Heteronuclear Diatomic Molecules Research Articles

Solution of Schrödinger Equation for Simple Diatomic Molecules Using One‐Parameter 1s Slater‐Type Orbitals Wave Function

ABSTRACTThe Schrödinger equation for simple homonuclear and heteronuclear diatomic molecules is analytically solved using one‐parameter Slater‐type orbitals (STOs) to approximate the electronic wave function within a molecular orbital (MO)‐like approach. The resulting total energies, equilibrium bond lengths, potential curves, and electron densities are presented in detail. Calculations using a selected orbital exponent accurately reproduce results from standard methods. Furthermore, the optimization of the orbital exponent allows for a more accurate representation of the electronic wave function, leading to the improved results of the total energy and the equilibrium bond length, as well as minimal computational cost. Seen in the heteronuclear diatomic molecule, the use of the one‐parameter STOs allows the transformation of the heteronuclear problem into the homonuclear one, revealing the electron repulsion effect on the orbital exponent parameter.

"Spatio-temporal symmetries of electronic chirality flips in oriented RbCs induced by two coincident laser pulses with circular ++,+-,-+,-- polarizations".

Recently it has been shown that two coincident well designed laser pulses with two different combinations of circular polarizations ( ++ or -+ ) can create chiral electronic densities in an oriented heteronuclear diatomic molecule. Subsequently, the chirality flips from the electronic Ra to Sa to Ra to Sa etc. enantiomers, with periods in the femtosecond (fs) and attosecond (as) time domains. The results were obtained by means of quantum dynamics simulations for oriented NaK. Here we investigate the electronic chirality flips in oriented RbCs induced by all possible ( ++ , -+ , +- , -- ) combinations of circular polarizations of two coincident well-designed laser pulses. Accordingly, the ++ and -- as well as the +- and -+ combinations generate opposite electronic enantiomers, e. g. Ra versus Sa, followed by opposite periodic chirality flips, e.g. form Ra to Sa to Ra to Sa etc. versus form Sa to Ra to Sa to Ra etc, with periods in the fs and as time domains, respectively. The laser induced spatio-temporal symmetries are derived from first principles and illustrated by quantum dynamics simulations.

Imaging Rovibrational Excitation of Scattered YO Molecules in Inelastic Collisions with Kr and Ne.

Energy transfer between atoms and molecules is fundamental to many physical and chemical processes, and understanding the mechanisms and outcomes of energy transfer is crucial for various applications in physics and chemistry. Here, the rovibrational excitation of YO(X 2Σ+) molecules with the collision of Kr and Ne has been studied in the laser-ablation crossed beam and time-sliced ion velocity map imaging setup in combination with the resonance enhanced multiphoton ionization scheme. Significant changes in the angular distribution for different rovibrational excitations of YO molecules are observed with the collision of Kr. The sharp forward distribution for low rovibrational excitation of YO(v' = 0, 1) molecules suggest that the weak attractive potential between Kr and YO is dominant at large impact parameters. Comparatively, the strong sideway distribution for highly rovibrationally excited YO(v' = 1, 2, 3, and 5) is due to rainbow scattering from the stronger attractive potential of Kr···YO at relatively small impact parameters. The more isotropic angular distribution in the highly rovibrationally excited YO(v' = 11) indicates the formation of a short-lived complex. A change in the angular distribution of scattered YO with different rovibrational excitations was also observed in the collisions of Ne. For YO as a heteronuclear diatomic molecule, collisions of the Y- and the O-end of YO with rare gases would affect the contribution of inelastic processes at different impact parameters.

Analyzing the photoassociation spectrum of ultracold 85Rb 133Cs molecule in (3)3Σ+ state.

We establish a theoretical model to analyze the photoassociative spectroscopy of 85Rb 133Cs molecules in the (3)3Σ+ state. The vibrational energy, spin-spin coupling constant, and hyperfine interaction constant of the (3)3Σ+ state are determined based on nine observed vibrational levels. Consequently, the Rydberg-Klein-Rees potential energy curve of the (3)3Σ+ state is obtained and compared with the ab initial potential energy curve. Our model can be adopted to analyze the photoassociative spectroscopy of other heteronuclear alkali-metal diatomic molecules in the (3)3Σ+ state.

