Core-valence Correlation Research Articles

Potential Energy Curves, Spectroscopic Parameters, and Spin–Orbit Coupling: A Theoretical Study on 24 Λ-S and 54 Ω States of C2+ Cation

The potential energy curves (PECs) of 24 Λ-S states and 54 Ω states of the C2(+) cation are studied in detail using an ab initio quantum chemical method. All the PEC calculations are made for internuclear separations from 0.09 to 1.11 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). All the Λ-S states involved dissociate into the first dissociation limit, C((3)Pg) + C(+)((2)Pu), of C2(+) cation, of which only the 2(2)Σg(-) and 2(4)Σg(-) are repulsive. The spin-orbit (SO) coupling effect is accounted for by the Breit-Pauli Hamiltonian with an aug-cc-pCVTZ basis set. To improve the quality of PECs, core-valence correlation and scalar relativistic corrections are included. Core-valence correlation corrections are taken into account with an aug-cc-pCVTZ basis set. Scalar relativistic correction calculations are done by the third-order Douglas-Kroll Hamiltonian approximation with the cc-pVQZ basis set. All the PECs are extrapolated to the complete basis set limit. The convergence observations of present calculations are made, and the convergent behavior is discussed with respect to the basis set and level of theory. With the PECs obtained by the MRCI+Q/CV+DK+56 calculations, the spectroscopic parameters of 22 Λ-S bound states of C2(+) cation are evaluated by fitting the first ten vibrational levels, which are obtained by solving the rovibrational Schrödinger equation using Numerov's method. In addition, the spectroscopic parameters of 51 Ω bound states generated from these Λ-S bound states are also obtained. The spectroscopic parameters are compared with those reported in the literature. Excellent agreement with available measurements is found. It is expected that the spectroscopic parameters of Λ-S and Ω states reported here are reliable predicted ones.

Theoretical study on ten Λ–S states of [formula omitted] anion: Potential energy curves, spectroscopy and spin–orbit couplings

The potential energy curves (PECs) of seventeen Ω states generated from the ten Λ–S states of the Si2- anion are studied in detail using an ab initio quantum chemical method for the first time. The PECs are calculated for internuclear separations from 0.10 to 1.20nm 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 Breit–Pauli Hamiltonian. Core–valence correlation and scalar relativistic corrections are considered. Core–valence correlation corrections are included using an aug-cc-pCVTZ basis set. Scalar relativistic correction calculations are made with the third-order Douglas–Kroll Hamiltonian approximation at the level of a cc-pV5Z basis set. Obvious effect of core–valence correlation corrections on the PECs is observed, in particular for the two lowest 2Πu and 2Σg+ Λ–S states. All the PECs are extrapolated to the complete basis set limit. The lowest 2Πu Λ–S state is found to be the ground state of Si2- anion. The convergence observations of present calculations are made and the convergent behavior is discussed with respect to the basis set and level of theory. The effects of core-electron correlations on the energy splitting are studied by the all-electron aug-cc-pCVTZ basis set. Using these PECs, the spectroscopic parameters of Λ–S and Ω states involved are determined. The vibrational manifolds are evaluated for each Λ–S and Ω state of non-rotation Si2- anion. It shows that the spectroscopic parameters and molecular constants of ten Λ–S and seventeen Ω states reported here can be expected to be reliable predicted ones.

Gaussian basis sets of quadruple zeta quality for potassium through xenon: application in CCSD(T) atomic and molecular property calculations

All-electron segmented contracted quadruple zeta valence plus polarization function (QZP) basis sets for the elements from K to Xe were constructed to be used in conjunction with the non-relativistic and Douglas–Kroll–Hess (DKH) Hamiltonians. The QZP-DKH set is obtained from the original QZP basis set, that is, the values of the contraction coefficients were re-optimized using the relativistic DKH Hamiltonian. This extends earlier works on segmented contracted QZ basis set for atoms H–Ar. At the coupled-cluster level of theory, the convergence of atomic ionization energy as well as of molecular spectroscopic constants as a function of basis set size is examined. Additional improvements on spectroscopic constants were achieved by applying corrections due to core–valence correlation and spin–orbit effects. This leads to estimates for the spectroscopic constants of various diatomics in gaseous phase. One verifies that the experimental and benchmark theoretical bond lengths, atomization energies, and harmonic vibrational frequencies can be reproduced well with the QZP-DKH set.

