate Perturbation Theory and Analytic Gradient Techniques. 1 Yarkony, David R. The Journal of Physical Chemistry A, Vol. 101, Issue 23 https://doi.org/10.1021/jp970137k	journal	June 1997
Electron Transition Current Density in Molecules. 1. Non-Born−Oppenheimer Theory of Vibronic and Vibrational Transitions Nafie, Laurence A. The Journal of Physical Chemistry A, Vol. 101, Issue 42 https://doi.org/10.1021/jp9706137	journal	October 1997
Quantum theory of concerted electronic and nuclear fluxes associated with adiabatic intramolecular processes Bredtmann, Timm; Diestler, Dennis J.; Li, Si-Dian Physical Chemistry Chemical Physics, Vol. 17, Issue 44 https://doi.org/10.1039/c5cp03982g	journal	January 2015
A simple method for deriving kinetic energy operators Wang, Xiao-Gang; Carrington, Tucker The Journal of Chemical Physics, Vol. 113, Issue 17 https://doi.org/10.1063/1.1313544	journal	November 2000
The diagonal Born–Oppenheimer correction beyond the Hartree–Fock approximation Valeev, Edward F.; Sherrill, C. David The Journal of Chemical Physics, Vol. 118, Issue 9 https://doi.org/10.1063/1.1540626	journal	March 2003
Phase integral theory, coupled wave equations, and mode conversion Littlejohn, Robert G.; Flynn, William G. Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 2, Issue 1 https://doi.org/10.1063/1.165918	journal	January 1992
General explanation of geometric phase effects in reactive systems: Unwinding the nuclear wave function using simple topology Althorpe, Stuart C. The Journal of Chemical Physics, Vol. 124, Issue 8 https://doi.org/10.1063/1.2161220	journal	February 2006
Analytic calculation of the diagonal Born-Oppenheimer correction within configuration-interaction and coupled-cluster theory Gauss, Jürgen; Tajti, Attila; Kállay, Mihály The Journal of Chemical Physics, Vol. 125, Issue 14 https://doi.org/10.1063/1.2356465	journal	October 2006
Born-Oppenheimer expansion at constant energy Mead, C. Alden The Journal of Chemical Physics, Vol. 125, Issue 20 https://doi.org/10.1063/1.2370992	journal	November 2006
Nonadiabatic corrections to the wave function and energy Pachucki, Krzysztof; Komasa, Jacek The Journal of Chemical Physics, Vol. 129, Issue 3 https://doi.org/10.1063/1.2952517	journal	July 2008
Analytic derivative couplings between configuration-interaction-singles states with built-in electron-translation factors for translational invariance Fatehi, Shervin; Alguire, Ethan; Shao, Yihan The Journal of Chemical Physics, Vol. 135, Issue 23 https://doi.org/10.1063/1.3665031	journal	December 2011
Adiabatic molecular properties beyond the Born–Oppenheimer approximation. Complete adiabatic wave functions and vibrationally induced electronic current density Nafie, Laurence A. The Journal of Chemical Physics, Vol. 79, Issue 10 https://doi.org/10.1063/1.445588	journal	November 1983
Coordinates for molecular dynamics: Orthogonal local systems Aquilanti, Vincenzo; Cavalli, Simonetta The Journal of Chemical Physics, Vol. 85, Issue 3 https://doi.org/10.1063/1.451223	journal	August 1986
Velocity-gauge formalism in the theory of vibrational circular dichroism and infrared absorption Nafie, Laurence A. The Journal of Chemical Physics, Vol. 96, Issue 8 https://doi.org/10.1063/1.462668	journal	April 1992
