Core-valence Correlation Research Articles

Theoretical study on thirteen Λ-S states of the SiN radical: potential energy curves, spectroscopic parameters and spin-orbit couplings

The spectroscopic properties of nineteen Ω states generated from the eight Λ-S bound states of SiN radicals are studied in detail using an ab initio quantum chemical method for the first time. The potential energy curves (PECs) are calculated by the complete active space self-consistent field method, which is followed by the internally contracted multireference configuration interaction approach with the Davidson modification (icMRCI+Q). The spin-orbit coupling is accounted for by the Breit-Pauli Hamiltonian using the cc-pCVTZ basis set. Scalar relativistic correction calculations are made using the third-order Douglas-Kroll Hamiltonian approximation at the level of a cc-pV5Z basis set. Core-valence correlation corrections are included with a cc-pCVTZ basis set. All the PECs are extrapolated to the complete basis set limit. The convergent behavior is discussed with respect to the basis set and level of theory. The effect of core-electron correlations on the energy splitting is studied. Using the PECs, the spectroscopic parameters of twelve Λ-S and nineteen Ω bound states are evaluated. At the icMRCI+Q/CV+DK+56 theoretical level, the spin-orbit coupling splitting energy of the A 2 ΠΛ-S state is found to be 88.45 cm-1, which agrees well with the recent measurements of 89.09 cm-1. Moreover, other spectroscopic parameters are also in fair agreement with their respective measurements. The effect of SO coupling on the vibrational levels is discussed. It shows that the spectroscopic parameters of the twelve Λ-S and nineteen Ω bound states reported here can be expected to be reliably predicted ones.

The H + CO ⇌ HCO reaction studied by ab initio benchmark calculations

The title reaction has been calculated using complete active space self-consistent field and internally contracted multi-reference configuration interaction, including Davidson correction, calculations. Dunning's correlation consistent atomic basis sets, together with several complete basis set extrapolation schemes, were employed. Core-valence and scalar relativistic effects were also taken into account, as well as anharmonicity of the vibrational modes. Core-valence correlation appears to have a large impact on the calculated frequencies, spectroscopic constants, and on the energetics. In particular, the best estimate for the HCO (DCO) formation barrier height at 0 K, 4.54 ± 0.14 (4.43 ± 0.14) kcal mol(-1) is larger than previous theoretical works and well above the usually accepted value of 2.0 ± 0.4 kcal mol(-1), measured at room temperature. Inclusion of temperature and entropy at 298 K does not seem to be able to solve this discrepancy. The present theoretical barrier height is therefore the recommended value. The exo-ergicity of the HCO (DCO) dissociation reaction, predicted to be -13.36 ± 0.57 (-14.72 ± 0.57) kcal mol(-1), is slightly below the experimental value. Finally, all tested density functionals fail to reproduce accurately both the formation and dissociation barriers.

An integrated experimental and quantum-chemical investigation on the vibrational spectra of chlorofluoromethane.

The vibrational analysis of the gas-phase infrared spectra of chlorofluoromethane (CH2ClF, HCFC-31) was carried out in the range 200-6200 cm(-1). The assignment of the absorption features in terms of fundamental, overtone, combination, and hot bands was performed on the medium-resolution (up to 0.2 cm(-1)) Fourier transform infrared spectra. From the absorption cross section spectra accurate values of the integrated band intensities were derived and the global warming potential of this compound was estimated, thus obtaining values of 323, 83, and 42 on a 20-, 100-, and 500-year horizon, respectively. The set of spectroscopic parameters here presented provides the basic data to model the atmospheric behavior of this greenhouse gas. In addition, the obtained vibrational properties were used to benchmark the predictions of state-of-the-art quantum-chemical computational strategies. Extrapolated complete basis set limit values for the equilibrium geometry and harmonic force field were obtained at the coupled-cluster singles and doubles level of theory augmented by a perturbative treatment of triple excitations, CCSD(T), in conjunction with a hierarchical series of correlation-consistent basis sets (cc-pVnZ, with n = T, Q, and 5), taking also into account the core-valence correlation effects and the corrections due to diffuse (aug) functions. To obtain the cubic and quartic semi-diagonal force constants, calculations employing second-order Møller-Plesset perturbation (MP2) theory, the double-hybrid density functional B2PLYP as well as CCSD(T) were performed. For all anharmonic force fields the performances of two different perturbative approaches in computing the vibrational energy levels (i.e., the generalized second order vibrational treatment, GVPT2, and the recently proposed hybrid degeneracy corrected model, HDCPT2) were evaluated and the obtained results allowed us to validate the spectroscopic predictions yielded by the HDCPT2 approach. The predictions of the deperturbed second-order perturbation approach, DVPT2, applied to the computation of infrared intensities beyond the double-harmonic approximation were compared to the accurate experimental values here determined. Anharmonic DFT and MP2 corrections to CCSD(T) intensities led to a very good agreement with the absorption cross section measurements over the whole spectral range here analysed.

