Experimental and quantum-chemical studies on the three-particle fragmentation of neutral triatomic hydrogen

Collective Multipole Expansions and the Perturbation Theory in the Quantum Three-Body Problem

“…Without loss of generality, we can assume that O is a scalar operator. This situation realizes, for example, in the case of the three-atomic molecular predissociation where O represents the operator of non-adiabatic couplings [5]. If the transition operator is a tensor O lm then the product Ψ jµ O lm can be decomposed into irreducible parts [9] so that the matrix element will be decomposed into the sum of matrix elements of the kind (20).…”

The Jahn–Teller effect in the 3 pe ′ Rydberg state of H 3 : review of experimental and ab initio determinations

“…This work was soon followed by the computations of Nager & Jungen [8], who used their frozen-core Rydberg ab initio method to predict numerous Rydberg states over a wide range of geometries. More recent potential surfaces of H 3 Rydberg states have been published in Mistrík et al [6] and Galster et al [19]. Among these, the highly correlated electronic wave functions and energies [6] obtained with the multi-reference code of Fink & Staemmler [20] based on the coupled electronpair approximation (CEPA) probably remain the most accurate values available today, and we shall use them below in an attempt to reevaluate the JT parameters of the npe , n = 3−5 Rydberg states.…”

“…The ab initio work on excited states of H 3 and H + 3 has been reported alternatively in terms of Dykstra coordinates [6,8,21], hyperspherical coordinates [19] or mass-scaled Jacobi coordinates [22]. In all these papers, the relationships between coordinates employed and the straightforward bond-length coordinates R 1 , R 2 , R 3 have been spelled out in detail.…”

“…We have used the ab initio 3pe surfaces from Mistrík et al [6] and Galster et al [19] in order to reexamine the JT parameters relevant for the npe Rydberg channel. This task has been performed previously by Staib & Domcke [7] on the basis of the theoretical surfaces from Nager & Jungen [8], and more recently by Mistrík et al [6] based on the new potential surfaces computed there.…”

“…We also attempt to redetermine the linear and quadratic JT splitting constants on the basis of the most sophisticated ab initio H 3 3pe potential surfaces existing to date. Although King & Morokuma [18] extracted a quadratic JT constant from their ab initio surface, to date, no quadratic constant for the later ab initio surfaces [6,8,19] has been reported; similarly, no quadratic constant has been extracted from the spectroscopic data of Herzberg et al [11,12]. While we focus in this work on the 3pe state of H 3 , we also consider the n = 4 and n = 5 members of the npe Rydberg series, for which ab initio potential energy surfaces also exist [6]; consideration of these surfaces provides information on the energy dependences of the quantum defect parameters.…”