Range Of Internuclear Distances Research Articles

Born-Oppenheimer potential forH2

The Born-Oppenheimer potential for the $^1\Sigma_g^+$ state of H$_2$ is obtained in the range of 0.1 -- 20 au, using analytic formulas and recursion relations for two-center two-electron integrals with exponential functions. For small distances James-Coolidge basis is used, while for large distances the Heitler-London functions with arbitrary polynomial in electron variables. In the whole range of internuclear distance about $10^{-15}$ precision is achieved, as an example at the equilibrium distance $r=1.4011$ au the Born-Oppenheimer potential amounts to $-1.174\,475\,931\,400\,216\,7(3)$. Results for the exchange energy verify the formula of Herring and Flicker [Phys. Rev. {\bf 134}, A362 (1964)] for the large internuclear distance asymptotics. The presented analytic approach to Slater integrals opens a window for the high precision calculations in an arbitrary diatomic molecule.

Use of complex configuration interaction calculations and the stationary principle for the description of metastable electronic states of HCl−

The complex multireference single- and double-excitation configuration interaction method has been employed to compute potential curves for the anion of the hydrogen chloride molecule. First, conventional CI calculations with real basis functions have been carried out to determine the potential curves of both HCl and its anion over a large range of internuclear distance. It is shown that adding basis functions with very small exponents leads to sharply avoided crossings for the HCl(-) potentials that greatly complicate the search for resonance states thought to be responsible for features observed in electron collision experiments. By limiting the number of such diffuse-type functions it is possible to describe resonance states at a highly correlated level and still account for their interaction with the continuum in which they are embedded. In the present study of the HCl(-) anion the complex basis function technique of Moiseyev-Corcoran and McCurdy-Resigno is employed to calculate the energy positions and line-widths of the resonance states. Two states of (2)Sigma(+) symmetry are calculated which have potentials that have significantly different shapes than that of the neutral ground state and thus contribute to the cross section for vibrational excitation of the neutral HCl molecule induced by low-energy electron collisions. The lower of these (1 (2)Sigma(+)) correlates smoothly with the bound anionic ground state at large internuclear distances and is seen to be responsible for the sharp peaks observed in the low-energy region of the spectrum. The upper state (3 (2)Sigma(+)) has a much larger bond length and is assigned to the broad bands observed with a maximum in the 2.5-3.0 eV range. The present calculations thus stand in contradiction to earlier claims that the above peaks are caused by so-called virtual states without a definite autoionization lifetime.

Theoretical Study of the LiCs Molecule: Adiabatic and Diabatic Potential Energy and Dipole Moment

For nearly all the states dissociating into Cs (6s, 6p, 5d, 7s, 7p, 6d, 8s) and Li (2s, 2p, 3s), we present an extensive adiabatic study for (1,3)Sigma(+), (1,3)Pi, and (1,3)Delta symmetries of the LiCs molecule. We have used an ab initio approach based on nonempirical pseudopotentials, parametrized l-dependent polarization potentials, and full configuration interaction calculations. A diabatisation procedure based on the effective Hamiltonian theory and an effective metric is used to produce the quasi-diabatic potential energy for all studied states. The spectroscopic constants (R(e), D(e), T(e), omega(e), omega(e)x(e), and B(e)) of these states are derived and compared with the available theoretical and experimental works. In addition to the potential energies, accurate permanent and transition dipole moment have been determined for a wide range of internuclear distances. The adiabatic permanent dipole moment for the first 10 (1)Sigma(+) electronic states has revealed ionic characters relating to electron transfer and yielding both Li(-)Cs(+) and Li(+)Cs(-) arrangements. The quasi-diabatic permanent moments show linear behaviors, especially at intermediate and large distance. The transition dipole moment between neighbor states has revealed many peaks located around the avoided crossing positions.