Performance of Density Functionals for Activation Energies of Zr-Mediated Reactions.

Coupled cluster CCSD(T) calculations with core-valence correlation and complete basis set (CBS) limit extrapolation are used to benchmark the performance of commonly used density functionals in computing energy barriers for Zr-mediated reactions involving zirconocene species. These reactions include (a) insertions of the Zr-H bond of Cp2Zr(H)Cl into C═C, C≡C, and C═O bonds and (b) C-H activations by Zr═N bond in Cp2Zr═NH. The best performing functionals are M06-L, M06, and M06-2X in the M06 series, all having mean unsigned deviations (MUD) less than 2 kcal/mol. The worst performing functional is OLYP, with a distinctly large MUD of more than 10 kcal/mol. Considering also the trends in barrier heights and the systematic barrier height deviation, our best recommended functional is M06-2X. In this work, DFT empirical dispersion correction (DFT-D3) is found to improve the performance of barrier height values for most functionals (especially of OLYP and B3LYP). With DFT empirical dispersion correction, we also recommend M06-2X for reaction barrier calculations of Zr-mediated reactions.

Extensive calculations on 12 Λ-S and 27 Ω states of PCl+ cation including spin–orbit coupling

The potential energy curves (PECs) of 27 Ω states generated from the 12 Λ-S states (X2Π, A2Π, 14Π, 24Π, 12Σ−, 22Σ−, 14Σ−, 24Σ−, 12Σ+, 14Σ+, 12Δ and 14Δ) of PCl+ cation are studied for the first time for internuclear separations from about 0.10 to 1.10nm using an ab initio quantum chemical method. All the 12 Λ-S states correlate to the first dissociation channel of PCl+ cation. Of these Λ-S states, the 24Π is found to be the repulsive one. The 14Σ+, 12Δ and 14Δ are found to be the inverted ones. And the 12Δ is found to possess the double wells. The PECs are calculated by the complete active space self-consistent field method, which is followed by the internally contracted multireference configuration interaction approach with the Davidson correction in combination with the correlation-consistent basis sets, aug-cc-pV(n+d)Z. The effect of core–valence correlation and scalar relativistic corrections on the spectroscopic parameters is briefly discussed. Scalar relativistic corrections are included by the third-order Douglas–Kroll Hamiltonian approximation at the level of a cc-pV5Z basis set. Core–valence correlation corrections are included with a cc-pCVTZ basis set. The convergent behavior of present calculations is discussed with respect to the basis set and level of theory. The spin–orbit coupling is accounted for by the state interaction method with the Breit–Pauli Hamiltonian using the all-electron cc-pCVTZ basis set. All the PECs are extrapolated to the complete basis set limit. The spectroscopic parameters are evaluated for the 11 Λ-S bound states and for the 23 Ω bound states, and are compared with available experimental and other theoretical results. Fair agreement has been found between the present spectroscopic parameters and the measurements. The energy splitting in the X2Π Λ-S state is calculated to be 346.11cm−1, close to the estimated measurements of 370cm−1. It demonstrates that the spectroscopic parameters reported here can be expected to be reliably predicted ones.

Systematic Theoretical Study of Non-nuclear Electron Density Maxima in Some Diatomic Molecules

First, exploratory calculations were performed to investigate the presence of non-nuclear maxima (NNMs) in ground-state electron densities of homonuclear diatomic molecules from hydrogen up to calcium at their equilibrium geometries. In a second stage, only for the cases in which these features were previously detected, a rigorous analysis was carried out by several combinations of theoretical methods and basis sets in order to ensure that they are not only calculation artifacts. Our best results support that Li2, B2, C2, and P2 are molecules that possess true NNMs. A NNM was found in values obtained from the largest basis sets for Na2, but it disappeared at the experimental geometry because optimized bond lengths are significantly inaccurate for this case (deviations of 0.10 Å). Two of these maxima are also observed in Si2 with CCSD and large basis sets, but they are no longer detected as core-valence correlation or multiconfigurational wave functions are taken into account. Therefore, the NNMs in Si2 can be considered unphysical features due to an incomplete treatment of electron correlation. Finally, we show that a NNM is encountered in LiNa, representing the first discovery of such electron density maxima in a heteronuclear diatomic system at its equilibrium geometry, to our knowledge. Some results for LiNa, found in variations in internuclear distances, suggest that molecular electric moments, such as dipole and quadrupole, are sensitive to the presence of NNMs.

