Excited States Of Diatomic Molecules Research Articles

Accuracy of the New Modified Morse Potential Energy Function for Ground and Excited States of Diatomic Molecules

Accuracy of the New Modified Morse Potential Energy Function for Ground and Excited States of Diatomic Molecules

First-principles calculation of excited states of diatomic molecules: a benchmark for the Gutzwiller conjugate gradient minimisation method

We recently proposed the Gutzwiller conjugate gradient minimisation (GCGM) method for efficient and accurate calculation of the ground state total energy of molecular and bulk systems. The GCGM method is developed under the framework of Gutzwiller wave function but goes beyond the commonly adopted Gutzwiller approximation to improve the accuracy and flexibility in treating the correlation effects. In this conference proceeding, we benchmark the GCGM method with the calculation of excited state potential energy curves of three diatomic molecules, namely H2, N2, and O2. Our calculations demonstrate the flexibility and reasonable accuracy of the method.

Structures and harmonic vibrational frequencies for excited states of diatomic molecules with CCSD(R12) and CCSD(F12) models

The equation-of-motion coupled-cluster method for excited states with the singles-and-doubles model (CCSD) has been implemented for ansatz 2 of the explicitly correlated CCSD(R12) and CCSD(F12) methods as part of the program package Dalton. In this model, an orthonormal complementary auxiliary basis set is used for the resolution-of-identity approximation in order to calculate the three-electron integrals needed for CCSD(R12) and CCSD(F12). The additional CCSD(R12) or CCSD(F12) terms introduced within ansatz 2, which are not present in ansatz 1, are derived and discussed with regard to the extra costs needed for their computation. As a first application the basis set convergence of equilibrium bond lengths and harmonic vibrational frequencies has been investigated for some singlet excited states of the diatomic molecules N(2), CO, BF, and BH. The calculated CCSD(F12) results show that the average absolute deviations of the bond lengths and frequencies from the basis set limits are below 0.1 pm and 5 cm(-1) as well as 0.05 pm and 1 cm(-1) for the triple- and quadruple-zeta basis sets, respectively. These deviations are shown to largely arise from the SCF basis set incompleteness errors.

Photoassociation of Ultracold Sodium Atoms

Using ultra-cold atoms a new technique of photoassociation spectroscopy has been developed. The technique has an unprecedented resolution and can be used to obtain high-resolution data on singly and doubly excited states of diatomic molecules. We describe the principle of the technique and show results for one specific case, namely the Na2 molecule.

The Fermi model as a key for understanding excited state potential energy curves

The interaction of a Rydberg electron with a ground-state atom is modelled using the Fermi approximation to obtain long-range potentials for various excited diatomic molecules. Particular attention is paid to the cases of degenerate and near-degenerate atomic Rydberg levels. Extensive comparisons are performed with recent ab initio calculations for 1Σ + and 3Σ + states of NaH and He 2, for up to the ninth state of a specified symmetry in the former. Overall, good qualitative and in some cases, quantitative agreement is found. For isolated states, the undulations in the potentials clearly reflect the nodal pattern of the Rydberg state involved and the magnitude is fixed in the Fermi approach by the electron-ground-state atom scattering length. When several atomic states are close in energy, in the Fermi model because of the factorizable nature of the interaction, only a single non-zero potential emerges from the remaining flat manifold. Such behaviour explains, for example, the presence of high barriers at large distances seen in ab initio calculations for the 1,3Σ + 4f states of NaH. For NaH, the Fermi results are generally better for the weaker triplet interactions than the singlets. In case of near-degenerate levels, the weaker interactions are normally described better than the stronger interaction, where avoided crossings (not included in this simple model) may be important. The Fermi model is also shown to yield a physically sound diabatic approach for excited states of diatomic molecules, allowing for a deeper understanding of the unusual shapes of the adiabatic curves. Limitations of the Fermi model are also discussed.

Undulations in potential curves analyzed using the Fermi model: LiH, LiHe, LiNe, andH2examples

The interaction of a Rydberg electron with a ground-state atom is modeled using the Fermi approximation to obtain long-range potentials for various excited diatomic molecules. Particular attention is paid to cases of degenerate and near-degenerate atomic Rydberg levels. Extensive comparisons are performed with recent ab initio calculations for 1 Σ + and 3 Σ + states of LiH and H 2 , also 2 Σ + states of LiHe, for up to the ninth state of a specified symmetry. Results for LiNe are also discussed. Overall, good qualitative and in some cases quantitative agreement is found. For isolated states, the undulations in the potentials clearly reflect the nodal pattern of the Rydberg state involved and the magnitude is fixed in the Fermi approach by the electron-ground-state atom scattering length. When several states are close in energy, in the Fermi model because of the factorizable nature of the interaction, only a single nonzero potential emerges from the remaining flat manifold. Such behavior explains, for example, the presence of high barriers at large distances seen in ah initio calculations for the 1 , 3 Σ + g , u n=3 states of molecular hydrogen. For the systems involving H the Fermi results are generally better for the weaker, triplet interactions than the singlets. In the case of near-degenerate levels the weaker interactions are normally described better than the stronger interaction, where avoided crossings (not included in this simple model) may be important. In LiHe, where the interactions are weaker, generally for separations larger than about 10a 0 the Fermi model obtains barrier positions within 1a 0 and maxima within 10 cm - 1 . For LiNe, because of the very small scattering length for electrons in neon, largely qualitative results are obtained. The Fermi model is also shown to yield a physically sound diabatic approach for excited states of diatomic molecules, allowing for a deeper understanding of the unusual shapes of the adiabatic curves. Limitations of the Fermi model are also discussed.

