Large Internuclear Distances Research Articles

Electronic states of NH and OH+

Ab initio calculations (LCAO-MO-SCF) nearing Hartree-Fock accuracy were made for a series of valence states of the molecules NH and OH+. The correlation energies of all states considered were calculated by a method used precedingly and described in this work. Good agreement with experimental data is found for a series of molecular properties such as equilibrium internuclear distances, term values, dissociation energies and ionization potentials; fair agreement is found for vibration frequencies and unharmonic constants. The precision of the present calculations allow definite predictions to be made concerning the relative energies of the singlet and triplet states in NH, and concerning the potential energy curves of unobserved singlets in OH+. Finally, the examination of the dissociation properties of the electronic states from calculations carried out at large internuclear distances, make it possible to reach conclusions concerning the eventual presence of potential maxima in their potential energy curves.

Observation of ultralong-range Rydberg molecules

Rydberg atoms have an electron in a state with a very high principal quantum number, and as a result can exhibit unusually long-range interactions. One example is the bonding of two such atoms by multipole forces to form Rydberg-Rydberg molecules with very large internuclear distances. Notably, bonding interactions can also arise from the low-energy scattering of a Rydberg electron with negative scattering length from a ground-state atom. In this case, the scattering-induced attractive interaction binds the ground-state atom to the Rydberg atom at a well-localized position within the Rydberg electron wavefunction and thereby yields giant molecules that can have internuclear separations of several thousand Bohr radii. Here we report the spectroscopic characterization of such exotic molecular states formed by rubidium Rydberg atoms that are in the spherically symmetric s state and have principal quantum numbers, n, between 34 and 40. We find that the spectra of the vibrational ground state and of the first excited state of the Rydberg molecule, the rubidium dimer Rb(5s)-Rb(ns), agree well with simple model predictions. The data allow us to extract the s-wave scattering length for scattering between the Rydberg electron and the ground-state atom, Rb(5s), in the low-energy regime (kinetic energy, <100 meV), and to determine the lifetimes and the polarizabilities of the Rydberg molecules. Given our successful characterization of s-wave bound Rydberg states, we anticipate that p-wave bound states, trimer states and bound states involving a Rydberg electron with large angular momentum-so-called trilobite molecules-will also be realized and directly probed in the near future.

Effects of the internuclear vector on the photoelectron angular distributions of H2 +

We study the photoelectron angular distributions (PADs) of diatomic molecule H2 + irradiated by intense laser fields using a nonperturbative scattering theory. We find that the internuclear vector may change the PADs. The PADs have qualitative changes with the increasing of the internuclear distance. The molecular orientation affect the symmetry of the PADs. When the internuclear vector is vertical or parallel to the laser polarization vector, the PADs are four-fold symmetric; for other case the PADs are two-fold symmetric. Due to the modulation effect resulting from the molecular multi-core nature, the size of the jet and the main lobe can be enlarged or reduced. The molecular modulation effect become obvious for large internuclear distance.

An ab initio multireference perturbation theory study on the manganese dimer

The potential energy curves of the ground state and of some excited states of the manganese dimer have been calculated over a wide range of internuclear distances using the second order n-electron valence state perturbation theory applied to a complete active space self-consistent field reference wave function. The ground state of Mn(2), for which also the third order NEVPT has been used, is calculated to be a singlet belonging to the Sigma(g) (+) symmetry, characterized by a large equilibrium internuclear distance R(e) of 3.7-3.8 A, by a low dissociation energy D(e) of 0.07-0.08 eV, and by a small harmonic frequency omega(e) of 43 cm(-1). The experimental evidence that Mn(2) is a van der Waals molecule is thus confirmed. Among the excited states, (11)Pi(u), which is usually indicated as the ground state by density functional theory studies, appears as a low-lying state with R(e)=2.50 A, D(e)=1.35 eV, and omega(e)=246 cm(-1).

Electronic Curves Crossing in Methyl Iodide by Spin–Orbit Ab Initio Calculation

An ab initio investigation of electronic curve crossing in a methyl iodide molecule is carried out using Spin–Orbit multiconfigurational quasidegenerate perturbation theory. The one-dimensional rigid potential curves and optimized effective curves of low-lying states, including Spin–Orbit coupling and relativistic effects, are calculated. The Spin–Orbit electronic curve crossing between 3Q0+and 1Q1, and the shadow minimum in potential energy curve of 3Q0+ at large internuclear distance are found in both sets of the curves according to the present calculations. The crossing position is in the range of RC–I = 0.2370 ± 00001 nm. Comparisons with other reports are presented.