Theoretical calculations on 12 Λ-S and 23 Ω states of CBr+ cation in the gas phase: Potential energy curves, spectroscopic parameters and spin–orbit coupling

The potential energy curves (PECs) of X1Σ+, a3Π, 13Σ+, 13Δ, 11Δ, 11Σ−, 13Σ−, 11Π, 21Σ+, 23Π, 21Π and 23Σ+ Λ-S states of CBr+ cation and corresponding 23 Ω states are calculated for the first time using the CASSCF method, which is followed by the internally contracted MRCI approach with the aug-cc-pVQZ basis set. All the Λ-S states involved are found to be bound and dissociate into the first dissociation limit of CBr+ cation. Of these Λ-S states, only the 13Σ+ and 13Σ− are inverted ones. The spin–orbit (SO) coupling is accounted for by the state interaction approach with the Breit–Pauli Hamiltonian. Core–valence correlation is included by a cc-pCVTZ basis set. Relativistic correction is calculated with the third-order Douglas–Kroll Hamiltonian approximation at the level of cc-pVQZ basis set. To obtain more reliable results, the PECs obtained by the MRCI calculations are corrected for size-extensivity errors by means of the Davidson modification. The PEC crossings of different Λ-S states are studied. With these PECs, the spectroscopic parameters of all the Λ-S and Ω states involved are obtained by fitting the first ten vibrational levels whenever available, which are calculated by solving the rovibrational Schrödinger equation using the Numerov's method. The spectroscopic parameters are compared with those reported in the literature. Excellent agreement is found between the present results and available measurements. In particular, the energy separation of 352.26cm−1 between the a3Π0+ and the a3Π1 Ω states agrees well with the measurements of 369±8cm−1, and the ωe results of 907.45 and 907.08cm−1 for the a3Π0+ and a3Π1 Ω states are in excellent agreement with the measurements of 906±2 and 903±6cm−1, respectively. These show that the spectroscopic parameters obtained in the present paper can be expected to be reliable predicted ones.

Correlation effects for nl-n′l′ transitions in nine isoelectronic sequences of silver ions

We present a comprehensive theoretical study of atomic characteristics of nine isoelectronic sequences of silver ions in a broad range of wavelengths and transitions. Energy levels and transitions probabilities are calculated for nl–n′l′ transitions particularly in Ag XLV, Ag XLIV, Ag XLII, Ag XXXVII, Ag XXXVI, Ag XXXV, Ag XIX, Ag XVIII, Ag XVII ions. Atomic structure and radiative characteristics of Li-like, Be-like, B-like, Na-like, Mg-like, Al-like, Cu-like, Zn-like and Ga-like silver ions are computed by multiconfiguration Dirac–Fock (MCDF) and relativistic configuration interaction calculations (RCI). The valence–valence, core–valence and core–core correlations are also considered. The calculated values including core–valence correlation are found to be similar and to compare very well with other theoretical and experimental values. We believe that our extensive calculated values can guide experimentalists in identifying the fine-structure levels in their future work.

Communication: Determining the lowest-energy isomer of Au8: 2D, or not 2D

A parallel numerical derivative code, combined with parallel implementation of the coupled-cluster method with singles, doubles, and non-iterative triples (CCSD(T)), is used to optimize the geometries of the low-energy structures of the Au8 particle. The effects of geometry relaxation at the CCSD(T) level and the combined effects of the basis set and core-valence correlations are examined and the results are compared with the corresponding second-order Møller-Plesset perturbation theory calculations. The highest-level computations, in which the single-point CCSD(T) calculations employing the correlation-consistent basis set of the cc-pVTZ quality and the associated relativistic effective core potential (ECP), both optimized for gold, and correlating the 5d(10)6s(1) valence and 5s(2)5p(6) semi-core electrons, are combined with the geometrical information obtained with the corresponding CCSD(T)/cc-pVDZ/ECP approach, favor the planar configuration, with the next three non-planar structures separated by 4-6 kcal/mol. In agreement with the earlier work, smaller-basis set CCSD(T) computations provide unreliable results for the relative energetics, even when the geometries are optimized at the CCSD(T) level.