Spectroscopic properties of AlC (X4∑-, B4∑-) molecule

The potential energy curves (PECs) of X4∑- and B4∑- states of the AlC molecule have been studied using highly accurate internally contracted multireference configuration interaction approach with the Davidson modification. The Dunning's correlation-consistent basis sets, aug-cc-pVnZ (n=D,T,Q,5,6) are used for the present study. To improve the quality of PECs, core-valence correlation and scalar relativistic corrections are considered. Core-valence correlation corrections are calculated with an aug-cc- pCVTZ basis set. Scalar relativistic correction calcualtions are made using the third-order Douglas-Kroll Hamiltonian approximation at the level of a cc-pV5Z basis set. Obvious effect on the PECs by the core-valence correlation and relativistic corrections has been observed. All the PECs are extrapolated to the complete basis set limit. The convergence observations of present calculations are made and the convergent behavior is discussed with respect to the basis set. Using these PECs, the spectroscopic parameters (TeReωeωexeωeyeBe and αe) of the X4∑- and B4∑- states are determined and compared with those reported in the literature. The vibration manifolds are evaluated for each state of non-rotation AlC molecule by numerically solving the radial Schrödinger equation of nuclear motion. For each vibrational state, the vibrational level and inertial rotation constants are obtained, which are in excellent accordance with the experimental findings.

A study on spectroscopic parameters of X2+, A2 and B2+ low-lying electronic states of SiN radical

The potential energy curves (PECs) of X2+, A2 and B2+ low-lying electronic states of SiN radical are investigated using the highly accurate valence internally contracted multireference configuration interaction (MRCI) approach combining the full valence complete active space self-consistent field method. In the present calculations, the basis sets used are correlation-consistent basis sets, aug-cc-pV6Z. The PECs determined by the MRCI calculations are corrected for size-extensivity errors by means of the Davidson modification (MRCI +Q). To obtain more reliable results, effects of the core-valence correlation and relativistic correction on the PECs are taken into account. The core-valence correlation correction is carried out with the cc-pCV5Z basis set The way to consider the relativistic correction is to use the second-order Douglas-Kroll Hamiltonian approximation, and the correction is performed at the level of cc-pV5Z basis set. With these PECs, the spectroscopic parameters are determined. A comparison with the experimental data shows that the present spectroscopic parameters are more accurate than the previous calculations.

Characterizing New Molecular Species: A Systematic Study of Stationary States on the Singlet [H, Se, Br] Potential Energy Surface

Structural characterization, infrared spectra, relative stability, dissociation energies and energy barrier for isomerization of new molecular species, HSeBr and HBrSe, were investigated at a high level of theory, CCSD(T)/CBS. HSeBr is predicted to be 44.95 kcal mol-1 more stable than HBrSe, with a barrier (ΔG#) for isomerization of 52.24 kcal mol-1. Due to the much smaller barrier for the reverse reaction, if formed, the less stable isomer is expected to be readily converted to HSeBr, except at cryogenic temperatures. The possibility of dissociation into atomic Se and HBr is also a likely one by a spin-orbit coupling mechanism. Heats of formation of SeBr and HSeBr were estimated to be 31.54 and 12.31 kcal mol-1, respectively, at 298.15 K. The effect of core-valence correlation on the structural parameters and harmonic frequencies was also evaluated, as well as the contribution of anharmonicity to the frequencies. Additional calculations performed with explicitly correlated wavefunctions showed promising results of fast convergence to the complete basis set (CBS) limit with relatively smaller basis sets.

