Range Of Internuclear Separations Research Articles

Predissociation dynamics of the hydroxyl radical (OH) based on a five-state spectroscopic model.

Multi-reference configuration interaction potential energy curves (PECs) and spin-orbit couplings for the X 2Π, A 2Σ+, 1 2Σ-, 1 4Σ-, and 1 4Π states of OH are computed and refined against empirical energy levels and transitions to produce a spectroscopic model. Predissociation lifetimes are determined by discretizing continuum states in the variational method nuclear motion calculation by restricting the calculation to a finite range of internuclear separations. Varying this range gives a series of avoided crossings between quasi-bound states associated with the A 2Σ+ and continuum states, from which predissociation lifetimes are extracted. 424 quasi-bound A 2Σ+ state rovibronic energy levels are analyzed, and 374 predissociation lifetimes are produced, offering good coverage of the predissociation region. Agreement with measured lifetimes is satisfactory, and a majority of computed results were within experimental uncertainty. A previously unreported A 2Σ+ state predissociation channel that goes via X 2Π is identified in the calculations. A Python package, binSLT, produced to calculate predissociation lifetimes, associated line broadening parameters, and lifetime uncertainties is made available. The PECs and other curves from this work will be used to produce a rovibronic ExoMol line list and temperature-dependent photodissociation cross sections for the hydroxyl radical.

Continuum solutions to the two–center Coulomb problem in prolate spheroidal coordinates

We present a computational and theoretical framework for solving the Schrödinger equation (SE) for the two–center Coulomb problem in prolate spheroidal coordinates when the energy of the SE is positive. A general and robust computer code has been produced that calculates the separation constants, spheroidal harmonic expansion coefficients, regular quasi–radial two–center Coulomb wave functions, and two–center Coulomb phase shifts. These quantities can be calculated over a range of internuclear separations, angular momentum projections, and continuum electron momenta. A representative set of results are presented and compared with previous calculations, excellent agreement is found in many cases while significant disagreements are found in others. Program summaryProgram title:spheroidal-cwCPC Library link to program files:https://doi.org/10.17632/nf5gw7vjnh.1Code Ocean capsule:https://codeocean.com/capsule/7638744Licensing provisions: MITProgramming language: Fortran 90Nature of problem: A robust and accurate computer code for calculating Coulomb wave functions in prolate spheroidal coordinate is necessary for the calculation of cross sections for photonionization, and electron and positron scattering on charged diatomic targets.Solution method: The angular solution is expanded in a series of spherical harmonics leading to the diagonalization of a pentadiagonal matrix. The eigenvectors contain the expansion coefficients and the eigenvalues are the separation constants which, unlike the SE in spherical coordinates, are also functions of the energy. The radial two–center Coulomb wave functions are started using a power series solution and then propagated using a linear multistep method. An asymptotic expansion is used to calculate the two–center Coulomb phase shift, and to normalize the radial wave function.Additional comments including restrictions and unusual features: Two–center Coulomb radial wave functions and phase shifts can be accurately calculated for internuclear separations from 0.001 to 60.0 a0, angular momentum projection |m| from 0 to 44, momentum k from 0.01 to 100.0 a.u., and a combined nuclear charge Z+ from 1 to 12.

Two-dimensional, finite-difference method of solving the Dirac equation for diatomic molecules revisited

Two-dimensional, fully numerical, finite-difference approach to the second-order Dirac equation for one-electron diatomics is revisited. Instead of using the transformation of variables to get rid of the singularities of σ-type spinors the Gaussian nuclear charge distribution model is employed. The approach is tested on the several lowest σ, π, δ and φ states of H, Kr and Th systems with the reference data of 12-digit accuracy provided by the GRASP and QRHF atomic codes. The method is also tested on H, Kr and Th systems. The energies of and states of H are converged to 9 significant figures and the relativistic correction to 6. In the case of the Th system the calculations for the state were performed for a range of internuclear separations a.u. and compared with the eXact 2-Component (X2C) and 4-component results. The agreement to within 1 milihartree or better is observed for all the separations greater than 0.2 a.u. Alas, the orbital energy of the system with a.u., could only be calculated with 0.1% accuracy. This problem also seems to haunt Sundholm's implementation of the method and we indicate the reasons behind the low accuracy at extremely short internuclear distances.

Shape Resonances in H_{2} as Photolysis Reaction Intermediates.

