Half-Projected and Projected Hartree-Fock Calculations for Singlet Ground States. i. four-Electron Atomic Systems

The half-projected Hartree-Fock function (HPHF ) for singlet states is defined as a linear combination of two Slater determinants, which contains only spin eigenfunctions with even quantum number. Using a self-consistent procedure based on the generalized Brillouin's theorem, the RHF , HPHF and PHF functions are deduced for the ground states of the Li^?, Be, B⁺, and C²⁺ systems, in a limited basis set. It is found that the HPHF function yields better energy values than the RHF function, very close to that of the PHF one. The HPHF scheme seems thus to be useful as a substitute for the PHF model, specially in the case of large electronic systems in which the latter method becomes unmanageable.     

Analysis of the half-projected Hartree–Fock function: Density matrix,natural orbitals,and configuration interaction equivalence

The half-projected Hartree–Fock function for singlet states (HPHF ) is analysed in terms of natural electronic configurations. For this purpose the HPHF spinless density matrix and its natural orbitals are first deduced. It is found that the HPHF function does not contain any contribution from odd-times excited configurations. It is seen in addition, in the case of the singlet ground states, this function is approximately equivalent to two closed-shell configurations, although the nature of the excited one depends on the nuclear geometry. An example is given in the case of the LiH ground state. Finally, the application of this model for studying systems of more that two atoms is criticized.     

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Spin-inversion dynamics in O₂ binding to a model heme complex, which consisted of Fe(II)-porphyrin and imidazole, were studied using nonadiabatic wave packet dynamics calculations. We considered three active nuclear degrees of freedom in the dynamics, including the motions along the Fe–O distance, Fe–O–O angle, and Fe out-of-plane distance. Spin-free potential energy surfaces for the singlet, triplet, quintet, and septet states were developed using density functional theory calculations, and spin–orbit coupling elements were obtained from CASSCF-level electronic structure calculations. The spin-inversion mainly occurred between the singlet state and one of the triplet states due to large spin–orbit couplings and the contributions of other states were extremely small. The present quantum dynamics calculations suggested that the narrow crossing region model plays a dominant role in the O₂ binding dynamics. In addition, the one-dimensional Landau–Zener model underestimated the nonadiabatic transition probability.     

Ab initio computations of spin-orbit interactions in polyatomic molecules. Splitting of sulfur LII,III states and singlet–triplet transitions in SO2

Spin-orbit interactions among the ground and the first few excited electronic states of SO₂, are computed with ab initio molecular wave functions and Gaussian atomic orbitals. All spin-other orbits contributions to the matrix elements are included. The computed intensity of the first singlet–triplet transition is found to be in broad agreement with experiment and sensitive to an extension of the configuration interaction expansion of molecular wave functions. Also, the splitting of sulfur L_{II ,III} states in SO₂ is derived as an example of large spin-orbit interactions among electronic states.     

Theoretical electronic studies of aluminum monobromide and aluminum monoiodide

By using CASSCF/MRCI methods, theoretical molecular calculations have been performed for 12 electronic states for AlBr molecule and 12 electronic states for AlI molecule in the representation ^2s+1Λ (neglecting spin‐orbit effects). Calculated potential energy curves are displayed. Spectroscopic constants including the harmonic vibrational wave number ω_e, the electronic energy T_e referred to the ground state and the equilibrium internuclear distance R_e are predicted for these singlet and triplet electronic states for both AlBr and AlI molecules. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