Dynamics of an ultracold weakly bound heteronuclear diatomic molecule in an ultrashort laser pulse

Dynamics of an ultracold weakly bound heteronuclear diatomic molecule in an ultrashort laser pulse

Lowest electronic states of neutral and ionic LiN

AbstractWe have investigated the potential energy curves (PECs) of the LiN heteronuclear diatomic molecule, including its ionic species LiN+ and LiN−, using explicitly correlated multi‐reference configuration interaction (MRCI‐F12) calculations in conjunction with the correlation consistent quintuple‐𝜁 basis set. The effect of core–valence correlation, scalar relativistic effects, and the size of the basis sets has been investigated. A comprehensive set of spectroscopic constants determined based on the above‐mentioned calculations are also reported for the lowest electronic states and all systems, including dissociation energies, harmonic and anharmonic vibrational frequencies, and rotational constants. Additional parameters, such as the dipole moments, equilibrium spin‐orbit constants, excitation energies, and rovibrational energy levels, are also documented. We found that the three triplet states of LiN, namely, X 3∑−, A 3Π, and 2 3∑−, exhibit substantial potential wells in the PEC diagrams, while the quintet states are repulsive in nature. The ground state of the anion also shows a deep potential well in the vicinity of its equilibrium geometry. In contrast, the ground and excited states of the cation are very loosely bound. Charge transfer properties of each of these states are also analyzed to obtain an in‐depth understanding of the interatomic interactions. We found that the core–valence correlation has a substantial effect on the calculated spectroscopic constants.

Elliptic Dichroism in the Above-Threshold Ionization of Molecules Induced by a Strong Laser Field.

Using a strong-field-approximation theory, we investigate the high-order above-threshold ionization of diatomic molecules exposed to the monochromatic and bichromatic elliptically polarized fields. We devote particular attention to the difference between the photoelectron momentum distributions obtained with fields with opposite helicity. This difference is quantified using the elliptic-dichroism parameter, which represents the normalized difference between the differential ionization rates calculated with driving fields with opposite helicity. We find that this parameter strongly depends on the molecular orientation with respect to the laser field. In addition, this dependence is different for molecules with different types of highest-occupied molecular orbital. In other words, we show that the molecular structure is imprinted onto the elliptic-dichroism parameter for both monochromatic and bichromatic driving fields. This is explained by analyzing the interferences between various partial contributions to the differential ionization rate. In this way, elliptic dichroism also serves as a tool to analyze the electron dynamics. Finally, for heteronuclear diatomic molecules, we show that the elliptic dichroism is different from zero even for the direct electrons, i.e., the electrons that after liberation go directly to the detector. In this case, the dependence on the molecular orientation is far more pronounced for a bichromatic driving field.

Coherent control of the vibrational dynamics of aligned heteronuclear diatomic molecules

We present an analytical pulse design protocol for controlling the vibrational dynamics of polar diatomic molecules within a given electronic state. Altering the potential energy function via the position-dependent electric permanent dipole moment, the vibrational state population dynamics is directly controlled using appropriately shaped laser pulses in the midinfrared regime. The optimal pulse shapes---that are expected to drive the molecule along user-defined quantum pathways---are obtained by reverse engineering, that is, solving the Schr\"odinger equation of the nuclei inversely in a relevant subspace. The proposed control scheme is validated by accurately solving the full time-dependent Schr\"odinger equation of the ${\mathrm{HeH}}^{+}$ molecular ion with two completely different methods: (1) propagating the complex population amplitudes of many field-free eigenstates or (2) propagating directly the nuclear wave packet on a grid. We find that besides smooth transitions, arbitrary Rabi oscillations as well as vibrational ladder climbing can be efficiently controlled with the present scheme. As a result, the molecule is successively excited beyond the potential barrier, leading to enhanced dissociation in the ground electronic state. Rotational effects and possible extensions of the presented control are also briefly discussed.