Shape resonances in H_{2}, produced as reaction intermediates in the photolysis of H_{2}S precursor molecules, are measured in a half-collision approach. Before disintegrating into two ground state H atoms, the reaction is quenched by two-photon Doppler-free excitation to the F electronically excited state of H_{2}. For J=13, 15, 17, 19, and 21, resonances with lifetimes in the range of nano- to milliseconds were observed with an accuracy of 30MHz (1.4mK). The experimental resonance positions are found to be in excellent agreement with theoretical predictions when nonadiabatic and quantum electrodynamical corrections are included. This is the first time such effects are observed in collisions between neutral atoms. From the potential energy curve of the H_{2} molecule, now tested at high accuracy over a wide range of internuclear separations, the s-wave scattering length for singlet H(1s)+H(1s) scattering is determined at a=0.2735_{31}^{39} a_{0}.

Vibrationally resolved electron impact electronic excitation of BeH

Beryllium is being adopted for plasma facing walls in fusion reactors. This has led to the observation of emissions from the A 2Π state of beryllium hydride. Use of these emissions to monitor Be erosion requires electron impact excitation rates. Cross sections for electron impact vibrational excitation within the X 2Σ+ state and vibrationally resolved electronic excitation to the A 2Π state are reported for BeH, BeD and BeT. Electron collisions are studied at a range of internuclear separations using the UK molecular R-matrix (UKRmol+) codes. Electronic excitation is studied both within the Franck–Condon approximation and by explicit averaging of the T-matrix elements. It is found that (a) inclusion of the effect of higher partial waves using the Born approximation leads to significant increases in the cross sections and (b) the Franck–Condon approximation underestimates the importance of collisions for which the vibrational state changes during electronic excitation.

Deeply bound ( 24DJ+5S1/2 ) Rb87 and Rb85 molecules for eight spin couplings

We observe long-range $^{85}$Rb and $^{87}$Rb (24$D$+5$S_{1/2}$) Rydberg molecules for eight different spin couplings, with binding energies up to 440~MHz and sub-percent relative uncertainty. Isotopic effects of the molecular binding energies arise from the different masses and nuclear spins. Because the vibrational states involve different spin configurations and cover a wide range of internuclear separations, the states have different dependencies on the $s$-wave and $p$-wave scattering phase shifts for singlet and triplet scattering. Fitting the spectroscopic data, we comprehensively determine all four scattering length functions over the relevant energy range as well as the zero-energy scattering lengths of the two $s$-wave channels. Our unusually high temperature and low density (180 $\mu$K, 1 $\times$ 10$^{11}$ cm$^{-3}$) suggest that the molecule excitation occurs through photoassisted collisions.

Line list for the ground state of CaF

The molecular potential energy function and electronic dipole moment function for the ground state of CaF were studied with MRCI, ACPF, and RCCSD(T) ab initio calculations. The RCCSD(T) potential function reproduces the experimental vibrational intervals to within ∼2 cm−1. The RCCSD(T) dipole moment at the equilibrium internuclear separation agrees well with the experimental value. Over a wide range of internuclear separations, far beyond the range associated with the observed spectra, the ab initio dipole moment functions are similar and highly linear. An extended Morse oscillator (EMO) potential function was also obtained by fitting the observed lines of the laboratory vibration-rotation and pure rotation spectra of the 40CaF X2Σ+ ground state. The fitted potential reproduces the observed transitions (v ≤ 8, N ≤ 121, Δv = 0, 1) within their experimental uncertainties. With this EMO potential and the RCCSD(T) dipole moment function, line lists for 40CaF, 42CaF, 43CaF, 44CaF, 46CaF, and 48CaF were computed for v ≤ 10, N ≤ 121, Δv = 0–10. The calculated emission spectra are in good agreement with an observed laboratory spectrum of CaF at a sample temperature of 1873 K.

Correlations of Rydberg orbitals of diatomic molecules

SynopsisCalculations of the potential energy curves of diatomic molecules are performed for the entire range of internuclear separation in order to correlate Rydberg orbitals at the united atom and separated atoms which are needed to properly assign highly excited Rydberg states.