Experimental and ab initio infrared study of χ-, κ ‐ and α-aluminas formed from gibbsite

χ-, κ- and α-alumina phases formed by dehydration of micro-grained gibbsite between 773 and 1573 K are studied using infrared spectroscopy (IR). The structural transitions evidenced by X-ray diffraction (XRD) were interpreted by comparing IR measurements with ab initio simulations (except for the χ form whose complexity does not allow a reliable simulation). For each phase, IR spectrum presents specific bands corresponding to transverse optical (TO) modes of Al–O stretching and bending under 900 cm −1. The very complex χ phase, obtained at 773 K, provides a distinctive XRD pattern in contrast with the IR absorbance appearing as a broad structure extending between 200 and 900 cm −1 resembling the equivalent spectra for γ-alumina phase. κ-alumina is forming at 1173 K and its rich IR spectrum is in good qualitative agreement with ab initio simulations. This complexity reflects the large number of atoms in the κ-alumina unit cell and the wide range of internuclear distances as well as the various coordinances of both Al and O atoms. Ab initio simulations suggest that this form of transition alumina demonstrates a strong departure from the simple pattern observed for other transition alumina. At 1573 K, the stable α-Αl 2Ο 3 develops. Its IR spectra extends in a narrower energy range as compared to transition alumina and presents characteristics features similar to model α-Αl 2Ο 3⋅ Ab initio calculations show again a very good general agreement with the observed IR spectra for this phase. In addition, for both κ- and α-Αl 2Ο 3, extra modes, measured at high energy (above 790 cm −1 for κ and above 650 cm −1 for α), can originate from either remnant χ-alumina or from surface modes.

Experimental and predicted Ag 2[formula omitted] absorption band strengths

Relative intensities in the absorption spectrum of the B 1 Π u − X 1 Σ g + band system of diatomic silver are measured for the first time. Analysis of these measurements is performed using Rydberg–Klein–Rees potential curves derived from the best available vibrational and rotational constants for this band system. Comparison of measured and calculated absorption band strength ratios for eleven vibrational bands reveals that the relative electronic transition moment function (ETMF) of the Ag 2 B− X system has a negative slope and decreases by ≈ 40 % over the 2.43–2.58 Å range of internuclear distance. The ETMF shows some nonlinear structure; however, the empirical error bars suggest that a linear model is appropriate, thus allowing the r-centroid approximation as a simplification in our analysis.

Spectroscopic investigations on HBr(X 1Σ +) molecule using MRCI method in combination with correlation-consistent quintuple basis set augmented with diffuse functions

The equilibrium internuclear separation, harmonic frequency, dissociation energy and potential energy curve (PEC) of the HBr(X 1Σ +) molecule have been investigated by using the highly accurate valence internally contracted multireference configuration interaction (MRCI) approach in combination with the correlation-consistent quintuple basis set augmented with diffuse functions, aug-cc-pV5Z, in the valence range. The PEC calculations cover the internuclear distance range from 0.08 to 2.08 nm. The PEC is fitted to the analytic Murrell–Sorbie function, which is used to reproduce the spectroscopic parameters, such as ω eχ e , α e , B e and D 0. The present D 0, D e , R e , ω e , ω eχ e , α e and B e are of 3.7665 eV, 3.9289 eV, 0.14195 nm, 2642.68 cm −1, 45.6118 cm −1, 0.23525 cm −1 and 8.40417 cm −1, respectively, which almost perfectly conform to the available measurements. With the potential determined at the MRCI/aug-cc-pV5Z level of theory, the total of 20 vibrational states is predicted when the rotational quantum number J is set to equal zero ( J = 0) by numerically solving the radial Schrödinger equation of nuclear motion. The complete vibrational levels, classical turning points, inertial rotation and centrifugal distortion constants are determined when J = 0 for the first time, which are in excellent agreement with the available experimental data.

Quantum chemical contribution to electron neutrino mass determination

Theoretical data have been obtained needed to analyze the experimental measurements of the T2 β-decay energy distribution near the end point. The energies of the six lowest 1∑+ states of HeT+ have been computed for internuclear distances 1.0 ≦4 R ≦ 4.0 bohr. The wavefunctions have been used to calculate the transition probabilities to these states from the electronic ground state of T2. Distribution of the probabilities over the final vibrational and rotational states has been evaluated including rotationally predissociating resonances. Using the stabilization method the 1∑+ resonance states of HeT+ above the ionization limit have been investigated. Preliminary potential energy curves for several of these states have been determined for a wide range of internuclear distances.