Geometries, vibrational frequencies, and excitation energies of a series of fluorine-substituted carbenes, FCX (X = H, F, Cl, Br, and I): A high-level multireference configuration interaction study

High-level calculations using internally contracted multireference configuration interaction including Davidson correction (icMRCI+Q) method have been carried out for the ground singlet states, the first excited states, and the lowest triplet states of a series of fluorine-substituted carbenes FCX (X = H, F, Cl, Br, and I). Equilibrium geometries and vibrational frequencies of the three electronic states, adiabatic transition energy of the first excited singlet state, as well as the ground singlet—lowest triplet energy gap (S-T gap) of each of FCX carbenes have been obtained. Effects of the basis set of icMRCI+Q calculation on the geometries and energies have been investigated. In addition, various corrections, including the scalar relativistic effect, spin-orbit coupling, and core-valence correlation, have been studied in calculating the transition energies and the S-T gaps, especially for heavy-atom carbenes. This results have been compared with previous calculations using a variety of methods. Our icMRCI+Q results are in very good agreement with the high-resolution laser-based spectroscopic results where available. Some structure and spectroscopic constants of the fluorine-substituted carbenes which are void in the literature have been provided with consistent high-level calculations. © 2013 Wiley Periodicals, Inc.

Energies and E1, M1, E2, and M2 transition rates for states of the 2s22p4, 2s2p5, and 2p6configurations in oxygen-like ions between F II and Kr XXIX

Based on relativistic wave functions from multiconfiguration Dirac-Hartree-Fock and configuration interaction calculations, E1, M1, E2, M2 transition rates, weighted oscillator strengths, and lifetimes are evaluated for the states of the (1s 2 )2s 2 2p 4 , 2s2p 5 , and 2p 6 configurations in all oxygen-like ions between F II and Kr XXIX. Valence and core-valence correlation effects were accounted for through single-double multireference (SD-MR) expansions to increasing sets of active orbitals. Computed energies are compared with the NIST recommended values, generally differing by less than 600 cm −1 . For some spectra, significantly larger differences are found and our results are in better agreement with Edlen interpolated values. For levels where experimental lifetimes are available, the agreement is within experimental uncertainty for all but a few lowly ionized spectra. Complete Online tables of energy levels and transition data are available.

Accurate calculations on 9 Λ-S and 28 Ω states of NSe radical in the gas phase: Potential energy curves, spectroscopic parameters and spin–orbit couplings

The potential energy curves (PECs) of 28 Ω states generated from 9 Λ-S states (X2Π, 14Π, 16Π, 12Σ+, 14Σ+, 16Σ+, 14Σ-, 24Π and 14Δ) are studied for the first time using an ab initio quantum chemical method. All the 9 Λ-S states correlate to the first two dissociation limits, N(4Su)+Se(3Pg) and N(4Su)+Se(3Dg), of NSe radical. Of these Λ-S states, the 16Σ+, 14Σ+, 16Π, 24Π and 14Δ are found to be rather weakly bound states. The 12Σ+ is found to be unstable and has double wells. And the 16Σ+, 14Σ+, 14Π and 16Π are found to be the inverted ones with the SO coupling included. The PEC calculations are made by the complete active space self-consistent field method, which is followed by the internally contracted multireference configuration interaction approach with the Davidson modification. The spin–orbit coupling is accounted for by the state interaction approach with the Breit-Pauli Hamiltonian. The convergence of the present calculations is discussed with respect to the basis set and the level of theory. Core-valence correlation corrections are included with a cc-pCVTZ basis set. Scalar relativistic corrections are calculated by the third-order Douglas-Kroll Hamiltonian approximation at the level of a cc-pV5Z basis set. All the PECs are extrapolated to the complete basis set limit. The variation with internuclear separation of spin–orbit coupling constants is discussed in brief for some Λ-S states with one shallow well on each PEC. The spectroscopic parameters of 9 Λ-S and 28 Ω states are determined by fitting the first ten vibrational levels whenever available, which are calculated by solving the rovibrational Schrödinger equation with Numerov’s method. The splitting energy in the X2Π Λ-S state is determined to be about 864.92cm−1, which agrees favorably with the measurements of 891.80cm−1. Moreover, other spectroscopic parameters of Λ-S and Ω states involved here are also in fair agreement with available measurements. It demonstrates that the spectroscopic parameters reported here can be expected to be reliable predicted ones.

