Singlet-triplet Energy Splitting Research Articles

Theoretical investigation on quinoline-based platinum (II) complexes as efficient singlet oxygen photosensitizers in photodynamic therapy

Geometry optimizations of the quinoline-based platinum (II) complexes (1-R, 2-R) and their related calculations on excited state energies, electronic absorption spectra and orbital populations have been carried out by the hybrid density functional theory (DFT) and its time-dependent approach (TD-DFT). The solvent effects on excitation energies are taken into account using the conductor-like polarizable continuum model (C-PCM). The red-shifted level of absorption bands, energy gaps between the singlet ground state (S 1) and the first triplet excited state (T 1) for each examined complex have been elaborated thoroughly as well. We find that the quinoline-8-thoil (ligand 2) induces much more significant red-shifted level than 8-hydroxyquinoline (ligand 1), and singlet-triplet splitting energy gaps of all examined complexes are bigger than threshold energy to yield singlet oxygen. It is revealed that the electronic red-shifted absorption bands originate from metal-to-ligand charge transfer (MLCT) transitions, and also shown that the quinoline-based Pt (II) complexes with strong donor groups could be considered as potential candidates for unearthing of novel photosensitizers in photodynamic therapy (PDT).

A computational study of the reactivities of four-membered heavy carbene systems

The potential energy surfaces for the chemical reactions of four-membered N-heterocyclic group 14 heavy carbene species have been studied using density functional theory (B3LYP/LANL2DZ). Five four-membered group 14 heavy carbene species, (i-Pr)(2) NP(NR)(2) E:, in which E = C, Si, Ge, Sn, and Pb, were chosen as the model reactants in this work. Also, four kinds of chemical reactions, C-H bond insertion, water addition, alkene cycloaddition, and dimerization, have been used to study the chemical reactivities of these group 14 four-membered N-heterocyclic carbene species. Basically, our present theoretical work predicts that the larger the ∠NEN bond angle of the four-membered group 14 heavy carbene species, the smaller the singlet-triplet splitting, the lower the activation barrier, and, in turn, the more rapid, its chemical reactions to various chemical species. Moreover, our theoretical investigations suggest that the relative carbenic reactivity decreases in the order: C > Si > Ge > Sn > Pb. That is, the heavier the group 14 atom (E), the more stable is its four-membered carbene toward chemical reactions. As a result, our results predict that the four-membered group 14 heavy carbene species (E = Si, Ge, Sn, and Pb) should be more kinetically stable than the observed carbene species and, thus, can be also readily synthesized and isolated at room temperature. Furthermore, the singlet-triplet energy splitting of the four-membered group 14 carbene species, as described in the configuration mixing model attributed to the work of Pross and Shaik, can be used as a diagnostic tool to predict their reactivities. The results obtained allow a number of predictions to be made.

Constrained active space unrestricted mean-field methods for controlling spin-contamination

We have recently proposed a novel approach for obtaining high-spin restricted open-shell Hartree-Fock wave functions by imposing constraints on the unrestricted Hartree-Fock (UHF) method [T. Tsuchimochi and G. E. Scuseria, J. Chem. Phys. 133, 141102 (2010)]. We here extend these ideas to the case where the constraints are released in an active space but imposed elsewhere. If the active space is properly chosen, our constrained UHF (CUHF) method greatly benefits from a controlled broken-symmetry effect while avoiding the massive spin contamination of traditional UHF. We also revisit and apply Löwdin's projection operator to CUHF and obtain multireference wave functions with moderate computational cost. We report singlet-triplet energy splittings showing that our constrained scheme outperforms fully unrestricted methods. This constrained approach can be readily used in spin density functional theory with similar favorable effects.

