Singlet Wave Functions Research Articles

The role of crystal packing on the optical response of trialkyltetrelethynyl acenes.

The electronic and optical responses of an organic semiconductor (OSC) are dictated by the chemistries of the molecular or polymer building blocks and how these chromophores pack in the solid state. Understanding the physicochemical nature of these responses is not only critical for determining the OSC performance for a particular application, but the UV/visible optical response may also be of potential use to determine aspects of the molecular-scale solid-state packing for crystal polymorphs or thin-film morphologies that are difficult to determine otherwise. To probe these relationships, we report the quantum-chemical investigation of a series of trialkyltetrelethynyl acenes (tetrel = silicon or germanium) that adopt the brickwork, slip-stack, or herringbone (HB) packing configurations; the π-conjugated backbones considered here are pentacene and anthradithiophene. For comparison, HB-packed (unsubstituted) pentacene is also included. Density functional theory and G0W0 (single-shot Green's function G and/or screened Coulomb function W) electronic band structures, G0W0-Bethe-Salpeter equation-derived optical spectra, polarized ϵ2 spectra, and distributions of both singlet and triplet exciton wave functions are reported. Configurational disorder is also considered. Furthermore, we evaluate the probability of singlet fission in these materials through energy conservation relationships.

Regulating Singlet-Triplet Energy Gaps through Substituent-Driven Modulation of the Exchange and Coulomb Interactions.

Control of the singlet-triplet energy gap (ΔEST) is central to realizing productive energy conversion reactions, photochemical reaction trajectories, and emergent applications that exploit molecular spin physics. Despite this, no systematic methods have been defined to tune ΔEST in simple molecular frameworks, let alone by an approach that also holds chromophore size and electronic structural parameters (such as the HOMO-LUMO gap) constant. Using a combination of molecular design, photophysical and potentiometric experiments, and quantum chemical analyses, we show that the degree of electron-electron repulsion in excited singlet and triplet states may be finely controlled through the substitution pattern of a simple porphyrin absorber, enabling regulation of relative electronically excited singlet and triplet state energies by the designed restriction of the electron-electron Coulomb (J) and exchange (K) interaction magnitudes. This approach modulates the ΔEST magnitude by controlling the densities of state in the occupied and virtual molecular orbital manifolds, natural transition orbital polarization, and the relative contributions of one electron transitions involving select natural transition orbital pairs. This road map, which regulates electron density overlaps in the occupied and virtual states that define the singlet and triplet wave functions of these chromophores, enables new approaches to preserve excitation energy despite intersystem crossing.

Time evolution of spin singlet in static homogeneous exchange and magnetic fields

Within the framework of an idealized theoretical model, we study the effect of external static homogeneous exchange and magnetic field on the spin part of the singlet wave function of two electrons. We begin by revising the traditional (textbook) approach to the spin singlet. Basing our own approach solely on the property of invariance under rotations of the coordinate system and using the theory of spinor invariants, we derive a generalized representation of the spin singlet whose main feature is that the spins are in mutually time-reversed states. We show that exactly this feature predetermines the actual form of the Hamiltonian of interaction with the external field and stipulates time evolution of the singlet. Some applications of these results to the theory of superconductivity and spin chemistry are presented. In particular, it is shown that the case of ferromagnetic superconductors constitutes a good illustration of the validity of our quantum-mechanical consideration.