Correlated electron-nuclear dynamics: Exact factorization of the molecular wavefunction Abedi, Ali; Maitra, Neepa T.; Gross, E. K. U. The Journal of Chemical Physics, Vol. 137, Issue 22 https://doi.org/10.1063/1.4745836	journal	December 2012
Electronic currents and Born-Oppenheimer molecular dynamics Patchkovskii, Serguei The Journal of Chemical Physics, Vol. 137, Issue 8 https://doi.org/10.1063/1.4747540	journal	August 2012
Systematic location of intersecting seams of conical intersection in triatomic molecules: The 1 2A′–2 2A′ conical intersections in BH2 Gordon, Mark S.; Glezakou, Vassiliki-Alexandra; Yarkony, David R. The Journal of Chemical Physics, Vol. 108, Issue 14 https://doi.org/10.1063/1.476318	journal	April 1998
Vector parametrization of the N-atom problem in quantum mechanics. I. Jacobi vectors Gatti, Fabien; Iung, Christophe; Menou, Michel The Journal of Chemical Physics, Vol. 108, Issue 21 https://doi.org/10.1063/1.476327	journal	June 1998
The exact molecular wavefunction as a product of an electronic and a nuclear wavefunction Cederbaum, Lorenz S. The Journal of Chemical Physics, Vol. 138, Issue 22 https://doi.org/10.1063/1.4807115	journal	June 2013
On the mathematical treatment of the Born-Oppenheimer approximation Jecko, Thierry Journal of Mathematical Physics, Vol. 55, Issue 5 https://doi.org/10.1063/1.4870855	journal	May 2014
Erratum: “The exact molecular wavefunction as a product of an electronic and a nuclear wavefunction” [J. Chem. Phys. 138, 224110 (2013)] Cederbaum, Lorenz S. The Journal of Chemical Physics, Vol. 141, Issue 2 https://doi.org/10.1063/1.4890075	journal	July 2014
Nuclear velocity perturbation theory for vibrational circular dichroism: An approach based on the exact factorization of the electron-nuclear wave function Scherrer, Arne; Agostini, Federica; Sebastiani, Daniel The Journal of Chemical Physics, Vol. 143, Issue 7 https://doi.org/10.1063/1.4928578	journal	August 2015
On the inclusion of the diagonal Born-Oppenheimer correction in surface hopping methods Gherib, Rami; Ye, Liyuan; Ryabinkin, Ilya G. The Journal of Chemical Physics, Vol. 144, Issue 15 https://doi.org/10.1063/1.4945817	journal	April 2016
Wave function continuity and the diagonal Born-Oppenheimer correction at conical intersections Meek, Garrett A.; Levine, Benjamin G. The Journal of Chemical Physics, Vol. 144, Issue 18 https://doi.org/10.1063/1.4948786	journal	May 2016
Communication: On the calculation of time-dependent electron flux within the Born-Oppenheimer approximation: A flux-flux reflection principle Albert, Julian; Hader, Kilian; Engel, Volker The Journal of Chemical Physics, Vol. 147, Issue 24 https://doi.org/10.1063/1.5011807	journal	December 2017
Non-adiabatic quantum reactive scattering in hyperspherical coordinates Kendrick, Brian K. The Journal of Chemical Physics, Vol. 148, Issue 4 https://doi.org/10.1063/1.5014989	journal	January 2018
Non-adiabatic mass correction to the rovibrational states of molecules: Numerical application for the H2+ molecular ion Mátyus, Edit The Journal of Chemical Physics, Vol. 149, Issue 19 https://doi.org/10.1063/1.5050401	journal	November 2018
On the calculation of time-dependent electron momenta within the Born-Oppenheimer approximation Schaupp, Thomas; Engel, Volker The Journal of Chemical Physics, Vol. 150, Issue 16 https://doi.org/10.1063/1.5092562	journal	April 2019