Structural, Spectroscopic and Vibrational Properties for Low-Lying Electronic States of LiCl

A multireference configuration interaction (MRCI) study has been carried out on the LiCl molecule. The potential energy has been calculated over a wide range of internuclear separation for the 21 low-lying electronic states of the LiCl molecule dissociating into Li (2S, 2P, 3S)+Cl (2P). The (4)1Σ+, (3)1Π, 1–33Σ+, 1–33Π, 1,3Δ, 1,3Σ−, (5)1Σ+, (4)3Σ+, (4)1Π, (4)3Π excited states are studied for the first time in theory. Molecular spectroscopic constants (Re,De, ωe, ωeχe, Be and αe) have been derived for the 9 bound states (X1Σ+, (3)1Σ+, (2)3Σ+, 1,3Δ, 1,3Σ−, (4)1Π, (4)3Π) with a regular shape, and the spectroscopic constants of ground states X1Σ+ are in good agreement with available experimental and theoretical values. The relative differences between experimental values and our values for Re, De,ωe, ωeχe, Be and αe are 1.02%, 0.60%, 1.72%, 9.46%, 2.0%, and 0.75%, respectively. Moreover, vibrational levels of 9 bound states, which have not been investigated experimentally, are computed.

Dynamical adiabatic theory of atomic collisions: The global structure of dynamical adiabatic potential energy curves

The concept of dynamical adiabatic states, originally proposed to describe one-electron atom(ion)-ion collision systems is developed and the properties of the corresponding dynamical adiabatic potential energy curves are studied for a complete range of internuclear separations $R$. The advantages of a dynamical adiabatic basis are threefold. First, it is compatible with the boundary conditions, whereas in standard adiabatic two-Coulomb center basis we have nonvanishing inelastic transitions when internuclear distance $R\ensuremath{\rightarrow}\ensuremath{\infty}$. Second, rotational transitions are transformed into radial transitions via a type of hidden crossings in contrast with the standard adiabatic basis, where these transitions could only be included by numerical close-coupling calculations. And third, the ionization process can be described using a basis of the complete discrete orthogonal wave packets, which is much more satisfactory for the process compared with the standard adiabatic approach where the continuum states which have no direct physical meaning are employed. Results of the calculation for the (HeH)${}^{2+}$ quasimolecular system are presented and discussed. Comparison is made with previous results derived by perturbation theory in the united-atom and separated atoms limits.

Low-energy electron collisions with O2: Test of the molecularR-matrix method without diagonalization

Electron collisions with O${}_{2}$ at scattering energies below 1 eV are studied in the fixed-nuclei approximation for a range of internuclear separations using the ab initio molecular R-matrix method. The ${}^{2}{\ensuremath{\Pi}}_{\mathrm{g}}$ scattering eigenphases and quantum defects are calculated. The parameters of the resonance and the energy of the bound negative ion are then extracted. Different models of the target that employ molecular orbitals calculated for the neutral target are compared with models based on anionic orbitals. A model using a basis of anionic molecular orbitals yields physically correct results in good agreement with experiment. An alternative method of calculation of the R matrix is tested, where instead of performing a single complete diagonalization of the Hamiltonian matrix in the inner region, the system of linear equations is solved individually for every scattering energy. This approach is designed to handle problems where diagonalization of an extremely large Hamiltonian is numerically too demanding.

Communication: Imaging wavefunctions in dissociative photoionization

The dissociative ionization dynamics of excited electronic states of the xenon dimer, Xe(2), have been studied using velocity map ion imaging (VMI). A one-colour, (2+1) resonant excitation scheme was employed to first excite and then ionize selected vibrational levels of the Xe(2) 6p (2)[(1)∕(2)](0) 0(g)(+) Rydberg state. Cationic fragments were then detected by the VMI. The data provide an outstanding example of the reflection principle in photodissociation with the full nodal structure of the Rydberg state wavefunctions clearly observed in the final Xe(+) kinetic energy distributions without the need for scanning the excitation energy. Fitting of the observed distributions provides detailed and precise information on the form of the Xe(2)(+) I((1)/(2)g) potential energy curve involved which is in excellent agreement with the results of photoelectron imaging studies [Shubert and Pratt, J. Chem. Phys. 134, 044315 (2011)]. Furthermore, the anisotropy of the product angular distributions yields information on the evolution of the electronic character of the ionic state with internuclear separation, R. The combination of the nature of dissociative ionization and the extent of the bound state wavefunctions provide information over an unusually wide range of internuclear separation R (ΔR > 0.75 Å). This would normally require scanning over a considerable energy region but is obtained in these studies at a fixed excitation energy.