High-order harmonic generation from diatomic molecules with large internuclear distance: The effect of two-center interference

We investigate the high-order harmonic generation (HHG) from diatomic molecules with large internuclear distance using a strong-field approximation model. We find that the hump and dip structure emerges in the plateau region of the harmonic spectrum and the location of this striking structure is sensitive to the laser intensity. Our model analysis reveals that two-center interference as well as the interference between different recombination electron trajectories is responsible for the unusual enhanced or suppressed harmonic yield at a certain order, and these interference effects are greatly influenced by laser parameters such as intensity.

Simple model of scalar-vector interaction for the relativistic two-center problem

The ground-state wave function and the energy term of a relativistic electron moving in the field of two fixed centers, when interaction of this particle with centers is described by two Coulomb and two Coulomb-like scalar potentials are calculated analytically by the linear combination of atomic orbitals method. By means of perturbation theory the asymptotic expansions (at small and large internuclear distances $R$) of the eigenvalues $E(R)$ of the system for arbitrary states are obtained. The dependence of critical charge ${Z}_{\text{cr}}$ and critical distance ${R}_{\text{cr}}$ from the scalar coupling constant was investigated.

Multiphoton Ion Pair Spectroscopy (MPIPS) with Ultrashort Laser Pulses for the H2 Molecule

Time-dependent Schrödinger equation, TDSE, simulations have been performed in order to prepare and study via MPIPS the evolution of vibrational wave packets on the ion pair electronic state potentials B''B1Sigma(u)(+) and Hh1Sigma(g)(+) of the H2 molecule. Using ab initio potential surfaces and transition moments, we present two- and three-photon excitation schemes with ultrashort pulses (tau <or= 10 fs) to prepare coherent superpositions of the two ion pair H(+)H(-) and H(-)H(+) states from the doorway B1Sigma(u)(+) state, which result from the strong radiative coupling between these two electronic states. The simulations are used to estimate the time evolution and recursion times of vibrational wave packets at large internuclear distances, usually not accessible by single-photon spectroscopy. Conditions for the localization of the ion pair states are proposed.

Electron correlation in the GK state of the hydrogen molecule

The second excited (1)Sigma(g)(+) state of the hydrogen molecule, the so-called GK state, has a potential energy curve with double minima. At the united atom limit it converges to the 1s3d configuration of He. At large internuclear distances R, it dissociates to two separated atoms, one in the ground state and another in the 2p excited state. Radial pair density calculations and natural orbital analyses reveal unusual effect of electron correlation around the K minimum of the potential energy curve. As R>2.0 a.u., a natural orbital of sigma(u) symmetry joins the two natural orbitals of sigma(g) symmetry at smaller R. The average interelectronic distance decreases as the internuclear distance increases from R=2.0 to 3.0 a.u. Around R=3.0 a.u. the singly peaked pair density curve splits into two peaks. The inner peak can be attributed to the formation of the ionic electron configuration (1s)(2), where both 1s electrons are on the same nucleus. As the two 1s electrons run into different nuclei, one of the two 1s electrons is promoted to the 2p state, which results in the outer peak in the pair density curve. The Rydberg 1s2p configuration persists as the nuclei stretch, and becomes dominant at large R where four natural orbitals, two of sigma(g) and two of sigma(u) symmetry, become responsible.

Control of electron transfer and high harmonic generation in the linear triatomic system at large internuclear distances with short intense laser fields

We numerically investigate high order harmonic generation (HHG) in the one electron linear H+– molecular system at large internuclear distances R = α and πα/2, where α is the ponderomotive radius, using ultra-short (two-cycles) intense (I > 1014 W cm −2) 800 nm laser pulses linearly polarized along the internuclear axis. We obtain the HHG spectra by solving exactly, in the Born–Oppenheimer approximation, the 3D time-dependent Schrodinger equation (TDSE). At large internuclear distances R, HHG spectra are obtained with an energy cut-off larger than the atomic maximum of I p + 3.17U p, where U p is the ponderomotive energy and I p is the ionization potential. The extended cut-off is shown to be related to the nature of electron transfer, whose direction is shown to depend critically on the absolute carrier envelope phase (CEP) of the ultrashort pulse. Constructive and destructive interferences in the HHG spectrum of coherent superpositions of electronic states in the H+– system are interpreted in terms of multiple electron trajectories from a time series analysis. Efficiencies of HHG are considerably enhanced by refocusing of the ionized electron trajectories with the neighbouring ion thus probing perturbative response of non-ionized electrons to few cycle intense laser pulses on attosecond time scales.