Split electrons in partition density functional theory

Partition density functional theory is a density embedding method that partitions a molecule into fragments by minimizing the sum of fragment energies subject to a local density constraint and a global electron-number constraint. To perform this minimization, we study a two-stage procedure in which the sum of fragment energies is lowered when electrons flow from fragments of lower electronegativity to fragments of higher electronegativity. The global minimum is reached when all electronegativities are equal. The non-integer fragment populations are dealt with in two different ways: (1) An ensemble approach (ENS) that involves averaging over calculations with different numbers of electrons (always integers) and (2) a simpler approach that involves fractionally occupying orbitals (FOO). We compare and contrast these two approaches and examine their performance in some of the simplest systems where one can transparently apply both, including simple models of heteronuclear diatomic molecules and actual diatomic molecules with two and four electrons. We find that, although both ENS and FOO methods lead to the same total energy and density, the ENS fragment densities are less distorted than those of FOO when compared to their isolated counterparts, and they tend to retain integer numbers of electrons. We establish the conditions under which the ENS populations can become fractional and observe that, even in those cases, the total charge transferred is always lower in ENS than in FOO. Similarly, the FOO fragment dipole moments provide an upper bound to the ENS dipoles. We explain why and discuss the implications.

A multiple scattering theoretical approach to time delay in high energy core-level photoemission of heteronuclear diatomic molecules

We present analytical expressions of momentum-resolved core-level photoemission time delay in a molecular frame of a heteronuclear diatomic molecule upon photoionization by a linearly polarized soft x-ray attosecond pulse. For this purpose, we start to derive a general expression of photoemission time delay based on the first order time dependent perturbation theory within the one electron and single channel model in the fixed-in-space system (atoms, molecules and crystals) and apply it to the core-level photoemission within the electric dipole approximation. By using multiple scattering theory and applying series expansion, plane wave and muffin-tin approximations, the core-level photoemission time delay is divided into three components, , and , which are atomic photoemission time delay, delays caused by the propagation of photoelectron among the surrounding atoms and the scattering of photoelectron by them, respectively. We applied a single scattering approximation to and obtained for a linearly polarized soft x-ray field with polarization vector parallel to the molecular axis for a heteronuclear diatomic molecule, where is the angle of measured photoelectron from the molecular axis. The core-level photoemission time delay is approximated well with this simplified expression in the high energy regime ( a.u.−1, where is the amplitude of photoelectron momentum ), and the validity of this estimated result is confirmed by comparing it with multiple scattering calculations for C 1s core-level photoemission time delay of CO molecules. shows a characteristic dependence on θ, it becomes zero at θ = 0°, exhibits extended x-ray absorption fine structure type oscillation with period at θ = 180°, where R is the bondlength, and gives just the travelling time of photoelectron from the absorbing atom to the neighbouring atom at θ = 90°. We confirmed these features also in the numerical results performed by multiple scattering calculations.

Profile of Energy Loss Spectrum in Impulsive Ion Collisions with Heteronuclear Diatomic Molecules: Effects of Mass Asymmetry in Target Molecule

Profile of Energy Loss Spectrum in Impulsive Ion Collisions with Heteronuclear Diatomic Molecules: Effects of Mass Asymmetry in Target Molecule

Theoretical aspects of radium-containing molecules amenable to assembly from laser-cooled atoms for new physics searches

We explore the possibilities for a next-generation electron-electric-dipole-moment experiment using ultracold heteronuclear diatomic molecules assembled from a combination of radium and another laser-coolable atom. In particular, we calculate their ground state structure and their sensitivity to parity- and time-reversal () violating physics arising from flavor-diagonal charge-parity () violation. Among these species, the largest -violating molecular interaction constants—associated for example with the electron electric dipole moment—are obtained for the combination of radium (Ra) and silver (Ag) atoms. A mechanism for explaining this finding is proposed. We go on to discuss the prospects for an electron EDM search using ultracold, assembled, optically trapped RaAg molecules, and argue that this system is particularly promising for rapid future progress in the search for new sources of violation.

