Notations, Spectroscopic Parameters, Energy Levels and Their Relationship to Effective Hamiltonian Formalism of Diatomic Molecules

This paper presents a part of the culmination of the collective efforts in developing a cohesive and consolidated enunciation of the spectroscopic parameters and their relationship to effective molecular Hamiltonians for diatomic formalism, linear four-atomic formalism and quasi-linearity, Watson Hamiltonian and the complexities in symmetric and asymmetric top spectral structures. All these considered together present a beautiful and consistent picture of molecular spectroscopy. In this paper we deal with the diatomic formalism. This paper forms our tribute to Professor K. Narahari Rao and in the second part of the paper we convoy our gratitude to him with a summary of his more than half century of work and an obituary. We will deal with other forms of molecular species which will be connected to optical pumping and/or interstellar space.     

Light scattering,origin invariant multipole moments and molecular property tensors: the case of electric-field-gradient-induced birefringence

A comparison of semiclassical and quantum versions of molecular light scattering theory at finite temperatures is presented. A general formulation of the semiclassical radiation model is developed to the point where its relationship to the corresponding QED formalism can be established: the classical scattered electric field is proportional to the same R-matrix element as that obtained from QED for the photon scattering amplitude. The result is valid for non-resonant scattering at T = 0. The semiclassical theory conventionally also inherits aspects of a classical molecular model, principally origin-dependent molecular multipole moments. Origin independent multipoles, and corresponding response functions can be defined if the theory is cast in terms of centre-of-mass and translation invariant internal coordinates. Such a choice of coordinates brings molecular light scattering theory into line with the theory of the molecular Schrödinger equation. This is illustrated for the case of a diatomic molecule. A specific application of these results of current interest is electric-field-gradient induced birefringence (EFGB) for which there are four competing theories in the literature. In this paper we examine the treatment of finite temperature effects in two semiclassical accounts of EFGB in polar molecules and identify a likely source of the discrepancy between them revealed in a recent ab initio computational study.     

Zero-width resonances in the context of Fano's configuration interaction formalism

ABSTRACT

We examine how to link two approaches for resonance width calculations, in a situation of crossing of two diatomic molecular potentials. One is the semiclassical formalism of Child. The other is Fano's configuration interaction approach leading to the Fermi golden rule. We build a case where the vanishing of the width in the two formalisms can be reduced to the same conditions.     

High-resolution spectroscopy on trapped molecular ions in rotating electric fields: A new approach for measuring the electron electric dipole moment

High-resolution molecular spectroscopy is a sensitive probe for violations of fundamental symmetries. Symmetry violation searches often require, or are enhanced by, the application of an electric field to the system under investigation. This typically precludes the study of molecular ions due to their inherent acceleration under these conditions. Circumventing this problem would be of great benefit to the high-resolution molecular spectroscopy community since ions allow for simple trapping and long interrogation times, two desirable qualities for precision measurements. Our proposed solution is to apply an electric field that rotates at radio frequencies. We discuss considerations for experimental design as well as challenges in performing precision spectroscopic measurements in rapidly time-varying electric fields. Ongoing molecular spectroscopy work that could benefit from our approach is summarized. In particular, we detail how spectroscopy on a trapped diatomic molecular ion with a ground or metastable ³Δ₁ level could prove to be a sensitive probe for a permanent electron electric dipole moment (eEDM).     

Laser-heating diamond anvil cell studies of simple molecular systems at high pressures and temperatures

We report the application of new laser-heating techniques and sample preparation procedures for simple molecular materials (diatomic molecules and water) under high pressure in the diamond anvil cell (DAC). Both continuous and pulsed laser heating was employed. We probed the materials using Raman spectroscopy and also by analyzing the time evolution of the temperature of the metallic coupler that is used to absorb laser radiation and heat the sample. Raman measurements of H₂, D₂, N₂, H₂O and O₂ show a broadening of intramolecular vibrations at high P−T conditions, indicating a decreasing molecular lifetime, and hence suggest an increasing molecular dissociation. In diatomic molecules the intramolecular bonding can be further probed by observations of sidebands corresponding to vibrational transitions from excited states; the energies of these sidebands imply intramolecular potentials that become increasingly less anharmonic as pressure is increased. We also show that the pulsed heating technique combined with instantaneous radiative temperature measurements provides a useful tool for studies of thermochemical properties and phase transformation boundaries.     

