scholarly journals High-precision evaluation of the vibrational spectra of long-range molecules

2001 ◽  
Vol 79 (2-3) ◽  
pp. 109-119
Author(s):  
C Tannous ◽  
J Langlois

Vibrational spectra of long-range molecules are determined accurately and to arbitrary accuracy with the Canonical Function Method. The energy levels of the 0–g and 1u electronic states of the 23Na2 molecule are determined from the ground state up to the continuum limit. The method is validated by comparison with previous results obtained for different potentials adapted to long-range molecules. PACS Nos.: 03.65-w, 31.15Gy, 33.20.Tp

2020 ◽  
Vol 2 (1) ◽  
Author(s):  
Yibing Shen ◽  
Phillip Isaac ◽  
Jon Links

We investigate the ground-state energy of a Richardson-Gaudin integrable BCS model, generalizing the closed and open p+ip models. The Hamiltonian supports a family of mutually commuting conserved operators satisfying quadratic relations. From the eigenvalues of the conserved operators we derive, in the continuum limit, an integral equation for which a solution corresponding to the ground state is established. The energy expression from this solution agrees with the BCS mean-field result.


Author(s):  
D. Porret ◽  
Frederick George Donnan

The continuous absorption spectra of gaseous bromine (Peskow 1917; Ribaud 1919; Gray and Style 1929; Acton, Aikin and Bayliss 1936) and of dissolved bromine (Bovis 1929; Gillam and Morton 1929) have been studied many times. They present a wide continuum (from about 30, 000 to 17, 000 cm. -1 .) with a maximum at 24, 000 cm. -1 . For the gas the continuum is preceded by two band systems on the long wave-length side. These systems converge at 19, 585 and 15, 896 cm. -1 . respectively. Acton, Aikin and Bayliss (1936) have shown that the continuum is not simple, and Mulliken (1936) and Darbyshire (1937) have pointed out that there are three overlapping continua corresponding to transitions from the ground state to three different excited electronic states. There are 3 II 0 + ← 1 Σ g , 3 II 1 ← 1 Σ g and 1 II ← 1 Σ g . The absorption spectrum of liquid bromine has been studied by Bovis (1929) form 18, 525 to 31, 750c cm. -1 . and by Camichel (1893) for two frequencies only (16, 978 and 18, 691 cm. -1 ).


1976 ◽  
Vol 54 (20) ◽  
pp. 2028-2049 ◽  
Author(s):  
H. Lew

Many bands of the [Formula: see text] electronic emission spectrum of H2O+, occurring in the wavelength region 4000–7500 Å, have been analyzed. These include bands that have been observed in the tails of comets. The wavelengths and wave numbers of all assigned lines are tabulated. Accurate rotational constants for the first three bending vibrational levels of the ground state are given, as well as energy levels in the upper and lower electronic states. The O—H bond distance and the H—O—H angle in the [Formula: see text] (0, 0, 0) level are found to be 0.9988 Å and 110.46° respectively. Some predicted microwave and infrared lines that may be of astrophysical interest are included.


1989 ◽  
Vol 03 (02) ◽  
pp. 125-133 ◽  
Author(s):  
C. ARAGÃO DE CARVALHO

We use the continuum limit of the Su-Schrieffer-Heeger model for linear polymers to construct its effective potential (Gibbs free energy) both at zero and finite temperature. We study both trans and cis-polymers. Our results show that, depending on a renormalization condition to be extracted from experiment, there are several possibilities for the minima of the dimerized ground state of cis-polymers. All calculations are done in the one-loop approximation.


1959 ◽  
Vol 37 (4) ◽  
pp. 700-707 ◽  
Author(s):  
H. Howard ◽  
G. W. King

The electronic energy levels of cis- and trans-bent planar centrosymmetric acetylene molecules, with [Formula: see text] and r cc = 1.383 Å, have been calculated by the LCAO/ASMO/CI procedure. The lowest energy state that can spectroscopically combine with the linear ground state is found to be of symmetry class Au belonging to the trans-bent molecule and to lie at 4.58 ev above the ground state. This compares favorably with the experimentally observed electronic transition of lowest energy which is of type (1Au−1∑g+) and at 5.24 ev. The lowest-energy allowed transition to a cis-bent state of these dimensions is at 9.39 ev, and hence this may not form part of the unanalyzed system of bands in the 2000–1500 Å region, as has been suggested. However, a transition to a trans-bent state of type (1Bu−1∑g+) is predicted to fall in this region. The energies of other electronic states are discussed in relation to the observed absorption systems of acetylene.


2020 ◽  
Vol 98 (1) ◽  
pp. 45-56 ◽  
Author(s):  
Israa Zeid ◽  
Rania Al Abdallah ◽  
Nayla El-Kork ◽  
Mahmoud Korek

For the alkali iodide molecules LiI, NaI, KI, and RbI, ab initio CASSCF/(MRCI+Q) calculations have been employed to investigate the adiabatic potential energy curves and the static dipole moment curves of the low-lying singlet and triplet electronic states in the representation 2S+1Λ(+/−). The spectroscopic constants Te, Re, ωe, Be, αe, the dipole moment μe, and the dissociation energies De have been computed for the bound states. Additionally, the percentage ionic character fionic around the equilibrium position of the ground state and the (2)1Σ+ state has been estimated. Using the canonical function approach, these calculations have been followed by a rovibrational calculation from which the rovibrational constants Ev, Bv, Dv, and the abscissas of the turning points Rmin and Rmax for the investigated bound states are calculated.


2010 ◽  
Vol 2010 ◽  
pp. 1-16 ◽  
Author(s):  
John R. Klauder

Recent proposals for a nontrivial quantization of covariant, nonrenormalizable, self-interacting, scalar quantum fields have emphasized the importance of quantum fields that obey affine commutation relations rather than canonical commutation relations. When formulated on a spacetime lattice, such models have a lattice version of the associated ground state, and this vector is used as the fiducial vector for the definition of the associated affine coherent states, thus ensuring that in the continuum limit, the affine field operators are compatible with the system Hamiltonian. In this article, we define and analyze the associated affine coherent states as well as briefly review the author's approach to nontrivial formulations of such nonrenormalizable models.


2020 ◽  
Vol 15 (1) ◽  
pp. 1-5
Author(s):  
Vitor Bento Souza ◽  
Germano Maioli Penello ◽  
Pedro Henrique Pereira ◽  
Deborah Sivco ◽  
Claire Gmachl ◽  
...  

In this work we present an InGaAs/InAlAs heterostructure lattice matched with InP that holds two leaky electronic states in the continuum. An optical analogy with Bragg mirrors is used to explain the origin and the desired characteristics of the leaky electronic state. Multipass waveguide absorption measurements were performed and theoretical calculations used to determine the energy levels involved in the optical transitions. The comparison between the theoretical and experimental oscillator strength shows the good optical quality of the sample.


The energy states of mixed molecular crystals in the rigid lattice are treated with special reference to impurity molecules differing only by isotopic substitutions from the host molecules. The perturbation Hamiltonian is treated explicitly, and the calculation made by an elaboration on the Green function method used by Koster & Slater for electron traps. Formulae for the energy levels and transition moments are given for dilute crystals and for crystals with any concentration of guests arranged in a superlattice. Virtual coupling between different guest molecules (trap-to-trap coupling) is considered, and limiting formulae derived.


Sign in / Sign up

Export Citation Format

Share Document