Ab Initio Potential Curves Research Articles

An improved density matrix functional by physically motivated repulsive corrections

An improved density matrix functional [correction to Buijse and Baerends functional (BBC)] is proposed, in which a hierarchy of physically motivated repulsive corrections is employed to the strongly overbinding functional of Buijse and Baerends (BB). The first correction C1 restores the repulsive exchange-correlation (xc) interaction between electrons in weakly occupied natural orbitals (NOs) as it appears in the exact electron pair density rho(2) for the limiting two-electron case. The second correction C2 reduces the xc interaction of the BB functional between electrons in strongly occupied NOs to an exchange-type interaction. The third correction C3 employs a similar reduction for the interaction of the antibonding orbital of a dissociating molecular bond. In addition, C3 applies a selective cancellation of diagonal terms in the Coulomb and xc energies (not for the frontier orbitals). With these corrections, BBC still retains a correct description of strong nondynamical correlation for the dissociating electron pair bond. BBC greatly improves the quality of the BB potential energy curves for the prototype few-electron molecules and in several cases BBC reproduces very well the benchmark ab initio potential curves. The average error of the self-consistent correlation energies obtained with BBC3 for prototype atomic systems and molecular systems at the equilibrium geometry is only ca. 6%.

Experimental and theoretical electron energy spectra due to ionizing collisions of metastable Ar*(3P2), Ar*(3P0) and Kr*(3P0) atoms with ground-state Hg atoms

Using a crossed-beams set-up, we have studied the electron energy spectra due to Penning and associative ionization in thermal energy collisions of state-selected metastable Ar*(4s 3P2, 3P0) and Kr*(5s 3P0) atoms with ground-state Hg atoms at an electron energy resolution of 30 meV. In all three cases the energy spectra exhibit a prominent peak located close to the energy difference between the metastable excitation energies and the Hg ionization energy; they show a sharp drop to lower and an extended tail towards higher electron energy with shapes which differ for the three systems. The energy-integrated ionization cross section for Ar*(3P0) exceeds that for Ar*(3P2) by about 30%. Excitation transfer to autoionizing Hg** states, resulting in a sharp additional structure, is only observed—as a weak channel—in Ar*(3P0) + Hg collisions. For the three investigated systems calculations of the electron energy spectra have been carried out within the local optical potential approximation. As input we use ab initio potential curves for the ionic exit channels as well as for the complex entrance channel potentials. Using these potentials (involving a scaled width for Kr* + Hg), impressive agreement with the experimental electron spectra is observed. In contrast, earlier empirical model potentials for the entrance channel are found to be inadequate. The calculated ionization rate coefficients at T = 300 K amount to (3.72, 5.26) × 10−10 cm3 s−1 for Ar*(3P2, 3P0) + Hg, respectively.

Close-coupling calculations of spectral line shape parameters for $\mathsf{Cd(5^3P_1 - 5^1S_0)}$ in a bath of noble gases

Line shape parameters of the intercombination line \(\rm 5^3P_1 - 5^1S_0\) of cadmium (\(\lambda = 326.1\) nm) perturbed by noble gas atoms are calculated by the quantum close-coupling method. Calculations are based on the ab initio potential curves determined by Czuchaj and Stoll. The obtained values of width and shift coefficients are compared with experimental data and some other theoretical results.

Emission spectra ofRb*Henexciplexes in a cold4Hegas

We report on the systematic observation of emission spectra of ${\mathrm{Rb}}^{*}{\mathrm{He}}_{n}$ exciplexes $(n=1,2,\dots{},6),$ realized by exciting Rb atoms to the ${5}^{2}P$ states $({\mathrm{Rb}}^{*})$ in a cold ${}^{4}\mathrm{He}$ gas. The observed broad spectral components are assigned to ${\mathrm{Rb}}^{*}{\mathrm{He}}_{n}$ $(n=1--6)$ using theoretical spectra obtained from ab initio potential curves. The dynamics of the exciplex formation is discussed, based on the observed temperature dependence of the spectra. The He gas density dependence of the spectra of ${\mathrm{Rb}}^{*}\mathrm{He}$ is understood as a change in the population distribution over the vibrational levels. The present results are compared with our previous work with Cs [K. Enomoto et al., Phys. Rev. A 66, 042505 (2002)], and differences are explained in terms of the difference in the fine-structure splitting. Furthermore, we show the emission spectrum observed after the excitation of Rb in liquid He and conclude that it is the fluorescence from the exciplex ${\mathrm{Rb}}^{*}{\mathrm{He}}_{6}.$