CCSDTQ Optimized Geometry of Water Dimer.

The equilibrium geometry of the lowest energy structure of water dimer [(H2O)2] has been investigated using coupled cluster theory. A hierarchy of conventional coupled cluster methods is utilized up to singles doubles triples and quadruples excitations (CCSDTQ). The geometry of (H2O)2 is also optimized using the explicitly correlated coupled cluster singles doubles and perturbative triples [CCSD(T)-F12b] method. Overall, we find that the effect of including excitations beyond CCSD(T) is smaller than inclusion of core-valence correlation and comparable to scalar-relativistic and adiabatic effects.

Spin–orbit coupling effects in the ground state and four low-lying excited valence states a1Δ, B3Σ−, 13Δ and 13Σ+ of SeS molecule

The potential energy curves (PECs) of 10Ω states generated from the five Λ–S valence states of SeS molecule are investigated in detail using an ab initio quantum chemical method for the first time. All the PEC calculations are made by the complete active space self-consistent field method, which is followed by the internally contracted multireference configuration interaction (MRCI) approach with the Davidson modification (MRCI+Q). The spin–orbit coupling effect is included in the present study by the Breit–Pauli Hamiltonian with the aug-cc-pV5Z basis set. Convergent behavior is discussed and excellent convergence is observed with respect to the basis set and level of theory. To improve the quality of PECs, core-valence correlation and scalar relativistic corrections are included. Core-valence correlation corrections are taken into account 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-pVQZ basis set. The PECs of all the Λ–S and Ω states are extrapolated to the complete basis set limit by the total-energy extrapolation scheme so that the residual errors behind the basis sets can be minimized. With the PECs including all the corrections used here, the spectroscopic parameters of five Λ–S and 10Ω states are calculated, which agree well with the measurements. The spectroscopic parameters of five Ω states (13Δ3, 13Δ2, 13Δ1, 13Σ0++ and 13Σ1+) reported here for the first time can be expected to be reliable predicted ones.

An ab Initio Investigation of Fluorobromo Carbene

Fluorobromo carbene, an important halogenated carbene in the stratospheric ozone depletion, has long been received considerable interest. However, the energy, structure, and dynamics of even the lowest excited states have not been well understood. In this paper, we performed a detail ab initio study on CFBr using complete active space second-order perturbation (CASPT2) and multireference configuration interaction (MRCI) method. We investigated the effect of basis set on the CASPT2 results of the ground X(1)A' state and the first excited singlet A(1)A" state. The potential energy surface (PES) of the A(1)A" state along C-Br bond distance was carefully examined at CASPT2/cc-pV5Z level, by optimizing C-F bond and F-C-Br angle at every C-Br bond length in contrast to fix them at the equilibrium values. On the basis of the PES, a reliable barrier height of the A(1)A" state was obtained from CASPT2 and MRCI+Q calculations with different basis sets, considering the scalar relativistic effect, spin-orbit coupling, and core-valence correlation. Finally, we carried out the first theoretical study on higher excited state with energy up to 7 eV. The present calculated results were compared with previous experimental and theoretical results where available. Our results will add some understanding and shed more light on the structure and dynamics of electronic states of CFBr radical.

Accurate ab initio study on the A2Π, 14Σ+, 14Π, 24Π and 16Σ+ electronic states of AlO radical including spin–orbit coupling

