Breit-Pauli Hamiltonian Research Articles

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.

Ab initio calculation on the low-lying excited states of [formula omitted] cation including spin–orbit coupling

Ab initio all-electron relativistic calculations of the low-lying excited states of Si2+ have been performed at MRCI+Q/AVQZ level. The calculated electronic states, including 12 doublet and 12 quartet Λ–S states, are correlated to the dissociation limit of Si(3Pg)+Si+(2Pu). Spin–orbit interaction is taken into account via the state interaction approach with the full Breit-Pauli Hamiltonian, which causes the entire 24 Λ–S states to split into 54Ω states. This is the first time that spin–orbit coupling (SOC) calculation has been performed on Si2+. The obtained potential energy curves (PECs) of Λ–S and Ω states are respectively depicted with the aid of the avoided crossing rule between the same symmetry. The spectroscopic constants of the bound Λ–S and Ω states are determined, and excellent agreements with the latest theoretical results are achieved.

Configuration interaction investigation including spin–orbit coupling effect for electronic states of IBr and its cation

Iodine monobromide (IBr) and its cation (IBr+), which play an important role in the stratospheric ozone depletion, have received much attention. However, the electronic states of IBr/IBr+ have not been well understood. In this paper, the potential energy curves (PECs) of low-lying electronic states for IBr/IBr+ were computed with high-level multireference configuration interaction (MRCI) method. The spin–orbit coupling effect was taken into account via the state interaction method with the full Breit–Pauli Hamiltonian. For IBr, the PECs of 12 Λ–S states correlated with the lowest dissociation limit of IBr molecule and 23Ω states generated from those Λ–S states were calculated. The spectroscopic constants of the bound states were obtained, which are consistent with previous experimental results. The two avoided crossing points between (2)0+/(3)0+ and (3)0+/(4)0+ were interpreted by analysis of Λ–S compositions of Ω states at various bond lengths. Based on potential energy curves and transition dipole moments, the radiative lifetime of 13Π1 was evaluated. For IBr+, the PECs of 12 Λ–S states and 4 low-lying Ω states were calculated, from which the spectroscopic constants were evaluated. Finally, the ionization energies from the neutral ground state (X1Σ+) to different ionic states (X2Π3/2, X2Π1/2, A2Π3/2 and A2Π1/2) were obtained.

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.

Energy levels, oscillator strengths, and radiative rates for Si-like Zn XVII, Ga XVIII, Ge XIX, and As XX

The energy levels, oscillator strengths, line strengths, and transition probabilities for transitions among the terms belonging to the 3s23p2, 3s3p3, 3s23p3d, 3s23p4s, 3s23p4p and 3s23p4d configurations of silicon-like ions (Zn XVII, Ga XVIII, Ge XIX, and As XX) have been calculated using the configuration-interaction code CIV3. The calculations have been carried out in the intermediate coupling scheme using the Breit–Pauli Hamiltonian. The present calculations have been compared with the available experimental data and other theoretical calculations. Most of our calculations of energy levels and oscillator strengths (in length form) show good agreement with both experimental and theoretical data. Lifetimes of the excited levels have also been calculated.

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.

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.

A four-component quadratic vibronic coupling approach to the Renner–Teller effect in linear triatomic molecules. The , manifold of BrCN+ and ClCN+

In this work, we present the four-component quadratic vibronic coupling model for the description of the Renner–Teller effect (RTE) in the presence of the spin–orbit coupling. The interaction of the two potential energy surfaces emerging from the cationic 2Π states of singly ionized linear triatomic molecules is described by the quadratic coupling constant c for the genuine RT repulsion and the second parameter, d, for a nonconstant spin–orbit coupling varying with the bond angle of the triatomic. The emergence of a linear RT constant in the presence of the spin–orbit operator was originally shown by Poluyanov and Domcke (2004 Chem. Phys. 301 111–27) and is based on the application of the Breit–Pauli Hamiltonian in combination with nonrelativistic wavefunctions. In contrast to this methodology, we generate the diabatic RT Hamiltonian in a 4-spinor basis where the symmetry transformation properties of the electronic and vibrational wavefunctions completely determine the RT matrix structure. Explicit access to highly correlated wavefunctions is not required in our approach. In addition, the four-component vibronic coupling model takes into account the full spatial orbital relaxation upon the inclusion of the spin–orbit coupling and is therefore well suited for heavy systems. The third parameter, p, accounting for a possible pseudo-Jahn–Teller interaction is not considered here, but it does not introduce a principal difficulty. As the initial systems for this study, we considered the BrCN+ and ClCN+ cations and determined the c and d parameters by a numerical fit to accurate adiabatic potential energy surfaces obtained by the relativistic Fock-space coupled-cluster method. New values for the computed linear RT parameter d amount to 14.7 ± 0.5 cm−1 for ClCN+ and 73.2 ± 0.7 cm−1 for BrCN+.

Energy Levels and the Landé -Factors for Singly Ionized Lanthanum

We have calculated the energies and the Landé -factors for 5d2, 5d6s, 6s2, 4f6p, 5d7s, 5d6d, 4f2, 6p2, 6s6d, 6s7s, 4f6s, 4f5d, 5d6p, 6s6p, 4f7s, 4f6d, 5d7p, and 6s7p excited levels of singly ionized lanthanum (La II). These calculations have been carried out by using the multiconfiguration Hartree-Fock method within the framework of the Breit-Pauli Hamiltonian (MCHF+BP) and the relativistic Hartree-Fock (HFR) method. The obtained results have been compared with other works available in the literature. A discussion of these calculations for La II in this study has also been in view of the MCHF+BP and HFR methods.

