Singlet-triplet Interaction Research Articles

Singlet-triplet interaction of the adiabatic terms [formula omitted] and [formula omitted] in the linear triatomic molecules

The paper introduces the 4x4 vibronic matrix that describes singlet–triplet interaction of adiabatic terms 1Σ+ and 3Σ+ via deformation π-modes of the linear triatomic system. Our analysis takes into account spin-orbital coupling in ab initio Breit-Pauli form in the framework of two-electronic model. It is shown that the symmetry operators of electronic Hamiltonian include both space operations (acting on electronic coordinates) and matrix operations (acting on electronic spins). Eigenvalues of vibronic matrix (i.e. potential energy surfaces) are invariants of the molecular symmetry group C∞ν. The 4x4 vibronic matrix includes 4 electrostatic parameters and 3 parameters caused by spin-orbital interaction.

The Singlet-Triplet Interaction of 3Π and 1Σ+ States in Linear Triatomic Molecules

The Singlet-Triplet Interaction of 3Π and 1Σ+ States in Linear Triatomic Molecules

Relativistic pseudo Renner effect of (3Π + 1Σ+) × π type in linear triatomic molecules

We present here two-electronic model, which describes singlet–triplet interaction of electronic terms 1Σ+ and 3Π in the linear triatomic molecules. Our analysis takes into account spin-orbital coupling terms in ab initio form of Breit-Pauli operator and uses symmetry properties of electronic Hamiltonian. It is shown that the symmetry operators of electronic Hamiltonian include both space operators and matrix operators.In our analysis we take into account only deformation π-modes. Resulting 7 × 7 vibronic matrix describes really relativistic pseudo Renner effect (3Π + 1Σ+) × π. Eigenvalues of vibronic matrix (i.e. potential energy surfaces) have axial symmetry.

Triplet exciton fine structure in Pt-rich polymers studied by circularly polarized emission under high magnetic field

Incorporating heavy atoms into polymer chains represents an effective way to generate emissive triplets. Here we used magneto-optical emission spectroscopy up to 17.5 Tesla for studying the fine structure of the triplet exciton in a series of Pt-rich \ensuremath{\pi}-conjugated polymers with various intrachain Pt concentrations. We found that their phosphorescence emission band shows substantial field-induced circular polarization (FICPO) up to 50% with an unusual, nonmonotonic field dependence at cryogenic temperature. From the field-induced energy splitting between left and right circularly polarized phosphorescence we obtained the effective $g$ factor of triplet exciton varying in the range of $\ensuremath{-}0.13\text{\ensuremath{-}}0.85$, which depends on the Pt concentration in the polymer chains. The FICPO of triplet emission originates from the population difference in spin sublevels, which is determined by thermal equilibrium subjected to spin-orbit coupling (SOC), exchange, and Zeeman interactions. Surprisingly we also observed FICPO in the fluorescence emission that results from the singlet-triplet interaction caused by the strong SOC. From these results we extracted the various interaction parameters that describe the exciton fine structure in these Pt-contained compounds.

Carbene-Metal-Amide Bond Deformation, Rather Than Ligand Rotation, Drives Delayed Fluorescence.

We report three characteristics of ideal thermally activated delayed fluorescence molecular systems apparent in carbene-metal-amides: (a) an exceptionally small singlet-triplet gap that effectively eliminates the thermal activation barrier to reverse intersystem crossing; (b) significant singlet oscillator strength promoting fluorescence in the region of this small barrier; and (c) enlarged spin-orbit coupling driving reverse intersystem crossing in this region. We carry out highly correlated quantum-chemical calculations to detail the relative energies of and spin-orbit couplings between the singlet and triplet states, finding that they fall closer together in energy and couple more strongly in going from the singlet ground-state to the triplet optimized geometry. This structural reorganization is defined not by rotation of the ligands but by a nontrivial bending of the carbene-metal-amide bond angle. This bending reduces carbene-metal-amide symmetry and enhances singlet-triplet interaction strength. We clarify that the reverse intersystem crossing triggering delayed fluorescence occurs around the coplanar triplet geometric optimum.