Accurate theoretical study on 18 Λ-S and 50 Ω states of CS in the gas phase: Potential energy curves, spectroscopic parameters, and spin-orbit coupling

The potential energy curves (PECs) of 50 Ω states generated from the 18 Λ-S states are studied for the first time using the complete active space self-consistent field method, which is followed by the internally contracted multireference configuration interaction approach with the Davidson modification. All the 18 Λ-S states correlate to the first dissociation limit, C((3)Pg) + S((3)Pg), of CS molecule, of which only the 2(5)Π is repulsive and the A(1)Π, A(') (1)Σ(+), and 2(3)Σ(+) possess double wells. The spin-orbit (SO) coupling is accounted for by the state interaction approach with the Breit-Pauli Hamiltonian. Core-valence correlation correction is taken into account with an all-electron cc-pCV5Z basis set. Scalar relativistic correction calculations are made by the third-order Douglas-Kroll Hamiltonian approximation at the level of a cc-pVTZ basis set. All the PECs are extrapolated to the complete basis set limit. The a(') (3)Σ(+), e(3)Σ(-), 1(5)Σ(+), 1(5)Π, and d(3)Δ are found to be the inverted Λ-S states with the SO coupling included. The spectroscopic parameters of 17 Λ-S and 41 Ω bound states are evaluated. The comparisons between the present results and available measurements are performed, and excellent agreement has been found. It shows that the spectroscopic results reported here can be expected to be reliable predicted ones.

Auxiliary basis sets for density-fitting second-order Møller-Plesset perturbation theory: Weighted core-valence correlation consistent basis sets for the 4delements Y-Pd

Auxiliary basis sets (ABS) specifically matched to the cc-pwCVnZ-PP and aug-cc-pwCVnZ-PP orbital basis sets (OBS) have been developed and optimized for the 4d elements Y-Pd at the second-order Møller-Plesset perturbation theory level. Calculation of the core-valence electron correlation energies for small to medium sized transition metal complexes demonstrates that the error due to the use of these new sets in density fitting is three to four orders of magnitude smaller than that due to the OBS incompleteness, and hence is considered negligible. Utilizing the ABSs in the resolution-of-the-identity component of explicitly correlated calculations is also investigated, where it is shown that i-type functions are important to produce well-controlled errors in both integrals and correlation energy. Benchmarking at the explicitly correlated coupled cluster with single, double, and perturbative triple excitations level indicates impressive convergence with respect to basis set size for the spectroscopic constants of 4d monofluorides; explicitly correlated double-ζ calculations produce results close to conventional quadruple-ζ, and triple-ζ is within chemical accuracy of the complete basis set limit.

Ab Initio Diabatic energies and dipole moments of the electronic states of RbLi molecule

For all states dissociating below the ionic limit Li(-) Rb(+) , we perform a diabatic study for (1) Σ(+) electronic states dissociating into Rb (5s, 5p, 4d, 6s, 6p, 5d, 7s, 4f) + Li (2s, 2p, 3s). Furthermore, we present the diabatic results for the 1-11 (3) σ, 1-8 (1,3) Π, and 1-4 (1,3) Δ states. The present calculations on the RbLi molecule are complementary to previous theoretical work on this system, including recently observed electronic states that had not been calculated previously. The calculations rely on ab-initio pseudopotential, core polarization potential operators for the core-valence correlation and full valence configuration interaction approaches, combined to an efficient diabatization procedure. For the low-lying states, diabatic potentials and permanent dipole moments are analyzed, revealing the strong imprint of the ionic state in the (1) Σ(+) adiabatic states. The transition dipole moment is used to evaluate the radiative lifetimes of the vibrational levels trapped in the 2 (1) Σ(+) excited states for the first time. In addition to the bound-bound contribution, the bound-free term has been evaluated using the Franck-Condon approximation and also exactly added to the total radiative lifetime.