Communication: An efficient algorithm for evaluating the Breit and spin–spin coupling integrals

We present an efficient algorithm for evaluating a class of two-electron integrals of the form r12⊗r12/r12(n) over one-electron Gaussian basis functions. The full Breit interaction in four-component relativistic theories beyond the Gaunt term is such an operator with n = 3. Another example is the direct spin-spin coupling term in the quasi-relativistic Breit-Pauli Hamiltonian (n = 5). These integrals have been conventionally evaluated by expensive derivative techniques. Our algorithm is based on tailored Gaussian quadrature, similar to the Rys quadrature for electron repulsion integrals (ERIs), and can utilize the so-called horizontal recurrence relation to reduce the computational cost. The CPU time for computing all six Cartesian components of the Breit or spin-spin coupling integrals is found to be only 3 to 4 times that of the ERI evaluation.

Ab Initio MRCI+Q Study on Low-Lying States of CS Including Spin–Orbit Coupling

Carbon monosulfide (CS), which plays an important role in a variety of research fields, has long received considerable interest. Due to its transient nature and large state density, the electronic states of CS have not been well understood, especially the interactions between different states. In this paper, we performed a detail ab initio study on the low-lying electronic states of CS by means of the internally contracted multireference configuration interaction method (including Davidson correction) with scalar relativistic correction using the Douglas-Kroll-Hess Hamiltonian. We focused on the spin-orbit coupling of the states via the state interaction method with the full Breit-Pauli Hamiltonian. The potential energy curves (PECs) of 18 Λ-S states correlated with the lowest dissociation limit of the CS molecule were calculated, as well as those of 50 Ω states generated from the Λ-S states. The spectroscopic constants of the bound states were obtained, which are in good agreement with previous available experimental and theoretical results. The state perturbations of the a(3)Π and A(1)Π states with other low-lying electronic states are discussed in detail, based on the calculated spin-orbit matrix as well as the PECs of the Ω states. Avoided crossing in the states of CS was indicated when spin-orbit coupling was taken into account. Finally, the allowed transition dipole moments as well as the lifetimes of the five lowest vibrational states of the A(1)Π1, A'(1)Σ(+)0(+) and a(3)Πi states were obtained.

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.

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.

Electron impact excitation for Ar VI

Radiative atomic and electron impact excitation data for Ar VI ion have been calculated using the AUTOSTRUCTURE code. The two-body non-fine structure operators of the Breit-Pauli Hamiltonian have been incorporated in AUTOSTRUCTURE, and for the collisional problem, we use the distorted wave approximation. We compare our radiative atomic results with the few available ones. To our best knowledge, there are no distorted wave collision strengths for Ar VI. Some discrepancies have been reported between our oscillator strengths and the only calculated ones using the MCHF method. We perform the same calculations with the UCL codes SST/DW/JAJOM and we compare with the present AUTOSTRUCTURE results.

Radiative lifetimes of spin forbidden a1Δ → X 3Σ− and spin allowed A3Π → X 3Σ− transitions and complete basis set extrapolated ab initio potential energy curves for the ground and excited states of CH−

The spin forbidden transition a(1)Δ → X(3)Σ(-) in CH(-) has been studied using the Breit-Pauli Hamiltonian for a large number of geometries. This transition acquires intensity through spin-orbit coupling with singlet and triplet Π states. The transition moment matrix including more than one singlet and triplet Π states was calculated at the multi-reference configuration interaction/aug-cc-pV6Z level of theory. The computed radiative lifetime of 5.63 s is in good agreement with the experimental (5.9 s) and other theoretical (6.14 s) results. Transition moment values of the spin allowed A(3)Π → X(3)Σ(-) transition have also been calculated at the same level of theory. Calculations show that the corresponding radiative lifetime is considerably low, 2.4 × 10(-7) s. Complete basis set extrapolated potential energy curves for the ground state of CH and the ground state and six low lying excited states (a(1)Δ, b(1)Σ(+), two (3)Π, and two (1)Π) of CH(-) are reported. These curves are then used to calculate the vibrational bound states for CH and CH(-). The computed electron affinity of CH supports the electron affinity bounds reported by Okumura et al. [J. Chem. Phys. 85, 1971 (1986)].

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.

Energetics and Mechanism of the Hydrogenation of XHn for Group IV to Group VII Elements X.

High-level ab initio calculations of the NESC/SOC/CCSD(T)/cc-pV5Z type (NESC, Normalized Elimination of the Small Component; SOC, spin-orbit coupling corrections using the Breit-Pauli Hamiltonian) are employed to determine the energetics of the 18 hydrogenation reactions XHn + H2 → XHn+1 + H with X = F, Cl, Br, I, O, S, Se, Te, N, P, As, Sb, Bi, C, Si, Ge, Sn, and Pb. Accurate reaction and activation enthalpies as well as the corresponding free energies are obtained by calculating vibrational, thermochemical, and entropy corrections with a cc-pVTZ basis set. Also calculated are accurate X-H bond dissociation enthalpies at 298 K. The reaction mechanism of all 18 reactions is analyzed using the unified reaction valley approach (URVA) and UMP2/6-31G(d,p) to determine each reaction valley with high accuracy (step size 0.005 to 0.03 amu(1/2) bohr). By analyzing the reaction path curvature, the mechanism can be partitioned into four to six reaction phases, in which the reaction complex XHn···H2 undergoes specific chemical transformations. The fate of the reaction complex is determined at an early stage in the entrance channel. Curvature peaks reflect the strength of the bonds being broken or formed and provide the basis for a quantitative justification of the Hammond-Leffler postulate.

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.