The potential energy curves (PECs) of 15 Ω states generated from five Λ–S states (A2Π, 14Σ+, 14Π, 24Π and 16Σ+) of AlO radical are studied in detail using high level ab initio quantum chemical method for the first time. All 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 (MRCI+Q). The spin–orbit coupling effect is included by the Breit–Pauli Hamiltonian with the aug-cc-pCVTZ basis set. Convergent behavior is discussed and excellent convergence has been observed with respect to the basis sets and level of theory. To improve the quality of PECs, core–valence correlation and scalar relativistic corrections are taken into account. Core–valence correlation corrections are included employing a cc-pCVQZ 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 by the total-energy extrapolation scheme. With these PECs including all the corrections used here, on the one hand, the spectroscopic parameters of all the Λ–S and Ω states are calculated, which are in reasonable agreement with the experimental and other theoretical results; on the other hand, the vibrational levels and inertial rotation constants of X2Σ+, A2Π, B2Σ+ Λ–S states as well as A2Π3/2 and A2Π1/2 Ω states are determined, which also agree well with the measurements. The vibrational levels and inertial rotation constants of A2Π3/2 and A2Π1/2 Ω states as well as the spectroscopic parameters of four Λ–S states (14Σ+, 14Π, 24Π and 16Σ+) and their corresponding 13 Ω states can be expected to be reliable predicted ones.

Theoretical studies on the SiC radical: electronic structure, spectroscopy and spin-orbit couplings

The potential energy curves (PECs) of twenty-five Λ-S states and twenty Ω states generated from eight Λ-S states of the SiC radical are calculated by using an ab initio quantum chemical method. The PEC calculations are performed for internuclear separations from 0.10 to 1.00 nm using the complete active space self-consistent field method, which is followed by the internally contracted multireference configuration interaction (MRCI) approach in combination with a correlation-consistent aug-cc-pV6Z basis set. To improve the quality of the PECs, core-valence correlation and relativistic corrections are included. Core-valence correlations are included using a cc-pCVTZ basis set. Relativistic corrections are calculated using the third-order Douglas-Kroll Hamiltonian approximation at the level of cc-pV5Z basis set. The spin-orbit coupling effect is accounted for by the Breit-Pauli Hamiltonian in combination with the aug-cc-pVTZ basis set. To obtain more reliable results, the PECs determined by the MRCI calculations are corrected for size-extensivity errors by means of the Davidson modification. The PECs are extrapolated to the complete basis set (CBS) limit by the total-energy extrapolation scheme. The spectroscopic parameters are obtained by fitting the vibrational levels, which are calculated by solving the ro-vibrational Schrodinger equation using the Numerov’s method. The spectroscopic results are compared with those reported in the literature. Excellent agreement has been found between the present results and the measurements. The vibrational manifolds of the first 30 vibrational states are calculated for each electronic state of the non-rotating radical. Comparison with the measurements demonstrates that the present results are accurate. The spectroscopic parameters and the molecular constants reported here are expected to be reliable predicted results.

Spectroscopic Parameters of X3Σ−, a1Δ, and A′3Δ Electronic States of SO Radical

The potential energy curves (PECs) of three low-lying electronic states (X3Σ, a1Δ, and A′3Δ) of SO radical have been studied by ab initio quantum chemical method. The calculations were carried out with the full valence complete active space self-consistent field method followed by the highly accurate valence internally contracted multireference configuration interaction (MRCI) approach in combination with correlation-consistent basis sets. Effects of the core-valence correlation and relativistic corrections on the PECs are taken into account. The core-valence correlation correction is carried out with the cc-pCVDZ basis set. The way to consider the relativistic correction is to use the second-order Douglas-Kroll Hamiltonian approximation, and the correction is performed at the level of cc-pV5Z basis set. To obtain more reliable results, the PECs determined by the MRCI calculations are also corrected for size-extensivity errors by means of the Davidson modification (MRCI+Q). These PECs are extrapolated to the complete basis set limit by the two-point energy extrapolation scheme. With these PECs, the spectroscopic parameters are determined.