Joint analysis of the attractive and repulsive regions of the Na2 a 3Σu+ state potential: A new empirical potential energy curve

Disagreements between empirical and ab initio potential curves of the Na2 a 3Σu+ state are examined. These disagreements are explained mainly by the influence of spin-rotation-type interactions with the effective constant γ≅−5.6⋅10−3 cm−1. A new potential energy function of this state is determined from the joint analysis of the continuous 2 3Σg+→a 3Σu+ and the discrete 3 3Πg→ a3Σu+ experimental spectra. The new potential function is able to reproduce all the available spectroscopic data within experimental accuracy, and is closer to the modern high quality ab initio potentials than all the earlier reported empirical potential functions.

Theoretical prediction of A30 +← X10 + and B31← X10 + spectra of the Zn–rare gas van der Waal's molecules

Excitation spectra arising from A 30 +← X 10 + and B 31← X 10 + electronic transitions in the Zn–rare gas (RG) van der Waal's molecules are calculated using the newly obtained ab initio potential curves for these species. The radial Schrödinger equation for nuclear motion was solved numerically with the calculated potentials to evaluate the corresponding vibrational levels and radial wavefunctions for the ground X 10 + and excited A 30 + and B 31 states of the Zn–RG complexes. The wavefunctions have been subsequently used in the calculation of the appropriate Franck–Condon factors to yield information on relative intensities of the vibrational bands produced by A 30 +← X 10 + and B 31← X 10 + transitions.

Cesium satellite band at 875.2 nm stemming from the Cs20g+(6 p2 P1/2+6 s2 S1/2) state

We measured a very distinct satellite band at 875.2 nm between two resonance lines of cesium. Spectral simulation using Spies and Meyer [#!ref1!#] ab initio potential curves and an appropriate transition dipole moment function was compared with experimental profile. Implications of the investigated satellite band at 875.2 nm in the field of ultracold cesium atom collisions are discussed with a special emphasize to new possibilities of the photoassociation of two ground state atoms leading to the formation of ultracold intermediate long-range molecules.

Ab initio quantum mechanical investigation of the photodissociation of HI and DI

The photoabsorption spectra of HI and DI are computed using ab initio potential curves and transition dipole moments. Partial absorption cross-sections and quantum yields for the production of the ground state ( 2 P 3/2 ) and the excited spin–orbit state ( 2 P 1/2 ) of iodine are calculated using the time-dependent wave packet formalism as functions of the excitation energy. Very good overall agreement with experimental data is obtained for the band total absorption spectrum and for the I( 2 P 1/2 ) quantum yield. The spin–rotational coupling of the a 3Π 0 + and A 1Π 1 states is estimated for the first time and is shown to play a negligible role in the HI photodissociation.

Double charge transfer spectroscopy for N 22+ and CO 2+ at vibrational resolution

Doubly charged molecular ions (dications) of N 2 and CO have been studied using a double charge transfer (DCT) spectrometer capable of resolving vibrational levels. The vibrational structures of low-lying singlet states are observed in the translational energy spectra of H − ions produced by double electron capture collisions of H + projectiles. The observed spectra are well reproduced using the theoretical Franck–Condon (FC) profiles calculated from the best available ab initio potential curves. This suggests that the DCT process obeys the FC principle, i.e., the vertical transition from a neutral molecule to the corresponding dication.

