Spectroscopic properties of the molecular ion in the 8kπ, 9kσ, 9lπ, 9lσ and 10oσ electronic states (original) (raw)
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International Journal of Quantum Chemistry, 2011
Starting with the Hamilton-Jacobi equation, Campos et al. have applied Hylleraas' method along with the series obtained by Wind-Jaffe to several molecular ions, among which the H + 2 system, to determine their electronic energies in different states. In this work, we have fitted the potential energy curves for the 2pπ, 3dσ , 4dσ , 4f π, 4f σ , 5gσ , and 6iσ electronic states of the H + 2 ion employing the Rydberg generalized function. From these fittings, the spectroscopic constants and the rovibrational energies have been determined by two distinct methods: Dunham's and the discrete variable representation. The theoretically obtained results are in a satisfactory agreement and are expected to provide a comparison source to future works in the experimental field.
International Journal of Quantum Chemistry, 2008
In this work, rovibrational energies and spectroscopic constants for the water−Ng complexes (Ng = He, Ne, Ar, Kr and Xe) were calculated through two different approaches (by solving the Nuclear Schrödinger equation and by applying the Dunham's method) and using two different potential energy curves (PEC). These PEC were determined using potential parameters obtained through molecular beam scattering experiments and accurate theoretical calculation, respectively. It was found that the theoretical rovibrational energies are in a good agreement (only for the lowest numbers of vibrational states) with those obtained through experimental PEC. Another important conclusions was regarding the calculated first two rovibrational energies for the H 2 O−Ar system, that are in a good agreement with the experimental data.
arXiv (Cornell University), 2023
We calculate accurate potential energy curves for a ground-state He + ion interacting with a He atom in the lowest-energy metastable 3 S electronic state. We employ the full configuration interaction method, equivalent to exact diagonalization, with results extrapolated to the complete basis set limit. The leading relativistic and adiabatic corrections are included using perturbation theory. We calculate rovibrational levels and spectroscopic constants of the He + 2 molecular ion in excited electronic states for three stable isotopologues. We predict the scattering lengths for ultracold ion-atom collisions. The theoretical data are presented with their uncertainties and agree well with previous results for the ground state. The reported results may be useful for the spectroscopy of the He + 2 molecular ion in the excited electronic state and collisional studies of He + ions immersed in ultracold gases of metastable He atoms.
Higher order spectroscopic constants and ionic potentials in molecular spectroscopy
Journal of Molecular Structure: THEOCHEM, 1983
Ionic Kratzer-type potentials (such as the Varshni V-potential) are shown to be consistent with all observed lower-and higher-order spectroscopic constants ae, wexe, p, and y, for over thirty diatomics of widely differing ionic characters. All higher Dunham coefficients can be derived from the first, which is itself related to the force constant. The ionic potentials are compared with other potentials discussed in the literature (Dunham, Morse, Simons-Parr-Finlan, Jordan). The deviations of Morse curves near r, from RKRcurves are completely predictable using an ionic potential as reference. The Calde? Ruedenberg constant, applicable to 160 diatomics, is consistently accounted for. Calculated vibrational levels for Li, on both sides of the minimum correspond with experimental levels within 0.6%, whereas computed AG(u)-values are accurate to within 1%. For the excited state, A '2: of Li, the same potential is also satisfactory. An ionic potential corrected for an atomic dissociation limit at r = -produces a finite solution at r = 0. In the case of Li, the energy at r = lo* A is of the same order of magnitude as the experimental fusion energy of two Li-nuclei into a single C-nucleus.
Journal of Physical Chemistry A, 2004
The polarizable valence-state-atoms-in-molecules (pVSAM) model describes the electron-pair bond in A-B molecules by superposing core-polarized A + B -, A -B + , and A:B structures, whose weights are determined by electronegativity equalization. The polarizable valence state potential energy curve (pVS-PEC) is derived through the systematic improvement of the valence state potential energy curve (VS-PEC) von Szentpály, L. J. Phys. Chem. A 1999, 103, 9313] and is given as U(R) ) -[(K 1 /R) + (K 2 /R 4 ) + (K 3 /R 7 )] + (T/R) exp(-λR). The first bracketed term contains the Coulomb, charge-induced dipole, and induced dipole-induced dipole terms, derived from weighted ionic and covalent bond-charge contributions. The potential is tested on a broad variety of homonuclear diatoms and heteronuclear halides and hydrides (a total of 52 molecules). The accuracies of the dimensionless vibration-rotation coupling constant (F) and the anharmonicity constant (G) for the halides of the alkali and coinage metals are significantly better than those of the Morse, Rydberg, simple bond-charge, and Rittner potentials. Adding core polarization to the VS-PEC reduces the average unsigned errors in the spectroscopic constants of 47 diatomic molecules from 17.1% to 7.5% in F and 18.9% to 7.8% in G, whereas those of the Morse potential amount to 32.6% and 31.4%, respectively. hydrides, has been tentatively rationalized 4,5 by the increasing importance of core-polarization and core-valence intershell correlation, both of which may be accounted for by a corepolarization potential (CPP). 17,18 To prove the point, we extend the VS-PEC into a form that takes core polarization into consideration. The polarizable valence-state-atoms-in-molecules (pVSAM) model links the ionic and covalent descriptions of the bond, using the concept of configuration mixing among contributing ionic and covalent (bond-charge) structures within the framework of the valencestate-atoms-in-molecules (VSAM) model. By incorporating polarization terms, a greater degree of accuracy is expected, and the advantage of physical interpretation is maintained, illustrated, and exploited.
