Ab initio investigation of the vibronic structure and the spin–orbit coupling in the XΠu state of C2D2

Results of an ab initio study of the Renner–Teller effect in the X²Π_u state of C₂D₂⁺ are presented. Potential curves for the trans- and cis-bending vibrations calculated by means of the internally contracted multireference configuration interaction method are employed. Vibronic energy levels and their splitting upon spin–orbit coupling are computed by means of a variational approach.     

Revisiting the nature of the ZnO ground state: Influence of spin–orbit coupling

Relativistic calculations of the low-lying electronic states of the ZnO molecule are performed for the Λ–Σ states, ¹Σ⁺, ¹Π, ¹Δ, ³Π and ³Σ⁻, at the CCSD(T) or MRCI level, using scalar relativistic energy-consistent pseudopotentials, and the EPCISO method for spin–orbit CI coupling. The ZnO ground state is assigned to 0⁺ symmetry and has ¹Σ⁺ character around the equilibrium region. The spectroscopic constants (r_e, ω_e) of the 0⁺ ground state are in good agreement with experimental results. Interpenetration of the vibrational levels of the two lowest 0⁺ states is also shown.     

Valence ab initio calculation of the potential-energy curves for the Ca<Subscript>2</Subscript> dimer

The electronic structure of the Ca₂ molecule has been investigated by use of a two-valence-electron semiempirical pseudopotential and applying the internally contracted multireference configuration interaction method with complete-active-space self-consistent-field reference wave functions. Core–valence correlation effects have been accounted for by adding a core-polarization potential to the Hamiltonian. The ground-state properties of the Ca₂ and Ca₂⁺ dimers have also been studied at the single-reference coupled-cluster level with single and double excitations including a perturbative treatment of triple excitations. Good agreement with experiment has been obtained for the ground-state potential curve and the only experimentally known A¹_u⁺ excited state of Ca₂. The spectroscopic parameters D_e and R_e deduced from the calculated potential curves for other states are also reported. In addition, spin–orbit coupling between the singlet and triplet molecular states correlating, respectively, with the (4p)¹P and (4p)³P Ca terms has been investigated using a semi-empirical two-electron spin–orbit pseudopotential. Acknowledgement.This work was supported by grant 5 P03B 082 21 from the Polish State Committee for Scientific Research (KBN).     

Vibronic effects accelerate the intersystem crossing processes of the through-space charge transfer states in the triptycene bridged acridine–triazine donor–acceptor molecule TpAT-tFFO

Quantum chemical studies employing combined density functional and multireference configuration interaction methods suggest five excited electronic states to be involved in the prompt and delayed fluorescence emission of TpAT-tFFO. Three of them, a pair of singlet and triplet charge transfer (CT) states (S₁ and T₁) and a locally excited (LE) triplet state (T₃), can be associated with the (Me → N) conformer, the other two CT-type states (S₂ and T₂) form the lowest excited singlet and triplet states of the (Me → Ph) conformer. The two conformers, which differ in essence by the shearing angle of the face-to-face aligned donor and acceptor moieties, are easily interconverted in the electronic ground state whereas the reorganization energy is substantial in the excited singlet state, thus explaining the two experimentally observed time constants of prompt fluorescence emission. Forward and reverse intersystem crossing between the singlet and triplet CT states is mediated by vibronic spin–orbit interactions involving the LE T₃ state. Low-frequency vibrational modes altering the distance and alignment of the donor and acceptor π-systems tune the S₁ and T₃ states (likewise S₂ and T₃) into and out of resonance. The enhancement of intersystem crossing due to the interplay of vibronic and spin–orbit coupling is considered a general feature of organic through-space charge-transfer thermally activated delayed fluorescence emitters.

DFT/MRCI quantum chemical studies suggest five excited electronic states to be involved in the prompt and delayed fluorescence emission of TpAT-tFFO.     

Theoretical electronic structure including spin–orbit effects of the alkali dimer cation

A theoretical study of the electronic structure of has been performed, including or not spin–orbit coupling. Potential energy curves for all the molecular states dissociating up to the limit Cs⁺ + Cs (8s ²S_1/2), i.e 26 states in the representation and 38 states in the representation Ω_g,u, are displayed. Equilibrium distances, transition energies and depths for the wells predicted at short and large range of internuclear separation R are reported. The existence of some of the long-range wells are confirmed by a long range model. Extensive tables of energy values versus internuclear distances are available at the following address: http://lasim.univ-lyon1.fr/allouche/cs2plus.htm.     