Singlet-triplet interaction in linear triatomic molecules

We present here two-electronic model, which describes singlet–triplet interaction 1π-3Σ+ in linear triatomic molecules. The analysis takes into account spin-orbital coupling terms in electronic Hamiltonian, as well as its symmetry properties. We give the symmetry operators of electronic Hamiltonian including space operators (acting on electronic coordinates) and matrix operators (acting on electronic spin). We consider only deformation π-modes and our resulting 5×5 vibronic matrix describes actual relativistic pseudo-Renner effect (1π-3Σ)×π. The eigenvalues of vibronic matrix (i.e. potential energy surfaces) have axial symmetry and represented by analytical expressions, include five electrostatic and three spin-orbital parameters.

Development of spin-orbit coupling for stochastic configuration interaction techniques.

To perform spin-orbit coupling calculations on atoms and molecules, good zeroth-order wavefunctions are necessary. Here, we present the software development of the Monte Carlo Configuration Interaction (MCCI) method, to enable calculation of such properties, where MCCI iteratively constructs a multireference wavefunction using a stochastic procedure. In this initial work, we aim to establish the efficacy of this technique in predicting the splitting of otherwise degenerate energy levels on a range of atoms and small diatomic molecules. It is hoped that this work will subsequently act as a gateway toward using this method to investigate singlet-triplet interactions in larger multireference molecules. We show that MCCI can generate very good results using highly compact wavefunctions compared to other techniques, with no prior knowledge of important orbitals. Higher-order relativistic effects are neglected and spin-orbit coupling effects are incorporated using first-order degenerate perturbation theory with the Breit-Pauli Hamiltonian and effective nuclear charges in the one-electron operator. Results are obtained and presented for B, C, O, F, Si, S, and Cl atoms and OH, CN, NO, and C2 diatomic radicals including spin-orbit coupling constants and the relative splitting of the lowest energy degenerate state for each species. Convergence of MCCI to the full configuration interaction result is demonstrated on the multireference problem of stretched OH. We also present results from the singlet-triplet interaction between the X3Σg- and both the a1Δg and b1Σg+ states of the O2 molecule. © 2017 Wiley Periodicals, Inc.

Singlet–triplet interaction in Group 2 M2O hypermetallic oxides

This ab initio study of Group 2 M2O hypermetallic oxides focuses mainly on the two heaviest members, Ba2O and Ra2O. In accordance with previous studies in our group on the Be, Mg, Ca and Sr hypermetallic oxides, we find that the BaOBa and RaORa molecules have a linear X∼1Σg+ ground electronic state and a very low lying first excited ã3Σu+ triplet electronic state. Special attention is placed on calculating and understanding how the singlet–triplet splitting and singlet–triplet interaction strength vary down the series. The calculations reveal that MgOMg shows the largest singlet–triplet splitting and does not fit into the overall trend down the Group 2 series of elements. However, in all cases the extent of the singlet–triplet interaction between vibronic levels of the X∼ and ã states is very small. On the experimental side, there is literature evidence for the formation of electronically excited Ba2O in oxidation reactions of barium dimers, and our calculations of excited singlet and triplet state energies support that assignment.

The Predicted Spectrum and Singlet–Triplet Interaction of the Hypermetallic Molecule SrOSr

In accordance with previous studies in our group on Be, Mg, and Ca hypermetallic oxides, we find that SrOSr has a linear X̃1Σ(g)+ ground electronic state and a very low lying first excited ã3Σ(u)+ triplet electronic state. No gas-phase spectrum of this molecule has been assigned yet, and to encourage and assist in its discovery we present a complete ab initio simulation, with absolute intensities, of the infrared absorption spectrum for both electronic states. The three-dimensional potential energy surfaces and the electric dipole moment surfaces of the X̃1Σ(g)+ and ã3Σ(u)+ electronic states are calculated using a multireference configuration interaction (MRCISD) approach in combination with internally contracted multireference perturbation theory (RS2C) based on complete active space self-consistent field (CASSCF) wave functions applying a Sadlej pVTZ basis set for both O and Sr and the Stuttgart relativistic small-core effective core potential for Sr. The infrared spectra are simulated using the MORBID program system. We also calculate vertical excitation energies and transition moments for several excited singlet and triplet electronic states in order to predict the positions and intensities of the most prominent singlet and triplet electronic absorption bands. Finally, for this heavy molecule, we calculate the singlet–triplet interaction matrix elements between close-lying vibronic levels of the X̃ and ã electronic states and find them to be very small.