1H-Phenalen-1-one: Photophysical Properties and Singlet-Oxygen Production

The efficiency of aromatic ketones as singlet-oxygen (¹O₂(¹Δ_g)) sensitizers can vary considerably with the electronic configuration of their lowest triplet state and the solvent used. Near-infrared measurements of tie luminescence of singlet oxygen have shown that the quantum yield of singlet-oxygen production (Φ_Δ) by 1H-phenalen-1-one ( 1 ) is close to unity in both polar (Φ_Δ = 0.97±0.03 in methanol) and non-polar solvents (Φ_Δ = 0.93±0.04 in benzene). Analysis of the absorption spectra of the ground state and phosphorescence measurements show that the lowest singlet and triplet states have dominant π, π* electronic configurations. The quantum yield of intersystem crossing (Φ_ISC) of 1 , determined by laser flash photolysis (partial-saturation method), is equal to unity. In comparison with other aromatic ketones, these parameters are important for the discussion of the surprisingly high Φ_ISC of 1 and the efficient energy transfer from its triplet state to molecular oxygen. The 1H-phenalen-1-one ( 1 ), being one of the most efficient singlet-oxygen sensitizers in both polar and non-polar media, could be used as a reference sensitizer, in particular in the area of relatively high energies of excitation.     

Projected BCS Tamm-Dancoff method for molecular electronic structures

A new Tamm–Dancoff method for the ground and excited states of molecular electronic systems is developed. The method begins with a number-projected BCS (PBCS ) wave function and is generated by excitations of particle pairs from the degenerate geminals in the PBCS wave function. A direct optimization of the PBCS wave function is accomplished with successive Bogoliubov transformations so that one-pair excitation terms in the Tamm-Dancoff expansion of the ground state vanish (the generalized Brillouin theorem). The spin-symmetry adapted first- and second-order Tamm–Dancoff bases and matrix elements are calculated by means of the CI expansion of the PBCS wave function with natural orbitals that diagonalize the BCS geminal matrix. Numerical calculations are presented for the H₄ system with D_2h and D_4h conformations and for methylene. The PBCS wave function is not a very good approximation for the ground state, accounting for only about half of the correlation energy. The second-order Tamm–Dancoff correction improves the result as much as the double excitation CI . The Tamm–Dancoff terms consisting of two triplet pairs coupled to a singlet, and those relaxing the constraint imposed on the pairwise excitations in the PBCS wave function are important.     

Ab initio calculations on urea

Multiconfiguration wave functions constructed from contracted Gaussian-lobe functions have been found for the ground and valence-excited states of urea. ICSCF molecular orbitals of the excited states were used as the parent configurations for the CI calculations except for the ¹A₁(π → π*) state. The ¹A₁(π → π*) state used as its parent configuration an orthogonal linear combination of natural orbitals obtained from the second root of a three-configuration SCF calculation. The lowest excited states are predicted to be the n π → π* and π → π* triplet states. The lowest singlet state is predicted to be the n π → π* state with an energy in good agreement with the one known UV band at 7.2 eV. The π → π* singlet state is predicted to be about 1.9 eV higher, contrary to several previous assignments which assumed the lowest band was a π → π* amide resonance band. The predicted ionization energy of 9.0 eV makes this and higher states autoionizing.     

Spiro[4.4]nonatetraene and its Positive and Negative Radical Ions: Molectronic Structure Investigations

The electronic structure of spiro[4.4]nonatetraene 1 as well as that of its radical anion and cation were studied by different spectroscopies. The electron‐energy‐loss spectrum in the gas phase revealed the lowest triplet state at 2.98 eV and a group of three overlapping triplet states in the 4.5 – 5.0 eV range, as well as a number of valence and Rydberg singlet excited states. Electron‐impact excitation functions of pure vibrational and triplet states identified various states of the negative ion, in particular the ground state with an attachment energy of 0.8 eV, an excited state corresponding to a temporary electron attachment to the 2b₁ MO at an attachment energy of 2.7 eV, and a core excited state at 4.0 eV. Electronic‐absorption spectroscopy in cryogenic matrices revealed several states of the positive ion, in particular a richly structured first band at 1.27 eV, and the first electronic transition of the radical anion. Vibrations of the ground state of the cation were probed by IR spectroscopy in a cryogenic matrix. The results are discussed on the basis of density‐functional and CASSCF/CASPT2 quantum‐chemical calculations. In their various forms, the calculations successfully rationalized the triplet and the singlet (valence and Rydberg) excitation energies of the neutral molecule, the excitation energies of the radical cation, its IR spectrum, the vibrations excited in the first electronic absorption band, and the energies of the ground and the first excited states of the anion. The difference of the anion excitation energies in the gas and condensed phases was rationalized by a calculation of the Jahn‐Teller distortion of the anion ground state. Contrary to expectations based on a single‐configuration model for the electronic states of 1 , it is found that the gap between the first two excited states is different in the singlet and the triplet manifold. This finding can be traced to the different importance of configuration interaction in the two multiplicity manifolds.     