Theoretical study of highly excited Σ and Π states of NaLi and experimental observation of the interacting 5Σ and 6Σ states

Theoretical multireference configuration interaction (MRDCI) calculations on the excited ¹Σ⁺ and ¹Π states of NaLi are presented. They improve the results of a previous study by two of the present authors, resolve some differences with other theoretical results and lead to overall good agreement with experimental observations. To extend the experimental data base of electronic states in NaLi, a previously unknown ¹Σ⁺ state is investigated by polarisation labelling spectroscopy. Comparison with accompanying and previous theoretical calculations leads to a conclusion that the observed system consists of two band systems switching smoothly from one adiabatic state to the other and allows assignment of the bands as 5¹Σ⁺ ← X¹Σ⁺ in the lower energy part and to 6¹Σ⁺ ← X¹Σ⁺ for higher energies.     

The ultraviolet photodissociation of DCl: H/D isotope effects on the Cl(P) atom spin–orbit branching

The photodissociation of jet-cooled DCl molecules subsequent to excitation in the long-wavelength tail of the first UV absorption band (A¹Π₁←X¹Σ⁺) has been investigated at five wavelengths in the range 200–220 nm. Ground state Cl(²P_3/2) and spin–orbit excited Cl^*(²P_1/2) photofragments were monitored using (2+1) resonance enhanced multiphoton ionization in a time-of-flight mass spectrometer. The product branching fractions are reported and compared with previous experimental results and high-level quantum mechanical calculations for HCl and DCl. A significant H/D isotope effect in the branching fractions is found at all the studied wavelengths, in quantitative agreement with recent theoretical predictions.     

MRCI potential energy curves and spectroscopic constants of the ground and low-lying excited states of HgCd

The multireference configuration interaction (MRCI) electronic energy calculations with different basis sets have been performed on the ground state (X¹Σ) and three low-lying excited states (³Σ, ¹Π and ³Π) of HgCd dimer. The obtained potential energy curves (PECs) are fit to analytical potential energy functions (APEFs) using the Murrell–Sorbie potential function. Spectroscopic constants are calculated using the APEFs. Based on the PECs, the vibrational levels of each state are predicted. Our equilibrium positions of the X¹Σ state and ³Π state are in excellent agreement with the experimental reports.     

Ab initio computation of the interaction energy curves for some low-lying states of CO which dissociate to ground-state3 P O and3 P C atoms

Summary We investigate the molecular electronic structure of the quintet states of CO which correspond to the C(³ P)+O(³ P) interaction at several levels of theory. We find the 1⁵⁺ state to be relatively deeply bound (D _e ca. 587 cm^–1) while the other quintets have relatively shallow potential wells (D _e<40 cm^–1) according to our multireference configuration interaction calculations which are counterpoise corrected for basis set superposition effects. Our results are in qualitative accord with the recent semiempirical estimates of Bussery and co-workers [(1989) Chem. Phys. 134:7].National Academy of Sciences, National Research Council, Air Force Astronautics Laboratory, Resident Research Associate 1987–89     

Nonadiabatic dissociation dynamics of ClHD van der Waals complex initiated by electron detachment of Cl–HD

Nuclear dynamics following the electron detachment of the Cl⁻–HD anion is investigated by a time-dependent wave packet propagation approach. Photodetachment of Cl⁻–HD promotes it to the van der Waals well region of the reactive ClHD potential energy surface. The latter is a manifold of three electronic states coupled by the electronic and (relativistic) spin-orbit coupling. Among the three surfaces, the electronic ground one is of ²Σ_1/2 type and yields products in their electronic ground state. The remaining two, ²Π_3/2 and ²Π_1/2, on the other hand, yield products in their excited electronic states. However, these two can yield products in their electronic ground state via nonadiabatic transitions to the ²Σ_1/2 state. The channel specific, HCl + D or DCl + H or Cl + HD, dissociation probabilities on this latter state are calculated both in the uncoupled and coupled surface situations. Separate initial transitions (via, photodetachment) to the ²Σ_1/2, ²Π_3/2 and ²Π_1/2 adiabatic electronic states of ClHD are considered in order to elucidate the nonadiabatic coupling effects on this important class of chemical reactions initiated by an electron detachment.     

Coordination chemistry of di-2-pyridylketone. Synthesis, spectroscopic investigations, X-ray studies and DFT calculations of Re(III) and Re(V) complexes

The paper presents a combined experimental and computational study of Re(III) and Re(V) complexes containing di-2-pyridylketone and its gem-diol form – [ReCl₃(dpk-N,O)(PPh₃)] (1), [ReCl₃(dpk-N,N′)(OPPh₃)] (2) and [ReOBr₃(dpk-OH)]·2(dpkH⁺Br⁻) (3). All the complexes have been characterized spectroscopically and structurally (by single-crystal X-ray diffraction). The complex 2 has been additionally studied by magnetic measurement. The magnetic behavior of 2 is characteristic of mononuclear octahedral Re(III) complex with d⁴ low-spin (³T_1g ground state) and arise because of the large spin–orbit coupling (ζ = 2500 cm⁻¹), which gives diamagnetic ground state. DFT and time-dependent (TD)DFT calculations have been carried out for [ReCl₃(dpk-N,N′)(OPPh₃)] and [ReOBr₃(dpk-OH), and their UV–vis spectra have been discussed on this basis.     