Effective non-adiabatic Hamiltonians for the quantum nuclear motion over coupled electronic states Mátyus, Edit; Teufel, Stefan The Journal of Chemical Physics, Vol. 151, Issue 1 https://doi.org/10.1063/1.5097899	journal	July 2019
Born–Oppenheimer and non-Born–Oppenheimer contributions to time-dependent electron momenta Schaupp, Thomas; Engel, Volker The Journal of Chemical Physics, Vol. 152, Issue 20 https://doi.org/10.1063/5.0004560	journal	May 2020
Modeling nonadiabatic dynamics with degenerate electronic states, intersystem crossing, and spin separation: A key goal for chemical physics Bian, Xuezhi; Wu, Yanze; Teh, Hung-Hsuan The Journal of Chemical Physics, Vol. 154, Issue 11 https://doi.org/10.1063/5.0039371	journal	March 2021
Time-dependent momentum expectation values from different quantum probability and flux densities Schaupp, Thomas; Renziehausen, Klaus; Barth, Ingo The Journal of Chemical Physics, Vol. 154, Issue 6 https://doi.org/10.1063/5.0039466	journal	February 2021
Analytic calculation of the Berry curvature and diagonal Born–Oppenheimer correction for molecular systems in uniform magnetic fields Culpitt, Tanner; Peters, Laurens D. M.; Tellgren, Erik I. The Journal of Chemical Physics, Vol. 156, Issue 4 https://doi.org/10.1063/5.0079304	journal	January 2022
Correlated three-dimensional electron-nuclear motion: Adiabatic dynamics vs passage of conical intersections Schaupp, Thomas; Engel, Volker The Journal of Chemical Physics, Vol. 156, Issue 7 https://doi.org/10.1063/5.0082597	journal	February 2022
The parallel-transported (quasi)-diabatic basis Littlejohn, Robert; Rawlinson, Jonathan; Subotnik, Joseph The Journal of Chemical Physics, Vol. 157, Issue 18 https://doi.org/10.1063/5.0122781	journal	November 2022
A mapping approach to surface hopping Mannouch, Jonathan R.; Richardson, Jeremy O. The Journal of Chemical Physics, Vol. 158, Issue 10 https://doi.org/10.1063/5.0139734	journal	March 2023
Representation and conservation of angular momentum in the Born–Oppenheimer theory of polyatomic molecules Littlejohn, Robert; Rawlinson, Jonathan; Subotnik, Joseph The Journal of Chemical Physics, Vol. 158, Issue 10 https://doi.org/10.1063/5.0143809	journal	March 2023
A multi-state mapping approach to surface hopping Runeson, Johan E.; Manolopoulos, David E. The Journal of Chemical Physics, Vol. 159, Issue 9 https://doi.org/10.1063/5.0158147	journal	September 2023
Which masses are vibrating or rotating in a molecule? Kutzelnigg, Werner Molecular Physics, Vol. 105, Issue 19-22 https://doi.org/10.1080/00268970701604671	journal	October 2007
Towards an exact factorization of the molecular wave function Parashar, Shubham; Sajeev, Y.; Ghosh, Swapan K. Molecular Physics, Vol. 113, Issue 19-20 https://doi.org/10.1080/00268976.2015.1074745	journal	September 2015
Vibronic mass computation for the EF–GK–H ¹Σ_g⁺ manifold of molecular hydrogen Mátyus, Edit; Ferenc, Dávid Molecular Physics, Vol. 120, Issue 19-20 https://doi.org/10.1080/00268976.2022.2074905	journal	May 2022
Energies and derivative couplings in the vicinity of a conical intersection 3. The 'most' diabatic basis Molecular Physics, Vol. 93, Issue 1 https://doi.org/10.1080/002689798169456	journal	January 1998
On factorization of molecular wavefunctions Jecko, Thierry; Sutcliffe, Brian T.; Woolley, R. Guy Journal of Physics A: Mathematical and Theoretical, Vol. 48, Issue 44 https://doi.org/10.1088/1751-8113/48/44/445201	journal	October 2015