A Theoretical Rationale why Furan‐side Monoadduct is More Favorable Toward Diadduct Formation in 8‐Methoxypsoralen and Thymine Complexes

The photoinduced mechanism of formation of mono- and diadducts between 8-MOP and thymine bases is studied using the ONIOM(MPWB1K/6-31 + G(d,p):B3LYP/6-31G(d,p):UFF) and B3LYP/6-31 + G(d,p) methods. The relevant cycloaddition displays favorable energy barriers and reaction energies in the triplet excited state, which involves the initial formation of a diradical followed by ring closure via singlet-triplet interaction. The monoadduct on the pyrone side is favored over the furan side when comparing reaction energies. The distinguishing feature in the formation of the monoadducts is that the furan-side adduct displays a better photostability, which is a relatively high-barrier exothermic reaction, and thus the energy balance of the monoadduct on the furan side toward final diadduct formation is favored.

Consecutive Reaction Mechanism for the Formation of Spore Photoproduct in DNA Photolesion

We have explored the potential energy profiles of TpT dinucleotides toward formation of a DNA photolesion product, spore photoproduct (SP), along the S(0), S(1), and T(1) states, by means of density functional theory and time-dependent density functional theory. Together with the spin density analysis, the consecutive mechanism for the SP formation can be established. The detailed reaction pathways have been revealed. All the adiabatic reaction pathways proceeding though S(1), T(1), or S(0) alone are shown to be energetically infeasible, while the nonadiabatic pathway involving both the T(1) and S(0) states corresponds to the lowest-energy path and is the most favorable in energy. The nonadiabatic pathway is rate-limited by the step of the hydrogen atom transfer proceeding in the T(1) state with a barrier of 14.2 kcal mol(-1) (11.9 kcal mol(-1) in bulk solution), whereas the subsequent C5-CH(2) bond formation toward the final SP formation occurs readily in S(0) after intersystem crossing from T(1) to S(0) via the singlet-triplet interaction. The results provide a rationale for the experimentally observed kinetic isotope effect after deuterium substitution at the 3'-T methyl group of TpT.

A Theoretical Rationale for Why Azetidine Has a Faster Rate of Formation Than Oxetane in TC(6–4) Photoproducts

The mechanism of formation of azetidine and oxetane in (6-4) photoproducts between thymine and imine-type cytosine is studied using the MPWB1K and B3LYP functionals together with the 6-31G(d,p) and 6-311++G(d,p) basis sets, in vacuum and bulk solvent. The photoinduced cycloaddition displays favorable energy barriers in the triplet excited state for formation of both azetidine and oxetane. The stepwise cycloaddition in the triplet excited state involves the initial formation of a diradical followed by ring closure via singlet-triplet interaction. The distinguishing feature in the formation of azetidine compared to that of oxetane is an intermediate H3' back-transfer to N3', which is a low-barrier exothermic reaction, and thus shifts the energy balance toward azetidine formation.

A triplet mechanism for the formation of thymine–thymine (6-4) dimers in UV-irradiated DNA

The reaction pathway for the photochemical formation of thymine-thymine (6-4) dimers in DNA is explored using hybrid density functional theory techniques in gas and in bulk solvent. It is concluded that the photo-induced cycloaddition displays favorable energy barriers in the triplet excited state. The stepwise cycloaddition in the triplet excited state involves the initial formation of a diradical followed by ring closure via singlet-triplet interaction. The key geometric features and electron spin densities are also discussed. The difference in barriers of H3' transfer for the lowest-lying triplet and singlet states shows that the singlet oxetane intermediate could catch the second photon to accelerate the rate of proton transfer, leading to formation of the Dewar structure. The present results provide a rationale for the formation of thymine-thymine (6-4) dimers in the triplet excited states.

