Core-valence Correlation Effects Research Articles

Transition probabilities and lifetimes of the low-lying levels of Fe XIV

The multi-configuration Dirac-Fock method is employed to calculate the transition energies, probabilities, and oscillator strengths for electric dipole allowed (E1) and forbidden (M1, E2, M2) lines for the 3s23p, 3s3p2, 3s23d, 3p3, and 3s3p3d configurations of Fe XIV. The lifetimes of all 40 levels of these low-lying configurations are also derived. The valence-valence and core-valence correlation effects are accounted for in a systematic way. Breit interactions and quantum electrodynamics (QED) effects are estimated in subsequent relativistic configuration interaction (CI) calculations. The present results are in good agreement with other available theoretical and experimental values, and therefore can be used for the further astrophysical investigations.

A theoretical study on CH2N2 isomers: structure and energetics

Five CH2N2 isomers, namely cyanamide, carbodiimide, diazomethane, isocyanamide and nitrilimine, have been investigated at a high level of accuracy. The singles and doubles coupled-cluster method including a perturbational correction for connected triple excitations, CCSD(T), in conjunction with correlation-consistent basis sets ranging in size from triple to quintuple zeta have been employed. Extrapolation to the complete basis set limit has been used with treatments of core-valence correlation effects in order to accurately predict structures, relative energies as well as N–H and C–H bond dissociation energies. The latter required to also investigate the HNNC radical with the same methodology used for CH2N2 isomers, while HCNN and HNCN data are available in the literature by the same authors (Puzzarini and Gambi in J Chem Phys 122:064316, 2005). For all the species studied, harmonic vibrational frequencies have also been evaluated at the CCSD(T) level in order to obtain zero-point corrections to total energies.

New ab Initio Potential Energy Surfaces for the Renner-Teller Coupled 11A′ and 11A′′ States of CH2

New ab initio potential energy surfaces (PESs) for the two lowest-lying singlet 11A′ and 11A′′ electronic states of CH2, coupled by the Renner-Teller (RT) effect and meant for the spectroscopic study, are presented. The surfaces are constructed using a dual-level strategy. The internally contracted multireference configuration interaction calculations with the Davidson correction, using the aug-cc-pVQZ basis set, are employed to obtain 3042 points at the lower level. The core and core-valence correlation effects are taken into account in the ab initio calculations with a modified optimized aug-cc-pCVQZ basis set for the higher-level points. The analytical representations of these PESs, with the inclusion of the nonadiabatic RT terms, are obtained by the nonlinear least-squares fit of the calculated points to three-body expansion. Quantum dynamical calculations are performed on these PESs, and the computed vibronic energy levels for the two singlet electronic states are in excellent agreement with experiment.

Configuration interaction and radiative decay rates in trebly ionized tungsten (W IV)

Radiative decay rates are obtained for the first time for allowed (E1) and forbidden (M1, E2) transitions in trebly ionized tungsten (W IV). Our calculations, motivated by strong interest for low-density plasmas and fusion research, illustrate in a convincing way the importance of core–valence correlation effects which substantially increase the lifetimes and, accordingly, decrease the transition probabilities of this heavy ion. Due to the lack of experimental data for W IV, the reliability of the theoretical ‘f’ values can only be tested by comparison of numerical results obtained with two independent (i.e. multiconfiguration Dirac–Fock and relativistic Hartree–Fock with core-polarization effects (HFR+CPOL)) methods well suited for investigating the atomic structure of heavy ions.

A theoretical study of the inversion and rotation barriers in Methyl-substituted Amines

Barrier heights of the internal rotation and inversion motions of methylamine, dimethylamine and trimethylamine molecules were calculated with the CCSD(T)//B3LYP methodology in combination with the cc-pVTZ, cc-pVQZ, and cc-pCVTZ basis sets of Dunning. The complete basis set (CBS) extrapolation procedure and core-valence (CV) correlation effects are also examined to the barrier heights. Our best estimate results (CCSD(T)/CBS+CV//B3LYP/cc-pVQZ) are in very good agreement with the experimental data, indicating the use of this methodology to provide accurate predictions of structures and barrier heights for other systems