Theoretical investigations of the reactivities of saturated five-membered ring N-heterocyclic carbenes with heavier Group 14 elements

The potential energy surfaces for the chemical reactions of group 14 carbenes have been studied using density functional theory (B3LYP/LANL2DZ). Five saturated five-membered-ring N-heterocyclic carbene Dipp[upper bond 1 start]N(CH(2))(2)N(Dipp)E[upper bond 1 end]: (five-ring-E:) species, where E = C, Si, Ge, Sn and Pb, have been chosen as model reactants in this work. Also, four kinds of chemical reactions; addition of water, methane insertion, alkene cycloaddition and dimerization, have been used to study the chemical reactivities of these group 14 carbenes. The present theoretical investigations suggest that the relative carbenic reactivity decreases in the order: C > Si > Ge > Sn > Pb. That is, the heavier the group 14 atom (E), the more stable is the carbene towards chemical reactions. This may be the reason that there have been many instances reported of the synthesis and characterization of stable group 14 five-membered-ring N-heterocyclic carbene species with various alkyl protecting substituents at room temperature. Furthermore, the singlet-triplet energy splitting of the five-ring-E:, as described in the configuration mixing model attributed to the work of Pross and Shaik, can be used as a diagnostic tool to predict their reactivities. The results obtained allow a number of predictions to be made.

On the nature of some biradicaloid and antiaromatic Vis/NIR‐chromophores

AbstractDyes derived from the biradicalic oxyallyl and cyclopentadienylium were calculated by time‐dependent density functional theory (TDDFT) and the characteristics of the prominent low‐energy transitions revealed by graphical means. According to theoretical and experimental studies, 4‐aminophenyl‐substituted dyes absorb intensely at long wavelengths up to the near infrared. If the amino groups are removed the absorption wavelengths are changed little. As found in the previous studies on the squaraine and croconaine oxyallyl dyes, the substituents play only a minor role in the spectral excitation. Charge‐transfer‐type excitations do not occur between the donor aryl substituents and the central oxyallyl or cyclopentadienylium acceptor group. This behaviour is exceptional since donor–acceptor compounds tend to produce charge‐transfer‐ or polymethine‐type electronic transitions. The hitherto rarely used electron density difference (EDD) maps clearly unveiled the spectral excitation features. The spectral excitation of the title compounds is predominantly localized at the oxyallyl and cyclopentadienylium groups, respectively. Characteristics of simple chromophoric compounds and of conventional CT‐ and polymethine dyes are given for comparison. The biradicaloid character of these dyes is supported by the calculated low singlet–triplet splitting energies. Spin properties were characterized in terms of expectation values of the S2‐operator and antiaromatic properties in terms of nucleus‐independent chemical shifts (NICS). According to the ΔES/T and <S2> criteria compounds with the acyclic oxyallyl fragment are more biradicaloid. The parent compounds oxyallyl, thioxyallyl and cyclopentadienylium, display extremely large <S2> values. These compounds are triplets in the ground state. The absorption wavelengths of selected biradicaloid species were also calculated by the multi‐reference SORCI method. Copyright © 2010 John Wiley & Sons, Ltd.

Correlated Electrons in Optically Tunable Quantum Dots: Building an Electron Dimer Molecule

We observe the low-lying excitations of a molecular dimer formed by two electrons in a GaAs semiconductor quantum dot in which the number of confined electrons is tuned by optical illumination. By employing inelastic light scattering we identify the intershell excitations in the one-electron regime and the distinct spin and charge modes in the interacting few-body configuration. In the case of two electrons, a comparison with configuration-interaction calculations allows us to link the observed excitations with the breathing mode of the molecular dimer and to determine the singlet-triplet energy splitting.

Theoretical investigations of the reactivities of lattice-framework carbene analogues of the group 14 elements