Anatomy of strong field ionization II: to dress or not to dress?

We analyse S-matrix-type approaches to strong-field ionization by an intense few-cycle laser pulse. We derive simple modifications of approximate S-matrix-type approaches that either neglect the effect of the ionic potential after ionization, or treat this potential perturbatively. We show how these modifications eliminate some crucial problems and artefacts, such as the ‘curse of the displaced atom’, associated with the choice of gauge in the strong field approximation. We then discuss how these approximate S-matrix-type approaches should be applied to dissociating molecules using the example of H. We show that suppression of electron tunnelling between the two fragments of the molecular ion introduces dramatic changes in the spectrum of high harmonic emission generated by an intense laser pulse that probes the molecular dissociation. For large internuclear distances and even when the active electron is fully delocalized between the two fragments, the high harmonic spectrum loses all traces of the conventional interference pattern associated with a two-centre molecular structure.

The quantum mechanical two-Coulomb-centre problem in the Dirac equation framework in 2+1 dimensions

With the help of perturbation theory the asymptotic expansions (at small and large internuclear distances R) of the eigenvalues (potential curves) E(R) of the two-Coulomb-centre problem in 2+1 dimensions are obtained. We compare the results obtained with the data from similar approximation for two-Coulomb-centre problem in 3+1 dimensions.

Laser Phase Control of High-Order Harmonic Generation at Large Internuclear Distance: TheH+−H2+System

Exact (Born-Oppenheimer) 3-D numerical solutions of the time-dependent Schrödinger equation are obtained for the one electron linear H+-H2+ atom-molecule system at large internuclear distance R in interaction with two-cycles intense (I>10(14) W cm(-2)) 800 nm laser pulses. High-order harmonic generation (HHG) spectra are obtained with an energy cutoff larger than the atomic maximum of I(p)+3U(p), where I(p) is the ionization potential and U(p) is the ponderomotive energy. At large R, this extended cutoff is shown to be related to the nature of electron transfer, whose direction is shown to depend critically on the carrier-envelope phase (CEP) of the ultrashort pulse. Constructive and destructive interferences in the HHG spectrum resulting from coherent superpositions of electronic states in the H+-H2+ system are interpreted in terms of multiple electron trajectories extracted from a time profile analysis.

Complex self-consistent field and multireference single- and double-excitation configuration interaction calculations for the Πg2 resonance state of N2−

Self-consistent field and multireference single- and double-excitation configuration interaction calculations employing the complex basis function technique are carried out for the (2)Pi(g) resonance state of the N(2) (-) molecule as well as several other anionic resonance states in the neighboring energy region. The results of calculations employing the same method for the (1)S (2s(2)) state of the He atom and the (1)Sigma(g) (+) (sigma(u) (2)) state of the H(2) molecule are found to be in good agreement with those of earlier work. The present theoretical treatment has succeeded for the first time in satisfying the rigorous criterion of the complex variational principle in computing the N(2) (-) resonance states, namely, a cusp in the plots of real versus imaginary components of the corresponding complex energies has been located at each internuclear distance. On this basis, it is found that the open-shell orbital in the lowest-energy adiabatic N(2) (-) resonance state of (2)Pi(g) symmetry changes its character from quite compact at large internuclear distance to relatively diffuse for r<2.3a(0). This is in contrast to all previous theoretical treatments of this system that have not rigorously satisfied the complex variational principle in their determination of this wave function.

Resonant charge exchange involving electronically excited states of nitrogen atoms and ions

Within the framework of the asymptotic theory the matrices for the exchange interaction potentials of the nitrogen ion, with electron shell ${p}^{2}$, and nitrogen atom, with electron shell ${p}^{3}$, are constructed. The hierarchy of interactions in the nitrogen molecular ion at large internuclear distances is constructed for different electronic states. On the basis of these interaction potentials, the cross sections of resonant charge exchange in slow collisions are evaluated for different values of electron momentum projections and then averaged over these momentum projections. The mobilities of nitrogen ions in atomic nitrogen are also derived.

