Potential Energy Curves, Spectroscopic Parameters, and Spin–Orbit Coupling: A Theoretical Study on 24 Λ-S and 54 Ω States of C₂⁺ Cation

Abstract

The potential energy curves (PECs) of 24 Λ-S states and 54 Ω states of the C2(+) cation are studied in detail using an ab initio quantum chemical method. All the PEC calculations are made for internuclear separations from 0.09 to 1.11 nm by the complete active space self-consistent field method, which is followed by the internally contracted multireference configuration interaction approach with the Davidson modification (MRCI+Q). All the Λ-S states involved dissociate into the first dissociation limit, C((3)Pg) + C(+)((2)Pu), of C2(+) cation, of which only the 2(2)Σg(-) and 2(4)Σg(-) are repulsive. The spin-orbit (SO) coupling effect is accounted for by the Breit-Pauli Hamiltonian with an aug-cc-pCVTZ basis set. To improve the quality of PECs, core-valence correlation and scalar relativistic corrections are included. Core-valence correlation corrections are taken into account with an aug-cc-pCVTZ basis set. Scalar relativistic correction calculations are done by the third-order Douglas-Kroll Hamiltonian approximation with the cc-pVQZ basis set. All the PECs are extrapolated to the complete basis set limit. The convergence observations of present calculations are made, and the convergent behavior is discussed with respect to the basis set and level of theory. With the PECs obtained by the MRCI+Q/CV+DK+56 calculations, the spectroscopic parameters of 22 Λ-S bound states of C2(+) cation are evaluated by fitting the first ten vibrational levels, which are obtained by solving the rovibrational Schrödinger equation using Numerov's method. In addition, the spectroscopic parameters of 51 Ω bound states generated from these Λ-S bound states are also obtained. The spectroscopic parameters are compared with those reported in the literature. Excellent agreement with available measurements is found. It is expected that the spectroscopic parameters of Λ-S and Ω states reported here are reliable predicted ones.

On the temperature dependence of the rate coefficient of formation of C$_2^+$ from C + CH+

“…The electronic structure of diatomics CH + and C + 2 was previously investigated in Green et al (1972); Petrongolo et al (1981); Kraemer & Roos (1987); Watts & Bartlett (1992); Shi et al (2013) and the spectroscopic properties of the related ground-states 1 Σ + and 4 Σ − g , respectively, were determined. C 2 H + was studied in Krishnan et al (1981) and Koch & Frenking (1990).…”

A theoretical investigation of the S2+ cation in the gas phase

“…21 As demonstrated in Table 1, we obtained the 18 ⌳-S electronic states, which dissociate into the first two dissociation limits. For convenience of comparison, the energy separations between the first two dissociation channels are collected.…”

“…Ĥ so is the SO part of the Breit−Pauli Hamiltonian. 21 Here, we include the SO coupling effect into the PEC calculations by the state interaction method with the Breit-Pauli Hamiltonian 33 at the cc-pCVTZ basis set level. Berning et al 34 thought that the Breit-Pauli operator could be very well approximated by an effective one-electron Fock operator.…”

Radiative Association of Atomic and Ionic Carbon

“…There are 24 molecular electronic states formed from C( 3 P ) and C + ( 2 P o ), namely, 2,4 Σ + g,u , 2,4 Σ − g,u (2), 2,4 Π g,u (2), 2,4 ∆ g,u (Chiu 1973;Shi et al 2013), however, we do not consider the 2 2 Σ − u , 2 2 Σ − g , 1 4 Π u , 2 4 Σ − u , 1 4 Σ + g , 2 4 Π u , 1 4 ∆ g and 2 4 Σ − g states because they are repulsive (Shi et al 2013) and will not be important for process (1).…”

“…calculations of Shi et al (2013). [Comprehensive tabulations of calculations by earlier workers (and some experimental data) were given by Shi et al (2013).]…”