Overlap-matched atomic orbitals

Single Slater-type orbitals can be determined which reproduce overlap integrals calculated using self-consistent-field atomic orbitals expressed in an extended basis set. Requirements and procedures for determining orbital parameters adequate for the chemically important range of internuclear distances are developed and applied to the more familiar elements. This method is applicable even in cases where no single exponential function is a generally good representation of the shape of the atomic orbital, such as the 3d function for a transition metal ion.

Quasi-relativistic treatment of the low-lying KCs states

The potential energy curves, permanent and transition dipole moments as well as spin-orbit and angular coupling matrix elements between the KCs electronic states converging to the lowest three dissociation limits were evaluated in the basis of the spin-averaged wavefunctions corresponding to pure Hund’s coupling case ( a). The quasi-relativistic matrix elements have been obtained for a wide range of internuclear distance by using of small (9-electrons) effective core pseudopotentials of both atoms. The core-valence correlation has been accounted for a large scale multi-reference configuration interaction method combined with semi-empirical core polarization potentials. The static dipole polarizabilities of the ground X 1 Σ + and a 3 Σ + states were extracted from the closed-shell coupled-cluster energies by the finite-field method. Among the singlet and triplet Σ + states manifold the pronounced avoided crossing effect between repulsive walls of the (2,3) 3 Σ + states has been discovered and analyzed by finite-difference calculation of radial coupling matrix elements. The resulting transition dipole moments and potentials were used to predict radiative lifetimes and emission branching ratios of excited vibronic states while the calculated angular coupling matrix elements were transformed to Λ -doubling constants of the (1,2) 1 Π states and magnetic g -factor of the ground state. The accuracies of the present results are discussed by comparing with experimental data and preceding calculations.

Configuration interaction calculations of annihilation rates for positronic complexes of alkali hydrides

Ab initio multireference single- and double-excitation configuration interaction (MRD-CI) wave functions have been employed to compute the annihilation rates (AR) of positronic molecular complexes of four alkali hydrides. The first step in these calculations is the evaluation of integrals of the two-particle Dirac delta function δ +− over pairs of electronic and positronic basis functions. MRD-CI wave functions calculated with the same basis are then employed to obtain expectation values of the δ +− operator ( Z eff), which in turn are proportional to the corresponding annihilation rates (AR) of the associated many-particle states. The importance of removing near-linear dependencies in the basis sets employed is stressed as well as the advisability of placing diffuse (small-exponent) functions in the basis only at the most electronegative center of the molecule. A tendency to underestimate the Z eff values is noted because of the impracticality of including sufficiently high-l basis functions in the basis for general molecular systems. However, comparison with the relatively accurate values for the four-electron e +LiH complex obtained by Quantum Monte-Carlo (QMC) and other methods indicates that the fractional error is nearly constant over a large range of internuclear distance, consistent with the expectation that missing correlation effects in the MRD-CI treatment are predominantly atomic in nature. A scaling procedure based on the asymptotic δ +− value, which is the same for all four alkali hydrides, is then shown to produce good agreement with the QMC AR data for e +LiH. The same procedure has been applied to the δ +− values for the positronic complexes of the heavier alkali hydrides for which no other theoretical results are available. Trends in the variation of the AR results with bond distance are discussed.

Theoretical spin-orbit structure of the alkali dimer cation K2+

A theoretical study of the electronic structure of [Formula: see text] including spin-orbit effects has been performed. Potential energy curves for the 58 molecular states in the representation Ωg,u are presented. Equilibrium distances, transition energies, depths for wells, and heights for humps predicted at short and large range of internuclear distances R are reported for all the bound states [Formula: see text] and Ωg,u dissociating to limits up to K++K(6p 2P3/2). Transition dipole moments have been calculated for all the allowed transitions among states [Formula: see text] dissociating to limits up to K+ +K(3d 2D). To the best of our knowledge, these are the first data reported for the Ωg,u states of [Formula: see text]. Extensive tables of energy values and transition dipole moments versus internuclear distances are available at the web address: http://www-lasim.univ-lyon1.fr/spip.php?rubrique99.PACS Nos.: 31.10.+z, 31.15.A–, 31.15.aj

Ab initio potential energy curves and transition dipole moments for the interaction of a ground state He with Na(3s–3p)

Potential energy curves of the states X 2Σ +, B (1) 2Σ + and A (1) 2Π of the NaHe molecule have been calculated accurately in a large range of internuclear distances R from SA-CASSCF-MRCI calculations, using molecular orbitals expanded in cc-pV5Z basis sets. Transition dipole moments have also been calculated for the X–B, X–A and A–B transitions, in the same range of R. Their long-range behaviour have been considered.