Accurate transition rates for intercombination lines of singly ionized nitrogen

The transition energies and rates for the $2{s}^{2}2{p}^{2}$ ${}^{3}{P}_{1,2}$--$2s2{p}^{3}$ ${}^{5}{S}_{2}^{o}$ and $2{s}^{2}2p3s$--$2{s}^{2}2p3p$ intercombination transitions have been calculated using term-dependent nonorthogonal orbitals in the multiconfiguration Hartree-Fock approach. Several sets of spectroscopic and correlation nonorthogonal functions have been chosen to describe adequately term dependence of wave functions and various correlation corrections. Special attention has been focused on the accurate representation of strong interactions between the $2s2{p}^{3}$ ${}^{1,3}{P}_{1}^{o}$ and $2{s}^{2}2p3s$ ${}^{1,3}{P}_{1}^{o}$levels. The relativistic corrections are included through the one-body mass correction, Darwin, and spin-orbit operators and two-body spin-other-orbit and spin-spin operators in the Breit-Pauli Hamiltonian. The importance of core-valence correlation effects has been examined. The accuracy of present transition rates is evaluated by the agreement between the length and velocity formulations combined with the agreement between the calculated and measured transition energies. The present results for transition probabilities, branching fraction, and lifetimes have been compared with previous calculations and experiments.

Effects of valence-valence, core-valence and core-core correlations on the fine-structure energy levels in Zn-like ions

We report on large ab initio calculation for the \(4s^2\)–4s4p transitions in the Zinc-like sequence, using the multi-configuration Dirac-Hartree-Fock method. Results for fine-structure energy levels, the wavelengths, transition rates and lifetimes between Z = 70 (Yb) and Z= 92 (U) are presented and compared with other theories and experiments. The calculated values including core-valence correlation are found to be similar and to compare very well with other theories and experiments values. We believe that our extensive calculated values can guide experimentalists in identifying the fine-structure levels in their future work.

Molecular core-valence correlation effects involving the post-d elements Ga–Rn: Benchmarks and new pseudopotential-based correlation consistent basis sets

Correlation consistent basis sets that are suitable for the correlation of the outer-core (n-1)spd electrons of the post-d elements Ga-Rn have been developed. These new sets, denoted by cc-pwCVXZ-PP (X=D,T,Q,5), are based on the previously reported cc-pVXZ-PP sets that were built in conjunction with accurate small-core relativistic pseudopotentials (PPs) and designed only for valence nsp correlation. These new basis sets have been utilized in benchmark coupled cluster calculations of the core-valence correlation effects on the dissociation energies and spectroscopic properties of several small molecules. As expected, the most important contribution is the correlation of the (n-1)d electrons. For example, in the case of the group 13 homonuclear diatomics (Ga(2),In(2),Tl(2)), this leads to a dissociation energy increase compared to a valence-only treatment from 1.5 to 3.2 kcal/mol, bond length shortenings from -0.076 to -0.125 Å, and harmonic frequency increases of 7-8 cm(-1). Even in the group 15 cases (As(2),Sb(2),Bi(2)), the analogous effects of (n-1)d electron correlation are certainly not insignificant, the largest values being +4.4 kcal/mol, -0.049 Å, and +9.6 cm(-1) for the effects on D(e), r(e), and ω(e), respectively. In general, the effects increase in magnitude down a group from 4p to 6p. Correlation of the outer-core (n-1)p electrons is about an order of magnitude less important than (n-1)d but larger than that of the (n-1)s. The effect of additional tight functions for Hartree-Fock and valence sp correlation was found to be surprisingly large, especially for the post-4d and post-5d elements. The pseudopotential results for the molecules containing post-3d elements are also compared to the analogous all-electron calculations employing the Douglas-Kroll-Hess Hamiltonian. The errors attributed to the PP approximation are found to be very small.

Predicting and characterizing new molecular species at a high-level theoretical approach: HSeCl, HClSe, and SeCl

New molecular species HSeCl, HClSe, and SeCl were investigated at a high level of theory, CCSD(T), with a series of correlation consistent basis sets with extrapolation to the CBS limit. Account has been taken for valence-only and core-valence correlation effects, and of anharmonic effects on the vibrational frequencies. HSeCl is 43.25 kcal mol −1 more stable than HClSe. A barrier (Δ G #) of 47.20 kcal mol −1 separates these species. Internuclear distances are generally overestimated by 0.008 Å in the valence-only correlation calculations. Inclusion of anharmonicity leads to much improved vibrational frequencies. For SeCl, we estimate Δ H f (0 K) = 23.96 and Δ H f (298.15 K) = 24.64 kcal mol −1; for HSeCl, we had 4.20 and 4.97 kcal mol −1, respectively.

