INTRODUCTION

Currently, applied problems of physicochemical mechanics in the ranges of both high and ultralow temperatures are becoming increasingly important [1]. Problems associated with calculation of the thermochemical and optical properties of real gas-phase media have wide practical applications [2]. Statistical methods for calculating the basic thermodynamic functions (including equilibrium constants) and rate constants of both direct and reverse chemical reactions have recently become very important. Their relatively easy implementation and versatility opens up wide opportunities for further use in solving a number of theoretical [3] and practical problems [4]. For example, they are used to solve the fundamental problem of quantitative aerothermodynamic analysis of supersonic flows surrounding a natural space object or spacecraft during its penetration into the planetary atmosphere [5]. The physicochemical parameters of gas-plasma media calculated by statistical methods can be used to predict cloud fragmentation and model the trajectory of divergent multipurpose clouds, and also to thoroughly analyze the dispersion of unburnt satellite fragments on the Earth surface. The precision optical properties of molecules formed during the thermal destruction of construction materials can also be used for remote sensing of combustion processes [6].

To implement this approach, it is necessary to perform quantum-mechanical modeling of the energy, radiation, thermodynamic, and kinetic properties of the most important atomic-molecular components of gas-phase media at the currently required experimental level of accuracy [7]. Laboratory modeling of high-energy gas-plasma processes of aeronomic and astrochemical interest [8], as well as optimization of the path of laser synthesis of ultracold molecular assemblies, obviously cannot be performed without taking into account the contributions of all weakly bound, quasibound, and continuum molecular states lying near the main (lowest energy) dissociation threshold of the molecules under study.

LASER-INDUCED FLUORESCENCE MOLECULAR SPECTRA NEAR THE DISSOCIATION THRESHOLD

Modern high- and ultrahigh-resolution experimental spectroscopy of small (diatomic) molecules is primarily used for studying the properties of highly excited rovibronic states of isolated molecules in the gas phase [9]. Laser-induced fluorescence (LIF) combined with dispersive emission analysis on a high-resolution Fourier transform spectrometer (FTS) is a proven and relatively simple but extremely informative method for the systematic study of the low-lying electronic states of molecules whose spectral linewidth is limited only by the Doppler effect [10]. By implementing various geometrical versions of the LIF optical scheme using one- or two-step laser excitation, it is possible to study in detail the fine and, sometimes, hyperfine structure of the rovibrational terms of various multiplicities in a wide range of internal excitation energies of the molecule [11]. Moreover, for strictly “off-diagonal” rovibronic transitions, characterized by very different shapes of interatomic potentials and a large relative shift of the potential curves of combined electronic states relative to each other, it is often possible to observe long (in terms of the vibrational levels of the lowest state) LIF progressions. The observed LIF progressions consist of a discrete (linear) part of the spectrum, which then smoothly transforms into a “structured” or “oscillatory” continuum and a short spectral region between these regions, which is responsible for optical transitions to the quasibound states of the molecule, lying just above the dissociation threshold [12].

Thus, accurate FTS measurement of the positions of rotational lines in the discrete part of the LIF spectrum makes it possible to study in detail the structural parameters of the molecule (including its hyperfine structure) up to the dissociation threshold, while the measurement of the intensity distribution in the continuum part of LIF provides information exclusively about the repulsive part of interatomic potentials, lying above the dissociation energy [13]. However, obtaining reliable information about the electronic-vibrational-rotational, fine, and hyperfine structure of an isolated molecule from precision LIF-FTS data still remains a nontrivial theoretical problem, since it requires quantum-mechanical modeling of the structural and dynamic properties of molecules at an unprecedentedly high (ideally, experimental) level of accuracy and detail [14].

GLOBAL NONADIABATIC ANALYSIS OF MOLECULAR STATES CONVERGING TO THE SAME DISSOCIATION LIMIT

From the theoretical viewpoint, an adequate description and reliable prediction of the properties of excited electronic states requires explicitly including intramolecular (nonadiabatic) interactions in calculation [15] and constructing spectroscopic models that make it possible to take into account the majority of intramolecular perturbations using a minimum set of physically significant parameters that are uniquely related to the electronic structure (structural parameters) of the molecule [16]. It is especially important to go beyond the conventional adiabatic approximation when describing the molecular levels localized near the dissociation threshold. This fundamental problem is caused by quasidegeneracy of the electronic atomic-molecular terms specified in the nonrelativistic model at the dissociation limit [17]. The degeneracy is obviously removed in a completely relativistic approximation, namely, when vector spin-orbital effects, as well as various hyperfine interactions caused by the nuclear spin, are taken into account [18]. However, taking into account relativistic interactions requires expensive electronic structure calculations and inevitably leads to rapidly growing number of electronic states under consideration, corresponding to the transition from pure a to pure c case of Hund coupling.