Parameter-free one-center model potential for an effective one-electron description of molecular hydrogen

For the description of an ${\mathrm{H}}_{2}$ molecule, an effective one-electron model potential is proposed which is fully determined by the exact ionization potential of the ${\mathrm{H}}_{2}$ molecule. In order to test the model potential and examine its properties, it is employed to determine excitation energies, transition moments, and oscillator strengths in a range of internuclear distances, $0.8\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.}<R<2.5\phantom{\rule{0.3em}{0ex}}\mathrm{a.u}$. In addition, it is used as a description of an ${\mathrm{H}}_{2}$ target in calculations of the cross sections for photoionization and for partial excitation in collisions with singly charged ions. The comparison of the results obtained with the model potential with literature data for ${\mathrm{H}}_{2}$ molecules yields a good agreement and encourages therefore an extended use of the potential in various other applications or in order to consider the importance of two-electron and anisotropy effects.

The ground electronic state of KCs studied by Fourier transform spectroscopy

We present here the first analysis of laser induced fluorescence (LIF) of the KCs molecule obtaining highly accurate data and perform a direct potential construction for the X (1)Sigma(+) ground state in a wide range of internuclear distances. KCs molecules were produced by heating a mixture of K and Cs metals in a heat pipe at a temperature of about 270 degrees C. KCs fluorescence was induced by different laser sources: the 454.5, 457.9, 465.8, and 472.7 nm lines of an Ar(+) laser, a dye laser with Rhodamine 6G dye (excitation at around 16 870 cm(-1)), and 850 and 980 nm diode lasers (11 500-11 900 and 10 200-10 450 cm(-1) tuning ranges, respectively). The LIF to the ground state was recorded by a Bruker IFS-125HR Fourier transform spectrometer with a spectral resolution of 0.03 cm(-1). Particularly, by applying the 850 nm laser diode we were able to observe LIF progressions to very high vibrational levels of the ground state close to the dissociation limit. The present data field contains 7226 term values for the ground state X (1)Sigma(+) and covers a range from v(")=0 to 97 with J(") varying from 12 to 209. More than 10 000 fluorescence lines were used to fit the ground state potential energy curve via the inverted perturbation approach procedure. The present empirical potential extends up to approximately 12.6 A and covers more than 99% of the potential well depth, it describes most of the spectral lines with an accuracy of about 0.003 cm(-1) and yields a dissociation energy of 4069.3+/-1.5 cm(-1) for the ground state X (1)Sigma(+). First observations of the triplet ground state a (3)Sigma(+) of KCs are presented, and preliminary values of few main molecular constants could be derived.

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).

Experimental mapping of the absolute magnitude of the transition dipole moment functionμe(R)of theNa2A Σ1u+−X Σ1g+transition

The absolute magnitude of the transition dipole moment function ${\ensuremath{\mu}}_{e}(R)$ of the $A\text{ }{^{1}\ensuremath{\Sigma}}_{u}^{+}\ensuremath{-}X\text{ }{^{1}\ensuremath{\Sigma}}_{g}^{+}$ band system of ${\text{Na}}_{2}$ was mapped experimentally over a relatively large range of internuclear distance $R$. The transition dipole moment matrix element of a set of rovibrational transitions between the $A\text{ }{^{1}\ensuremath{\Sigma}}_{u}^{+}$ and $X\text{ }{^{1}\ensuremath{\Sigma}}_{g}^{+}$ states was measured using the Autler-Townes effect. By employing the $R$-centroid approximation, or a fit to a polynomial function involving higher order $R$ centroids, ${\ensuremath{\mu}}_{e}$ as a function of the internuclear distance was obtained. These Autler-Townes effect based measurements yield the absolute magnitude of ${\ensuremath{\mu}}_{e}$, which can be used to test ab initio theoretical transition dipole moment functions or to ``normalize'' experimental transition moment functions obtained from intensity measurements, which in general give only the relative behavior of ${\ensuremath{\mu}}_{e}(R)$.