The potential energy surfaces for the chemical reactions of lattice-framework group 14 heavy carbene species have been studied using density functional theory (B3LYP/LANL2DZ) and the Gibbs free energy method. Five lattice-framework group 14 heavy carbene species, L-F-X: , where X = C, Si, Ge, Sn, and Pb, have been chosen as model reactants in this study. Also, four kinds of chemical reactions, O-H bond insertion, C-H bond insertion, alkene cycloaddition, and dimerization, have been used to study the chemical reactivities of these species. Basically, our present theoretical work predicts that the larger the ∠C(1)XC(2) bond angle of the lattice-framework group 14 heavy carbene species, the smaller the singlet-triplet splitting, the lower the activation barrier, and, therefore, the greater the rates of its chemical reactions with various other species. Moreover, the theoretical investigations suggest that the relative lattice-framework reactivity decreases in the order: C > Si > Ge > Sn ≫ Pb. That is, the heavier the group 14 atom (X), the more stable is its lattice-framework carbene towards chemical reactions. As a result, we predict that the L-F-Pb should be stable, and can be synthesized and isolated at room temperature. Furthermore, the singlet-triplet energy splitting of the lattice-framework group 14 carbene species, as described in the configuration mixing model attributed to the work of Pross and Shaik, can be used as a diagnostic tool to predict their reactivities. The results obtained allow a number of predictions to be made.

Theoretical study of the mechanisms of [3+2] cycloaddition reactions of trimetallaallenes [MMM] (M = C, Si, Ge, Sn, and Pb)

The potential energy surfaces for the cycloaddition reactions of 16 valence-electron trimetallaallene species have been studied using density functional theory (B3LYP/LANL2DZ). Seven trimetallaallene species of the form [double bond splayed left]M=M=M[double bond splayed right] with five-membered-rings where M = C, Si, Ge, Sn, and Pb, have been chosen as model reactants in this work. Also, the alkene cycloaddition has been used to study the chemical reactivities of these 16 valence-electron trimetallaallene species. The present theoretical investigations suggest that their relative reactivity increases in the order: C=C=C < Si=Si=Si < Si=Ge=Si < Ge=Si=Ge < Ge=Ge=Ge < Sn=Sn=Sn < Pb=Pb=Pb. That is, less electronegative and heavier main group atoms will lead to a smaller ΔE(st) and, in turn, will facilitate the [3 + 2] cycloaddition reactions to alkenes. Furthermore, the singlet-triplet energy splitting of the 16 valence-electron trimetallaallene species, as described in the configuration mixing model attributed to the work of Pross and Shaik, can be used as a diagnostic tool to predict their reactivities. The results obtained allow a number of predictions to be made.

Electrical control of singlet-triplet entanglement in lateral quantum dot molecules

We study effects of spin-orbit coupling and electron-electron correlation, which can be electrically tuned, on the singlet-triplet entanglement in double lateral quantum dots charged with two electrons. We have found that the magnetic character of a double-dot system can be changed from diamagnetic to paramagnetic, only by adjusting the strength of spin-orbit coupling. Coulomb interaction leads to an unusual singlet-triplet energy splitting, accompanied by a shift of this transition energy to the lower magnetic field side in the energy spectrum.

Silicon-rich/silica multilayers: A means to provide a link between the excitonic 1D quantum confinement and the photoluminescence parameters

The photoluminescence properties—intensity I PL, emission energy E PL and decay lifetime τ PL—of silicon-rich silicon oxide (SRSO)/silica (SO) multilayers are investigated as a function of the optical pump flux ( φ) of an argon laser and the measurement temperature in four kinds of samples corresponding to different SRSO sublayer thicknesses (namely 0.7, 1.4, 3.3 and 4.5 nm). The excitons created by the incident laser light mainly within the SRSO layers or at the SRSO/silica interface are confined in the multilayer growth direction (normal to the layers). This so-called 1D exciton quantum confinement effect has been independently described by two models (the state filling, the electron–hole exchange interaction). It is shown in this paper that both models are complementary since we have been able to reproduce, on the one hand, flux dependence of main PL features (energy, intensity and lifetime) of all fabricated samples and on the other hand, the evolution of the singlet–triplet energy splitting as a function of the SRSO sublayer thickness.