Non-Adiabatic Crossing of Energy Levels Zener, C. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 137, Issue 833 https://doi.org/10.1098/rspa.1932.0165	journal	September 1932
Quantum flux densities for electronic–nuclear motion: exact versus Born–Oppenheimer dynamics Schaupp, Thomas; Engel, Volker Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 380, Issue 2223 https://doi.org/10.1098/rsta.2020.0385	journal	March 2022
Internal or shape coordinates in then-body problem Littlejohn, Robert G.; Reinsch, Matthias Physical Review A, Vol. 52, Issue 3 https://doi.org/10.1103/PhysRevA.52.2035	journal	September 1995
Total angular momentum conservation in ab initio Born-Oppenheimer molecular dynamics Bian, Xuezhi; Tao, Zhen; Wu, Yanze Physical Review B, Vol. 108, Issue 22 https://doi.org/10.1103/PhysRevB.108.L220304	journal	December 2023
Bloch Electrons in a Magnetic Field Blount, E. I. Physical Review, Vol. 126, Issue 5 https://doi.org/10.1103/physrev.126.1636	journal	June 1962
Extension of the Foldy-Wouthuysen Transformation Blount, E. I. Physical Review, Vol. 128, Issue 5 https://doi.org/10.1103/physrev.128.2454	journal	December 1962
On the Quantum Correction For Thermodynamic Equilibrium Wigner, E. Physical Review, Vol. 40, Issue 5 https://doi.org/10.1103/physrev.40.749	journal	June 1932
On the Dirac Theory of Spin 1/2 Particles and Its Non-Relativistic Limit Foldy, Leslie L.; Wouthuysen, Siegfried A. Physical Review, Vol. 78, Issue 1 https://doi.org/10.1103/physrev.78.29	journal	April 1950
Geometric phases in the asymptotic theory of coupled wave equations Littlejohn, Robert G.; Flynn, William G. Physical Review A, Vol. 44, Issue 8 https://doi.org/10.1103/physreva.44.5239	journal	October 1991
Diagonalization of multicomponent wave equations with a Born-Oppenheimer example Weigert, Stefan; Littlejohn, Robert G. Physical Review A, Vol. 47, Issue 5 https://doi.org/10.1103/physreva.47.3506	journal	May 1993
Adiabatic motion of a neutral spinning particle in an inhomogeneous magnetic field Littlejohn, Robert G.; Weigert, Stefan Physical Review A, Vol. 48, Issue 2 https://doi.org/10.1103/physreva.48.924	journal	August 1993
Newtonian adiabatics unified Goldhaber, Alfred S. Physical Review A, Vol. 71, Issue 6 https://doi.org/10.1103/physreva.71.062102	journal	June 2005
Adiabatic electronic flux density: A Born-Oppenheimer broken-symmetry ansatz Pohl, Vincent; Tremblay, Jean Christophe Physical Review A, Vol. 93, Issue 1 https://doi.org/10.1103/physreva.93.012504	journal	January 2016
Molecular geometric phase from the exact electron-nuclear factorization Requist, Ryan; Tandetzky, Falk; Gross, E. K. U. Physical Review A, Vol. 93, Issue 4 https://doi.org/10.1103/physreva.93.042108	journal	April 2016
Asymptotic analysis of the Berry curvature in the E ⊗ e Jahn-Teller model Requist, Ryan; Proetto, César R.; Gross, E. K. U. Physical Review A, Vol. 96, Issue 6 https://doi.org/10.1103/physreva.96.062503	journal	December 2017
Exact Factorization of the Time-Dependent Electron-Nuclear Wave Function Abedi, Ali; Maitra, Neepa T.; Gross, E. K. U. Physical Review Letters, Vol. 105, Issue 12 https://doi.org/10.1103/physrevlett.105.123002	journal	September 2010
Exact Factorization-Based Density Functional Theory of Electrons and Nuclei Requist, Ryan; Gross, E. K. U. Physical Review Letters, Vol. 117, Issue 19 https://doi.org/10.1103/physrevlett.117.193001	journal	November 2016