Ab initio study of spin–orbit interaction in the ground electronic states of XH (X = C, Si, Ge and Sn) molecules

Electronic structure and spectroscopic properties for the ground electronic states of CH, SiH, GeH and SnH molecules were obtained using the multiconfigurational self-consistent field followed by spin–orbit multireference multistate perturbation theory. Spin–orbit splitting calculations for ground states of the four molecules were carried out with model core potential (MCP) and all-electron (AE) methods. MCP results are compared with corresponding AE values to estimate the accuracy of the saving cost MCP calculations. The potential energy curves, calculated for the Ω states CH(X₁²Π_1/2 and X₂²Π_3/2), SiH(X₁²Π_1/2 and X₂²Π_3/2), GeH(X₁²Π_1/2 and X₂²Π_3/2) and SnH(X₁²Π_1/2 and X₂²Π_3/2) using the MCP method, were fitted to analytical potential energy function using Murrell–Sorbie potential energy function. Based on the analytical potential energy function, force constants and spectroscopic constants for the Ω states were obtained.     

Solvent effects on optically detected magnetic resonance in triplet spin labels

We have calculated solvent effects on the zero-field splitting (ZFS) constants induced by electron spin–spin coupling (SSC) in the low-lying triplet states of azaaromatic molecules in solutions using multiconfiguration self-consistent-field wave functions and the polarizable continuum model. The second-order spin–orbit coupling (SOC) contribution to the splitting of the ^3* states is found to be almost negligible, and the calculations therefore provide a good estimate of the ZFS parameters and their solvent dependence based only on the electron spin–spin coupling expectation values. The correlation between the shift in the ZFS and the phosphorescence frequency that has been observed in optically detected magnetic resonance experiments in low-temperature glasses is supported by our direct SSC calculations without taking SOC into account. This makes it possible to distinguish between the two theories that earlier were proposed to explain the inhomogeneous broadening of triplet state spectra, and discard the one that is exclusively based on the SOC-induced mixing of the singlet and triplet states.Contribution to the Jacopo Tomasi Honorary IssueAcknowledgments. This work was supported (B. M.) by the Swedish Royal Academy of Science (KVA). This work was also supported by the Norwegian Research Council through a grant of computer time from the Program for Supercomputing. We are grateful to B. Schimmelpfenning for his valuable assistance in the computations.     

All‐electron relativistic computations on the low‐lying electronic states,bond length,and vibrational frequency of CeF diatomic molecule with spin–orbit coupling effects

Ab initio all‐electron computations have been carried out for Ce⁺ and CeF, including the electron correlation, scalar relativistic, and spin–orbit coupling effects in a quantitative manner. First, the n‐electron valence state second‐order multireference perturbation theory (NEVPT2) and spin–orbit configuration interaction (SOCI) based on the state‐averaged restricted active space multiconfigurational self‐consistent field (SA‐RASSCF) and state‐averaged complete active space multiconfigurational self‐consistent field (SA‐CASSCF) wavefunctions have been applied to evaluations of the low‐lying energy levels of Ce⁺ with [Xe]4f¹5d¹6s¹ and [Xe]4f¹5d² configurations, to test the accuracy of several all‐electron relativistic basis sets. It is shown that the mixing of quartet and doublet states is essential to reproduce the excitation energies. Then, SA‐RASSCF(CASSCF)/NEVPT2 + SOCI computations with the Sapporo(‐DKH3)‐2012‐QZP basis set were carried out to determine the energy levels of the low‐lying electronic states of CeF. The calculated excitation energies, bond length, and vibrational frequency are shown to be in good agreement with the available experimental data. © 2018 Wiley Periodicals, Inc.     

An ab initio study of electronic spectra and excited-state properties of 7-azaindole in vapour phase and aqueous solution

The geometries of 7-azaindole (7AI), its tautomer (7AT), and 7AI–H₂O and 7AT–H₂O complexes were optimised in the ground state and some low-lying singlet excited states using the 3-21G basis set. Differences of total energies of the optimised ground and excited states and the vertical excitation energies of these systems were used to explain the observed electronic spectra. Effect of solvation of these systems in bulk water was studied using the polarized continuum model (PCM). The mode of binding of a water molecule in the S₂(n–π^*) excited state of 7AI was found to be quite different from those in its ground and π–π^* excited states. It is shown that crossing of the lowest two singlet excited-state potential surfaces S₁(π–π^*) and S₂(n–π^*) of 7AI occurs in the vapour phase under geometry relaxation while on interaction with water, the S₂(n–π^*) excited state is raised up appreciably going even above the S₃(π–π^*) excited state. Ground- and excited-state molecular electrostatic potential mapping was carried out, which led to valuable information regarding the nature of excited states of the above-mentioned systems.     