Ab initio MRSDCI study on the low-lying electronic states of the lithium chloride molecule (LiCl)

Potential energy curves (PECs) for the low-lying states of the lithium chloride molecule (LiCl) have been calculated using the internally contracted multireference single- and double-excitation configuration interaction (MRSDCI) method with the aug-cc-PVnZ (AVnZ) and aug-cc-PCVnZ (ACVnZ) basis sets, where n = T, Q, and 5. First, we calculate PECs for 7 spin-orbit (SO)-free Λ-S states, X(1)Σ(+), A(1)Σ(+), (3)Σ(+), (1)Π, and (3)Π, and then obtain PECs for 13 SO Ω states, X0(+), A0(+), B0(+), 0(-)(I), 0(-)(II), 1(I), 1(II), 1(III), and 2, by diagonalizing the matrix of the electronic Hamiltonian plus the Breit-Pauli SO Hamiltonian. The MRSDCI calculations not including core orbital correlation through the single and double excitations are also performed with the AV5Z and ACV5Z basis sets. The Davidson corrections (Q0) are added to both the Λ-S and Ω state energies. Vibrational eigenstates for the obtained X(1)Σ(+) and X0(+) PECs are calculated by solving the time-independent Schrödinger equation with the grid method. Thus, the effects of basis set, core orbital correlation, and the Davidson correction on the X(1)Σ(+) and X0(+) PECs of LiCl are investigated by comparing the spectroscopic constants calculated from the PECs with one another and with experiment. It is confirmed that to accurately predict the spectroscopic constants we need to include core-electron correlation in the CI expansion and use the basis sets designed to describe core-valence correlation, i.e., ACVnZ. The SO PECs presented in this paper will be of help in the future study of diatomic alkali halide dynamics.

On the accuracy of explicitly correlated coupled-cluster interaction energies — have orbital results been beaten yet?

The basis set convergence of weak interaction energies for dimers of noble gases helium through krypton is studied for six variants of the explicitly correlated, frozen geminal coupled-cluster singles, doubles, and noniterative triples [CCSD(T)-F12] approach: the CCSD(T)-F12a, CCSD(T)-F12b, and CCSD(T)(F12*) methods with scaled and unscaled triples. These dimers were chosen because CCSD(T) complete-basis-set (CBS) limit benchmarks are available for them to a particularly high precision. The dependence of interaction energies on the auxiliary basis sets has been investigated and it was found that the default resolution-of-identity sets cc-pVXZ/JKFIT are far from adequate in this case. Overall, employing the explicitly correlated approach clearly speeds up the basis set convergence of CCSD(T) interaction energies, however, quite surprisingly, the improvement is not as large as the one achieved by a simple addition of bond functions to the orbital basis set. Bond functions substantially improve the CCSD(T)-F12 interaction energies as well. For small and moderate bases with bond functions, the accuracy delivered by the CCSD(T)-F12 approach cannot be matched by conventional CCSD(T). However, the latter method in the largest available bases still delivers the CBS limit to a better precision than CCSD(T)-F12 in the largest bases available for that approach. Our calculations suggest that the primary reason for the limited accuracy of the large-basis CCSD(T)-F12 treatment are the approximations made at the CCSD-F12 level and the non-explicitly correlated treatment of triples. In contrast, the explicitly correlated second-order Mo̸ller-Plesset perturbation theory (MP2-F12) approach is able to pinpoint the complete-basis-set limit MP2 interaction energies of rare gas dimers to a better precision than conventional MP2. Finally, we report and analyze an unexpected failure of the CCSD(T)-F12 method to deliver the core-core and core-valence correlation corrections to interaction energies consistently and accurately.

Investigation of spectroscopic properties and spin-orbit splitting in the XΠ² and AΠ² electronic states of the SO ⁺cation.

