Range Of Internuclear Distances Research Articles

Accurate Analytic Potential Energy Function andSpectroscopic Study for G1Πg State of Dimer 7Li2

The reasonable dissociation limit for theG1Πg state of dimer 7Li2 is determined.The equilibrium internuclear distance,dissociation energy, harmonic frequency, vibrationalzero energy, and adiabatic excitation energy are calculated usinga symmetry-adapted-cluster configuration-interaction method incomplete active space in Gaussian03 program package at such numerousbasis sets as 6-311++G, 6-311++G(2df,2pd), 6-311++G(2df,p), cc-PVTZ,6-311++G(3df,3pd), CEP-121G, 6-311++G(2df,pd), 6-311++G(d,p),6-311G(3df,3pd),D95(3df,3pd), 6-311++G(3df,2p), 6-311++G(2df), 6-311++G(df,pd)D95V++, and DGDZVP. The complete potential energy curves are obtainedat these sets over a wide internuclear distance range and haveleast squares fitted to Murrell–Sorbie function. The conclusionshows that the basis set 6-311++G(2df,p) is a most suitable onefor the G1Πg state. At this basis set,the calculated spectroscopic constants Te, De, E0,Re, ωe, ωeχe, αe,and Be are of 3.9523 eV, 0.813 06 eV, 113.56 cm−1,0.320 15 nm, 227.96 cm−1, 1.6928 cm−1,0.004 436 cm−1, and 0.4689 cm−1,respectively, which are in good agreementwith measurements whenever available. Thetotal 50 vibrational levels and corresponding inertial rotationconstants are for the first time calculated and compared withavailable RKR data. And good agreement with measurements is obtained.

Dissociative Double Ionization of CO2: Dynamics, Energy Levels, and Lifetime

In a kinematically complete experiment on the dissociative double ionization of CO2 by electron impact, spontaneous and metastable decay have been observed via the channel CO2(2+) --> CO+ + O+. The metastable decay shows a lifetime of 5.8 +/- 1.5 micros. The measured kinetic energy release spectrum of the dissociation shows one broad peak. To understand the observed features, ab initio potential energy surface (PES) for the ground electronic state of CO2(2+) was computed using a multireference configuration interaction method and a correlation-consistent polarized-valence quadruple-zeta basis set, for a range of internuclear distances and O-C-O bond angles, and an analytic fit of the PES was obtained. The computed PES clearly indicates the metastability of the dication and yields a barrier height and an asymptotic limit in fair agreement with the reported data. A time-dependent quantum mechanical approach was used to compute the ground vibrational state wave function of CO2 in its ground electronic state. Assuming a Franck-Condon transition, the same function was taken to be the initial wave function at time t = 0 for the time evolution on the fitted PES for the ground electronic state of CO2(2+). The autocorrelation function was computed and Fourier transformed to obtain the excitation spectrum. Upon convolution with the instrument resolution function, the kinetic energy release spectrum was obtained, in good agreement with the experimental results, particularly at lower energies. The discrepancies at higher energies are attributed to the noninclusion of the excited states of CO2(2+) in the dynamical study.

Role of the electric dipole moment in positron binding to the ground and excited states of the BeO molecule

Self-consistent-field and multireference single- and double-excitation configuration interaction (CI) calculations have been carried out for various electronic states of the beryllium oxide molecule and their positron-attached counterparts. Particular emphasis is placed on the correlation between the polarity of a given BeO state and the magnitude of the positron binding energy as the internuclear distance is varied. Potential curves are computed for all BeO states that correlate with the first three atomic limits for this system and good agreement is found between the experimental and calculated spectroscopic constants in all cases. The present level of CI treatment is known to underestimate the positron affinities of atoms by at least several tenths of an eV, and this fact needs to be taken into account in evaluating the results for positron binding to molecules. The lowest BeO excited states (3,1Pi) are not found to bind with a positron in the Franck-Condon region due to their comparatively small dipole moments caused by O to Be charge transfer relative to the X 1Sigma+ ground state, which in turn does have a fairly sizeable positron affinity. The situation changes significantly as dissociation proceeds, however, with both 4,2Pi and 2Sigma+ positronic states lying several tenths of an eV lower than their neutral counterparts over a broad range of internuclear distance.

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, ∞).

Relationship between the Charge Distribution and Dipole Moment Functions of CO and the Related Molecules CS, SiO, and SiS

The dipole moment functions of the titled molecules are written as the sum of a charge and induced atomic dipole contribution and the distance dependence interpreted in terms of these components. These two contributions have opposite signs over a large range of internuclear distances, and when they have equal magnitudes, the dipole moment vanishes. This happens with CO near the equilibrium bond length and is responsible for its small dipole moment. The dipole moment of CS is 0.770(ea0), rather large for a diatomic in which the two atoms have essentially the same electronegativities; this is because for CS, the two components of the dipole moment have the same sign at equilibrium and reinforce one another.