Singlet-Triplet States Interaction Regions in DNA/RNA Nucleobase Hypersurfaces.

The present study provides new insight into the intrinsic mechanisms for the population of the triplet manifold in DNA nucleobases by determining, at the multiconfigurational CASSCF/CASPT2 level, the singlet-triplet states crossing regions and the main decay paths for their lowest singlet and triplet states after near-UV irradiation. The studied singlet-triplet interacting regions are accessible along the minimum energy path of the initially populated singlet bright (1)ππ* state. In particular, all five natural DNA/RNA nucleobases have, at the end of the main minimum energy path and near a conical intersection of the ground and (1)ππ* states, a low-energy, easily accessible, singlet-triplet crossing region directly connecting the lowest singlet and triplet ππ* excited states. Adenine, thymine, and uracil display additional higher-energy crossing regions related to the presence of low-lying singlet and a triplet nπ* state. These funnels are absent in guanine and cytosine, which have the bright (1)ππ* state lower in energy and less accessible nπ* states. Knowledge of the location and accessibility of these regions, in which the singlet-triplet interaction is related to large spin-orbit coupling elements, may help to understand experimental evidence such as the wavelength dependence measured for the triplet formation quantum yield in nucleobases and the prevalence of adenine and thymine components in the phosphorescence spectra of DNA.

A Triplet Mechanism for the Formation of Cyclobutane Pyrimidine Dimers in UV-Irradiated DNA

The reaction pathways for the photochemical formation of cyclobutane thymine dimers in DNA are explored using hybrid density functional theory techniques. It is concluded that the thymine-thymine [2 + 2] cycloaddition displays favorable energy barriers and reaction energies in both the triplet and the singlet excited states. The stepwise cycloaddition in the triplet excited state involves the initial formation of a diradical followed by ring closure via singlet-triplet interaction. The triplet mechanism is thus completely different from the concerted singlet state cycloaddition processes. The key geometric features and electron spin densities are also discussed. Bulk solvation has a major effect by reducing the barriers and increasing the diradical stabilities. The present results provide a rationale for the faster cycloreaction observed in the singlet excited states than in the triplet excited states.

Single Molecule Modulation Spectroscopy of Conjugated Polymers

This paper describes a new single molecule spectroscopy approach for the investigation of triplet-triplet and singlet-triplet interactions in conjugated polymers. The technique involves the irradiation of isolated single, mulitchromophoric, conjugated polymer molecules by a repetitive sequence of variable-intensity microsecond time scale excitation pulses. The fluorescence intensity is synchronously time-averaged for thousands of cycles of the pulse sequence to yield a high signal-to-noise fluorescence transient on the microsecond time scale. The transient can be analyzed with kinetic models to obtain quantitative information about the kinetics of triplet-triplet exciton annihilation and the quenching of singlet excitons by triplet excitons in conjugated polymers.

A statistical approach for the study of singlet–triplet interactions in small polyatomic molecules

Surface electron ejection by laser excited metastable (SEELEM) and laser induced fluorescence (LIF) spectroscopies are complementary techniques that can be employed to provide both qualitative and quantitative insights into the mechanisms of singlet–triplet coupling in small polyatomic molecules. Two qualitatively distinct singlet–triplet coupling mechanisms are examined here in order to reveal the statistical signatures by which they can best be distinguished. These interaction mechanisms are: direct coupling between a “bright” S1 state and an entire background manifold of “dark” triplet states; and “doorway-mediated” indirect coupling in which the bright state couples to the manifold of dark states through the intermediary of one doorway state of unique vibronic character. Our goal in this paper is to present and explain the basis for the effectiveness of statistical methods with which complex LIF/SEELEM spectra may be processed so as to distinguish qualitatively between these two mechanistic possibilities. The trends obtained from these statistical methods are also shown to encode information about some characteristic quantitative features of the triplet perturbers, such as their coupling strength to the bright state S1. The development of the statistical methods described in this paper was motivated by our experiments on acetylene. Acetylene has certain useful dynamical features which make it a good model system for this study. The statistical measures developed distinguish conclusively between the direct and doorway-mediated coupling schemes, because each scheme is shown here to give rise to characteristic statistical signatures in the SEELEM and LIF spectra. Qualitative results from a preliminary real data set analyzed using the statistical approach proposed here are also presented in order to demonstrate the effectiveness of these statistical measures.

