Empirical Potential Curves Research Articles

New observation and analysis of the ultracold Cs2 0u+ and 1g long-range states at the asymptote 6S1/2+6P1/2

Photoassociation of ultracold Cs atoms is reported in magneto-optical trap with the modulation technique. Trap loss spectroscopy of the ultracold Cs2 molecules has been obtained experimentally. Spectroscopy data are expended to the red detuned of 70cm-1 below the 6S1/2+6P1/2 dissociation limit. Several new low lying vibrational levels belongs to the 0u+ and 1g states are identified and analyzed. The long range molecular coefficients C3 for the 0u+ and 1g states are obtained, and the corresponding empirical potential curves are derived with the spectroscopy data.

Full empirical potential curves for the X(1)Σ(+) and A(1)Π states of CH(+) from a direct-potential-fit analysis.

All available "conventional" absorption/emission spectroscopic data have been combined with photodissociation data and translational spectroscopy data in a global analysis that yields analytic potential energy and Born-Oppenheimer breakdown functions for the X(1)Σ(+) and A(1)Π states of CH(+) and its isotopologues that reproduce all of the data (on average) within their assigned uncertainties. For the ground X(1)Σ(+) state, this fully quantum mechanical "Direct-Potential-Fit" analysis yielded an improved empirical well depth of 𝔇e = 34 362.8(3) cm(-1) and equilibrium bond length of re = 1.128 462 5 (58) Å. For the A(1)Π state, the resulting well depth and equilibrium bond length are 𝔇e = 10 303.7(3) cm(-1) and re = 1.235 896 (14) Å, while the electronic isotope shift from the hydride to the deuteride is ΔTe = - 5.99(±0.08) cm(-1).

High sensitive photoassociation spectroscopy of the Cs molecular [formula omitted] and 1 g long-range states below the 6S 1/2 + 6P 3/2 limit

Highly sensitive photoassociation spectroscopy is reported using the modulation technique in a Cs atom magneto-optical trap. Spectral data are extended to red detunings of 70 cm −1 below the Cs 6S 1/2 + 6P 3/2 dissociation limit. Long vibrational progressions are assigned to the 0 u + and 1 g long-range molecular excited states. Some low-lying vibrational levels are first observed for the 0 u + and 1 g states. By fitting the experimental data using the semiclassical LeRoy–Bernstein equation, the long-range molecular coefficients C 3 of the 0 u + and 1 g states are obtained. The present C 3 values are closest to the theoretical values compared with the experimental results reported in earlier publications. Empirical potential curves in the long-range region are derived from these data.

Theoretical study of differential charge-transfer cross sections for Ne4++He collisions at low energies.

A quantal two-channel calculation is applied to study charge-transfer differential cross sections in ${\mathrm{Ne}}^{4+}$ on He collisions at laboratory impact energies from 220 to 500 eV. The experimental data of Tunnell et al. were used to fit empirical potential curves and coupling terms from which the observed oscillatory structures in the differential cross sections were analyzed. In contrast with the double-charge-transfer process in ${\mathrm{C}}^{4+}$ on He, where the oscillations in the differential cross sections are attributed to pure Stueckelberg oscillations, we demonstrated that the differential cross sections for charge transfer in ${\mathrm{Ne}}^{4+}$ on He exhibit many fine fast oscillations and the observed structures are due to the envelopes of these unresolved fast oscillations. Classical deflection functions are used to help in interpreting the calculated oscillations.

Empirical determination of the potential curves of the ground state and the first two excited states of Kr 2

The potential curves of the first two excited states of the krypton dimer have been determined by means of an iterative semiempirical procedure, i.e. by comparing calculated bound-free Franck-Condon factors with experimental spectra, with experimental data from the literature also included. For the ground state, the existing empirical potential curves need to be modified in the region of small internuclear distances. Spectra simulated on the basis of the resulting potential curves show the best agreement with experimental data.

Direct Determination of Pure-State Density Matrices. I. Some Simple Introductory Calculations

A method is developed for the semiempirical determination of an electron density in small diatomic molecules. The method involves primarily the electrostatic and virial theorems and empirical potential curve data. The density has been determined, using Slater-type basis functions, for the molecules ${\mathrm{H}}_{2}^{+}$, ${\mathrm{H}}_{2}$, ${\mathrm{He}}_{2}$, ${\mathrm{Li}}_{2}$, and ${\mathrm{N}}_{2}$. Expectation values are calculated and compared to exact or Hartree-Fock values. A theoretical discussion of the semiempirical densities via a natural-orbital analysis is given. These analyses show that (a) the electrostatic and virial theorems are effective when used to determine unknown parameters in a first-order density but that (b) some additional means must be provided to ensure $N$ representability.

POTENTIAL ENERGY CURVES AND DISSOCIATION PRODUCTS OF THE K2 MOLECULE

A R.K.R.V. calculation has been performed for the [Formula: see text] and B1Πu state of the K2 molecule. By fitting an empirical potential curve to the known true potential curve (the one obtained by the R.K.R.V. method) the dissociation energies of the corresponding states can be estimated. These estimated values allow the states of the dissociated atom to be determined. We have used the four-parameter Lippincott and the five-parameter Hulburt–Hirschfelder functions to approximate the R.K.R.V. curves of the two states. The agreement between the curves is of the same type as already found in previous cases.

Electron Affinities of Some Halogen Molecules and the Charge-Transfer Frequency

In an attempt to fix the value of the vertical electron affinity of the iodine molecule EI2v the potential curve for I2— has been constructed from semiempirical considerations. From this curve the value of EI2v is estimated to be 1.7±0.5 eV, in apparent contradiction to the value around 0 eV indicated by the electron-capture experiments. It is suggested that the electron-capture experiment may measure the vertical energy for capture to give an excited state of the I2— ion, thus explaining the discrepancy. Having fixed the value for EI2v, the relationship predicting the charge transfer frequency for iodine complexes is reexamined critically. By fitting curves to the data for three different types of complexes (π donors with I2, amine donors with I2, and complexes with I atoms), three sets of empirical constants required to force the fit are determined. An attempt is then made to calculate these sets of constants from a priori considerations. The success of this treatment supports the general theory, indicating especially that no major terms have been omitted from the estimation of the energy difference, W1—W0. Furthermore, the general argument supports the value of EI2v obtained in the earlier part of the paper as well as the reliability of the estimation of the other parameters. The analysis supports the perpendicular model for the geometry of the complexes between I2 and π donors. Finally, similar analyses are presented for other halogens; Br2, Cl2, and ICl. Estimates of the vertical electron affinity for these halogens from the empirical potential curves agree reasonably well with estimates from the charge transfer frequency, in support of the results for I2.