Study on spectroscopic parameters and molecular constants of CS+(X2Σ+) and CS+(A2Π) by MRCI

The potential energy curves (PECs) of CS+(X2Σ+) and CS+(A2Π) have been investigated using the full valence complete active space self-consistent field (CASSCF) method through the highly accurate valence internally contracted multireference configuration interaction (MRCI) approach over the internuclear separation range from 0.05 to 0.60 nm. In the present calculations, the basis sets for S and C are both aug-cc-pV6Z. The spectroscopic parameters of three main isotopes (12C32S+, 12C33S+, 12C34S+) have been determined. The present D0, De, Re, ωe, ωeχe, αe and Be for 12C32S+(X2Σ+) are 6.4694 eV, 6.5542 eV, 0.14975 nm, 1371.89 cm-1, 7.5746 cm-1, 0.006481 cm-1 and 0.8616 cm-1, respectively; and those for CS+(A2Π) are 4.8460 eV, 4.9084 eV, 0.16449 nm, 1009.31 cm-1, 6.4970 cm-1, 0.006110 cm-1 and 0.7134 cm-1, respectively, which have been compared with those of previous results reported in the literature. And the comparison shows that the present results and the experimental results are in excellent agreement with each other. With the PECs of CS+(X2Σ+) and CS+(A2Π) determined here, the vibrational states for each electronic state are determined when the rotational quantum number J equals zero (J = 0). For the first 30 vibrational states, the vibrational level G(υ), inertial rotation constant Bυ and centrifugal distortion constant Dυ for 12C32S+(X2Σ+) and 12C32S+(A2Π) are evaluated when J = 0, which are in good accordance with the available RKR data.

Spectroscopic parameters and molecular constants of CSe(X1Σ+) radical

The spectroscopic and molecular properties of CSe(X1Σ+) radical are investigated using the complete active space self-consistent field (CASSCF) method followed by the highly accurate valence internally contracted multireference configuration interaction (MRCI) approach. The potential energy curve (PEC) is calculated over the internuclear separation range from 0.08 to 2.5 nm at the basis sets, aug-cc-pV5Z for C and aug-cc-pV5Z-pp for Se atom. The spectroscopic parameters (D0, De, Re, ωe, ωexe, αe and Be) of six isotope molecules (12C74Se, 12C76Se, 12C77Se, 12C78Se, 12C80Se and 12C82Se) are evaluated using the PEC of CSe(X1Σ+) radical. The spectroscopic parameters are compared with those reported in the literature, and excellent agreement is found between them. With the PEC of CSe(X1Σ+) radical obtained here, a total of 81 vibrational states of 12C80Se species are predicted when J = 0 by numerically solving the radical Schrödinger equation of nuclear notion. For each vibrational state of every isotope species, the vibrational levels, classical turning points and inertial rotation constants are reported, which are in agreement with the available experimental data.

Performance of multireference and equation-of-motion coupled-cluster methods for potential energy surfaces of low-lying excited states: Symmetric and asymmetric dissociation of water

Multireference (MR), general-model-space (GMS), state-universal (SU) coupled-cluster (CC) method that considers singly (S) and doubly (D) excited cluster amplitudes relative to the reference configurations spanning the model space (GMS SU CCSD), as well as its externally corrected (ec) version (N,M)-CCSD that employs N-reference MR CISD as an external source of higher-than-pair cluster amplitudes in a M-reference GMS CCSD, are employed to investigate low-lying states of the water molecule. The emphasis is on a generation of several low lying states belonging to the same symmetry species. Cuts of the potential energy surface (PES) corresponding to the breaking of a single OH bond and leading to the OH+H fragments, as well as the simultaneous breaking of both bonds into the O+2H are considered. Relying on a simple ab initio model that enables a comparison with the exact full configuration interaction energies, the performance of the GMS-based methods is assessed in the whole relevant range of internuclear separations. It is shown that the ec (N,M)-CCSD version provides best results for both the singlet and the triplet states considered. The same cuts of the PES are then explored using a realistic aug-cc-pVTZ basis set. For triplets, the use of high-spin (M(S)=1) references is to be preferred.