Strong-field ionization of heteronuclear diatomic molecules using an orthogonally polarized two-color laser field

We apply the improved molecular strong-field approximation to investigate high-order above-threshold ionization (HATI) of heteronuclear diatomic molecules by an orthogonally polarized two-color (OTC) laser field. The OTC field consists of two linearly polarized components with frequencies $r\ensuremath{\omega}$ and $s\ensuremath{\omega}$, where $r$ and $s$ are integers, and $\ensuremath{\omega}$ is the fundamental frequency. The molecule is aligned in the OTC laser field polarization plane. We show that the photoelectron momentum distribution obeys one reflection symmetry which is valid for arbitrary values of the relative phase between the OTC field components in the case when $r+s$ is odd. For molecules oriented along the polarization axis ${z}_{L}$ of the $r\ensuremath{\omega}$ component (${\ensuremath{\theta}}_{L}={0}^{\ensuremath{\circ}}$) and $r$ even and $s$ odd, the HATI spectrum exhibits the reflection symmetry with respect to the ${z}_{L}$ axis. When the molecular orientation is along the ${x}_{L}$ axis, which is perpendicular to the polarization axis of the $r\ensuremath{\omega}$ component (${\ensuremath{\theta}}_{L}={90}^{\ensuremath{\circ}}$), the spectrum exhibits the reflection symmetry with respect to the ${x}_{L}$ axis for $r$ odd and $s$ even. In addition, we analyze the asymmetry in the photoelectron spectra of heteronuclear molecules by comparing them with the photoelectron spectra obtained ionizing a homonuclear diatomic molecule. We also explore the influence of the shift of the relative phase by ${180}^{\ensuremath{\circ}}$ on the HATI spectra. We explain some characteristics of the obtained HATI spectra using a generalization of the classical two-dimensional simple man's model which includes ionization probabilities calculated using the imaginary-time method. Finally, we analyze the interference minima for different heteronuclear diatomic molecules and for particular values of the emission angle, laser-field parameters, and internuclear distance. These minima are well fitted with the curve obtained using the derived condition for the two-center destructive interference minima.

Potential Energy Surfaces for Water Interacting with Heteronuclear Diatomic Molecules: H2O–HF as a Case Study

We present an analytical model, suitable for molecular dynamics applications, of a five-dimensional potential energy surface, based on the expansion in spherical harmonics, for non-linear-triatomic molecule (C2v) – heteronuclear-diatomic molecule systems, with both molecules having a rigid structure. The method consists in the exact transformation of quantum chemical input data related to a minimal number of significant configurations. This approach is applied to the case study of H2O–HF at various levels of theory. The interaction potential has been analyzed and compared with state-of-art theoretical models. Pros and cons of the method are presented and discussed.

Multiconfiguration Density-Coherence Functional Theory.

This paper presents a new theory called multiconfiguration density coherence functional theory (MC-DCFT). This theory provides a new route to define density functionals for multiconfiguration wave functions, in particular by using the one-particle density matrix in the coordinate representation. The theory is illustrated by calculating the dissociation curve of four heteronuclear and homonuclear diatomic molecules, namely, H2, F2, N2, and HF, using density coherence functionals converted from PBE, BLYP, and PW91. By introducing two parameters in the converted density functionals, we are able to calculate bond dissociation energies of comparable accuracy as those calculated by multiconfiguration pair-density functional theory (MC-PDFT) and complete active space second-order perturbation theory (CASPT2). This demonstrates that it would be possible to build a successful multiconfiguration density functional theory based on density coherence.

High-order harmonic generation by aligned heteronuclear diatomic molecules in an orthogonally polarized two-color laser field

Using the molecular strong-field approximation, we investigate high-order harmonic generation by heteronuclear diatomic molecules exposed to an orthogonally polarized two-color laser field, which consists of two mutually orthogonal linearly polarized fields with frequencies $$r\omega $$ and $$s\omega $$ . Here, r and s are integers and $$\omega $$ is the fundamental frequency. The harmonic emission rate and the harmonic ellipticity can be controlled using the laser-field parameters, in particular the relative phase and the intensity ratio of the laser-field components. The value of the relative phase, for which the emission rate is optimal, and the position of the cutoff can be estimated using a classical model. Also, we analyze the harmonic emission rate and the harmonic ellipticity as functions of the molecular orientation, which can also be used as a control parameter. Two types of minima are present in the spectra, depending on r and s. For $$r+s$$ even, interference minima are present in the spectra of the T-matrix component either parallel or perpendicular to the internuclear axis. Using quantum-orbit theory and the saddle-point method, we derive a condition for the interference minima, which relates the molecular orientation angle $$\theta _L$$ and the harmonic order n. The corresponding curves in the ( $$\theta _L$$ , n) plane well reproduce the minima of the numerically calculated spectra. For $$r+s$$ odd, minima are present in the spectra for a particular molecular orientation angle. These minima are explained using the explicit form of the T-matrix element. A heteronuclear as opposed to a homonuclear molecule affords a larger region in the parameter space where both the harmonic ellipticity and the harmonic intensity vary smoothly and both are large.

