Reduced Potential Curve Method Research Articles

Remark on the ground state potentials and dissociation energies of the alkali hydrides

The ground state Rydberg—Klein—Rees (RKR) potentials and the corresponding molecular constants of the alkali hydrides, recommended in a recent article by S twalley et al. ( J. Phys. Chem. Ref. Data, to be published [1]) are critically evaluated in the framework of the reduced potential curve (RPC) scheme. A comparison with the older RPC analysis of the ground states of the alkali hydrides is briefly discussed. The efficiency of the RPC method for the detection of errors in the RKR potential (spectroscopic constants) and for the estimation of the dissociation energy is emphasized. Although the RKR potentials of NaH and RbH are known only up to 54 and 57% of D e, respectively, the RPC method permitted here at least a substantial reduction of the uncertainty in the lower limit of D e(NaH) (by 70 cm −1) and in the lower and upper limits of D e(RbH) (by 250 and 500 cm −1, respectively) which are now estimated as 15 870, 14 230 and 14 680 cm −1, respectively. The RPC picture even suggests that the values 14 380 and 14 580 cm −1 may possibly be taken as reasonable limits for D e(RbH). Accurate extensions of the inner wings of the potentials of NaH, RbH and CsH were calculated using the generalized reduced potential curve (GRPC) method. The limit of error of these extensions should be smaller than 0.002 Å if the potentials are correct.

Reduced potential curves of the excited states of alkali diatomic molecules

The reduced potential curve (RPC) method has so far been successfully employed for the discussion of the ground states of diatomic molecules, however, its efficacy in the complicated world of the excited states has been doubted by some spectroscopists. The present paper should prove that such doubts are in general unjustified. It is shown that, for an excited state of definite symmetry and order (e.g., 1 1Πu, 2 1Πu, etc.) in a group of affiliated molecules, e.g., the group of homo- or heteronuclear alkali diatomic molecules, the same rules hold in the reduced potential curve (RPC) scheme as have been shown before to hold for the ground state. Small deviations and also anomalies with respect to this rule exist for some excited states as must, of course, be expected. The RPC method just seems most suited to visualize such anomalies. Rydberg–Klein–Rees (RKR) and theoretical ab initio calculated potentials are studied in reduced form. The RPC scheme makes possible a systematic comparative study of excited states of diatomic molecules. The RPC method may be also used for detection of errors (inaccuracies) in the analysis of the spectrum or of deficiencies in the theoretical calculation, and for estimation of the potentials of excited states.

Application of the reduced-potential curve method for the detection of errors or inaccuracies in the analysis of spectra and for the construction of internuclear potentials of diatomic molecules: Alkali diatomic molecules.

Errors in the Rydberg-Klein-Rees potentials for the ground and B-excited states of LiNa and LiK and in the ground-state potential of RbCs are detected using the reduced-potential curve (RPC) method and shown to be due to errors or inaccuracies in the analysis of the spectrum. Using the rules of the RPC scheme, estimates for the left limbs of the ground- and B-state potentials of LiNa and LiK are given which are quite accurate for the ground states. With the use of the RPC method, we also give estimates of the ground-state potentials of ${\mathrm{Rb}}_{2}$ and RbCs up to the dissociation limit. The RPC method is further employed for a calculation of accurate internuclear potentials from inaccurate theoretical ab initio potential curves for a series of molecules. These procedures could be useful for a prediction of the spectrum. The examples should illustrate the predictive and constructive power of the RPC method.

Reducedab initio theoretical internuclear potentials of diatomic molecules

Ab initio theoretical ground state potentials of diatomic molecules calculated with the use of the variational CI-MO (configuration interaction method based on molecular orbitals) are analyzed with the use of the RPC (reduced potential curve) method. It is shown on a series of examples that the following statement is true even for inaccurateab initio calculations: in reduced form, the theoretical potential coincides to a high degree of accuracy with the reduced RKR (Rydberg-Klein-Rees) potential calculated from the spectroscopic data. Thus, with the use of the RPC method, even inaccurateab initio calculations (in particular for heavier molecules) may be used for the construction of rather accurate internuclear potentials and hence obtain a practical significance. The statement also holds for excited states if strong perturbations are not present.

A comparative study of the ground state internuclear potentials of alkali hydrides and estimation of dissociation energies with the use of the RPC (reduced potential curve) method

The RKR potential curves for the ground states of alkali hydrides, calculated in recent years by several authors on the basis of new measurements employing modern techniques, have been analyzed with the use of the RPC method. The ground state reduced potential curves of the alkali hydrides are found to coincide to a high degree of approximation. This group of molecules (together with the group of dialkali molecules reported elsewhere) are slightly anomalous compared to the ground states of other diatomic molecules. The RPC method is used to critically evaluate the dissociation energies of the alkali hydrides using the noncrossing rule of the RPC scheme. This evaluation is essentially in accord with other recent values of dissociation energy.

Applications of the reduced potential curve method to mercury halides and Bi 2

Recently published ground state RKR potential curves of mercury halides are analyzed by using the RPC (reduced potential curve) method. It is shown that these potential curves are quantitatively incorrect, although the sequence of the potential curves of HgCl, HgBr and HgI yields a qualitatively correct picture of the sequence of diatomic molecules with increasing atomic numbers in the RPC scheme. This failure is caused by issufficient rotational analysis and an extrapolation by Morse-curve fitting. A similar analysis is given for a ground state RKR curve of Bi 2. These examples illustrate a possible application of the RPC method.

Ab initio calculations of the ground state potential function of the hydroxyl anion by means of the many-body Rayleigh-Schrödinger perturbation theory

Many-body Rayleigh-Schrödinger perturbation theory (MB-RSPT) up to third order applied to OH- in the range of interatomic distances from 0.0815 to 0.1175 nm. The energy data obtained are combined with the experimental RKR (ground state) potential of HF, and, a ground state potential of OH- is constructed (over a wide range of internuclear distances) within the framework of the reduced potential curve method. With the use of this potential the corresponding rotation-vibration Schrödinger equation is solved for 16OH-. The computed spectroscopic constants are compared with best reported calculations and available experimental evidence. The comparison indicates that MB-RSPT may be used as an adequate (and convenient) tool for the study of negative ions.

Ground state potential curve of Te 2 by the reduced potential curve method

The ground state potential curve of the Te 2 molecule has been constructed using the reduced potential curve (RPC) method. The resulting potential curve which could be obtained almost up to the dissociation limit may be supposed to approximate the exact adiabatic potential curve to a degree of accuracy at present unattainable by any other method known.

Ground-State Reduced Potential Curve (RPC) and the Anomaly of Cl2

The study of ground-state reduced potential curves indicates that either there is some error in the analysis of the spectrum and/or in the values of molecular constants of the Cl2 molecule or a nonnegligible perturbation of the ground state of Cl2 exists. In case the analysis of the spectrum and the values of the molecular constants are correct, the RPC method then leads to the following conclusion: The perturbation of the electronic states of halogens, predicted in order to explain the remarkably anomalous intensities of the band spectra, is, in I2, of the type proposed by Van Vleck whereas, for Cl2, the interpretation suggested by Mulliken holds.

Evaluation of the interatomic potential functions for rare gases with the use of the reduced potential curve method

Evaluation of the interatomic potential functions for rare gases with the use of the reduced potential curve method