Jet spectroscopy, structure, anomalous fluorescence, and molecular quantum beats of silylidene (H2C=Si), the simplest unsaturated silylene

The jet-cooled B̃ 1B2–X̃ 1A1 spectrum of silylidene, the simplest unsaturated silylene, has been observed for the first time. H2C=Si and D2C=Si have been produced by an electric discharge through tetramethylsilane and tetramethylsilane-d12 vapor diluted in argon at the exit of a supersonic expansion. Rotational analysis of the 000 bands yielded the following substitution structures: rs″(CSi)=1.706(5) Å, rs″(CH)=1.099(3) Å, θs″(HCH)=114.4(2)°, rs′(CSi)=1.815(5) Å, rs′(CH)=1.073(4) Å, and θs′(HCH)=133.7(1)°. The electronic transition consists primarily of strong electronically allowed perpendicular bands, but a weaker system of vibronically induced parallel bands has also been assigned. Transitions involving Δv=2 changes in the ν6 (b2) mode show up prominently in the spectrum, due to a very large change in the vibrational frequency on excitation. Silylidene has very interesting excited state decay dynamics. Anomalous S2−S0 fluorescence is observed due to the very large S2−S1 energy gap. Rotational level specific intensity anomalies are found in the laser induced fluorescence spectra. Collision-free fluorescence decay curves exhibit superimposed quantum beats for almost all the accessible rotational levels in the 000 bands of H2CSi and D2CSi. Density of states arguments lead to the conclusion that most of the beat patterns are due to coupling with high vibrational levels of the ground state, although two examples of hyperfine splittings associated with singlet–triplet interactions have also been found.

High resolution near-infrared electronic spectroscopy of HCBr

The rotationally resolved spectrum of the HCBr à 1A″(0,2,0)←X̃ 1A′(0,0,0) Ka=0←1 transition between 12760 and 12850 cm−1 was obtained for the first time at Doppler-limited resolution using a transient frequency-modulation absorption technique. Rotational structure of HC 79Br and HC 81Br was identified and analyzed. The analysis shows R″(C–Br)=1.852 Å and R′(C–Br)=1.749 Å. The observed band indicates a linear–bent transition. This yields an upper limit of approximately 1600 cm−1 for the barrier to linearity above the zero-point energy for the à 1A″ state. Perturbations caused by singlet–triplet interactions were also found in the observed spectrum. The analysis of these perturbations indicates a very low-lying ã 3A″ state.

Spin-orbit interactions from self consistent field wavefunctions

Effects of the spin-orbit Hamiltonian HLS , including both the spin-same orbit and spin-other orbit terms, are studied at the self consistent field (SCF) level of theory. Separate calculations are carried out for each state considered, and biorthogonal orbitals are constructed for the evaluation of matrix elements. Doublet-doublet and singlet-triplet interactions are discussed. The evaluation of the Gaussian basis function integrals is described in a Cartesian component representation, these integrals being directly related to one and two electron second derivative integrals. This new SCF spin-orbit code is used to (i) determine the spatial dependence of the spin-orbit parameters for the Renner-Teller 2B1, 2A1 states of H2O+, (ii) determine the spin-orbit splitting of the 2Π states of OH as a function of bond-length and (iii) calculate the radiative lifetime of the a 3Σ+ state of NO+. In each case these calculations are compared with more sophisticated configuration interaction studies, but it is found that the evaluation of these effects near equilibrium geometries at the SCF level is sufficiently accurate, provided that a large basis set is used.