Zunlue Zhu

MRCI study on spectroscopic and molecular properties of B1Δg, , C1Πg, , and 11Δu electronic states of the C2 radical

The potential energy curves (PECs) of six electronic states (B1Δg, , C1Πg, , and 11Δu) of the C2 radical have been investigated using the full valence complete active space self-consistent field (CASSCF) method followed by the highly accurate valence internally contracted multireference configuration interaction (MRCI) approach in conjunction with the correlation-consistent aug-cc-pV6Z basis set for internuclear separations from 0.05 to 2.0 nm. The effects on the spectroscopic parameters (Te , D 0, De , Re , ωe , ωexe , ωeye , αe , βe , γe and Be ) of the core–valence correlation and relativistic corrections are taken into account. The way to consider the relativistic corrections is to employ the second-order Douglas–Kroll Hamiltonian approximation. The core–valence correlation correction is performed at the cc-pCV5Z basis set. And the relativistic correction is carried out at the level of the cc-pV5Z basis set. In order to obtain reliable PECs, the Davidson modification is also included in the study. These spectroscopic parameters have been compared in detail with those of previous investigations reported in the literature, and excellent agreement has been found between the present results and the available experimental data. The first 20 vibrational states are computed for all these electronic states when the rotational quantum number J equals zero, and the vibrational levels, inertial rotation and centrifugal distortion constants of the B1Δg and electronic states are reported when J = 0, which are in excellent agreement with the available measurements. Comparison with the available experimental data shows that the present molecular constants are both reliable and accurate.

MRCI study of spectroscopic and molecular properties of X2Πg, a 4Πu, A2Πu, b 4 , D2Δg and B2 electronic states of ion

The potential energy curves (PECs) of six low-lying electronic states (X2Πg, a 4Πu, A2Πu, b 4 , D2Δg and B2 ) of ion were studied by the ab initio quantum chemical method. The calculations were carried out with the full valence complete active space self-consistent field (CASSCF) method followed by the highly accurate valence internally contracted multireference configuration interaction (MRCI) approach in combination with large correlation-consistent basis sets. Effects on the PECs of the core–valence correlation and relativistic corrections are taken into account. The way to consider the relativistic correction is to use the second-order Douglas–Kroll Hamiltonian (DKH2) approximation. The core–valence correlation correction is carried out with the cc-pCVQZ basis set, and the relativistic correction is performed at the level of cc-pVQZ 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 (CBS) limit by the two-point total-energy extrapolation scheme. With these PECs, the spectroscopic parameters (Te , De , D 0, Re , ωe , ωexe , αe and Be ) are determined and compared with those reported in the literature. The conclusion can be reached that the effect on the spectroscopic parameters of the core–valence correlation correction is larger than that of the relativistic correction. With the PECs obtained by the MRCI + Q/CV+DK+56 calculations, the vibrational levels and inertial rotation constants of the first 26 vibrational states are determined for these electronic states of non-rotating ion. Comparison with the experimental data shows that the present spectroscopic parameters and molecular constants are accurate.

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 Numerovs 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.

Accurate theoretical spectroscopic investigations of the 20 Λ-S and 58 Ω states of O2+ cation including the spin–orbit coupling effect

