Spin-orbit Coupling Integrals Research Articles

MRCI+Q study on the electronic structure and spectroscopy of the low-lying electronic states of HgBr including spin-orbit coupling

Due to attractive candidate for the laser application and searching for the permanent electric dipole moment of the electron (eEDM), mercury bromide (HgBr) is of much interest to researchers. However, detailed information of the electronic structure of HgBr is still lacking, especially for spin-orbit interactions in excited states. In this work, high-level configuration interaction calculations of low-lying states correlating to the lowest two dissociation limits Hg(1S) + Br(2P) and Hg(3P) + Br(2P) of HgBr are carried out. In order to ensure good accuracy, the Davidson correction and spin-orbit coupling (SOC) effect are all taken into consideration in our computations. The potential energy curves (PECs) of 14 Λ-S states and 30 Ω states are determined. Based on the PECs, the spectroscopic constants of the bound states are obtained, most of which have not been reported in previous studies. The calculated SOC integrals of 22Σ+-22Π indicate a strong spin-orbit interaction, which can explain the apparent perturbations between B2Σ+1/2 and C2Π1/2 found in the HgBr fluorescence excitation spectrum. Finally, to reveal more detail on transition properties of excited states, transition dipole moments of C2Π1/2-X2Σ+1/2, D2Π3/2-X2Σ+1/2, and B2Σ+1/2-X2Σ+1/2 transitions and radiative lifetimes of C2Π1/2, D2Π3/2, and B2Σ+1/2 are determined.

Transition properties between low-lying electronic states of SiO+

In this work, we investigate the potential energy curves (PECs), transition dipole moments (TDMs) and spin-orbit couplings for low-lying electronic states of SiO+ based on ab initio calculations. The PECs of seventeen low-lying electronic states are calculated by the internally contracted multireference configuration interaction (icMRCI) method with the Davidson correction, as well as the basis set extrapolation, core-valence (CV) correction and scalar relativistic correction. The Schrödinger equation of nuclear movement is solved over the PEC to obtain the rotational and vibrational energy levels, which are used to fit the spectroscopic parameters. The Einstein coefficients, Franck-Condon factors and oscillator strengths for dipole-allowed transitions are calculated with the PECs and TDMs. The radiative lifetimes of some excited states are also obtained. Our calculated radiative lifetime of 67.8 ns for B2Σ+(υ′ = 0) is in excellent agreement with the recent experimental measurement of 66 ± 2 ns. The spin-orbit coupling integrals related to the X2Σ+, A2Π, B2Σ+, 14Σ+, 14Π and 14Σ− states are calculated using the Breit-Pauli Hamiltonian. In addition, the effects of spin-orbit couplings on the potential energies of the Λ-S electronic states are discussed.

Spectroscopic investigations of transition properties for the electronic states of PN+ correlating to two lowest dissociation limits

The PN+ cation is regarded as a candidate of ions which may exist in the interstellar medium. Accurate transition properties are desired to identify the spectra from astronomical observation. However, transition data of PN+ are relatively limited. In this work, the state-of-the-art ab initio calculations are carried out to investigate the low-lying electronic states of PN+ correlating to two lowest dissociation limits, its transition properties and its spin-orbit couplings. For the X2Σ+ and A2Π states, the calculated spectroscopic constants agree well with previous experimental data. For the other electronic states, the accuracy of the spectroscopic parameters is also ensured by comparing with previous theoretical results. Then, transition probabilities of dipole allowed transition systems are calculated. The radiative lifetimes of vibrational levels for the A2Π, 14Π, 14Δ, 14Σ−, and 24Π states are also evaluated. Such transition data can be used in the identification of PN+ in the laboratory or the interstellar space. Finally, the predissociation of 14Σ− (υ' = 1)→16Σ+, 14Σ− (υ' = 15)→16Π and 14Δ (υ'= 19)→16Π are analyzed with the help of spin-orbit coupling integrals.

A full-pivoting algorithm for the Cholesky decomposition of two-electron repulsion and spin-orbit coupling integrals.

A significant reduction in the computational effort for the evaluation of the electronic repulsion integrals (ERI) in ab initio quantum chemistry calculations is obtained by using Cholesky decomposition (CD), a numerical procedure that can remove the zero or small eigenvalues of the ERI positive (semi)definite matrix, while avoiding the calculation of the entire matrix. Conversely, due to its antisymmetric character, CD cannot be directly applied to the matrix representation of the spatial part of the two-electron spin-orbit coupling (2e-SOC) integrals. Here, we present a computational strategy to achieve a Cholesky representation of the spatial part of the 2e-SOC integrals, and propose a new efficient CD algorithm for both ERI and 2e-SOC integrals. The proposed algorithm differs from previous CD implementations by the extensive use of a full-pivoting design, which allows a univocal definition of the Cholesky basis, once the CD δ threshold is made explicit. We show that 2δ is the upper limit for the errors affecting the reconstructed 2e-SOC integrals. The proposed strategy was implemented in the ab initio program Computational Emulator of Rare Earth Systems (CERES), and tested for computational performance on both the ERI and 2e-SOC integrals evaluation. © 2017 Wiley Periodicals, Inc.