A fully ab initio potential curve of near-spectroscopic quality for OH − ion: importance of connected quadruple excitations and scalar relativistic effects

A benchmark study has been carried out on the ground-state potential curve of the hydroxyl anion, OH −, including detailed calibration of both the 1-particle and n-particle basis sets. The CCSD(T) basis set limit overestimates ω e by about 10 cm −1, which is only remedied by inclusion of connected quadruple excitations in the coupled cluster expansion — or, equivalently, the inclusion of the 2π orbitals in the active space of a multireference calculation. Upon inclusion of scalar relativistic effects (−3 cm −1 on ω e), a potential curve of spectroscopic quality (sub-cm −1 accuracy) is obtained. Our best computed EA(OH), 1.828 eV, agrees to three decimal places with the best available experimental value. Our best computed dissociation energies, D 0(OH −)=4.7796 eV and D 0(OH)=4.4124 eV, suggest that the experimental D 0(OH)=4.392 eV may possibly be about 0.02 eV too low.

A CASSCF/MRCI study of the low-lying Rydberg states of CIO

An ab initio calculation has been performed on the lowest seven doublet and six quartet Rydberg states of CIO at the CASSCF/MRCI level and with basis sets suitable for the extended molecular orbitals of such states (aug-cc-pVTZ with up to eleven extra Gaussian functions). Calculations on the quartet states reveal the energy ordering of Rydberg orbitals to be 4sσ, 4pπ, 4pσ;, 3dδ, 3dσ and 3dπ. The calculated doublet ab initio potential curves confirm experimental assignments of the C2Σ- and F2Σ- states but require reassignments for the symmetries of the D (2Δ), E (2Π) and H (2Δ) Rydberg states. These revisions are supported by spin-orbit coupling calculations that suggest the separation between the Ω components is small. In addition, a 2Σ+ state has been identified as the likely upper state for two previously unassigned vibronic bands recorded in absorption studies.

Ab initio potential curves of the fragments and diatomics-in-molecules potential energy surfaces for the SH⋯Kr complex

Potential curves of the SH, KrH and KrS molecules needed for the diatomics-in-molecules (DIM) treatment of the ground and excited states of the SH(X,A)⋯Kr complex have been computed at the SOCI/CASSCF level. The ionic and ion-pair states of these diatomic fragments which play an essential role in the DIM model of intermolecular interactions have been considered as well. The new results for the ion-pair states of SH are compared to the corresponding data for OH. The curves for KrS and XeS [M. Yamanishi, K. Hirao, K. Yamashita, J. Chem. Phys. 108 (1998) 1514] are discussed. The main features of the empirical potential surfaces of the SH⋯Kr complex are reproduced by the DIM technique.

Spectroscopic quality ab initio potential curves for CH, NH, OH and HF. A convergence study

A calibration study has been carried out on the ground-state potential curves of CH, NH, OH and HF. Using uncontracted spdfgh or spdfghi basis sets in conjunction with treatments of core correlation and imperfections in the CCSD(T) method, re and ωe of the first-row diatomic hydrides can on average be reproduced to within 0.0002 Å and 1 cm−1, respectively, as can the first 4–6 vibrational quanta. The CCSD(T) basis set limit systematically overestimates ωe by 4–9 cm−1 and underestimates re by 0.0003–0.0006 Å. Higher anharmonicities exhibit pronounced basis set sensitivity, which is markedly reduced upon uncontracting the basis set.

Charge transfer in collisions ofC2+ions with H atoms at low-keV energies: A possible bound state ofCH2+

Electron capture in ${\mathrm{C}}^{2+}+\mathrm{H}$ collisions is studied theoretically by using a semiclassical molecular representation with nine molecular states for the doublet manifold at collision energies above 10 eV. The ab initio potential curves and nonadiabatic coupling matrix elements for the ${\mathrm{CH}}^{2+}$ system are obtained from the multireference single- and double-excitation configuration interaction method. The adiabatic potential curves show no bound state for the $1{}^{2}{\ensuremath{\Sigma}}^{+}$ state, but a very shallow well in the $2{}^{2}{\ensuremath{\Sigma}}^{+}$ potential, suggesting a possibility of a bound state of ${\mathrm{CH}}^{2+}.$ The corresponding total and partial cross sections for charge transfer are found to be in a reasonable agreement with experiment in shape, but the present magnitude is found to be larger by nearly a factor of 2 at the high-energy end.