Fully automated incremental evaluation of MP2 and CCSD(T) core, core-valence and valence correlation energies

A recently proposed coupled cluster evaluation of core–core and core-valence correlation effects within the incremental scheme has been extended to perturbative treatments. The accuracy of the approach is demonstrated at the MP2 and CCSD(T) level of theory for various systems from different areas of chemistry, i.e. a binuclear titanium complex, a diallylmagnesium compound, a Hg 4 cluster and various hydration complexes of the sodium cation. Besides the convergence of individual correlation contributions arising from the core and/or valence electron systems the basis set dependence of the contributions was also monitored. Results within chemical accuracy of 1 kcal/mol in the total energies are typically obtained at third order of the incremental expansion. Furthermore a few reasonable simplifications of the incremental core-valence treatment are proposed, which allow a large number of individual calculations to be omitted a priori without a significant loss of accuracy.

Theoretical investigation of ionized HSO and SOH

The anharmonic force-fields of HSO+ and SOH+ have been determined employing the CCSD(T) methodology and the correlation consistent basis sets. The calculated fundamental frequencies of SOH+ are 1009, 1149 and 3317 cm−1, for the υSO, υbend and υOH, respectively. For HSO+ the computed fundamentals are 1060, 1190 and 2307 cm−1, for the υbend, υSO and υSH, respectively. The vibrational frequency observed at 1150 ± 160 cm−1 for HSO+, which was tentatively assigned to the bending-mode, is close to our computed value for the SO-stretching mode. Thus revision of the assignment is suggested. The computed ionization potentials for HSO and SOH are 9.933 and 10.096 eV, respectively. The former value is in excellent agreement with the experimental measurement, 9.918 ± 0.016 eV. The onset to triplet HSO+ is calculated at 11.115 eV, in reasonable agreement with the experimental value 11.15 ± 0.04 eV. To estimate the of HSO+ and SOH+ we considered relativistic, core-valence and higher-order correlation effects. The recommended values are (HSO+) = 223.6 ± 0.5 and (SOH+) = 230.7 ± 0.5 kcal/mol. Finally, employing the experimental ionization potential of HSO and the (HSO+) we recommend (HSO) = −5.5 ± 0.5 and (SOH) = −2.0 ± 0.5 kcal/mol.

On the enthalpy of formation of thiophene

Thiophene is an important contaminant of petroleum-derived fuels, and it also plays an important role in molecular electronics. We have calculated the enthalpy of formation of thiophene employing the CCSD(T) methodology and the cc-pV(X + d)ZX = T,Q,5 basis sets. At the CCSD(T)/CBS limit and including corrections for scalar relativistic effects, anharmonic effects, spin–orbit and core-valence correlation effects, the estimated enthalpy of formation is 25.15-1+0.5 kcal/mol. Our estimation is 2.3 kcal/mol lower than the experimental value. The discrepancies between experiment and theory are expected to be increased if higher-order correlation effects are taken into account. Thus, a new determination of the experimental value is highly recommended. Finally, we discuss the problems faced to make this estimation, in particular the determination of accurate Zero-point energy corrections and the evaluation of core-valence correlation effects.

Exploring biorthonormal transformations of pair-correlation functions in atomic structure variational calculations

Multiconfiguration expansions frequently target valence correlation and correlation between valence electrons and the outermost core electrons. Correlation within the core is often neglected. A large orbital basis is needed to saturate both the valence and core–valence correlation effects. This in turn leads to huge numbers of configuration state functions (CSFs), many of which are unimportant. To avoid the problems inherent to the use of a single common orthonormal orbital basis for all correlation effects in the multiconfiguration Hartree–Fock (MCHF) method, we propose to optimize independent MCHF pair-correlation functions (PCFs), bringing their own orthonormal one-electron basis. Each PCF is generated by allowing single- and double-excitations from a multireference (MR) function. This computational scheme has the advantage of using targeted and optimally localized orbital sets for each PCF. These pair-correlation functions are coupled together and with each component of the MR space through a low dimension generalized eigenvalue problem. Nonorthogonal orbital sets being involved, the interaction and overlap matrices are built using biorthonormal transformation of the coupled basis sets followed by a counter-transformation of the PCF expansions. Applied to the ground state of beryllium, the new method gives total energies that are lower than the ones from traditional complete active space (CAS)-MCHF calculations using large orbital active sets. It is fair to say that we now have the possibility to account for, in a balanced way, correlation deep down in the atomic core in variational calculations.

