II electronic states

The expressions for the rotational energy levels (i.e., also involving the end-over-end rotations, not considered in the previous works) of linear triatomic molecules in doublet and triplet II electronic states that take into account a spin orbit interaction and a vibronic coupling were derived in two milestone studies by Hougen [72,32]. In them, the isomorfic Hamiltonian was inboduced, which has later been widely used in treating linear molecules (see, e.g., [55]). 

Figure 9. Energy difference (absolute value) between the components of the X II electronic State of HCCS as a function of coordinates p, P2, and y. Curves represent the square root of the second of functions given by Eq. (77) (with e, = —0.011, 2 = 0.013, 8,2 = 0.005325) for fixed values of coordinates p, and P2 (attached at each curve) and variable Y = 4>2 Here y = 0 corresponds to cis-planar geometry and y = 71 to trans-planar geometry. Symbols results of explicit ab initio calculations.

Hamiltonian equations, 627-628 perturbative handling, 641-646 II electronic states, 631-633 vibronic coupling, 630-631 ABC bond angle, Renner-Teller effect, triatomic molecules, 611-615 ABCD bond angle, Renner-Teller effect, tetraatomic molecules, 626-628 perturbative handling, 641-646 II electronic states, 634-640 vibronic coupling, 630-631 Abelian theory, molecular systems, Yang-Mills fields ... 

II electronic states, 634-640 theoretical background, 625-626 triatomic molecules, 611-615 pragmatic models, 620-621 Ab initio multiple spawning (AIMS) conical intersection location, 491-492 direct molecular dynamics, 411-414 theoretical background, 360-361 Adiabatic approximation geometric phase theory ... 

Hamiltonian equations, 627-628 II electronic states, 632-633 triatomic molecules, 587-598 minimal models, 615-618 Hartree-Fock calculations ... 

HCCS radical, Renner-Teller effect, tetraatomic molecules, II electronic states, 633-640 H2D molecule, non-adiabatic coupling, two-state molecular system, 107-109 HD2 molecule, permutational symmetry isotopomers, 713-717 potential energy surfaces, 692-694 Heaviside function ... 

II electronic states, 638-640 vibronic coupling, 628-631 triatomic molecules, 594-598 Hamiltonian equations, 612-615 pragmatic models, 620-621 Kramers doublets, geometric phase theory linear Jahn-Teller effect, 20-22 spin-orbit coupling, 20-22 Kramers-Kronig reciprocity, wave function analycity, 201 -205 Kramers theorem ... 

A electronic states, 647—653 II electronic states, 641-646 triatomic molecules, minimal models, 615-618... 

Appendix A Perturbative Handling of the Renner-Teller Effect and Spin-Orbit Coupling in II Electronic States of Tetraatomic Molecules... 

As in the case of II electronic states of tetraatomic molecules, because of generally high degeneracy of zeroth-order vibronic leves only several particular (but important) coupling cases can be handled efficiently in the framework of the perturbation theory. We consider the following particular cases ... 

As is well known, linear molecules represent an exception of the JT theorem. The degeneracy of II electronic states is lifted in second order of the bending amplitude, the degeneracy of A electronic states is lifted in fourth order, etc., see [35-38] for reviews. 

Figure 3. Low-energy vibronic spectrum in a II electronic state of a linear triatomic molecule, computed for various values of the Renner parameter 6 and spin-orbit constant Aso (in cm ). The spectrum shown in the center of figure (e = —0.17, Aso = —37cm ) corresponds to the A II state of NCN [28,29]. The zero on the energy scale represents the minimum of the potential energy surface. Solid lines K = 0 vibronic levels dashed lines K = 1 levels dash-dotted lines K = 2 levels dotted lines K = 3 levels. Spin-vibronic levels are denoted by the value of the corresponding quantum number P P = + S note that S is in this case spin quantum number).

In this section, we consider II electronic state (A = 1) of ABBA type molecules. The additional Hamiltonian H is of the form... 

In the lowest order (quadratic) approximation for II electronic states of asymmetrical (ABCD) tetraatomics, the electronic matrix elements (60) have the forms [18,152,153] ... 

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