Geometric phases and the Bohr-Sommerfeld quantization of multicomponent wave fields Littlejohn, Robert G.; Flynn, William G. Physical Review Letters, Vol. 66, Issue 22 https://doi.org/10.1103/physrevlett.66.2839	journal	June 1991
General linear mode conversion coefficient in one dimension Littlejohn, Robert G.; Flynn, William G. Physical Review Letters, Vol. 70, Issue 12 https://doi.org/10.1103/physrevlett.70.1799	journal	March 1993
Space-Adiabatic Perturbation Theory in Quantum Dynamics Panati, Gianluca; Spohn, Herbert; Teufel, Stefan Physical Review Letters, Vol. 88, Issue 25 https://doi.org/10.1103/physrevlett.88.250405	journal	June 2002
Theory of electronic transitions in slow atomic collisions Delos, John B. Reviews of Modern Physics, Vol. 53, Issue 2 https://doi.org/10.1103/revmodphys.53.287	journal	April 1981
Diabolical conical intersections Yarkony, David R. Reviews of Modern Physics, Vol. 68, Issue 4 https://doi.org/10.1103/revmodphys.68.985	journal	October 1996
Gauge fields in the separation of rotations andinternal motions in the n-body problem Littlejohn, Robert G.; Reinsch, Matthias Reviews of Modern Physics, Vol. 69, Issue 1 https://doi.org/10.1103/revmodphys.69.213	journal	January 1997
Theoretical Study of Geometric Phase Effects in the Hydrogen-Exchange Reaction Juanes-Marcos, J. C. Science, Vol. 309, Issue 5738 https://doi.org/10.1126/science.1114890	journal	August 2005
Time-dependent electron momenta from Born-Oppenheimer calculations Schaupp, Thomas; Albert, Julian; Engel, Volker The European Physical Journal B, Vol. 91, Issue 6 https://doi.org/10.1140/epjb/e2018-90113-x	journal	June 2018
When the exact factorization meets conical intersections... Agostini, Federica; Curchod, Basile F. E. The European Physical Journal B, Vol. 91, Issue 7 https://doi.org/10.1140/epjb/e2018-90117-6	journal	July 2018
Conical Intersections: Electronic Structure, Dynamics and Spectroscopy Domcke, Wolfgang; Yarkony, David R.; Köppel, Horst Advanced Series in Physical Chemistry, Vol. 15 https://doi.org/10.1142/5406	book	July 2004
Vibrational Circular Dichroism Stephens, P. Annual Review of Physical Chemistry, Vol. 36, Issue 1 https://doi.org/10.1146/annurev.physchem.36.1.213	journal	January 1985
Theorie der unelastischen Stösse zwischen Atomen E. C. G., Stueckelberg, Birkhäuser https://doi.org/10.5169/seals-110177	text	January 1932

Similar Records

Molecular anions and the Born-Oppenheimer approximation

Thesis/Dissertation · 1987 · OSTI ID:6955703

Kendall, R A

Non-Born-Oppenheimer path in anti-Hermitian dynamics for nonadiabatic transitions

Journal Article · 2006 · Journal of Chemical Physics · OSTI ID:20783224

Takatsuka, Kazuo

Density-Matrix Based Extended Lagrangian Born–Oppenheimer Molecular Dynamics

Journal Article · 2020 · Journal of Chemical Theory and Computation · OSTI ID:1843167

Niklasson, Anders Mauritz N.

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
Born-Oppenheimer approximation
Coordinate transformations
Hamiltonian mechanics
Perturbation theory
Potential energy surfaces
Power series
Quantum chemical dynamics

Title: Diagonalizing the Born–Oppenheimer Hamiltonian via Moyal perturbation theory, nonadiabatic corrections, and translational degrees of freedom

Citation Formats

References (102)

Similar Records

Related Subjects