普适性双原子分子解析势能函数的研究

提出了一种构造解析势能函数的新方法,由此得到了一种既适用于中性双原子分子又适用于带电双原子分子离子的解析势能函数。本文用八种基本类型的双原子分子——同核中性基态双原子分子Na₂-X1Σ+_g,同核中性激发态双原子分子C₂-A1Π_u,同核带电基态双原子分子离子He+₂-X2Σ+_u,同核带电激发态双原子分子离子N+₂-B2Σ+_u,异核中性基态双原子分子NaLi-X1Σ+_g,异核中性激发态双原子分子BH-B1Σ+,异核带电基态双原子分子离子(BC)--X3Π,异核带电激发态双原子分子离子(CS)+-A2Π等共21个算例对势能函数进行了验证并与RKR (Rydberg-Klein-Rees)实验数据进行了比较,计算结果与RKR数据符合很好。     

Symmetry-adapted tensorial formalism to model rovibrational and rovibronic spectra of molecules pertaining to various point groups

We present a short review on the tensorial formalism developed by the Dijon group to solve molecular spectroscopy problems. This approach, originally devoted to the rovibrational spectroscopy of highly symmetrical species (spherical tops) has been recently extended in several directions: quasi-spherical tops, some symmetric and asymmetric tops, and rovibronic spectroscopy of spherical tops in a degenerate electronic state. Despite its apparent complexity (heavy notations, quite complex mathematical tools), these group theoretical tensorial methods have a great advantage of flexibility: a systematic expansion of effective terms for any rovibrational/rovibronic problem up to a given order is automatically generated. Inclusion of all possible interaction terms for any polyad scheme is therefore easy. This makes such an approach suitable for many types of molecular problems, not only the most symmetric ones.     

Perturbed Morse oscillator calculations of vibrational effects on quadrupole coupling in alkali halides

Formulas are obtained for the variation of the quadrupole coupling constant with vibrational state of an ionic diatomic molecule, using the pertubed Morse oscillator formalism. Results are apllied to NaF, KF, RbF, CsF and KCI, and compared with measured values. Systematic discrepancies are noted, which for the alkali fluorides increase with the atomic number of the alkali metal. Possible explanations include a variation of ionicity with vibrational states and a departure from 1/r³ dependencies of the electric field gradient. Calculations of dependencies of eQq on molecular rotation are also presented.     

Fast fragmentation in core-excited molecules

Symmetry breaking is an important phenomenon connected to the excitation of core electrons in molecules. The fundamental question of whether inner-shell electronic-state orbitals are delocalized, and what the underlying mechanism for breaking the symmetry of a molecule upon dissociation are the subject of much debate, especially for the case of diatomic molecules. One method for studying molecular fragmentation, which is based upon a symmetry picture, is multicoincidence ion spectroscopy. Here we give a brief presentation of some of the applications of this technique, where symmetry, nuclear motion and the temporal signature are of importance.     

Cooling of a nanomechanical resonator in presence of a single diatomic molecule

We propose a theoretical scheme for coupling a nanomechanical resonator to a single diatomic molecule via microwave cavity mode of a driven LC$LC$ resonator. We describe the diatomic molecule by a Morse potential and find the corresponding equations of motion of the hybrid system by using Fokker–Planck formalism. Analytical expressions for the effective frequency and the effective damping of the nanomechanical resonator are obtained. We analyze the ground state cooling of the nanomechanical resonator in presence of the diatomic molecule. The results confirm that presence of the molecule improves the cooling process of the mechanical resonator. Finally, the effect of molecule’s parameters on the cooling mechanism is studied.     

Quantum effects at low-energy atom–molecule interface

The effects of quantum interference in inter-conversion between cold atoms and diatomic molecules are analysed in this study. Within the framework of Fano’s theory, continuum-bound anisotropic dressed state formalism of atom–molecule quantum dynamics is presented. This formalism is applicable in photo- and magneto-associative strong-coupling regimes. The significance of Fano effect in ultracold atom–molecule transitions is discussed. Quantum effects at low-energy atom–molecule interface are important for exploring coherent phenomena in hitherto unexplored parameter regimes.     

E.S.R. spectrum of the radical produced by ultra-violet irradiation in solid azobisisobutyronitrile

The coupled τ operator formalism is applied to derive exact and approximate selection rules that govern the rotational state distribution of products following an interaction between a diatomic molecule and a free atom. The analysis is performed for a two-channel system in which one of the atoms is infinitely heavy.     