On the low-lying electronic states of BiF

Relativistic CI calculations on the low-lying states of BiF(0⁺, 1, 2, 0⁺(II)) arising from the σ²π² configuration are carried out. Comparison calculations of the λ-s states without spin-orbit interaction (³Σ⁻, ¹Σ⁺ and ¹Δ) are also presented. These calculations enable the assignment of three experimentally observed low-lying states. In addition, the properties of a new state (2) are calculated (yet to be observed). The calculated dissociation energy of the ground state is 2.63 eV. The potential energy surfaces of the low-lying electronic states of BiF reveal interesting avoided crossings. Our calculations clarify the earlier assignment of the electronic transitions of BiF.     

Singlet oxygen generation in PUVA therapy studied using electronic structure calculations

The ability of furocoumarins to participate in the PUVA (Psoralen + UV-A) therapy against skin disorders and some types of cancer, is analyzed on quantum chemical grounds. The efficiency of the process relies on its capability to populate its lowest triplet excited state, and then either form adducts with thymine which interfere DNA replication or transfer its energy, generating singlet molecular oxygen damaging the cell membrane in photoactivated tissues. By determining the spin–orbit couplings, shown to be the key property, in the intersystem crossing yielding the triplet state of the furocoumarin, the electronic couplings in the triplet–triplet energy transfer process producing the singlet oxygen, and the reaction rates and lifetimes, the efficiency in the phototherapeutic action of the furocoumarin family is predicted as: khellin < 5-methoxypsoralen (5-MOP) < 8-methoxypsoralen (8-MOP) < psoralen < 4,5′,8-trimethylpsoralen (TMP) < 3-carbethoxypsoralen (3-CPS), the latter being the most efficient photosensitizer and singlet oxygen generator.     

Chromophore-radical excited state antiferromagnetic exchange controls the sign of photoinduced ground state spin polarization

A change in the sign of the ground-state electron spin polarization (ESP) is reported in complexes where an organic radical (nitronylnitroxide, NN) is covalently attached to a donor–acceptor chromophore via two different meta-phenylene bridges in (bpy)Pt(CAT-m-Ph-NN) (mPh-Pt) and (bpy)Pt(CAT-6-Me-m-Ph-NN) (6-Me-mPh-Pt) (bpy = 5,5′-di-tert-butyl-2,2′-bipyridine, CAT = 3-tert-butylcatecholate, m-Ph = meta-phenylene). These molecules represent a new class of chromophores that can be photoexcited with visible light to produce an initial exchange-coupled, 3-spin (bpy˙⁻, CAT⁺˙ = semiquinone (SQ), and NN), charge-separated doublet ²S₁ (S = chromophore excited spin singlet configuration) excited state. Following excitation, the ²S₁ state rapidly decays to the ground state by magnetic exchange-mediated enhanced internal conversion via the ²T₁ (T = chromophore excited spin triplet configuration) state. This process generates emissive ground state ESP in 6-Me-mPh-Pt while for mPh-Pt the ESP is absorptive. It is proposed that the emissive polarization in 6-Me-mPh-Pt results from zero-field splitting induced transitions between the chromophoric ²T₁ and ⁴T₁ states, whereas predominant spin–orbit induced transitions between ²T₁ and low-energy NN-based states give rise to the absorptive polarization observed for mPh-Pt. The difference in the sign of the ESP for these molecules is consistent with a smaller excited state ²T₁ – ⁴T₁ gap for 6-Me-mPh-Pt that derives from steric interactions with the 6-methyl group. These steric interactions reduce the excited state pairwise SQ-NN exchange coupling compared to that in mPh-Pt.

A change in the sign of the ground state electron spin polarization (ESP) is reported in complexes where an organic radical (nitronylnitroxide, NN) is covalently attached to a donor–acceptor chromophore via two different meta-phenylene bridges.     

The ligand-ligand and spin-orbit interactions in Fe(phen) 3 +2 and Ru(phen) 3 +2 ions

To explain the differences in the spectral properties of the complex ions (–)-Fe(phen) ₃ ⁺² and (–)-Ru(phen) ₃ ⁺² the interaction between the ligands and spin-orbit coupling energies have been calculated. It is shown that the spinorbit coupling energy in case of Ru(II) complex is more important than the ligand-ligand interaction. This leads to a sequence of the lowest excited states ³A₂<¹A₂<¹E.