Thus, a detailed analysis of the energy and radiation properties of the electronically excited molecular states localized near the same dissociation limit requires the development of new methods of nonadiabatic analysis that fully take into account both strong local and relatively weak regular spin-orbital and hyperfine interactions. The most rigorous accounting of nonadiabatic interactions is based on solving a system of coupled radial equations (so-called vibration channels) (CVCs) [3, 16]. When considering regular perturbations caused by interaction with a large (in the limit, infinite) number of remote electronic states, the reduced version of the CVC method is often used [19], in which this effect is taken into account by modifying both diagonal and off-diagonal matrix elements of the original matrix of the molecular Hamiltonian using Van Vleck contact transformations. To implement the CVC method evidently requires an ab initio calculation of not only the potential energy curves of the electronic states in question [20], but also of the matrix elements of intramolecular (spin-orbital, hyperfine, electronic-rotational, etc.) interactions between them as explicit functions of the internuclear distance R.

Moreover, to perform a global nonadiabatic analysis of the electronic states of diatomic molecules converging to a common atomic limit, it is necessary to additionally solve the following related problems.

–All weakly bound, quasibound, and continuum states of a molecule should be simultaneously considered within the framework of the same quantum-chemical approximation (nonadiabatic model). The standard effective Hamiltonian method is evidently not suitable here because of the abrupt change in the strength and nature of intramolecular interactions with a change in the interatomic distance R.

–The conventional adiabatic approximation based on the separation of variables is completely violated at the dissociation limit, since the nonrelativistic electronic states become quasidegenerate. Consequently, all nonadiabatic interactions, including spin-orbital and hyperfine ones, must be taken into account explicitly.

–The rovibrational wave functions for weakly bound, quasibound, and continuum levels of the molecule: (1) satisfy the fundamentally different boundary conditions at R → ∞, (2) are localized in an extremely wide range of internuclear distances 0 > R > 100 Å, and (3) have an irregular nodal structure and rapidly changing vibration amplitude [21]. This makes it very difficult to identify the levels, since the vibrational quantum number is no longer good within the framework of the nonadiabatic CVC approach because of violations of the hypotheses of the oscillatory theorem [22]. In this situation, a remedy may be increasing the efficiency of the numerical solution of the CVC system by analytically transforming the standard radial coordinate into the reduced analogs [23].

–The precision ab initio calculation of the electronic structure of excited molecular states should be performed within the framework of both the a and c cases of Hund coupling in order to obtain reliable estimates of the potential energy curves and all the necessary (primarily, spin-orbital and electronic-rotational) nonadiabatic matrix elements in the widest possible range of R.

In order to check the adequacy of the constructed nonadiabatic model, it is also necessary:

–to achieve systematic reproduction of the experimental terms not directly involved in the nonlinear optimization of spectral model parameters at the level of accuracy of their spectroscopic measurement;

–to perform a test for mass invariance of the optimized electronic parameters of the given nonadiabatic model by reproducing the properties of minor isotoplogues when explicitly replacing the reduced molecular mass in the CVC equations;

–based on the optimized parameters of the CVC model, to calculate the distribution of relative intensities in the observed LIF-FTS progressions and compare them with the measured values; and

–to predict the values of radiative lifetimes, as well as magnetic Lande factors and intrinsic (permanent) dipole moments of the rovibronic levels of the molecule, and compare them with the available experimental analogs.

It was shown, using the global nonadiabatic analysis of high-resolution LIF-FTS spectra of the KCs molecule as an example [10–13], that the nonadiabatic model discussed in this report makes it possible to reproduce, with unprecedentedly high (sub-Doppler) accuracy, the fine and hyperfine structure of rovibronic terms, as well as the probabilities of radiation transitions involving fully mixed electronic states localized near the main dissociation threshold.

CONCLUSIONS

The possibility of laboratory experimental and theoretical modeling of the energy and radiation characteristics of the bound, quasibound, and continuum states of diatomic molecules localized near the dissociation threshold at a currently required experimental level of accuracy was demonstrated using the literature and original data as an example. It was shown that in combination with precision ab initio quantum-chemical calculations of the electronic structure and the global nonadiabatic analysis of quasidegenerate rovibronic states converging to the same dissociation limit, LIF-FTS experiments make it possible to study the structural and dynamic properties of isolated molecules in a very wide range of their electronic-vibrational-rotational excitation. The bound, quasibound, and continuum rovibronic states of molecules play a key role in the formation of stable molecular assemblies during photoassociation and laser-induced assembly of ultracold atoms, and also make a significant contribution to the physicochemical characteristics of molecules at high temperatures, especially in the absence of conditions for using the local thermodynamic equilibrium approximation.

The weakly bound rovibronic states of a molecule, localized near its dissociation threshold, actively participate in the formation of stable assemblies of molecules both during spontaneous and laser-stimulated association of colliding atoms, leading to efficient cooling of the reaction medium. This process of radiation formation and cooling of gas-phase molecules can occur both under laboratory and uncontrolled space conditions, both at elevated and very low translational temperatures.