Interaction potentials for Br−–Rg (Rg=He–Rn): Spectroscopy and transport coefficients

High-level ab initio CCSD(T) calculations are performed in order to obtain accurate interaction potentials for the Br(-) anion interacting with each rare gas (Rg) atom. For the Rg atoms from He to Ar, two approaches are taken. The first one implements a relativistic core potential and an aug-cc-pVQZ basis set for bromine, an aug-cc-pV5Z basis set for Rg, and a set of bond functions placed at the midpoint of the Rg-Br distance. The second one uses the all-electron approximation with aug-cc-pV5Z bases further augmented by an extra diffuse function in each shell. Comparison reveals close similarity between both sets of results, so for Rg atoms from Kr to Rn only the second approach is exploited. Calculated potentials are assessed against the previous empirical, semiempirical, and ab initio potentials, and against available beam scattering data, zero electron kinetic energy spectroscopic data, and various sets of the measured ion mobilities and diffusion coefficients. This multiproperty analysis leads to the conclusion that the present potentials are consistently good for the whole series of Br(-)-Rg pairs over the whole range of internuclear distances covered.

1Σ u and 1Π u states of the hydrogen molecule: Nonadiabatic couplings and vibrational levels

Nonadiabatic coupling matrix elements are computed for six lowest 1 Σ u + and four lowest 1Π u electronic states of H 2 in a wide range of internuclear distances. These matrix elements are used together with the adiabatic potentials to determine the bound ro-vibrational levels of the 10 electronic states for rotational quantum numbers J ⩽ 10. The computed energies agree quite well with existing experimental term values. However, some of the experimental levels should be assigned differently.

Theoretical determination of the electronic structure of KH +

Potential energy curves and dipole moments have been determined over a large range of internuclear distances, for all molecular states dissociating up to the asymptote K(4d) + H + (i.e. for 22 2Λ (+) electronic states). Calculations have been performed through a model potential type method. Spectroscopic constants of the bound states are presented and characteristics of the humps are also reported. Both results are compared with available data.

Threshold effects in the photoassociation of cold atoms: R−6 model in the Milne formalism

The general trends of the energy dependence of the photoassociation probability in the threshold range are obtained by introducing the simplest asymptotic model to describe the ground molecular state. It consists in a R−6 potential limited at short range by a repulsive wall, with a tuneable position chosen to reproduce the scattering length of the system. The introduction of reduced units of length and energy allows the systematic investigation of all pairs of alkali atoms. The use of the Milne phase–amplitude formalism is suitable to analyse the breaking of the quasi-classical approximation. The universal trends of the threshold behaviour of collisional properties are analysed and exhibit clearly the importance of the scattering length value. Two particular solutions of the amplitude equation are studied, corresponding to integration from inward or outward, and analytic expressions are given. Both solutions are smoothly connected through the whole range of internuclear distance, extending the results of different authors to the description of states with larger binding energy.

Ab initio and quantum-defect calculations for the Rydberg states of ArH

Potential energy curves were evaluated for the ground and thirteen low-lying excited electronic states of the ArH molecule over a wide range of internuclear distances by the multi-reference averaged quadratic coupled cluster method. The ab initio energy differences and transition dipole moments were used to estimate Einstein emission coefficients, absorption oscillator strengths and radiative lifetimes. Diagonal and off-diagonal quantum defects, as functions of internuclear distance, were extracted from ab initio potentials of the lowest Rydberg states of the neutral ArH molecule by taking account of configuration interaction between Rydberg series converging to the ground and two electronic excited states of the ArH(+) cation. The derived quantum-defect functions were used to generate manifolds of higher excited Rydberg states. The agreement between experimental and calculated energies and radiative transition probabilities was found to be as good as or better than that obtained by earlier calculations.

Simple Three-Parameter Model Potential for Diatomic Systems: From Weakly and Strongly Bound Molecules to Metastable Molecular Ions

Based on a simplest molecular-orbital theory of H(2)(+), a three-parameter model potential function is proposed to describe ground-state diatomic systems with closed-shell and/or S-type valence-shell constituents over a significantly wide range of internuclear distances. More than 200 weakly and strongly bound diatomics have been studied, including neutral and singly charged diatomics (e.g., H(2), Li(2), LiH, Cd(2), Na(2)(+), and RbH(-)), long-range bound diatomics (e.g., NaAr, CdNe, He(2), CaHe, SrHe, and BaHe), metastable molecular dications (e.g., BeH(++), AlH(++), Mg(2)(++), and LiBa(++)), and molecular trications (e.g., YHe(+++) and ScHe(+++)).