QCD Theory of the Hadrons and Filling the Yang–Mills Mass Gap

The rank-3 antisymmetric tensors which are the magnetic monopoles of SU(N) Yang–Mills gauge theory dynamics, unlike their counterparts in Maxwell’s U(1) electrodynamics, are non-vanishing, and do permit a net flux of Yang–Mills analogs to the magnetic field through closed spatial surfaces. When electric source currents of the same Yang–Mills dynamics are inverted and their fermions inserted into these Yang–Mills monopoles to create a system, this system in its unperturbed state contains exactly three fermions due to the monopole rank-3 and its three additive field strength gradient terms in covariant form. So to ensure that every fermion in this system occupies an exclusive quantum state, the Exclusion Principle is used to place each of the three fermions into the fundamental representation of the simple gauge group with an SU(3) symmetry. After the symmetry of the monopole is broken to make this system indivisible, the gauge bosons inside the monopole become massless, the SU(3) color symmetry of the fermions becomes exact, and a propagator is established for each fermion. The monopoles then have the same antisymmetric color singlet wavefunction as a baryon, and the field quanta of the magnetic fields fluxing through the monopole surface have the same symmetric color singlet wavefunction as a meson. Consequently, we are able to identify these fermions with colored quarks, the gauge bosons with gluons, the magnetic monopoles with baryons, and the fluxing entities with mesons, while establishing that the quarks and gluons remain confined and identifying the symmetry breaking with hadronization. Analytic tools developed along the way are then used to fill the Yang–Mills mass gap.

Chi _{c1} and chi _{c2} polarization as a probe of color octet channel

We analyze joint LHC data on the production of chi _{c1} and chi _{c2} mesons together with the polarization data obtained very recently by the CMS Collaboration at sqrt{s} = 8 TeV. Our consideration is based on the k_T-factorization approach and nonrelativistic QCD formalism for the formation of bound states. The observed polar anisotropy of chi _{c1} and chi _{c2} decays can be described as a combined effect of the color-singlet and color-octet contributions. We extract the corresponding long-distance matrix elements from the fits. Our fits point to unequal color singlet wave functions for chi _{c1} and chi _{c2} states.

Diradicalar Character and Ring Stability of Mesoionic Heterocyclic Oxazoles and Thiazoles by Ab Initio Mono and Multi-Reference Methods.

Mesoionics are neutral compounds that cannot be represented by a fully covalent or purely ionic structure. Among the possible mesomeric structures of these compounds are the diradical electronic configurations. Theoretical and experimental studies indicate that some mesoionic rings are unstable, which may be related to a significant diradical character, that until then is not quantified. In this work, we investigated the diradical character of four heterocycles: 1,3-oxazol-5-one, 1,3-oxazol-5-thione, 1,3-thiazole-5-one, and 1,3-thiazole-5-thione. The oxazoles are known to be significatively less stable than thiazoles. DFT and ab initio single (B3LYP, MP2, CCSD, and QCISD) and ab initio multi-reference (MR-CISD) methods with three basis sets (6-311+G(d), aug-cc-pVDZ, and aug-cc-pVTZ) were employed to assess the diradical character of the investigated systems, in gas phase and DMSO solvent, from three criteria: (i) HOMO-LUMO energy gap, (ii) determination of energy difference between singlet and triplet wave functions, and (iii) quantification of the most significant diradical character (y0, determined in the unrestricted formalism). All of the results showed that the diradical character of the investigated systems is very small. However, the calculated electronic structures made it possible to identify the possible origin of the oxazoles instability, which can help the design of mesoionic systems with the desired properties.

Photophysics of BODIPY-Based Photosensitizer for Photodynamic Therapy: Surface Hopping and Classical Molecular Dynamics.

Halogenated BODIPY derivatives are emerging as important candidates for photodynamic therapy of cancer cells due to their high triplet quantum yield. We probed fundamental photophysical properties and interactions with biological environments of such photosensitizers. To this end, we employed static TD-DFT quantum chemical calculations as well as TD-DFT surface hopping molecular dynamics on potential energy surfaces resulting from the eigenstates of the total electronic Hamiltonian including the spin-orbit (SO) coupling. Matrix elements of an effective one-electron spin-orbit Hamiltonian between singlet and triplet configuration interaction singles (CIS) auxiliary wave functions are calculated using a new code capable of dealing with singlets and both restricted and unrestricted triplets built up from up to three different and independent sets of (singlet, alpha, and beta) molecular orbitals. The interaction with a biological environment was addressed by using classical molecular dynamics (MD) in a scheme that implicitly accounts for electronically excited states. For the surface hopping trajectories, an accelerated MD approach was used, in which the SO couplings are scaled up, to make the calculations computationally feasible, and the lifetimes are extrapolated back to unscaled SO couplings. The lifetime of the first excited singlet state estimated by semiclassical surface hopping simulations is 139 ± 75 ps. Classical MD demonstrates that halogenated BODIPY in the ground state, in contrast to the unsubstituted one, is stable in the headgroup region of minimalistic cell membrane models, and while in the triplet state, the molecule relocates to the membrane interior ready for further steps of photodynamic therapy.