Black hole binaries and light fields: Gravitational molecules

We show that light scalars can form quasibound states around binaries. In the nonrelativistic regime, these states are formally described by the quantum-mechanical Schr\"odinger equation for a one-electron heteronuclear diatomic molecule. We performed extensive numerical simulations of scalar fields around black hole binaries, showing that a scalar structure condenses around the binary---we dub these states ``gravitational molecules.'' We further show that these are well described by the perturbative, nonrelativistic description.

Spectroscopic properties of open shell diatomic molecules using Piris natural orbital functionals.

Spectroscopic properties such as equilibrium distances, vibrational constants, rotational constants, dissociation energies, and excitation energies are calculated for nine heteronuclear diatomic molecules (PH, NF, NH, NO, CS, AlF, ClF, BeO and CF) using an interactive pair model (PNOF7s), that has been generalized for spin multiplet states, and its second order perturbation variant, NOF-MP2, which was also generalized for multiplets. The results obtained are compared with Complete Active Space (CASSCF) and Complete Active Space Perturbation Theory (CASPT2). It is shown that the potential energy curves provided by the PNOF functional for open shell diatomic molecules are in acceptable agreement with those from CASSCF and CASPT2. The spectroscopic constants depending at most on the second derivative of the potential energy are in good agreement with experiment, while those requiring the evaluation of the third and fourth derivatives show larger deviations from experiment and from those predicted by CASPT2. Thus, it is shown that the PNOF functional extension to multiplets is an alternative approach in predicting spectroscopic constants of molecules where static correlation plays an important role, like the open shell heteronuclear diatomic molecules studied in this work.

Absolute Band Intensity of the Iodine Monochloride Fundamental Mode for Infrared Sensing and Quantitative Analysis.

Iodine monochloride (ICl) is a potential off-gas product of molten salt reactors; monitoring this heteronuclear diatomic molecule is of great interest for both environmental and safety purposes. In this paper, we investigate the possibility of infrared monitoring of ICl by measuring the far-infrared absorption cross section of its fundamental band near 381 cm-1. We have performed quantitative studies of the neat gas in a 20 cm cell at 25, 35, 50, and 70 °C at multiple pressures up to ∼9 Torr and investigated the temperature and pressure dependencies of the band's infrared cross section. Quantitative measurements were problematic due to sample adhesion to the cell walls and windows as well as reactions/possible hydrolysis of ICl to form HCl gas. Effects were mitigated by measuring only the neat gas, using short measurement times, and subtracting out the partial pressure of the HCl(g). The integrated band strength is shown to be temperature independent and was found to be equal to 9.1 × 10-19 (cm2/molecule) cm-1. As expected, the temperature dependence of the band profile showed only a small effect over this limited temperature range. We have also investigated using the absorption data along with inverse least squares multivariate methods for the quantitative monitoring of ICl effluent concentrations under different scenarios using infrared (standoff) sensing and compare these results with traditional Beer's law (univariate) techniques.

Rivalry between Regium and Hydrogen Bonds Established within Diatomic Coinage Molecules and Lewis Acids/Bases.

A theoretical study of the complexes formed by Ag2 and Cu2 with different molecules, XH (FH, ClH, OH2 , SH2 , HCN, HNC, HCCH, NH3 and PH3 ) that can act as hydrogen-bond donors (Lewis acids) or regium-bond acceptors (Lewis bases) was carried out at the CCSD(T)/CBS computational level. The heteronuclear diatomic coinage molecules (AuAg, AuCu, and AgCu) have also been considered. With the exception of some of the hydrogen-bonded complexes with FH, the regium-bonded binary complexes are more stable. The AuAg and AuCu molecules show large dipole moments that weaken the regium bond (RB) with Au and favour those through the Ag and Cu atoms, respectively.