Singlet−Triplet Energy Splitting and Excited States of Phenylnitrene

The vertical and adiabatic singlet-triplet energy splittings (Delta E ST) of phenylnitrene were computed by a variety of multireference configuration interaction and perturbation theory methods employing basis sets of up to quadruple-xi quality and extrapolation to the complete basis set limit. The vertical and adiabatic energy gaps are 18.9 and 15.9 kcal mol (-1), respectively, the latter in reasonable agreement with the revised experimental value of 15.1 +/- 0.2 kcal mol (-1). The energy difference between both states at the geometry of the a (1)A 2 singlet state was also considered and amounts to 13.8 kcal mol (-1). In obtaining accurate state energy splittings, basis set completeness turns out to be a more important issue than the level of dynamical electron correlation treatment. Density functional theory that is frequently employed to investigate phenylnitrenes and their rearrangements yields varying results and, depending on the functional, gives adiabatic energy differences between 9 and 16 kcal mol (-1). The b (1)A 1 state has a similar geometry as the ground state of 1 and is 31 kcal mol (-1) higher in energy. According to best estimates, the next higher singlet states, c (1)A 1 and d (1)B 1, are 57 and 72 kcal mol (-1) above the ground state. In the triplet manifold, vertical excitation energies to the A (3)B 1 and B (3)A 2 states are 71 and 77 kcal mol (-1), respectively.

Compression effects in helium-like atoms [formula omitted] constrained by hard spherical walls

Ground and lowest triplet S state energies and other properties are obtained for confined helium-like atoms { Z = 1 , … , 5 } spherically enclosed by impenetrable boxes of varying size. Wave functions are variationally optimized within generalized Hylleraas bases fulfilling appropriate boundary conditions. For all systems, enhanced confinement leads to increased total energies and singlet–triplet energy splittings.

Theoretical Investigations of the Reactivities of Cationic Six-membered Carbene Analogues of Group 14 Elements

The potential energy surfaces for the chemical reactions of cationic six-membered group 14 heavy carbene species have been studied using density functional theory (B3LYP/LANL2DZ) and CCSD (CCSD/LANL2DZ//B3LYP/LANL2DZ) methods. Five six-membered group 14 cationic heavy carbene species, [HC(CMeNPh)2E:](+), where E = C, Si, Ge, Sn, and Pb, have been chosen as model reactants in this work. Also, four kinds of chemical reaction, C-H bond insertion, multiple bond cycloaddition, dimerization, and O-H bond insertion, have been used to study the chemical reactivities of these group 14 cationic carbene species. Basically, our present theoretical work predicts that the larger the angle NEN bond angle and the smaller the singlet-triplet splitting of the carbene, the lower its activation barriers will be and, in turn, the more rapid are its chemical reactions with other species. Moreover, the theoretical investigations suggest that the relative carbenic reactivity decreases in the order C > Si > Ge > Sn > Pb. That is, the heavier the group 14 atom (E), the more stable is its cationic carbene toward chemical reaction. As a result, we predict that the cationic six-membered group 14 carbene species (E = C, Si, Ge, Sn, and Pb) should be stable, readily synthesized, and isolated at room temperature. Our computational results are in good agreement with the available experimental observations. Furthermore, the singlet-triplet energy splitting of the carbene, as described in the configuration mixing model attributed to the work of Pross and Shaik, can be used as a diagnostic tool to predict its reactivities. The results obtained allow a number of predictions to be made.

Electronic Structure of the Alkyne-Bridged Dicobalt Hexacarbonyl Complex Co2 μ-C2H2 (CO)6: Evidence for Singlet Diradical Character and Implications for Metal−Metal Bonding

A series of ab initio calculations are presented on the alkyne-bridged dicobalt hexacarbonyl cluster Co2 micro-C2H2 (CO)6, indicating that this compound has substantial multireference character, which we interpret as evidence of singlet diradical behavior. As a result, standard theoretical methods such as restricted Hartree-Fock (RHF) or Kohn-Sham (RKS) density functional theory cannot properly describe this compound. We have therefore used complete active space (CAS) methods to explore the bonding in and spectroscopic properties of Co2 micro-C2H2 (CO)6. CAS methods identify significant population of a Co-Co antibonding orbital, along with Co-pi* back-bonding, and a relatively large singlet-triplet energy splitting. Analysis of the electron density and related quantities, such as energy densities and atomic overlaps, indicates a small but significant amount of covalent bonding between cobalt centers.

