An unusually large nonadiabatic error in the BNB molecule

Journal of Chemical Physics

Volumn 133, Issue 17, 2010, Pages

  Stanton, John F ^a  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ADIABATIC POTENTIALS; ANTISYMMETRIC STRETCHING MODE; CONICAL INTERSECTION; COUPLED ELECTRONIC STATE; ENERGY LEVEL; FORCE CONSTANTS; HIGH-ACCURACY; MODEL SYSTEM; NON-ADIABATIC; NON-ADIABATIC CONTRIBUTIONS; NON-ADIABATICITY; NONADIABATIC CORRECTIONS; ONE DIMENSION; ORDERS OF MAGNITUDE; QUANTUM CHEMICAL CALCULATIONS; RELATIVISTIC CORRECTION; VIBRATIONAL ENERGIES; VIBRATIONAL ENERGY LEVELS; VIBRATIONAL FREQUENCIES; VIBRONIC COUPLING; VIBRONIC INTERACTIONS; ZERO-POINT VIBRATIONAL ENERGIES;

ELECTRONIC STATES; QUANTUM CHEMISTRY;

MOLECULES;

EID: 78650676171     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3505217     Document Type: Article

References (21)

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2. Meaning that all of the states that are treated explicitly are only weakly coupled to the remaining electronic states. The KDC Hamiltonian can be viewed as resulting from a block diagonalization of the molecular Hamiltonian projected onto the crude Born-Huang basis, in which the interacting state block is "dressed" by the weak coupling between it and the remaining states. It is this effect that builds in the "following of the nuclei" property of the wavefunctions and other slow variations with nuclear geometry. See Ref. for more discussions.
3. N) term.
4. Such approach is of course problematic when conical intersections occur. Then, the surface is pathological, and a variational adiabiatic calculation of energy levels is clearly an unwise pursuit. This paper largely focuses on systems such as the ground and first excited states of BNB, where (at least the interesting regions of) the adiabatic potential energy surfaces do not coincide at any point.
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6. Some analysis along the lines of those presented here were in H. Köppel, Ph.D. thesis, TU München, 1979, and has found its way into his lecture notes entitled "Molecular photoexcitation and spectroscopy for strongly coupled potential surfaces," especially around p. 50 See also H. Köppel, in Conical Intersections: Electronic Structure, Dynamics and Spectroscopy, edited by, W. Domcke, D. R. Yarkony, and, H. Köppel, (World Scientific, Singapore, 2004), pp. 175-204 10.1142/9789812565464-0004 Another example where a similar calculation was done, although the case was far less diabolical than BNB and the nonadiabatic correction was small, was R. Lefebvre and M. Garcia Sucre, Int. J. Quantum Chem. IJQCB2 0020-7608 1, 339 (1967). 10.1002/qua.560010640
7. It should be noted that the term "nonadiabatic error," as used in this paper, has a very specific definition; that is, it refers to the difference between vibronic level spacings involving the zero-point and low-lying vibrational states, in a quite specific way in this paper.
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11. It should still be said that this is not as poor an approximation as it might seem. For example, while the asymmetric stretching force constants are very different on the two adiabatic surfaces of BNB relevant to this draft, the two diabatic electronic states involved have great qualitative similarities: they both can be viewed as arising from the closed-shell BNB anion by removal of an electron from nonbonded lone pair orbitals (out of phase for the ground state neutral, and in phase for the excited 2 g- state). One would expect two such diabatic potentials to be very similar. This is essentially the justification for this frequently invoked approximation.
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