Accurate configuration-interaction calculation of transitions in Sn II

A large-scale Breit–Pauli configuration-interaction calculation has been undertaken of all possible 85 E1 optically allowed and intersystem transitions in Sn II among the 22 energetically lowest-lying levels. We have presented a discussion of a sequence of increasingly complex calculations, performed in the LS coupling scheme, in which we have satisfied the necessary criterion in order that we could be confident that a satisfactory convergence of all important valence and core–valence correlation effects had been attained. Judging by the extensive checks we have subjected our results to, we estimate realistic uncertainties in the region of 5% for the stronger transitions studied, achieving an accuracy required for the proposed applications in astrophysical and fusion research. It is encouraging that we can propose possible deficiencies in the theoretical models of previous calculations in an attempt to account for disparities with present data. Although the observed consistency between our results and the greater part of experimental measurements is a comforting indication of reliability, the analysis is not without its discrepancies. We would argue, however, that the present work, representing the most accurate data available to date, warrants further elaborate experimental study. Our calculated fine-tuned oscillator strength for the astrophysically important transition at 1400.5 Å fl = 1.205 ± 0.060 puts into question the conclusions of Sofia et al (Sofia U J, Meyer D M and Cardelli J A 1999 Astrophys. J. 522 L137) that they measured gas-phase ratios of Sn/H in the interstellar medium that appear to be supersolar.

Accurate computational thermochemistry from explicitly correlated coupled-cluster theory

Explicitly correlated coupled-cluster theory has developed into a valuable computational tool for the calculation of electronic energies close to the limit of a complete basis set of atomic orbitals. In particular at the level of coupled-cluster theory with single and double excitations (CCSD), the space of double excitations is quickly extended towards a complete basis when Slater-type geminals are added to the wave function expansion. The purpose of the present article is to demonstrate the accuracy and efficiency that can be obtained in computational thermochemistry by a CCSD model that uses such Slater-type geminals. This model is denoted as CCSD(F12), where the acronym F12 highlights the fact that the Slater-type geminals are functions f(r 12) of the interelectronic distances r 12 in the system. The performance of explicitly correlated CCSD(F12) coupled-cluster theory is demonstrated by computing the atomization energies of 73 molecules (containing H, C, N, O, and F) with an estimated root-mean-square deviation from the values compiled in the Active Thermochemical Tables of σ = 0.10 kJ/mol per valence electron. To reach this accuracy, not only the frozen-core CCSD basis-set limit but also high-order excitations (connected triple and quadruple excitations), core–valence correlation effects, anharmonic vibrational zero-point energies, and scalar and spin–orbit relativistic effects must be taken into account.

Core–valence correlation effects in the ground and low-lying excited states of GaN

We present careful analysis of the accuracy of molecular properties of the GaN molecule calculated by the Coupled Cluster CCSD(T) method including the core–valence correlation effects. We demonstrate that calculations of the core–valence correlation effects with basis sets which were optimised considering just valence electrons of the gallium atom lead to unreliable results. Our objective is to find the relation between the accuracy and the oversimplification due to the use of aug-cc-pVXZ basis sets when 3d and eventually also 3s3p electrons are correlated with these basis sets, having in mind calculations of larger systems. We observe the oscillatory behaviour of molecular properties with increasing cardinal basis set number X in the aug-cc-pVXZ series. This is the main deficiency of this more economical basis set. Extrapolation to the complete basis set limit with this series is only possible starting with the aug-cc-pVQZ basis. Regular behaviour with increasing X show results with the aug-cc-pCVXZ series. Reasonable molecular properties are provided by the ANO-RCC basis sets with 3d 104s 24p 1 correlated electrons of Ga.