Benchmark ab initio potential curves for the light diatomic hydrides. Unusually large nonadiabatic effects in BeH and BH

In order to assess the relative importance of the intrinsic error in high-level conventional ab initio methods and errors inherent in the Born–Oppenheimer approximation, benchmark quality potential curves and spectroscopic constants have been computed for the light diatomic hydrides H 2, LiH, BeH, and BH. The intrinsic error is found to be comparable to or smaller than the nonadiabatic effects. Revised spectroscopic constants are proposed for BeH. BH is predicted to have an unusually large nonadiabatic contribution of about 0.0025 Å to its bond length. Previous arguments favoring the use of atomic rather than nuclear masses are further corroborated.

Natural bond orbital analysis of steric interactions

We describe an ab initio procedure for extracting the Pauli exchange antisymmetry (“steric”) contributions to molecular potential energy in the framework of self-consistent-field molecular orbital (SCFMO) theory. This “natural steric analysis” method is based on natural bond orbital (NBO) representation of the SCFMO wave function, which allows the steric exchange energy to be approximated as an energy difference between “preorthogonal” and final NBOs, analogous to the procedure of Sovers et al. [J. Chem. Phys. 49, 2592 (1965)]. We show how the total NBO steric exchange energy can in turn be approximated in terms of pairwise-additive interactions between localized bonding units, comparable to the empirical steric potentials of molecular mechanics models. The accuracy of NBO steric analysis is tested in applications to various rare-gas interactions (expected to be of pure steric exchange type), and excellent agreement is found with the full ab initio potential curves over a wide range of separations. Limitations of the simple pairwise-additive model of steric exchange interactions are noted and characterized.

Electron capture in collisions of H^{+} ions with S atoms and its reverse process below kilo-electron-volt energies

Electron capture in ${\mathrm{H}}^{+}+\mathrm{S}{(}^{3}{P,}^{1}D)$ collisions is studied theoretically by using a semiclassical molecular representation with five molecular channels from the initial ground and excited states at collision energies above 10 eV. Electron capture in ${\mathrm{S}}^{+}$ ${(}^{4}S)+\mathrm{H}(1\mathrm{}\mathrm{s})$ collisions is also investigated by using three molecular channels in order to assess the earlier estimation which gave the rate constant of ${10}^{\ensuremath{-}15}{\mathrm{cm}}^{3}/\mathrm{s}$ at ${10}^{4}\mathrm{K}$ for the process. The ab initio potential curves and nonadiabatic coupling matrix elements for the ${\mathrm{HS}}^{+}$ system are obtained from multireference single- and double-excitation configuration-interaction calculations employing relatively large basis sets. Dominant capture channels corresponding to the $[{\mathrm{H}+\mathrm{S}}^{+}{(}^{2}P)]$ and $[{\mathrm{H}+\mathrm{S}}^{+}{(}^{2}D)]$ states lie lower by 0.2 and 1.4 eV, and 1.34 and 2.5 eV from the initial ground $[{\mathrm{H}}^{+}+\mathrm{S}{(}^{3}P)]$ and excited $[{\mathrm{H}}^{+}+\mathrm{S}{(}^{1}D)]$ states, respectively. The present results show that electron capture from the excited species is found to be rather weak at lower energies. But it rapidly becomes comparable to that from the ground state. Electron capture in ${\mathrm{S}}^{+}$ ${(}^{4}S)+\mathrm{H}$ collisions proceeds through the two-step mechanism at lower energies, and therefore, the cross section is found to be small with the value less than ${10}^{\ensuremath{-}17}{\mathrm{cm}}^{2}$ below 1 keV, thus supporting the earlier estimation.

Charge Transfer Rate in Collisions of H+Ions with Si Atoms

Charge transfer in Si(3P, 1D) + H+ collisions is studied theoretically by using a semiclassical molecular representation with six molecular channels for the triplet manifold and four channels for the singlet manifold at collision energies above 30 eV, and by using a fully quantum mechanical approach with two molecular channels for both triplet and singlet manifolds below 30 eV. The ab initio potential curves and nonadiabatic coupling matrix elements for the HSi+ system are obtained from multireference single- and double-excitation configuration interaction (MRD-CI) calculations employing a relatively large basis set. The present rate coefficients for charge transfer to Si+(4P) formation resulting from H+ + Si(3P) collisions are found to be large with values from 1 × 10–10 cm3 s–1 at 1000 K to 1 × 10–8 cm3 s–1 at 100,000 K. The rate coefficient for Si+(2P) formation, resulting from H+ + Si(3P) collisions, is found to be much smaller because of a larger energy defect from the initial state. These calculated rates are much larger than those reported by Baliunas & Butler, who estimated a value of 10–11 cm3 s–1 in their coronal plasma study. The present result may be relevant to the description of the silicon ionization equilibrium.