Topological Analysis of the Electron Density Distribution in Perturbed Systems. I. Effect of Charge on the Bond Properties of Hydrogen Fluoride

Within the framework of the molecular orbital (MO) theory, the addition of one electron to the 4sigma antibonding orbital of the neutral (F...H) system or the removal of one electron from its pi nonbonding orbitals, leading to (F...H)- and to (F...H)+, has permitted the investigation of these charge perturbations on the bond properties of the hydrogen fluoride molecule by using the topological analysis of rho(r). For (F...H), (F...H)-, and (F...H)+, the topological and energetic properties calculated at the F...H bond critical point (BCP) have been related to the 3sigma bonding molecular orbital (BMO) distribution, as this orbital is the main contributor to rho(r) at the interatomic surface. The analysis has been carried out at several F...H internuclear distances, ranging from 0.8 to 3.0 A. As far as the BMO distribution results from its interaction with the average Coulomb and exchange potential generated by the charge filling the other MOs, and in particular by the pi and 4sigma electrons, the comparison between the BCP properties calculated for the charged systems and those corresponding to the neutral one permits the interpretation of the differences in terms of the charge perturbation on BMO. Along with the BCP properties of (F...H), (F...H)-, and (F...H)+, the interaction energy magnitudes of these systems have been also calculated within the same range of internuclear distances, indicating that the applied perturbations do not break the F-H bond but soften it, giving rise to the stable species (F-H)- and (F-H)+. Comparing the three systems at their equilibrium geometries, the most stable configuration, which corresponds to the unperturbed (F...H) system, shows the highest quantity and the most locally concentrated charge density distribution, along with the largest total electron energy density magnitude, at the interatomic surface as a consequence of the BMO contraction toward the fluorine nucleus in (F...H)+ and of the BMO expansion toward both nuclei in (F...H)-. On the other hand, if the comparison is carried out at the equilibrium distance of (F...H) (d(eq)0), this one exhibits both the smallest total energy density magnitude and the largest quantity of bonding charge at the interatomic surface. Hence, being the signature of the most stable configuration, the characteristic magnitudes of the neutral system rho(d(eq)0), inverted triangle2 rho(d(eq)0), and H(d(eq)0) appear as boundary conditions at the interatomic surface of its unperturbed and relaxed electron distribution.

Characterization of a Closed-Shell Fluorine−Fluorine Bonding Interaction in Aromatic Compounds on the Basis of the Electron Density

A bond path linking two saturated fluorine atoms is found to be ubiquitous in crowded difluorinated aromatic compounds. The bond path is shown to persist for a range of internuclear distances (2.3-2.8 A) and a range of relative orientations of the two C-F internuclear axes. The F. . .F bonding is shown to exhibit all the hallmarks of a closed-shell weak interaction. The presence of such a bond path can impart as much as 14 kcal/mol of local stabilization to the molecule in which it exists, a stabilization that can be offset or even overwhelmed by destabilization of other regions in the molecule. Several other weak closed-shell interactions were also found and characterized including F. . .C, F. . .O, and C. . .C interactions, hydrogen bonding, dihydrogen bonding, and hydrogen-hydrogen bonding. This study represents another example of the usefulness and richness of the bond path concept and of the theory of atoms in molecules in general.

Theoretical study of the ArH+ electronic states

Potential energy curves, permanent multipole and transition dipole moments were evaluated for the ground and low-lying excited electronic states of the ArH+ cation over a wide range of internuclear distance by the multireference averaged quadratic coupled cluster method (MR-AQCC). The electric dipole polarisability of the ground X 1sigma state was evaluated by the finite-field method. The permanent multipole moments and dipole polarisabilities corresponding to the ArH+ X 1sigma+ state were used to estimate quantum defect functions of the nonpenetrating d- and f-complex Rydberg states of neutral ArH molecule. The ground state dipole function and potential were tested by a simulation of intensity distributions in the rovibrational deltav = 1 bands, radiative lifetimes and rotational g-factors for the X 1sigma+ state.

Polarizability functions of diatomic homonuclear molecules: Semiempirical approach

A semiempirical method is discussed to construct the polarizability functions for a diatomic homonuclear 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 nuclear equilibrium position of the molecule. The method is applied to calculate the polarizability functions of N$_2$ and O$_2$ molecules in the range of internuclear distances (0, ∞).

Ab initio calculation of molecular hydrogen electronic states’ properties: fine structure spin–spin constants

The aim of this work is the ab initio study of the properties of the electronically excited states of the H2 molecule for progressively higher states. Computations are performed using the recent DYCI code developed by Mitrushenkov. The DYCI code allows the very accurate calculation of the energies of molecular electronic excited states and of their properties such as transition moments, fine structure constants (spin–orbit and spin–spin), non-adiabatic coupling matrix elements. Fine structure spin–spin constants for Rydberg series np3Π u (n = 2,3,4), nd3Π g (n = 3,4,5), nd3Δ g (n = 3,4) and for the first three states have been calculated for a range of internuclear distances spanning 0.6 to 12 bohr. Comparison with available experimental results is provided.