Dissociation of the Fluorine Molecule

The primary purpose of the present study is to resolve the discrepancy that exists between the two most recently published dissociation energies for the fluorine molecule [D0(F2)] and, consequently, for the associated heats of formation of the fluorine atom [ΔfH0°(F)]. We hope to provide a reliable, well-established theoretical estimate for these thermochemical quantities. To this end, a high-accuracy coupled-cluster-based composite ab initio model chemistry has been utilized. The protocol involves contributions of up to pentuple excitations in coupled-cluster theory augmented with basis set extrapolation techniques and additional corrections beyond the nonrelativistic and Born–Oppenheimer approximations. The augmented core–valence correlation consistent basis set families, aug-cc-pCVXZ, have been successively used, in some cases, up to octuple-ζ quality. Our best theoretical results for D0(F2) and ΔfH0°(F) obtained in this study are 154.95 ± 0.48 and 77.48 ± 0.24 kJ/mol, respectively. Because conflicting theoretical results are also reported about the existence of a barrier along the dissociation curve of F2, extensive multireference configuration interaction and coupled-cluster calculations have been performed using reference orbitals taken from all-electron complete active space self-consistent field computations. Extrapolations from the results obtained with the aug-cc-pCVXZ (X = T, Q, 5) basis sets clearly indicate that the barrier indeed exists. It is located at 3.80 ± 0.20 Å along the dissociation curve with a height of 42 ± 10 μEh (∼0.11 ± 0.03 kJ/mol). Because of the neglect of this effect during the evaluation of the raw experimental data used to obtain D0(F2) = 154.52 ± 0.12 kJ/mol and ΔfH0°(F) = 77.26 ± 0.06 kJ/mol [Stevens; et al. J. Phys. Chem. A 2010, 114, 13134], an additional error should be attached to these latter values. Obviously, the barrier does not affect either the experimental results, D0(F2) = 154.92 ± 0.10 kJ/mol and ΔfH0°(F) = 77.46 ± 0.05 kJ/mol [Yang; et al. J. Chem. Phys. 2005, 122, 134308; 2007, 127, 209901], which are based on the ion-pair dissociation of the molecule, or the data calculated theoretically. It is also noteworthy that our best estimates are in excellent agreement with those obtained from the ion-pair dissociation experiment.

Spin–orbit coupling splitting in the X2Π, A2Δ, B2Σ−, C2Σ+, D2Σ+, F2Π and a4Σ− Λ–S states of SiH radical

The potential energy curves (PECs) of eleven Ω states generated from the seven Λ–S bound states of SiH radical are studied in detail using an ab initio quantum chemical method. The PECs are calculated for internuclear separations from about 0.10 to 1.00nm by the CASSCF method, which is followed by the internally contracted MRCI approach with the Davidson modification. The spin–orbit coupling is accounted for with the Breit–Pauli Hamiltonian. Core–valence correlation corrections are included with an aug-cc-pCVTZ basis set. Scalar relativistic correction calculations are made by the third-order Douglas–Kroll Hamiltonian approximation at the level of a cc-pV5Z basis set. To discuss the effect of core–electron correlations on the spectroscopic parameters, in particular on the Te, the all-electron basis set, aug-cc-pCVTZ with and without core–electron correlations, is employed to calculate the spin–orbit coupling splitting in the X2Π Λ–S state. The all-electron aug-cc-pCVTZ basis set with core–electron correlations is chosen for the present spin–orbit coupling studies. The convergent behavior of present calculations is discussed with respect to the basis set and level of theory. All the PECs are extrapolated to the complete basis set limit. The spectroscopic parameters of seven Λ–S and eleven Ω bound states are evaluated. The splitting energy of X2Π Λ–S state is determined as 141.12cm−1, which agrees well with the recent measurements of 142.896cm−1. Moreover, other spectroscopic parameters are also in excellent agreement with available measurements. It demonstrates that the spectroscopic parameters of eleven Ω bound states reported here can be expected to be reliable predicted ones.

Is near-“spectroscopic accuracy” possible for heavy atoms and coupled cluster theory? An investigation of the first ionization potentials of the atoms Ga–Kr