Improved molecular constants for low vibrational levels of the [formula omitted] state of 7Li 2

We report new high resolution spectroscopic data for the lowest vibrational levels v = 0–3 for the F ( 4 ) 1 Σ g + state of 7Li 2. A new ab initio potential energy curve, that covers a wide range of internuclear distance, is also reported.

Combined analysis of the PFOODR data on the a 3Σ u + , 23Πg, 23Σ g + , 33Πg, and 43Σ g + states of the K2 molecule

The known and new heterogeneous spectral data on the triplet states a 3Σ u + , 23Πg, 23Σ g + , 33Πg, and 43Σ g + of the K2 dimer are simultaneously fitted. The data published in J. Mol. Spectrosc. 234, 41 (2005) are refined. The new information used in the analysis contains the data on the 23Σ g + state, which have not been considered previously. The range of internuclear distances where the potential function of the lowest triplet state a 3Σ u + is defined is extended.

Ab initiocalculations on thea3Σ+ustate properties of dimer7Li2

The comparison between single-point energy scanning (SPES) and geometry optimization (OPT) in determining the equilibrium geometry of the a3Σ+u state for 7Li2 is made at numerous basis sets such as 6-311++G(2df), cc-PVTZ, 6-311++G(2df,p), 6-311G(3df,3pd), 6-311++G(2df,2pd), D95(3df,3pd), 6-311++G, DGDZVP, 6-311++G(3df,2pd), 6-311G(2df,2pd), D95V++, CEP-121G, 6-311++G(d,p), 6-311++G(2df,pd) and 6-311++G(3df,3pd) in full active space using a symmetry-adapted-cluster/ symmetry-adapted-cluster configuration-interaction (SAC/SAC-CI) method presented in Gaussian03 program package. The difference of the equilibrium geometries obtained by SPES and by OPT is reported. Analyses show that the results obtained by SPES are more reasonable than those obtained by OPT. We have calculated the complete potential energy curves at these sets over a wide internuclear distance range from about 3.0a0 to 37.0a0, and the conclusion is that the basis set cc-PVTZ is the most suitable one. With the potential obtained at cc-PVTZ, the spectroscopic data (Te, De, D0, ωe,ωeχe, and Be) are computed and they are 1.006 eV, 338.71 cm−1, 307.12 cm−1, 64.88 cm−1, 3.41 cm−1, 0.0187 cm−1 and 0.279 cm−1, respectively, which are in good agreement with recent measurements. The total 11 vibrational states are found at J=0. Their corresponding vibrational levels and classical turning points are computed and compared with available RKR data, and good agreement is found. One inertial rotation constant (Bv) and six centrifugal distortion constants (Dv Hv, Lv, Mv, Nv and Ov) are calculated. The scattering length is calculated to be −27.138a0, which is in good accord with the experimental data.

Ab initiocalculation on accurate analytic potential energy functions and harmonic frequencies of c3∑g+and B1∏ustates of dimer7Li2

The comparison between single-point energy scanning (SPES) and geometry optimization (OPT) in determining the equilibrium geometries of c3∑g+ and B1∏u states of dimer 7Li2 is made at numerous basis sets by using a symmetry-adapted-cluster configuration-interaction (SAC-CI) method in the Gaussian 03 program package. In this paper the difference of the equilibrium geometries obtained by SPES and by OPT is reported. The results obtained by SPES are found to be more reasonable than those obtained by OPT in full active space at the present SAC-CI level of theory. And the conclusion is attained that the cc-PVTZ is a most suitable basis set for these states. The calculated dissociation energies and equilibrium geometries are 0.8818 eV and 0.3090 nm for c3∑g+ state, and 0.3668 eV and 0.2932 nm for B1∏u state respectively. The potential energy curves are calculated over a wide internuclear distance range from about 2.5a0 to 37a0 and have a least-squares fit into the Murrell-Sorbie function. According to the calculated analytic potential energy functions, the harmonic frequencies (ωe) and other spectroscopic data (ωeχe, Be and αe) are calculated. Comparison of the theoretical determinations at present work with the experiments and other theories clearly shows that the present work is the most complete effort and thus represents an improvement over previous theoretical results.