Charged cores in ionized $\mathsf{{^{4}He}}$ clusters II: Ab initio calculations for the $\mathsf{{He_{2}^{ + } + He}}$ system and Many-Body fitting of the computed points

Experimental and theoretical studies in large, ionized helium clusters have suggested the presence of structures in which a diatomic (and occasionally triatomic) charged molecular core is surrounded by nearly neutral atoms which are bound to it by weaker forces. The understanding of the interactions between the He2 + system and one of the neutral He atoms of the cluster is therefore crucial in order to understand the microscopic dynamics of the post-ionization evolution. The first part of this work [Eur. Phys. J. D 21, 323 (2002)] reported the Potential Energy Surface (PES) for the interaction between the He2 + and an He atom and described its bound states. Since dynamical calculations require a more extensive variable range of the relevant PES to be sampled, we present here a further, more detailed study in which we span a larger configurational space for the three internal coordinates of the title system. In particular, we have included a greater range of internuclear distances of the molecular ion. The resulting ab initio values have been numerically fitted via an analytic expression in terms of the three internuclear distances within the He3 + system. As a first step in the analysis of the dynamics we have calculated the vibrational coupling terms which involve the ionic core vibrational wave functions and the interaction of the latter molecule with the external helium atom. They reveal interesting features and properties that are here discussed.

VariationalR-matrix calculations for singly and doubly excited singlet gerade channels inH2

Variational ab initio R-matrix theory is combined with generalized multichannel quantum defect theory, implemented in spheroidal coordinates, to calculate clamped-nuclei {sup 1}{sigma}{sub g}{sup +}, {sup 1} product {sub g}, and {sup 1}{delta}{sub g}{sup +} electron-ion scattering phase shift matrices for H{sub 2}. The calculations cover the bound state region below H{sub 2}{sup +} 1{sigma}{sub g}, the resonance region between H{sub 2}{sup +} 1{sigma}{sub g} and H{sub 2}{sup +} 1{sigma}{sub u}, and they extend beyond the H{sub 2}{sup +} 1{sigma}{sub u} threshold. They span the range of internuclear distances 1{<=}R{<=}5 a.u. The use of spheroidal instead of spherical coordinates allows a restricted partial wave expansion to be used, thus yielding a compact set of interaction parameters pertaining to the electron-ion scattering dynamics in H{sub 2}. The accuracy of our fixed-nuclei quantum defects is generally of the order of about 0.02. At the same time the quantum defect matrices obtained here exhibit a smooth behavior across the ionization thresholds and their elements also vary rather smoothly with internuclear distance. These results represent a step toward the goal of constructing a unfied theoretical description of ionization and dissociation fragmentation dynamics of H{sub 2}.

Electronic–Rotational Coupling and c1 –u–b1 +gTransition Probability in the Oxygen Molecule

A theory was proposed for the formation of intensity of the forbidden singlet–singlet c1Σ u – → b1Σ g + transition in the oxygen molecule. The dipole moments of transitions that contribute to the formation of the intensity of the c–b transition in the range of internuclear distances of 1.2–2.0 A were calculated using the configuration interaction method with a valence triple-zeta basis set. Based on these results, the electric dipole moment for the c1Σ u – → b1Σ g + transition was calculated.

Potential energy curves of diatomic molecular ions from high-resolution photoelectron spectroscopy. I. The first six electronic states of Ar2+.

High-resolution photoelectron spectroscopic data have been used to determine the potential energy curves of the first six electronic states of Ar2+. The potential energy functions properly include the effects of the long-range interactions and of the spin-orbit interaction and are of spectroscopic accuracy (1-2 cm(-1)) over a wide range of internuclear distances. The total number of adjustable parameters could be reduced to only 12 by truncating the long-range interaction series after the R(-6) term and assuming an R-independent spin-orbit coupling constant. This assumption was verified to be valid to an accuracy of +/-2 cm(-1) over the range of internuclear distances between 3.0 and 4.6 A. The interaction potential proposed by Siska [P. E. Siska, J. Chem. Phys. 85, 7497 (1986)] was generalized to a form that is expected to be sufficiently flexible to describe chemical bonding in other diatomic molecular ions. The potential energy curves are more accurate than the best available ab initio curves by two orders of magnitude and provide quantitative information on dissociation energies and equilibrium internuclear distances. The local maximum between the two potential wells of the I(1/2g) state was determined to lie 62 cm(-1) below the Ar(1S0)+Ar(+)(2P(3/2)) dissociation limit, and the II(1/2g) state is found to be significantly more bound (De=177 cm(-1)) than previously assumed.