Singlet–triplet splittings as obtained from the Xα-scattered wave method: A theoretical analysis

The theoretical determination of singlet–triplet splittings of the excited states of closed-shell molecules is discussed with emphasis on the use of the Xα–scattered wave method. With this method, splittings can be computed in two independent ways. Both will have corrections due to orbital relaxation effects. The singlet–triplet splittings obtained with the Xα–scattered wave method for several large organic molecules are reviewed. It is seen that the results using the two splitting formulas differ by a large amount; in fact, they differ by the magnitude of the computed splitting. We provide a criterion for choosing the results obtained with one method over the other by showing that they both give upper bounds to the best result obtainable within the framework of the model. However, because of the large differences between the two methods, the quantitative value of the splitting should be viewed with caution.     

Carbon-beryllium binding in CH2Be

Ab initio molecular orbital theory is used to study carbon-beryllium binding in the lowest singlet and triplet states of CH₂Be. When electron correlation is included, both singlet and triplet states are significantly bound relative to the ground states of CH₂ and Be fragments.     

Rationally Investigating the Influence of T1 Location on Electroluminescence Performance of Aryl Amine Modified Phosphine Oxide Materials

The correspondence between triplet location effect and host‐localized triplet–triplet annihilation and triplet–polaron quenching effects was performed on the basis of a series of naphthyldiphenylamine (DPNA)‐modified phosphine oxide hosts. The number and ratio of DPNA and diphenylphosphine oxide was adjusted to afford symmetrical and unsymmetrical molecular structures and different electronic environments. As designed, the first triplet (T₁) states were successfully localized on the specific DPNA chromophores. Owing to the meso‐ and multi‐insulating linkages, identical optical properties and comparable electrical performance was observed, including the same first singlet (S₁) and T₁ energy levels to support the similar singlet and triplet energy transfer and the close frontier molecular orbital energy levels. This established the basis of rational investigation on T₁ location effect without interference from other optoelectronic factors.     

The Low‐Lying Excited States of 2,2′‐Bithiophene: A Theoretical Analysis

The low‐energy regions of the singlet→singlet, singlet→triplet, and triplet→triplet electronic spectra of 2,2′‐bithiophene are studied using multiconfigurational second‐order perturbation theory (CASPT2) and extended atomic natural orbitals (ANO) basis sets. The computed vertical, adiabatic, and emission transition energies are in agreement with the available experimental data. The two lowest singlet excited states, 1¹B_u and 2¹B_u, are computed to be degenerate, a novel feature of the system to be borne in mind during the rationalization of its photophysics. As regards the observed high triplet quantum yield of the molecule, it is concluded that the triplet states 2³A_g and 2³B_u, separated about 0.4 eV from the two lowest singlet excited states, can be populated by intersystem crossing from nonplanar singlet states.     