Rotationally resolved near-threshold photoionization of the 1b1 valence orbital of H2O and D2O

Results of theoretical studies of rotationally resolved ion distributions for near-threshold photoionization of the 1b1 valence orbital of H2O and D2O are reported and compared with measured spectra. Agreement between the calculated and measured spectra is very encouraging. The calculated and measured spectra reveal both type a and type c transitions in contrast to type c transitions only expected in an atomiclike picture. Type a transitions arise from odd (mainly p wave) angular momentum components of the photoelectron matrix elements which are due to l mixing in the electronic continua. These type a transitions are quite molecular in origin and are similar to nonatomiclike transitions seen in resonance enhanced multiphoton ionization of excited states of diatomic molecules. Useful rotational selection rules are also obtained.

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.

Strongly bound doubly excited states of diatomic molecules

Theoretical calculations are given which show the existence of strongly bound doubly excited states. These states show significant decreases in R e and increases in ω e compared to the ground state. Examples include B 2 and B 2 +, but the discussion is general and may lead to the discovery of many such states.

Perturbation theory with model zero-order approximation for Li2 molecules

In this work, for the example of calculation of the excited state B /sup 1/Pi/sub u/ of the Li/sub 2/ molecule, we formulate a systematic approach to description of the excited states of diatomic molecules based on perturbation theory with the zero-order approximation model potential and with effective correction for correlation effects as higher order perturbation effects.

The vibrational force constant and transition stress for diatomic molecules

The approximate orbital additivity of vibrational force constants for diatomic molecules is demonstrated. For a given molecule or molecular ion, vibrational force constants of excited electronic states associated with a particular configuration are approximately equal, provided configuration interaction can be neglected. The transition stress associated with an electronic transition strongly affects the vibrational motion. The vibrational force constant is shown to depend on the transition stress. The general relation between the force constant and the bond length for excited states is discussed. Molecular constants of excited states of diatomic molecules and molecular ions can be calculated from the transition stress. These calculated values are in good agreement with experimental results or with the theoretical values obtained by ab initio calculation.

TB3 - Measurement of vibrational-vibrational exchange of highly excited states of diatomic molecules where the collisional probability is approaching unity

An experimental method, employing a fast population perturbation technique, is described to measure the vibrational-vibrational ( VV ) collisional probability P\min{r,r-1}\max{\upsilon,\upsilon+1} of a diatomic molecule for large vibrational quantum numbers r and υ. The relaxation of the perturbed gain of a pair of vibrational levels is a function of the vibrational populations and VV rate constants K\min{\upsilon,\upsilon+1}\max{r,r,-1} . The numerical inversion of the VV master rate equations determining this relaxation does not give unique value for K\min{r,r-1}\max{\upsilon,\upsilon+1} (or P\min{r,r-1}\max{\upsilon,\upsilon+1} ), but lower bounds can be evaluated and with empirical formulas, having several adjustable constants, it can be shown that probabilities of the order of unity are required to satisfy the experimental data. The method has been specifically applied to the CO molecule, but other molecules such as HX(X = F, C1, Br), NO, etc., could also be measured.

Morse Potentials for Excited States of Diatomic Molecules

A model is presented, according to which the nuclear potential functions of the various electronic states of a diatomic molecule form a one-parameter family of Morse functions. The variable parameter represents the fraction of the valence electrons which are in antibonding orbitals. By using the properties of the ground state to determine the Morse constants, a relation between ωe and re of the various electronic states is obtained. This relation reproduces the observed data rather accurately. Somewhat cruder predictions of vibrational anharmonicity, ωeχe, and of dissociation energies are also obtained. Properties of molecular ions and of bonds in polyatomic molecules are also obtained from the model. The measure of bond strength obtained from the model is similar to that deduced from electron configurations in the usual way.

Unified Orbital Theory of the Excited States of the Fluorine Molecule

The unification of the atomic orbital and molecular orbital theories of the excited states of diatomic molecules is achieved by means of semi-localized orbitals. In particular the classification of the states of the fluorine molecule arising from the interaction of two fluorine atoms in their ground state is discussed. Quantitative calculations are made for the 1Σg+ and 3Σu+ states and a comparison of the singlet-triplet separation energies and binding energies from the three methods is made. Both two electron and eighteen electron calculations are made. The better molecular orbital calculations give a lower triplet than a singlet state. In the eighteen electron calculation the atomic and semi-localized orbital methods coincide, and the 1Σg+ state is found to be the ground state.

The molecular orbital theory of chemical valency. XII. The excited states of diatomic molecules

A method is developed for the solution of the wave equation for two electrons in the presence of two centres. The work of Lennard-Jones & Pople (1951) on the ground state of such a system is generalized so as to apply to all the excited states. Full advantage is taken of the symmetry properties of the wave functions, both in three-dimensional and six-dimensional space, to reduce the wave equation to a number of component parts, each of a particular symmetry type. This leads to sets of equations with characteristic symmetry properties appropriate to singlet states and triplet states, whether even or odd, positive or negative in the standard notation (1∑-g).