Configuration interaction study of electronic structures of CdCl including spin-orbit coupling

Adiabatic potential energy curves (PECs) and the dipole moments (DMs) for the 14 low-lying Λ-S states of CdCl were computed at configuration interaction method including Davidson correction (+Q). To quantitatively evaluate the spin-orbit coupling (SOC) effect, the SOC integrals involving the X2Σ+ and 22Σ+ were investigated. The spectroscopic constants of 9 bound Λ-S states and 4 lowest bound Ω states were derived. Moreover, the radiative lifetimes of the vibrational levels of bound states were predicted for the first time. Finally, the feasibility and challenges of laser cooling of CdCl were discussed based on a three-laser cooling scheme.

Enhanced spin-orbit coupling driven by state mixing in organic molecules for OLED applications

We investigate the energy gap variation as well as spin-orbit coupling (SOC) integrals between various low-lying singlet and triplet excited states for a series of fluorescein derivatives. We find that when the electron-donating property of the substituent group on the benzene moiety of fluorescein is gradually increased, the charge transfer states are lowered in energy and a mixing with nearby ππ* or nπ* states occurs, which causes a twisting in the p orbital on the carbonyl group and a non-zero SOC integral between the originally non-coupled 1ππ* and 3ππ* states. We also find an enhancement of about 3–4 times in the SOC integrals upon sulfur substitution for the oxygen in the carbonyl groups, and that with substantial energy lowering in ππ* and especially in nπ* states, the SOC between the S1 state with energetically close triplet states is also increased significantly, signifying the possibility of enhanced phosphorescence or thermally-delayed fluorescence emission.

Perturbative treatment of spin-orbit coupling within spin-free exact two-component theory.

This work deals with the perturbative treatment of spin-orbit-coupling (SOC) effects within the spin-free exact two-component theory in its one-electron variant (SFX2C-1e). We investigate two schemes for constructing the SFX2C-1e SOC matrix: the SFX2C-1e+SOC [der] scheme defines the SOC matrix elements based on SFX2C-1e analytic-derivative theory, hereby treating the SOC integrals as the perturbation; the SFX2C-1e+SOC [fd] scheme takes the difference between the X2C-1e and SFX2C-1e Hamiltonian matrices as the SOC perturbation. Furthermore, a mean-field approach in the SFX2C-1e framework is formulated and implemented to efficiently include two-electron SOC effects. Systematic approximations to the two-electron SOC integrals are also proposed and carefully assessed. Based on benchmark calculations of the second-order SOC corrections to the energies and electrical properties for a set of diatomic molecules, we show that the SFX2C-1e+SOC [der] scheme performs very well in the computation of perturbative SOC corrections and that the "2eSL" scheme, which neglects the (SS|SS)-type two-electron SOC integrals, is both efficient and accurate. In contrast, the SFX2C-1e+SOC [fd] scheme turns out to be incompatible with a perturbative treatment of SOC effects. Finally, as a first chemical application, we report high-accuracy calculations of the (201)Hg quadrupole-coupling parameters of the recently characterized ethylmercury hydride (HHgCH2CH3) molecule based on SFX2C-1e coupled-cluster calculations augmented with second-order SOC corrections obtained at the Hartree-Fock level using the SFX2C-1e+SOC [der]/2eSL scheme.

Valence–Rydberg electronic states of N2: spectroscopy and spin–orbit couplings

Using ab initio methodology, we compute the potential energy curves and spin–orbit coupling integrals of the N2 electronic states located in the 0–120 000 cm−1 energy domain. In our analysis, we focus mostly on those located outside the Franck–Condon region accessible from the ground state of N2, i.e. the two strongly bound states 13Σg− and 11Γg, and the weakly bound state 23Σg−, in addition to several repulsive states. We characterize them spectroscopically and we compute their spin–orbit couplings to the close lying singlets, triplets and quintets. This work completes our knowledge on the electronic states of N2 that may be important intermediates during N + N collisions and for the dynamics of the N2 singlet, triplet and quintet VUV photodissociation.

