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Chemical Bonding
Published in Alan Cottrell, An Introduction to Metallurgy, 2019
The hydrogen molecular ion H2+, i.e. one electron and two protons, provides the simplest example of a covalent bond. In Fig. 4.2 we show the protons, 1 and 2, at a fixed distance R and the electron, e, at distances r1 and r2 from them. The wave equation of this electron is then obtained directly by substituting V=−14πε0(e2r1+e2r2)
Quantum Chemistry Methods for Molecular Disordered Materials
Published in Alexander Bagaturyants, Vener Mikhail, Multiscale Modeling in Nanophotonics, 2017
Alexander Bagaturyants, Vener Mikhail
The simplest diatomic system is the hydrogen molecular ion H2+ $ \text{H}_{\text{2}}^{\text{ + }} $ (see Fig. 3.1). It contains two hydrogen nuclei and one electron. Just as the hydrogen atom has been considered as a prototypical system for other atoms, the hydrogen molecular ion may serve as a prototypical system for diatomic molecules. Many general properties of electronic wave functions in diatomic systems can be understood from studying the properties of solutions for H2+ $ \text{H}_{\text{2}}^{\text{ + }} $ . Though the problem of electronic states in H2+ $ \text{H}_{\text{2}}^{\text{ + }} $ allows an exact solution in prolate spheroidal coordinates, this solution is not transparent. Instead, we consider a simple way of constructing an approximate molecular one‐electron wave function as a linear combination of atomic one‐electron wave functions. Molecular one‐electron wave functions are generally called molecular orbitals (MOs) $ \text{(MOs)} $ . Atomic one‐electron wave functions (atomic orbitals, AOs) are considered in many textbooks (see, for example, Refs. [2–6]). Therefore, this approximation is called MO LCAO (where the abbreviation LCAO stands for linear combination of atomic orbitals).
Black-body radiation-induced photodissociation and population redistribution of weakly bound states in H2 +
Published in Molecular Physics, 2022
The hydrogen molecular ion (HMI) is the simplest molecular system and can be used to test quantum electrodynamics and to determine fundamental constants by comparing experimental and theoretical transition frequencies [1,2]. While ab initio theory reached a level of relative accuracy for H and HD [3,4], a comparable experimental accuracy has only been achieved for the HD isotopologue [1,2,5]. In these experiments, rovibrationally-cold HD ions are held in a radio-frequency trap and sympathetically cooled to reach the Lamb-Dicke regime in order to suppress Doppler effects during the spectroscopic interrogation.
Precision measurement of quasi-bound resonances in H2 and the H + H scattering length
Published in Molecular Physics, 2022
K.-F. Lai, E. J. Salumbides, M. Beyer, W. Ubachs
To predict transition frequencies for the F0-X transitions, term values of the electronic state were calculated using Born-Oppenheimer [72], adiabatic [73] and relativistic [74] potential energy curves. Leading order radiative corrections were taken into account by using the corresponding curves of the hydrogen molecular ion [75]. Nonadiabatic energies for the F0 states are reported for J = 0−5 in Ref. [76] and were obtained from a coupled-equations calculation including several gerade states. In the spirit of Ref. [77] the energy difference between the reported nonadiabatic and the current adiabatic term values are parametrised as , relating a to homogeneous and b to heterogeneous interactions. The found parameters and are expected to predict F0 term values with an accuracy of around 1 . These renewed computations for the F0(J) levels energies were performed since values for the highest J-levels were lacking in [78]. Based on a comparison with experimental values for F0(J) at low J [79] the present computations are shown to be more accurate. Values for F0(J), for the J-values relevant to the present study, are listed in Table 2.
Generalized Sturmian Functions in prolate spheroidal coordinates
Published in Molecular Physics, 2021
D. M. Mitnik, F. A. López, L. U. Ancarani
We present now the results of our calculations and make a comparison with the data provided in the literature. We start by applying the GSF iterative method for both the ground and some m = 0 excited states of the hydrogen molecular ion for which and thus . Next, we consider asymmetric (heteronuclear) molecular ions with . Finally, for , we will show how the GSF direct method yields the ground and several excited states in a single run.