SCF and CI Studies of Hund's rules for the effects of electronic correlation and delocalization. I

In connection with the reinterpretation of Hund's multiplicity rules for molecules, a detailed study has been made of the energy differences in the total energy and its components for the triplet and singlet Π_u states of the hydrogen molecule and the analogous states of the four- and six-membered hydrogen atom rings. For the hydrogen molecule, both SCF and CI studies indicated that the outer electron is considerably more contracted in the triplet than in the singlet state. In both approximations, the energy difference is dominated for all bond distances of chemical and physical significance by the electron-nuclear attraction component and not by the electron repulsion component as predicted by simple first-order perturbation theory. Although the correlation energy for each of the states is of the same magnitude as the energy differences considered here, the difference of the correlation energies is much smaller. It had little effect on the qualitative differences between these states of the hydrogen molecule. For the four- and six-membered rings, SCF studies were made on the lowest singlet and triplet states where one electron was promoted from the σ_g to a Π_u orbital. Even though the coupled electrons were more delocalized in these cases, the electron repulsion became relatively more important. However in all cases, the lower state had the highest electron repulsion energy and lower electron-nuclear attraction. The triplet state continued to have the more contracted outer open-shell orbital.     

Half-projected Hartree–Fock natural orbitals for defining CAS–SCF active spaces

We have extended the range of systems to which the half-projected Hartree–Fock (HPHF ) method has been applied, including the triplet state of the wave function. In our implementation, DIIS overcomes the convergence difficulties reported in earlier studies. HPHF allows generation of a symmetry-broken wave function in regions of the potential energy surface where the RHF wave function is triplet-stable. The fractionally occupied natural orbitals (FONOS ) of the HPHF wave function are good starting vectors for CAS –SCF calculations. A CAS –SCF in the space defined by the HPHF FONOS should be used instead of the unrestricted natural orbital CAS –SCF method in regions of triplet stability and for small active space problems. We draw extensive comparisons between the results of both the UNO –CAS and HPNO –CAS methods and those of full CAS –SCF calculations. © 1993 John Wiley & Sons, Inc.     

Pressure dependence of triplet formation in acridine and phenazine vapours

The pressure dependence of T₁ formation in acridine and phenazine vapours was studied between 0.05 torr and 40 torr of an added buffer gas, by microsecond flash photolysis. In contrast to the pressure dependence of anthracene triplet formation, in the heterocyclic compounds the triplet absorption increases slightly with pressure up to 1 torr and then decreases strongly with an increase in pressure up to 30–40 torr. These effects were confirmed by the slight increase followed by a decrease with time of the integrated areas of the T₁ acridine spectra observed at much shorter times by means of nanosecond flash photolysis. The absorption of the lowest triplet was found to have an induction period more than one order of magnitude longer than the laser pulse or the singlet lifetimes revealing that the T₁ state is not populated directly from S₁ but via other electronic triplet states. The pressure effects on triplet formation are interpreted in terms of a reversible intersystem crossing S₁ ? T₁ associated with vibrational relaxation in the triplet states.     

Efficient Direct Reverse Intersystem Crossing between Charge Transfer-Type Singlet and Triplet States in a Purely Organic Molecule

In the field of organic light-emitting diodes, thermally activated delayed fluorescence (TADF) materials have achieved great performance. The key factor for this performance is the small energy gap (ΔE_ST) between the lowest triplet (T₁) and singlet excited (S₁) states, which can be realized in a well-separated donor-acceptor system. Such systems are likely to possess similar charge transfer (CT)-type T₁ and S₁ states. Recent investigations have suggested that the intervention of other type-states, such as locally excited triplet state(s), is necessary for efficient reverse intersystem crossing (RISC). Here, we theoretically and experimentally demonstrate that our blue TADF material exhibits efficient RISC even between singlet CT and triplet CT states without any additional states. The key factor is dynamic flexibility of the torsion angle between the donor and acceptor, which enhances spin-orbit coupling even between the charge transfer-type T₁ and S₁ states, without sacrificing the small ΔE_ST. This results in excellent photoluminescence and electroluminescence performances in all the host materials we investigate, with sky-blue to deep-blue emissions. Among the hosts investigated, the deepest blue emission with CIE coordinates of (0.15, 0.16) and the highest EQE_MAX of 23.9 % are achieved simultaneously.