The potential energy curves (PECs) of the X2Π and A2Π electronic states of the SO+ ion are calculated using the complete active space self-consistent field method, which is followed by the internally contracted multireference configuration interaction (MRCI) approach for internuclear separations from 0.08 to 1.06 nm. The spin-orbit coupling effect on the spectroscopic parameters is included using the Breit-Pauli operator. To improve the quality of PECs and spin-orbit coupling constant (A0), core-valence correlation and scalar relativistic corrections are included. To obtain more reliable results, the PECs obtained by the MRCI calculations are corrected for size-extensivity errors by means of the Davidson modification (MRCI+Q). At the MRCI+Q/aug-cc-pV5Z+CV+DK level, the A0 values of the SO+(X2Π1/2, 3/2) and SO+(A2Π1/2, 3/2) are 362.13 and 58.16 cm−1 when the aug-cc-pCVTZ basis set is used to calculate the spin-orbit coupling splitting, and the A0 of the SO+(X2Π1/2, 3/2) and SO+(A2Π1/2, 3/2) are 344.36 and 52.90 cm−1 when the aug-cc-pVTZ basis set is used to calculate the spin-orbit coupling splitting. The conclusion is drawn that the core-valence correlations correction makes the A0 slightly larger. The spectroscopic results are obtained and compared with those reported in the literature. Excellent agreement exists between the present results and the measurements. The vibrational manifolds are calculated, and those of the first 30 vibrational states are reported for the J = 0 case. Comparison with the measurements shows that the present vibrational manifolds are both reliable and accurate.

Spin-orbit splitting in the X2Π, a4Π, B2Π and H2Π electronic states of the NS radical

The potential energy curves (PECs) of ten Ω states (X2Π1 / 2,3 / 2, a4Π1 / 2,1 / 2,3 / 2,5 / 2, B2Π1 / 2,3 / 2 and H2Π1 / 2,3 / 2) generated from four Λ-S states (X2Π, a4Π, B2Π and H2Π) of the NS radical are studied in detail for the first time using an ab initio quantum chemical method. All the PEC calculations are performed for internuclear separations from 0.10 to 1.11 nm by the complete active space self-consistent field method followed by the internally contracted multireference configuration interaction approach with the Davidson modifications (MRCI + Q). The spin-orbit coupling (SO) effect is accounted for by the Breit- Pauli Hamiltonian. To discuss the effect on the energy splitting by the core-electron correlations, two all-electron basis sets, cc-pCVTZ and cc-pVTZ, are used for the SO coupling calculations. To improve the quality of the PECs, core-valence correlation and relativistic corrections are included. Core-valence correlation corrections are included with a cc-pCVTZ basis set. Relativistic correction calculations are carried out using the third-order Douglas-Kroll Hamiltonian approximation at the level of a cc-pV5Z basis set. The spectroscopic parameters of four Λ-S states and ten Ω states are calculated. Excellent agreement is found between the present results and the measurements. Using the PECs obtained by the MRCI + Q/AV5Z + CV + DK + SO calculations, the G(υ), Bυ and Dυ are calculated for each vibrational state of each Ω state, and those of the first 30 vibrational states are reported for the X2Π1 / 2, X2Π3 / 2, B2Π1 / 2 and B2Π3 / 2 states of the 14N32S radical. The spectroscopic parameters of four Ω states of the a4Π and the G(υ), Bυ and Dυ of the X2Π1 / 2, X2Π3 / 2, B2Π1 / 2 and B2Π3 / 2 states reported here are expected to be reliable predicted results.