Treatment of singlet–triplet splitting of a set of phenylene ethylenes organic molecules by TD-DFT

Density-functional theory (DFT), and its time-dependent (TD) version, is applied to investigate the singlet–triplet energy splitting of a set of single molecules useful constituents of opto-electronics devices. The splitting relates to the singlet and triplet exciton formation rates and thus might influence the quantum efficiency for electro-luminescence. Systematic calculations are performed to address the origin of the discrepancies between experimental and calculated values. The results are found to strongly depend on the DFT level employed (pure and hybrid GGA and meta-GGA approaches) which makes difficult the choice of an accurate enough automated approximation for DFT-based studies in the field of nano-photonics.

Theoretical Studies of the [2 + 4] Diels−Alder Cycloaddition Reactions of Alkene Analogues of the Group 13 Elements with Toluene

The potential energy surfaces for the cycloaddition reactions of formally double-bonded molecules containing group 13 elements have been studied using density functional theory (B3LYP/LANL2DZ). Five group 13 alkene analogues, ArX=XAr, where X = B, Al, Ga, In, and Tl, have been chosen as model reactants in this work. Our present theoretical work predicts that the smaller the singlet-triplet splitting in ArX=XAr, the lower the activation barrier and, in turn, the more rapid are its [4 + 2] cycloaddition reactions. Moreover, the theoretical investigations suggest that the relative dimeric reactivity decreases in the order B > Al > Ga > In > Tl. That is, the heavier the group 13 atom (X), the more stable is its dimetallene toward chemical reactions. In consequence, our results predict that the dimetallenes containing heavier group 13 elements (in particular, X = Ga, In, and Tl) should be stable and should be readily synthesized and isolated at room temperature. This is in good agreement with available experimental observations. Besides this, the singlet-triplet energy splitting of a dimetallene, as described in the configuration mixing model attributed to the work of Pross and Shaik, can be used as a diagnostic tool to predict its reactivity. The results obtained allow a number of predictions to be made.

Theoretical Designs for Neutral Five-Membered Carbene Analogues of the Group 13 Elements: A New Target for Synthesis

Potential energy surfaces for the chemical reactions of neutral five-membered group 13 carbenoids have been studied using density functional theory (B3LYP/LANL2DZ). Five five-membered group 13 carbenoid species, HCMeP(PhN)2X, where X = B, Al, Ga, In, and Tl, have been chosen as model reactants in this work. Also, three kinds of chemical reaction, C-H bond insertion, alkene cycloaddition, and dimerization, have been used to study the chemical reactivities of these group 13 carbenoids. Our present theoretical work predicts that the larger the angleNXN bond angle in the neutral five-membered group 13 carbenoid, the smaller the singlet-triplet splitting, the lower the activation barrier, and, in turn, the more rapid are its various chemical reactions. Moreover, the theoretical investigations suggest that the relative carbenoidic reactivity decreases in the order B > Al > Ga > In > Tl. That is, the heavier the group 13 atom (X), the more stable is its carbenoid with respect to chemical reactions. As a result, we predict that the neutral five-membered group 13 carbenoids (X = Al, Ga, In, and Tl) should be stable, readily synthesized, and isolated at room temperature. Furthermore, the neutral five-membered group 13 carbenoid singlet-triplet energy splitting, as described in the configuration mixing model attributed to the work of Pross and Shaik, can be used as a diagnostic tool to predict their reactivities. The results obtained allow a number of predictions to be made.

A theoretical study on phosphasilylenes CPSi-X (X=H, CN, NH 2 and OMe)