Polarizability functions of heteronuclear diatomic molecules: Semiempirical approach

A semiempirical method is discussed to construct the polarizability functions for a diatomic heteronuclear molecule as a piecewise-continuous function that exhibits physically correct behavior at small and large internuclear distances and agrees with the polarizability function near the equilibrium position of the molecule nuclei. The method is applied to calculate the static polarizability functions of LiH, HF, HCl and CO molecules in the range of internuclear distances [0, ∞).

Charge-resonance effect on harmonic generation by symmetric diatomic molecular ions in intense laser fields

In present paper we develop an analytic theory for the harmonic generation of symmetric diatomic molecular ions beyond two-level model, emphasizing the influence of charge-resonance (CR) states those are strongly coupled to electromagnetic fields for large internuclear distance. With taking into account the continuum states that is ignored in the two-level model and become important for intense laser case, our model is capable to produce spectrum for the whole range of harmonic orders consisting of a molecular plateau due to the CR transition and an atomic-like plateau for a long-wavelength excitation, and in good agreement with numerical results from directly solution of the Schr\"odinger equation. Our theory also identifies the crucial role of the CR states in the fine structure of harmonic spectrum and shows that the harmonic generation in molecular system can be effectively controlled by adjusting the internuclear distance.

High-order above-threshold ionization in stretched molecules

By numerical solution of the time-dependent Schr\"odinger equation, highly accurate electron spectra are calculated for strong-field ionization of a one-dimensional $\mathrm{H}_{2}{}^{+}$ molecular ion at large internuclear distances. Compared to the atomic spectra, we find additional cutoffs at high electron energies. The classical model for ionization (simple-man's model) adapted to the molecular geometry predicts cutoffs up to $50{U}_{\mathrm{p}}$, where ${U}_{\mathrm{p}}$ is the ponderomotive potential. The cutoffs correspond to various scattering scenarios of the tunneled electron from the molecular sites. For certain internuclear distances the agreement between the classical predictions and the numerical spectra is unsatisfactory. We propose a modified simple-man's model based on complex electron trajectories, allowing for electrons appearing in the continuum with nonzero initial velocity from the tunneling ionization process. Agreement of the resulting cutoffs with the numerical results is recovered.

Analysis of light-induced frequency shifts in the photoassociation of ultracold metastable helium atoms

We present an exhaustive analysis of the light-induced frequency shifts of the photoassociation lines of ultracold metastable 4He* atoms in a magnetic trap. The measurements of the shifts of several vibrational levels bound in the purely long-range J = 1, 0u+ potential linked to the 23S1–23P0 asymptote were reported in a previous paper (Kim et al 2005 Europhys. Lett. 72 548), and are analysed here. The simplicity of this system makes it very appropriate for a detailed study. Indeed, the purely long-range character of the excited potential allows one to calculate exact excited molecular wavefunctions and to use asymptotic expansions at large internuclear distances of the ground-state wavefunctions appearing in Franck–Condon-type integrals. Moreover, the number of collisional channels to be considered is strongly reduced by the absence of hyperfine structure for 4He* and the use of polarized ultracold atoms and polarized light. This allows us to derive semi-analytical expressions for the shifts showing explicitly their linear dependences on the s-wave scattering length a of spin polarized metastable 4He* atoms. This explains how it is possible to derive the measurement of a from these shifts.

The K2 23Πg State: New Observations and Analysis

Totally 3045 transitions into the 2(3)Pi(g) v = 0-42, J = 0-103, Omega = 0, 1, 2 rovibrational levels have been observed by infrared-infrared double resonance fluorescence excitation and two-photon spectroscopy. Molecular constants including the spin-orbit interaction parameters are obtained. Although the K2 2(3)Pi(g) state dissociates to the 4s + 3d atomic limit, it is strongly mixed with the 3P ionic states in the range of the potential well. This mixing results in a relatively large equilibrium internuclear distance Re = 5.254 A and a larger spin-orbit constant A0 approximately 14.17 cm(-1) than that of the atomic limit -2.33 cm(-1). Strong perturbations of the 2(3)Pi(g) levels observed are attributed to the spin-orbit coupling with the 4(1)Sigma(g)+ state.