The potential energy curves (PECs) are calculated for the 20 Λ-S states (X2Πg, A2Πu, B2Σ−g, a4Πu, b4Σ−g, b′4Πg, c4Σ−u, 12Σ+g, 12Σ+u, 12Σ−u, 14Σ+g, 14Σ+u, 14Δg, 14Δu, 16Σ+g, 16Σ+u, 16Πg, 16Πu, 24Πg and 24Πu) of O2+ cation and their corresponding 58 Ω states. Of these 20 Λ-S states, the 16Πu state is found to be repulsive. The 12Σ+g, 14Σ+u, c4Σ−u and 14Δu states are found to possess the double well. The b4Σ−g, 16Σ+g, 14Σ+u, a4Πu, A2Πu, 16Πg and 24Πg states are found to be inverted with the spin–orbit coupling effect included. The b′4Πg, 16Πg, 16Σ+g, 14Σ+u and 14Δu states, and the second well of the 12Σ+g state are found to be the weakly bound states. The b′4Πg state is found to possess one well with one barrier. 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 aug-cc-pV6Z basis set. The core–valence correlation and scalar relativistic corrections are included. The convergent behaviour of present calculations is discussed with respect to the basis set and theoretical level. The spin–orbit coupling effect is accounted for. The PECs are extrapolated to the complete basis set limit. The spectroscopic parameters are evaluated, and compared with available measurements. It demonstrates that the spectroscopic parameters reported here can be expected to be reliably predicted ones.

Geometric shielding correction approach for total cross sections of electron scattering by C6H6, C6F6, C6H12, C6H14, C6F14, C8H16, C8H18 and C8F18 at 30-5000 eV

Taking into consideration the contributions of the geometric shielding effect in the molecule, an empirical fraction, which depends on the energy of the incident electrons, the targets molecular dimension and the atomic and electronic numbers in the molecule, is presented. Using this empirical fraction, a new formulation of the additivity rule is proposed. The total cross sections for electron scattering by eight larger polyatomic molecules (C6H6, C6F6, C6H12, C6H14, C8H16, C8H18, C6F14 and C8F18) are calculated using the new additivity rule at the Hartree–Fock level for impact energies ranging from 30 to 5000 eV. The quantitative total cross sections are compared with those obtained by experiments and other theories, and good agreement is attained above 100 eV or so. The new results for C6F14 and C8F18 are also presented although no experimental and theoretical data are available for comparison in the present energy region. In these calculations, the atoms are represented by the spherical complex optical potential, which is composed of static, exchange, polarization and absorption terms.

Accurate predictions of spectroscopic and molecular properties of 27 Λ-S and 73 Ω states of AsS radical

The PECs are calculated for the 27 Λ-S states and their corresponding 73 Ω states of AsS radical. Of these Λ-S states, only the 2(2)Δ and 5(4)Π states are replulsive. The 1(2)Σ(+), 2(2)Σ(+), 4(2)Π, 3(4)Δ, 3(4)Σ(+), and 4(4)Π states possess double wells. The 3(2)Σ(+) state possesses three wells. The A(2)Π, 3(2)Π, 1(2)Φ, 2(4)Π, 3(4)Π, 2(4)Δ, 3(4)Δ, 1(6)Σ(+), and 1(6)Π states are inverted with the SO coupling effect included. The 1(4)Σ(+), 2(4)Σ(+), 2(4)Σ(-), 2(4)Δ, 1(4)Φ, 1(6)Σ(+), and 1(6)Π states, the second wells of 1(2)Σ(+), 3(4)Σ(+), 4(2)Π, 4(4)Π, and 3(4)Δ states, and the third well of 3(2)Σ(+) state are very weakly-bound states. The PECs are extrapolated to the CBS limit. The effect of SO coupling on the PECs is discussed. The spectroscopic parameters are evaluated, and compared with available measurements and other theoretical ones. The vibrational properties of several weakly-bound states are determined. The spectroscopic properties reported here can be expected to be reliably 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.

Calculations of 21 Λ-S and 42 Ω states of BC molecule: Potential energy curves, spectroscopic parameters and spin-orbit coupling effect