Multireference coupled‐cluster methods for ground and low‐lying excited states. A benchmark illustration on CH + potentials

AbstractMultireference (MR), general‐model‐space (GMS), state‐universal (SU) coupled‐cluster (CC) method that considers singly (S) and doubly (D) excited cluster amplitudes relative to the reference configurations spanning the model space (GMS SU CCSD), as well as its externally corrected (ec) version (N,M)‐CCSD that uses N‐reference MR CISD as an external source of higher‐than‐pair cluster amplitudes in a M‐reference GMS CCSD, are used to investigate low‐lying states of the CH+ ion. Relying on a simple ab initio model that enables a comparison with the exact full configuration interaction energies, the performance of the GMS‐based methods is assessed in the whole relevant range of internuclear separations. It is shown that the ec (N,M)‐CCSD version provides best results for both the singlet and the triplet states considered. For triplets, the use of high‐spin (MS = 1) references is to be preferred. The GMS‐based MR SU CC results for the ten low‐lying states of CH+ clearly indicate the usefulness and reliability of these approaches. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010

Theoretical study of the X Σ2+ states of the neutral CM–RG complexes (CM=coinage metal, Cu, Ag, and Au and RG=rare gas, He–Rn)

We present high level ab initio potential energy curves for the X Σ2+ electronic states of the CM–RG complexes; where CM is a coinage metal, CM=Cu, Ag and Au and RG is a rare gas, RG=He–Rn. These potentials are calculated over a range of internuclear separations, R, and the energy at each point is corrected for basis set superposition error and extrapolated to the basis set limit. Spectroscopic constants are determined from the potentials so obtained and are compared to available experimental data. The impact of core-valence correlation to the overall interactions within the complexes involving the lighter RG atoms is also considered. We find that there is a surprising continuous decrease in Re in these species from CM-He to CM-Rn and show that this is likely due to a combination of sp hybridization and small amounts of charge transfer.

Spectroscopic investigations on the HCl(X2Π) ion using coupled-cluster theory in combination with the correlation-consistent quintuple basis set augmented with diffuse functions

The coupled-cluster singles-doubles-approximate-triples [CCSD(T)] theory in combination with the correlation-consistent quintuple basis set augmented with diffuse functions (aug-cc-pV5Z) is used to investigate the spectroscopic properties of the HCl+(X2Π) ion. The accurate potential energy curve is calculated over the internuclear separation range from 0.051 to 2.51 nm and is fitted to the analytic Murrell-Sorbie function, which is used to accurately determine the spectroscopic parameters such as D0, De, ωeχe, αe, and Be. The present D0, De, Re, ωe, ωeχe, αe, and Be values are of 4.6316, 4.7964 eV, 0.13157 nm, 2684.463, 53.116, 0.3165, and 9.9412 cm−1, respectively, which conform almost perfectly with the available measurements. With the potential obtained at the UCCSD(T)/aug-cc-pV5Z level of theory, a total of 26 vibrational states have been predicted for the first time when the rotational quantum number J is set equal to zero (J = 0) by numerically solving the radial Schrödinger equation of nuclear motion with the Numerov method. The complete vibrational levels, classical turning points, inertial rotation, and centrifugal distortion constants are reproduced from the potential of the HCl+(X2Π) ion when J = 0 for the first time, which are in excellent agreement with the available experiments. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010

Multiphoton ionization of H+2 at critical internuclear separations: non-Hermitian Floquet analysis

We present ab initio time-dependent non-Hermitian Floquet calculations of multiphoton ionization (MPI) rates of hydrogen molecular ions subject to an intense linearly polarized monochromatic laser field with a wavelength of 800 nm. The orientation of the molecular axis is parallel to the polarization vector of the laser field. The MPI rates are computed for a wide range of internuclear separations R with high resolution in R and reproduce resonance and near-threshold structures. We show that enhancement of ionization at critical internuclear separations is related to resonance series with higher electronic states. The effect of two-centre interference on the MPI signal is discussed.

Theoretical investigations on the SH+(X3Σ−) ion using coupled-cluster theory in combination with the correlation-consistent quintuple basis set augmented with diffuse functions

The coupled-cluster singles-doubles-approximate-triples [CCSD(T)] theory in combination with the correlation-consistent quintuple basis set augmented with diffuse functions (aug-cc-pV5Z) is used to investigate the spectroscopic properties of the SH+( X3Σ−) ion. The accurate potential energy curve is calculated over the internuclear separation range from 0.09 to 2.46 nm and is fitted to the analytic Murrell-Sorbie function, which is used to accurately determine the spectroscopic parameters such as De, ωeχe, αe, and Be. The present De, Re, ωe, ωeχe, αe, and Be values are 3.69119 eV, 0.13644 nm, 2,556.429 cm−1, 49.290 cm−1, 0.289 cm−1, and 9.2677 cm−1, respectively, which are in excellent agreement with the available measurements. With the potential obtained at the UCCSD( T)/aug-cc-pV5Z level of theory, a total of 21 vibrational states is predicted when 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 reproduced from the potential energy curve of the SH+( X3Σ−) ion when J = 0 for the first time. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009