MRCI study on electronic spectrum of 13 electronic states of SiP molecule

The potential energy curves (PECs) of the X2Π, A2Σ+, a4Σ+, B2Π, c4Δ, C2Σ+, d4Σ−, D2Φ, E2Σ−, G2Δ, H2Π, I2Σ+ and f4Δ electronic states of the SiP molecule are calculated employing an ab initio quantum chemical method. The PEC calculations are performed for internuclear separations from 0.10 to 1.10nm using the complete active space self-consistent field (CASSCF) method, which is followed by the internally contracted multireference configuration interaction (MRCI) approach in combination with a correlation-consistent aug-cc-pV6Z basis set. To improve the quality of the PECs, core-valence correlation and scalar relativistic corrections are included. Scalar relativistic correction calculations are carried out using the third-order Douglas-Kroll Hamiltonian approximation at the level of a cc-pV5Z basis set. Core-valence correlation corrections are included using a cc-pCVQZ basis set. The PECs obtained by the MRCI calculations are corrected for size-extensivity errors by means of the Davidson modification. The PECs are extrapolated to the complete basis set limit. The spectroscopic parameters are obtained by fitting the vibrational levels, which are calculated by solving the ro-vibrational Schrödinger equation. The spectroscopic results are compared in detail with those reported in previous literature. Excellent agreement is found between the present spectroscopic results and the experimental ones. Using the Breit-Pauli operator, the spin–orbit (SO) coupling effect on the spectroscopic parameters is included in the X2Π, D2Φ and H2Π electronic states at the level of a cc-pCVTZ basis set. The energy separation of the X2Π and A2Σ+ electronic states is accurately determined by including the Davidson modification, SO coupling and core-valence correlation and scalar relativistic corrections. Using the PECs determined by the MRCI+Q/CV+DK+56 calculations, the G(υ), Bυ and Dυ are calculated for each vibrational state of each electronic state, and those of the first 20 vibrational states are reported for each electronic state of the non-rotation 29Si31P molecule. Comparison with the measurements demonstrates that the present results are accurate. The spectroscopic parameters of the a4Σ+, B2Π, c4Δ, d4Σ−, D2Φ, E2Σ−, G2Δ, H2Π, I2Σ+ and f4Δ electronic states and the G(υ), Bυ and Dυ of all the electronic states obtained here are expected to be reliable predicted results.

Relativistic segmented contraction basis sets with core-valence correlation effects for atoms 57La through 71Lu: Sapporo-DK-nZP sets (n = D, T, Q)

For the 15 lanthanide atoms 57La through 71Lu, we report Sapporo-DK-nZP sets (n = D, T, Q), which are natural extensions of the Sapporo-(DK)-nZP sets for lighter atoms and efficiently incorporate the correlation among electrons in the N through P shells as well as the relativistic effect. The present sets well describe the correlation among the 4s and 4p electrons, which are important in the excitation of 4f electrons. Atomic test calculations of 57La, 58Ce, 59Pr, and 60Nd at configuration interaction with the Davidson correction level of theory confirm high performance of the present basis sets. Molecular test calculations are carried out for 57LaF and 70YbF diatomics at the coupled-cluster level of theory. The calculated spectroscopic constants approach smoothly to the experimental values as the quality of the basis set increases.

Extensive ab initio study of the electronic states of CP radical including spin–orbit coupling

The potential energy curves (PECs) of 18 Λ–S states and 13 Ω states generated from six Λ–S states of the CP radical are studied in detail using an ab initio quantum chemical method. All the PEC calculations are performed for internuclear separations from 0.10 to 1.11nm 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 (SO) coupling effect is accounted for by the Breit-Pauli Hamiltonian. To discuss the effect on the energy splitting by the core-electron correlations, two all-electron basis sets, cc-pCVTZ and cc-pVTZ, are used for the SO coupling calculations. In order to improve the quality of the PECs, core–valence correlation and scalar relativistic corrections are included. Core–valence correlation corrections are taken into account with a cc-pCVTZ basis set. Scalar relativistic correction calculations are carried out using the third-order Douglas-Kroll Hamiltonian approximation at the level of a cc-pV5Z basis set. The spectroscopic parameters of 17 Λ–S bound states and 13 Ω states are calculated. When the core-electron correlations are used to calculate the SO coupling splitting by the all-electron cc-pCVTZ basis set and when the core–valence correlation and scalar relativistic corrections are included in the PECs, the SO coupling splitting energy between the A2Π3/2 and A2Π1/2 Ω states is 153.63cm−1, which agree well with the measurements of 157.87cm−1. Moreover, other spectroscopic parameters are also in excellent agreement with the available experimental ones. It demonstrates that the spectroscopic parameters of 14Σ+, 14Δ, 14Π, 22Π, 16Σ+, 14Σ−, 32Π, 12Δ, 12Σ−, 22Δ, 22Σ−, 24Δ, 24Σ− and 26Σ+ Λ–S states and 13 Ω states reported here can be expected to be reliable predicted ones.

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.