The potential energy curves (PECs) were calculated for the 42 Ω states generated from the 21 Λ-S states (X(4)Σ(-), A(4)Π, B(4)Σ(-), a(2)Π, b(2)Σ(-), c(2)Δ, d(2)Σ(+), e(2)Π, 3(2)Π, 4(2)Π, 5(2)Π, 2(2)Σ(-), 3(2)Σ(-), 2(2)Σ(+), 3(2)Σ(+), 2(2)Δ, 3(2)Δ, 1(4)Σ(+), 2(4)Π, 1(4)Δ and 1(2)Φ), which originated from the lowest two dissociation channels, B((2)Pu)+C((3)Pg) and B((2)Pu)+C((1)Dg), of the BC molecule. The PECs were calculated for internuclear separations from 0.08 to 1.10 nm using the CASSCF method, which was followed by the icMRCI approach with the aug-cc-pV6Z basis set. Of these 21 Λ-S states, the e(2)Π, 2(2)Δ, 2(2)Σ(-), 4(2)Π, 1(2)Φ and 3(2)Δ possess the double wells. The A(4)Π, a(2)Π, c(2)Δ, 2(4)Π, 4(2)Π, 5(2)Π, 1(4)Δ and 1(2)Φ states are inverted with the spin-orbit coupling (SOC) effect taken into account. The first well of e(2)Π state and the second well of 4(2)Π and 2(2)Δ states do not have any vibrational states whether with or without the SOC effect included. All the Λ-S and Ω states involved in this paper are bound states. Scalar relativistic correction was included by the third-order Douglas-Kroll Hamiltonian approximation at the level of an aug-cc-pV5Z basis set. Core-valence correlation correction was included at the level of an aug-cc-pCV5Z basis set. The SOC effect was accounted for by the state interaction method with the Breit-Pauli Hamiltonian and the all-electron cc-pCV5Z basis set. The PECs of all the states were extrapolated to the complete basis set limit. The spectroscopic parameters were obtained. The vibrational properties of several Λ-S and Ω states with the relatively shallow wells were evaluated. The SOC effect on the spectroscopic parameters is not obvious for almost all the states. The spectroscopic properties reported in this paper can be expected to be reliably predicted ones.

MRCI study on the spectroscopic parameters and molecular constants of the X1Σ+, a3Σ+, A1Π and C1Σ− electronic states of the SiO molecule

The potential energy curves (PECs) of the X(1)Σ(+), a(3)Σ(+), A(1)Π and C(1)Σ(-) electronic states of the SiO molecule are studied using an ab initio quantum chemical method. The calculations have been made employing the complete active space self-consistent field (CASSCF) method, which is followed by the valence internally contracted multireference configuration interaction (MRCI) approach in combination with several correlation-consistent basis sets. The effect on the PECs by the core-valence correlation and relativistic corrections is included. The way to consider the relativistic correction is to use the third-order Douglas-Kroll Hamiltonian approximation. The core-valence correlation correction is carried out with the cc-pCVQZ basis set, and the relativistic correction is performed at the level of the cc-pVQZ 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). The PECs of these electronic states are extrapolated to the complete basis set limit by the total-energy extrapolation scheme. Employing these PECs, the spectroscopic parameters are calculated and compared with those reported in the literature. With these PECs determined by the MRCI+Q/CV+DK+56 calculations, by solving the radial Schrödinger equation of nuclear motion, 110 vibrational states for the X(1)Σ(+), 69 for the a(3)Σ(+), 54 for the A(1)Π and 67 for the C(1)Σ(-) electronic state are predicted when the rotational quantum number J equals zero. The vibrational manifolds of the first 20 vibrational states are reported and compared with the available RKR data for each electronic state. On the whole, as expected, the most accurate spectroscopic parameters and molecular constants of the SiO molecule are obtained by the MRCI+Q/CV+DK+56 calculations. And the present molecular constants of the a(3)Σ(+), C(1)Σ(-) and A(1)Π electronic states determined by the MRCI+Q/CV+DK+56 calculations should be good prediction for future laboratory experiment.

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, 1(4)Σ+, 1(4)Π, 2(4)Π and 1(6)Σ+) 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 A(2)Π3/2 and A2Π1/2 Ω states as well as the spectroscopic parameters of four Λ-S states (1(4)Σ+, 1(4)Π, 2(4)Π and 1(6)Σ+) and their corresponding 13 Ω states can be expected to be reliable predicted ones.