Regardless of the theory used for understanding atomic construction, equations that define atomic spectra must include as a derivative the Rydberg equation describing hydrogen and other single-electron ions. The following work product is evidence that defining all elemental spectra is achievable by merely changing some assumptions. The first assumption is that using integers in calculating spectra is incorrect. The second is that spin values for electrons in atoms begin at a ground state level and increase in spin-1 increments due to adding photons of spin-1. The third assumption is that photons are dual spin-1/2 composites. Using spin-1/2 as a basis produces a set of Rydberg-style equations providing spectra for all elements and their many ionic forms. The presented examples, hydrogen through neon, plus phosphorus, a spin-1/2 nucleus, reveal the equation behavior for elements of varying character. Unfortunately, determining which spectral lines dominate in multiple electron atoms is not straightforward without a solid theoretical underpinning. Current theory is lacking or it would be able to provide a similar solution. The term ‘preliminary’ in the title indicates that more than one equation solution exists for multi-electron ions. The equation sets provided represent the most logical and reasonable solutions. Although dominant line prediction is not yet forthcoming, an explanation for photon production using a combination of equation components is proffered. The enclosed information should lead to a full explanation once solutions for all elements are determined and examined in detail and theory further develops.
Theory and energetics of mass spectra
Mass Spectrometry, 1975
Ab initio Self-consistent Field Calculations including Electron Correlation.-An important distinction must be drawn between ab initio SCF calculations using extended basis sets and those using minimal basis Only the former are expected to give results of Hartree-Fock accuracy in the single-particle approximation (which ignores electron correlation). These calculations are very expensive for polyatomic molecules, and minimal basis set calculations are therefore more generally performed. With judicious choice of basis functions for particular systems, results within a few kcal mol-' of the Hartree-Fock limit can be obtained using minimal basis sets.5 But even with results of this accuracy erroneous conclusions may be drawn because electron correlation is ignored in the Hartree-Fock
Properties of high-lying vibrational states of the molecular ion
Molecular Physics, 2006
Calculations are presented for the vibrational states of H þ 3 on a potential with the correct dissociation properties (Molec. Phys., 98, 261 ) using both Radau and Jacobi coordinates. This potential is found to support horseshoe states at low to intermediate energies. Near the dissociation limit a new class of long-range states, called asymptotic vibrational states (AVS), is found. These states are similar to those suggested to explain the observed near-dissociation spectrum of H þ 3 . The possible consequences of such states are discussed.
The dependence of multipole moments and polarizabilities on external fields appears in many applications including biomolecular molecular mechanics, optical non-linearity, nanomaterial calculations, and the perturbation of spectroscopic signatures in atomic clocks. Over a wide range of distances, distributed multipole and polarizability potentials can be applied to obtain the variation of atom-centered atoms-in-molecules electric properties like bonding-quenched polarizability. For cylindrically symmetric charge distributions, we examine single-center and atom-centered effective polarization potentials in a non-relativistic approximation for Rydberg states. For ions, the multipole expansion is strongly origin-dependent, but we note that origin-independent invariants can be defined. The several families of invariants correspond to optimized representations differing by origin and number of terms. Among them, a representation at the center of dipole polarizability optimizes the accuracy of the potential with terms through 1/r 4 . We formulate the single-center expansion in terms of polarization-modified effective multipole moments, defining a form related to the source-multipole expansion of Brink and Satchler. Atom-centered potentials are an origin independent alternative but are limited both by the properties allowed at each center and by the neglected effects like bond polarizability and charge flow. To enable comparisons between single-center effective potentials in Cartesian or spherical form and two-center effective potentials with differing levels of mutual induction between atomic centers, we give analytical expressions for the bond-length and origin-dependence of multipole and polarizability terms projected in the multipole and polarizability expansion of Buckingham. The atom-centered potentials can then be used with experimental data and ab initio calculations to estimate atoms-in-molecules properties. Some results are given for BaF + and HF showing the utility and limitations of the approach. More detailed results on X 1 Σ + CaF + are published separately. Published by AIP Publishing. [http://dx.