Recent developments in ab initio coupled cluster (CC) theory and correlation consistent basis sets have ushered in an era of unprecedented accuracy when studying the spectroscopy and thermodynamics of molecules containing main group elements. These same developments have recently seen application to heavier inorganic or transition metal-containing species. The present work benchmarks conventional single reference coupled cluster theory (up to full configuration interaction for valence electron correlation and coupled cluster with up to full pentuple excitations (CCSDTQP) for core-valence correlation) and explicitly correlated coupled cluster methods [CC with single, double, and perturbative triple substitutions (CCSD(T)-F12)] for the atomic ionization potentials of the six 4p elements (Ga-Kr), a property with experimental error bars no greater than a few cm(-1). When second-order spin orbit coupling effects are included, a composite methodology based on CCSD(T) calculations yielded a mean signed error of just -0.039 kcal mol(-1) and a mean unsigned error of 0.043 kcal mol(-1). Inclusion of post-CCSD(T) correlation corrections reduced both of these values to -0.008 kcal mol(-1) and 0.025 kcal mol(-1), respectively, with the latter corresponding to an average error of just 9 cm(-1). The maximum signed error in the latter scheme was just -0.043 kcal mol(-1) (15 cm(-1)).

Calculations on thirteen Λ–S states of PO radical: Electronic structure, spectroscopy and spin–orbit coupling

This paper presents the potential energy curves (PECs) of X2Π, B2Σ+, B′2Π, C2Σ−, C′2Δ, 32Π, a4Π, b4Σ−, 14Δ, 24Δ, 14Σ+, 16Σ+ and 16Π Λ–S states and the PECs of 16 Ω states generated from the eight bound Λ–S states of PO radical. All the PECs are calculated by the CASSCF method, which is followed by the internally contracted MRCI approach with the Davidson modification. The spin–orbit coupling is included by the state interaction approach with the Breit–Pauli Hamiltonian. The convergent behavior is observed and discussed with respect to the correlation-consistent basis set and level of theory. The effect on the energy splitting by core-electron correlations is studied. To improve the quality of PECs, core-valence correlation corrections are included by a cc-pCVTZ basis set. Scalar relativistic correction calculations are made by the third-order Douglas–Kroll Hamiltonian approximation at the level of a cc-pV5Z basis set. All the PECs are extrapolated to the complete basis set limit. With these PECs, the spectroscopic parameters of 10 Λ–S and 16 Ω bound states are evaluated. The vibrational manifolds of the first 16 vibrational states are evaluated for each Λ–S and Ω state of non-rotation radical. With the PECs obtained by the MRCI+Q/CV+DK+56+SO calculations, the SO coupling splitting energy of X2Π Λ–S state is determined as 225.18cm−1, which agrees well with the measurements of 224.17cm−1. Moreover, other spectroscopic parameters and molecular constants calculated here are also in excellent agreement with the available measurements. It shows that the spectroscopic parameters and molecular constants reported here can be expected to be reliable predicted ones.

Extensive ab initio study of the electronic states of S2 molecule including spin-orbit coupling

The potential energy curves (PECs) of 15 Λ-S states and 24 Ω states generated from the 13 Λ-S bound states of the S2 molecule are investigated in detail using an ab initio quantum chemical method. The PECs are calculated for internuclear separations from 0.12 to 1.10 nm by the complete active space self-consistent field method, which is followed by the internally contracted multireference configuration interaction approach with the Davidson modification (MRCI + Q). The spin-orbit (SO) coupling effect is accounted for by the Breit–Pauli Hamiltonian. To discuss the effect on the energy splitting by the core-electron correlations, the all-electron basis set, cc-pCVTZ with and without 2s2p correlations, is used for the SO coupling calculations of the A3 and B′3Πg Λ-S states since their measurements can be found in the literature. By comparison, the cc-pCVTZ basis set with 2s2p correlations is chosen for the SO coupling calculations of 13 Λ-S bound states. To improve the quality of PECs, core-valence correlation and scalar relativistic corrections are included. Scalar relativistic correction calculations are made using the third-order Douglas–Kroll Hamiltonian (DKH3) approximation at the level of a cc-pV5Z basis set. Core-valence correlation corrections are taken into account with a cc-pCVTZ basis set. The spectroscopic parameters of 13 Λ-S bound states and 24 Ω states are calculated. With the PECs obtained by the MRCI + Q/aug-cc-pV6Z + CV + DK + SO calculations, the SO coupling splitting energies are 379.25 cm−1 between the A′3 and A′2 Ω state, 83.40 cm−1 between the A1 and A0− Ω state and 210.91 cm−1 between the B′2 and B′1 Ω state, which agree well with the corresponding measurements of 383, 77.51 and 209 cm−1, respectively. Moreover, other spectroscopic parameters are also in excellent agreement with the measurements. It demonstrates that the spectroscopic parameters of 24 Ω states reported here for the first time can be expected to be reliable predicted ones.