Electronic conductance via atomic wires: a phase field matching theory approach

A model is presented for the quantum transport of electrons, across finite atomic wire nanojunctions between electric leads, at zero bias limit. In order to derive the appropriate transmission and reflection spectra, familiar in the Landauer-Büttiker formalism, we develop the algebraic phase field matching theory (PFMT). In particular, we apply our model calculations to determine the electronic conductance for freely suspended monatomic linear sodium wires (MLNaW) between leads of the same element, and for the diatomic copper-cobalt wires (DLCuCoW) between copper leads on a Cu(111) substrate. Calculations for the MLNaW system confirm the correctness and functionality of our PFMT approach. We present novel transmission spectra for this system, and show that its transport properties exhibit the conductance oscillations for the odd- and even-number wires in agreement with previously reported first-principle results. The numerical calculations for the DLCuCoW wire nanojunctions are motivated by the stability of these systems at low temperatures. Our results for the transmission spectra yield for this system, at its Fermi energy, a monotonic exponential decay of the conductance with increasing wire length of the Cu-Co pairs. This is a cumulative effect which is discussed in detail in the present work, and may prove useful for applications in nanocircuits. Furthermore, our PFMT formalism can be considered as a compact and efficient tool for the study of the electronic quantum transport for a wide range of nanomaterial wire systems. It provides a trade-off in computational efficiency and predictive capability as compared to slower first-principle based methods, and has the potential to treat the conductance properties of more complex molecular nanojunctions.     

Quantitative Auger analysis of ion-implanted boron and arsenic in polycrystalline silicon

Quantitative analysis of boron and arsenic in silicon has been made by Auger electron spectroscopy with the in-situ ion milling technique. Ion-implanted boron and arsenic in polycrystalline silicon was used as standard samples. The experimental results indicate that the semi-empirical formalism for quantitative Auger analysis is valid for impurity concentrations less than a few percent. Excellent linear relationship has been obtained between the implanted dose and the normalized Auger signal intensity within ±10% for boron and ±20% for arsenic in silicon.     

The effective rotational hamiltonian for open-shell molecules

A formalism for obtaining the effective rotational hamiltonian for any open-shell molecule is described. This effective hamiltonian is shown to be formed of series of irreducible tensors composed of real and fictitious angular momentum operators. The operations of these tensors may in all cases be restricted to a particular electronic state. Application of such a formalism should be particularly valuable in the interpretation of the high resolution spectra (zero-field microwave, gas-phase electron resonance, etc.) of open-shell molecules, for it follows that the experimental data may always be interpreted without explicit reference to electronic states other than that wherein the spectrum originates. Useful rules are given which determine the relevant orders of tensors in the series and the method is illustrated for the case of a ³Σ diatomic molecule.     

Noise-immune cavity-enhanced optical heterodyne molecular spectroscopy: Current status and future potential

As a result of a combination of an external cavity and modulation techniques, noise-immune cavity-enhanced optical heterodyne molecular spectroscopy (NICE-OHMS) is one of the most sensitive absorption techniques, capable of reaching close-to-shot-noise sensitivities, down to 5×10^-13 fractional absorption at 1 s averaging. Due to its ability to provide sub-Doppler signals from weak molecular overtone transitions, the technique was first developed for frequency standard applications. It has since then also found use in fields of molecular spectroscopy of weak overtone transitions and trace gas detection. This paper describes the principles and the unique properties of NICE-OHMS. The historical background, the contributions of various groups, as well as the performance and present status of the technique are reviewed. Recent progress is highlighted and the future potential of the technique for trace species detection is discussed. PACS  33.80.-b; 07.57.-c; 42.62.Fi     

Electric flux distribution in photodetachment of heteronuclear diatomic molecular negative ion

The photodetachment of a hetero-nuclear diatomic molecular negative ion is studied by using a two-centre model. An analytic formula is presented for the electron flux distribution of a heteronuclear diatomic molecular negative ion. Taking HF^- as an example, we calculated the electron flux distributions of this ion for various detached electron energies. The results show that the electron flux distributions exhibit oscillatory structures, which are caused by the interference effect between the two nuclei. Besides, the laser light polarization also has a great influence on the electron flux distribution. The oscillation amplitude is the largest when the laser polarization is parallel to the z-axis; when the laser polarization is perpendicular to the z-axis, the oscillation almost vanishes. This study provides a new understanding of the photodetachment of a heteronuclear diatomic molecular negative ion.     

Accurate studies on the full vibrational energy spectra and molecular dissociation energies for some electronic states of N<Subscript>2</Subscript> molecule

It is usually very difficult to directly obtain molecular dissociation energy D _e and all accurate high-lying vibrational energies for most diatomic electronic states using modern experimental techniques or quantum theories, and it, is also very difficult to give accurate analytical expression for diatomic molecular dissociation energy. This study proposes a new analytical formula for obtaining accurate molecular dissociation energy based on the LeRoy and Bernstein’s energy expression in dissociation limit. A set of full vibrational energy spectra for some electronic states of N₂ molecule are studied using the algebraic method (AM) suggested recently, and the corresponding accurate molecular dissociation energies are evaluated using the proposed new formula and high-lying AM vibrational energies. The results show that the AM spectra and the new theoretical dissociation energies agree excellently with experimental data, and thereby providing a new physical approach to generating accurate dissociation energies for electronic states of diatomic molecules.