Accurate ab initio spin–orbit predissociation lifetimes of the A states of SH and SH+

Accurate ab initio calculations are performed at the aug-cc-pV6Z/MRCI level of theory on the potential energy curves of SH (A2Σ+, 4Σ−, 2Σ−, 4Π) and SH+ (A3Π, 5Σ−), and on their respective mutual spin–orbit coupling integrals. These data are incorporated into Fermi golden rule computations allowing deducing the predissociation lifetimes for SH A2Σ+ and SH+ A3Π rovibrational levels and their corresponding deuterated species. An excellent agreement is found between the experimentally known values and ours, allowing reliable lifetime predictions for the upper A state rovibrational levels not measured yet.

Optimal axes of Siberian snakes for polarized proton acceleration

Accelerating polarized proton beams and storing them for many turns can lead to a loss of polarization when accelerating through energies where a spin rotation frequency is in resonance with orbit oscillation frequencies. First-order resonance effects can be avoided by installing Siberian Snakes in the ring, devices which rotate the spin by 180 degrees around the snake axis while not changing the beam's orbit significantly. For large rings, several Siberian Snakes are required. Here a criterion will be derived that allows to find an optimal choice of the snake axes. Rings with super-period four are analyzed in detail, and the HERA proton ring is used as an example for approximate four-fold symmetry. The proposed arrangement of Siberian Snakes matches their effects so that all spin-orbit coupling integrals vanish at all energies and therefore there is no first-order spin-orbit coupling at all for this choice, which I call snakes matching. It will be shown that in general at least eight Siberian Snakes are needed and that there are exactly four possibilities to arrange their axes. When the betatron phase advance between snakes is chosen suitably, four Siberian Snakes can be sufficient. To show that favorable choice of snakes have been found, polarized protons are tracked for part of HERA-p's acceleration cycle which shows that polarization is preserved best for the here proposed arrangement of Siberian Snakes.

Ab initio spin–orbit coupling SCF calculation of parity-violating energy of chiral molecules

The spin–orbit coupling SCF (SOC-SCF) wavefunction was obtained on the basis of Breit–Pauli Hamiltonian and generalized spin-orbitals and was used to calculate the parity-violating energy, E pv, of chiral molecules. For the twisted HOOH molecule, the magnitude of SOC-SCF E pv is comparable with those of RPA, MC-LR, and DHF methods, and 2 or 3 times as large as that calculated by sum-over-state perturbation theory (SOS-PT). Moreover, the SOC-SCF method gave a reliable variation in the E pv value for the conformational change of l-alanine zwitterion ( l-ALAZ), indicating that the SOC was introduced appropriately into the SOC-SCF wavefunction. Calculations for several chiral molecules have suggested that the [5s2p/3s] basis set was acceptable for the SCF–SCF E pv calculation of large molecules. The contribution of one- and two-electron spin–orbit coupling terms to E pv was analyzed by dividing the E pv values in parts. It was confirmed that only one-center terms of the spin–orbit coupling integrals are sufficient in the SOC-SCF E pv calculation, although both one- and two-electron terms should be included. The SOC-SCF method with the [5s2p/3s] basis set was applied to l-ALAZ in aqueous solution, and the E pv map was created as a function of two torsion angles, ϕ for the NH 3 group and θ for the CO 2 group. In the ( ϕ, θ) map of E pv, the positive E pv area is wider than the negative one, and the averaged E pv value was +2.1×10 −20 hartree, indicating that l-ALAZ is more unstable than d-ALAZ in aqueous solution due to the parity-violating weak neutral current interaction.

Spin–orbit coupling in oxygen containing diradicals

Intermediate diradicals which occur in the Paterno–Büchi photocycloaddition and in the Norrish type I photoreactions have been calculated taking into account the spin–orbit coupling (SOC) between the singlet (S) and triplet (T) states. Reaction paths for the photocycloaddition of formaldehyde to ethene and the diradical products of the α-cleavage of cyclohexanone have been optimized by the MNDO CI method for a number of different singlet and triplet states. SOC integrals are calculated by an effective one-electron approximation. Intermediate diradicals in the Paterno–Büchi reaction and the SOC effects are also studied ab initio with CAS SCF geometry optimization in a TZV basis set. Both methods predict a large SOC matrix element between the S and T states in the course of the C–C attack, while the SOC integral is two orders of magnitude smaller for the diradical produced in the C–O attack. In the Norrish type I photoreaction the oxygen atom also produces some nonzero contribution to the SOC integral which governs intersystem crossing in a ·C–C· diradical. For the diradicals produced by the α-cleavage of cyclohexanone a vibronic interaction is responsible for the SOC mixing between the lowest S and T states. The importance of one-center versus two-center SOC contributions in diradicals is briefly discussed.