Correlation consistent basis sets for molecular core-valence effects with explicitly correlated wave functions: The atoms B–Ne and Al–Ar

Correlation consistent basis sets have been optimized for accurately describing core-core and core-valence correlation effects with explicitly correlated F12 methods. The new sets, denoted cc-pCVnZ-F12 (n=D, T, Q) and aug-cc-pC(F12)VnZ (n=D, T, Q, 5), were developed by augmenting the cc-pVnZ-F12 and aug-cc-pVnZ families of basis sets with additional functions whose exponents were optimized based on the difference between all-electron and valence-electron correlation energies. The number of augmented functions added is fewer, in general, than in the standard cc-pCVnZ and cc-pwCVnZ families of basis sets. Optimal values of the geminal Slater exponent for use with these basis sets in MP2-F12 calculations are presented and are also recommended for CCSD-F12b calculations. Auxiliary basis sets for use in the resolution of the identity approximation in explicitly correlated calculations have also been optimized and matched to the new cc-pCVnZ-F12 series of orbital basis sets. The cc-pCVnZ-F12 basis sets, along with the new auxiliary sets, were benchmarked in CCSD(T)-F12b calculations of spectroscopic properties on a series of homo- and heteronuclear first and second row diatomic molecules. Comparing the effects of correlating the outer core electrons in these molecules with those from conventional CCSD(T) at the complete basis set limit, which involved calculations with new cc-pCV6Z basis sets for the second row elements that were also developed in the course of this work, it is observed that the F12 values are reasonably well converged already at just the triple-zeta level.

Effects of valence-valence, core-valence, and core-core correlations on the fine-structure energy levels in Al-like ions

This paper reports on multiconfiguration Dirac-Hartree-Fock calculations for both allowed and intercombination transitions and fine structure referring to the levels of a term in highly charged aluminum like ions. Results for fine-structure energy levels, the term splitting, the wavelengths, transition rates, and thereby the branching ratios and lifetimes for the Al-like $3{s}^{2}3p$-$3s3{p}^{2}$ transitions in the ions Fe XIV--Au LXVII are reported and compared with other theories and experiments, using the codes GRASP2K. Our calculated fine-structure energy levels are in excellent agreement with the experimental results and the experimentally compiled energy values of the National Institute for Standards and Technology wherever available. The calculated values including core--valence correlation are found to be similar and to compare very well with other theoretical and experimental values for medium-$Z$ ions. For higher $Z$ the inclusion of the valence correlation gives results in excellent agreement with those from many-body perturbation theory. We believe that our extensive calculated values can guide experimentalists in identifying the fine-structure levels in their future work. From our radiative decay rates we have also calculated radiative lifetimes of some fine-structure levels. In this calculation we also predict new data for several fine-structure levels where no other theoretical and/or experimental results are available.

Theoretical characterisation of the SSO, cyclic SOS and SOS isomers

The SSO, cyclic SOS and open SOS isomers have been investigated, employing the CCSD(T) methodology and the cc-pV(X + d)Z X = 3, 4, 5, 6 basis sets. The anharmonic force fields have been calculated to predict the fundamental vibrational frequencies, rotational constants, vibration-rotation corrections, anharmonic corrections to zero-point energies, and structural parameters. At the CCSD(T)/CBS limit and including corrections for scalar relativistic effects, complete quadruple excitations, spin-orbit and core-valence correlation effects, the estimated enthalpies of formation are −13.9 ± 1, 32.1 ± 1, and −51.2 ± 1 kcal/mol, for SSO, cyclic-SOS and open-SOS, respectively. Finally, it was found that the asymmetric SO stretch of the open and cyclic SOS isomers are located in a nearly identical position and it is likely that SOS also maybe present in the surface of Io.

Hyperfine quenching of the 3s3p 3P0 level in Mg-like ions

Hyperfine quenching rates of the 3s3p3P0 level in Mg-like ions were calculated using the GRASP2K package based on the multi-configuration Dirac–Hartree–Fock method. Valence and core-valence correlation effects were accounted for in a systematic way. Breit interactions and QED effects were included in the subsequent relativistic CI calculations. Calculated rates were compared with other theoretical values and with experiment, and a good agreement with the latest experimental value for the ion (Rosenband et al 2007 Phys. Rev. Lett. 98 220801) was found. Furthermore, we showed in detail the contributions from Breit interaction and QED effects to concerned physical properties. Finally, electronic data were presented in terms of a general scaling law in Z that, given isotopic nuclear spin and magnetic moment, allows hyperfine-induced decay rates to be estimated for any isotope along the isoelectronic sequence.