Singlet–triplet energy splittings (Δ E s–t,X) for 24 CPSi-X silylenic reactive intermediates, are compared and contrasted at 10 levels of theory: B1LYP/6-31++G**, B3LYP/6-31++G**, MP2/6-31G*, HF/6-311++G**, B1LYP/6-311++G**, B3LYP/6-311++G**, MP2/6-311++G**, MP4(SDTQ)/6-311++G**, QCISD(T)/6-311++G** and CCSD(T)/6-311++G** (where X=H, CN, NH 2 and OMe). Singlet (s) and/or triplet (t) CPSi-X, are confined to the following three structures: 3-X-2-phospha-1-silacyclopropenylidene ( 1 s-X, 1 t-X); [(X-phosphino)methylene]silylene ( 2 s-X, 2 t-X); or X-methylidynephosphinesilylene ( 3 s-X, 3 t-X). The relative orders of Δ E s–t,X as functions of substituents (X) are different for each structure. All the singlet state silylenes appear more stable than their corresponding triplet states. Among all isomeric sets of silylenes studied, the least stable silylene emerges as triplet acyclic 2 t-X. Good linear correlations are found between the LUMO–HOMO energy gaps of the singlet acyclic silylenes 2 s-X and 3 s-X, and their corresponding Δ E s–t,X, calculated at B3LYP/6-311++G**. Relative energies of the divalent 3 s-X and/or 3 t-X structures are plotted as a function of the divalent bond angle ∠X–Si–CN. The singlet and triplet states of CPSi-H cross at 127°. Substituents widen the cross point angles. The global minimum, among CPSi-H and CPSi-CN species, appears to be the singlet cyclic 1 s-X. The global minimum among CPSi-NH 2 and CPSi-OMe silylenes turnsout to be the singlet acyclic 3 s-X.

Confined helium atom low-lying S states analyzed through correlated Hylleraas wave functions and the Kohn-Sham model

Calculation including the electron correlation effects is reported for the ground 1 1S and lowest triplet 1 3S state energies of the confined helium atom placed at the center of an impenetrable spherical box. While the adopted wave-functional treatment involves optimization of three nonlinear parameters and 10, 20, and 40 linear coefficients contained in wave functions expressed in a generalized Hylleraas basis set that explicitly incorporates the interelectronic distance r12, via a Slater-type exponent and through polynomial terms entering the expansion, the Kohn-Sham model employed here uses the Perdew and Wang exchange-correlation functional in its spin-polarized version within the local-density approximation (LDA) with and without the self-interaction correction. All these calculations predict a systematic increase in the singlet-triplet energy splitting toward the high confinement regime, i.e., when the box radius is reduced. By using the variational results as benchmark, it is found that the LDA underestimates the singlet-triplet energy splitting, whereas the self-interaction correction overestimates such a quantity.

In search of triplet ground state GeCNX germylenes (X = H, F, Cl, and Br): An ab initio and DFT study

Singlet–triplet energy splittings for 24 GeCNX germylenic reactive intermediates are compared and contrasted at 10 levels of theory: B1LYP/6-311++G**, B3LYP/6-311++G**, MP3/6-311+G*, MP3/LANL2DZ, MP2/6-311++G**, MP4(SDTQ)/6-311++G**, QCISD(T)/6-311++G**, CCSD(T)/6-311++G**, G1 and G2 (where X = H, F, Cl, and Br). Singlet ( s) and/or triplet ( t) GeCNX, are confined to the following three structures: 3-X-2-aza-1-germylacyclopropenylidene ( 1 s- X , 1 t- X ), [(X-imino)methylene]germylene ( 2 s- X , 2 t- X ), or X-cyanogermylene ( 3 s- X , 3 t- X ). For every of these three structures the order of singlet–triplet energy separations (Δ E s– t, X ), appears as a function of electro-negativity (F > Cl > Br > H). Fascinatingly, two triplet structures 2 t- H and 3 t- H appear more stable than their corresponding singlet states. Good linear correlations are found between the LUMO–HOMO energy gaps of the singlet germylenes, and their corresponding singlet–triplet energy separations, calculated at B3LYP/6-311++G**. Relative energies of the divalent 3 s- X and/or 3 t- X structures are plotted as a function of the divalent bond angle ∠X-Ge-CN, where the singlet and triplet germylenes GeCNH cross at 134°. Little germanium d orbital valence participation is found in the cyclic triplet structures 1 t- X . The global minimum, among six GeCNH species, appears to be the singlet cyclic 1 s- H . However, the global minima among the other eighteen GeCNX (X≠H) species appear to be the singlet acyclic 3 s- X . Among all the calculation methods employed, B3LYP appears as the method of choice.