Charge transfer in collisions of B2+(2S,2P) and B3+(1S) ions with He atoms below 200 keV.

Charge transfer in ${\mathrm{B}}^{2+}$${(}^{2}$S${,}^{2}$P)+He and in ${\mathrm{B}}^{3+}$${(}^{1}$S)+He collisions is studied theoretically by using a semiclassical molecular representation with 8 and 12 molecular channels for ${\mathrm{B}}^{2+}$ and ${\mathrm{B}}^{3+}$ on He systems, respectively, at collision energies between 200 eV and 200 keV for the former and between 600 eV and 50 keV for the latter. The ab initio potential curves and nonadiabatic coupling matrix elements are obtained from the multireference single- and double-excitation configuration-interaction (MRD-CI) calculations for the ${\mathrm{B}}^{2+}$-He system and a pseudopotential-modified configuration-interaction method for the ${\mathrm{B}}^{3+}$-He system. The present cross sections for charge transfer by the ground state ${\mathrm{B}}^{2+}$ ions are found to have a broad maximum with a magnitude as large as 2\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}15}$ ${\mathrm{cm}}^{2}$ at 100 keV and those by an excited ${\mathrm{B}}^{2+}$${(}^{2}$P) state are found to be larger by a factor of 6 than those by the ground state in the same energy regime. ${\mathrm{B}}^{2+}$-excitation cross sections are smaller than those for charge transfer below 1 keV, while they increasingly dominate above this energy. The present total charge-transfer cross section for ${\mathrm{B}}^{3+}$ in collisions with He is similar to that obtained in earlier work by Gargaud et al. [J. Phys. B 27, 3985 (1994)] both in magnitude and energy dependence, but is found to show slightly different ${\mathrm{B}}^{2+}$(2s) and ${\mathrm{B}}^{2+}$(2p) production ratio. \textcopyright{} 1996 The American Physical Society.

Electron capture in collisions of O2+(3P) ions with He atoms at energies below 10 keV: The effect of metastable O2+(1D) ions.

Electron capture in ${\mathrm{O}}^{2+}$${(}^{3}$P${,}^{1}$D)+He collisions is studied theoretically by using a semiclassical molecular representation with six molecular channels at collision energies above 50 eV and by using a fully quantum-mechanical molecular representation with three \ensuremath{\Pi} channels below these energies. The ab initio potential curves and nonadiabatic coupling matrix elements for the ${\mathrm{HeO}}^{2+}$ system are obtained from multireference single- and double-excitation configuration-interaction calculations employing a relatively large basis set. The present total cross sections for electron capture by the ground-state ${\mathrm{O}}^{2+}$ ions are found to be in reasonable accord with those calculated by Gargaud, Bacchus-Montabonel, and McCarroll [J. Chem. Phys. 99, 4495 (1993)] below 30 eV/u but are slightly larger above this energy. Partial cross sections for the l distribution are also slightly different. Cross sections for electron capture by the metastable ${\mathrm{O}}^{2+}$ ions decrease much more sharply than those for the ground-state ion as the energy is lowered, reaching a difference between them approximately as large as one to two orders of magnitude below 100 eV. The present rate coefficient for the reaction is approximately ${10}^{\mathrm{\ensuremath{-}}9}$ ${\mathrm{cm}}^{3}$/s above 10 000 K, suggesting that the small rate coefficient of about ${10}^{\mathrm{\ensuremath{-}}12}$ ${\mathrm{cm}}^{3}$/s at 20 000 K observed by Kwang and Fang [Phys. Rev. Lett. 71, 4127 (1993)] for electron capture by the ground-state ion might be caused, in part, by a mixture of ground and metastable ions in their experiment. \textcopyright{} 1996 The American Physical Society.