Ligand- and Metal-Based Reactivity of a Neutral Ruthenium Diolefin Diazadiene Complex: The Innocent, the Guilty and the Suspicious.

Coordination of the diazadiene diolefin ligand (trop2dad) to ruthenium leads to various complexes of composition [Ru(trop2dad)(L)]. DFT studies indicate that the closed‐shell singlet (CSS), open‐shell singlet (OSS), and triplet electronic structures of this species are close in energy, with the OSS spin configuration being the lowest in energy for all tested functionals. Singlet‐state CASSCF calculations revealed a significant multireference character for these complexes. The closed‐shell singlet wavefunction dominates, but these complexes have a significant (≈8–16 %) open‐shell singlet [d7‐RuI(L)(trop2dad.−)] contribution mixed into the ground state. In agreement with their ambivalent electronic structure, these complexes reveal both metal‐ and ligand‐centered reactivity. Most notable are the reactions with AdN3, diazomethane, and a phosphaalkyne leading to scission of the C−C bond of the diazadiene (dad) moiety of the trop2dad ligand, resulting in net (formal) nitrene, carbene, or P≡C insertion in the dad C−C bond, respectively. Supporting DFT studies revealed that several of the ligand‐based reactions proceed via low‐barrier radical‐type pathways, involving the dad.− ligand radical character of the OSS or triplet species.

Core excitations of the solid oxygen ε phase: periodic hybrid density functional theory studies with localized atomic basis

The e and the superconducting ζ oxygen phases at high pressures consist of (O2)4 cuboid unit cells. Previous lattice optimizations and vibrational calculations with periodic hybrid density functional theory using atomic basis sets addressed the evolution of the lattice parameters, Raman and infrared spectra as well as the e–ζ phase transition pressure; in all cases, the results found with hybrid exchange–correlation (XC) functionals are in excellent agreement with experiments. We address here the evolution of the core 1s–σ u * and 1s–1π g * transitions for the low-pressure regime of the e phase with GGA and hybrid-type XC functionals. Again, hybrid XC functionals yield a better agreement with K-edge results for the pressure evolution in the 10–40 GPa range for which experimental data are available. However, a slower dependence of the 1π g * excitation with pressure is found with respect to experimental data, irrespective of whether a GGA or hybrid-type XC functional is used. We provide arguments to explain the poorer theoretical description for the 1π g * excitation as arising from the rather strong multireference character of the unit cell singlet wavefunction in the low-pressure regime. Some general conclusions are drawn concerning the accuracy of hybrid versus GGA-type exchange correlation functionals for this complex system.

Molecular Road Map to Tuning Ground State Absorption and Excited State Dynamics of Long-Wavelength Absorbers.

Realizing chromophores that simultaneously possess substantial near-infrared (NIR) absorptivity and long-lived, high-yield triplet excited states is vital for many optoelectronic applications, such as optical power limiting and triplet-triplet annihilation photon upconversion (TTA-UC). However, the energy gap law ensures such chromophores are rare, and molecular engineering of absorbers having such properties has proven challenging. Here, we present a versatile methodology to tackle this design issue by exploiting the ethyne-bridged (polypyridyl)metal(II) (M; M = Ru, Os)-(porphinato)metal(II) (PM'; M' = Zn, Pt, Pd) molecular architecture (M-(PM')n-M), wherein high-oscillator-strength NIR absorptivity up to 850 nm, near-unity intersystem crossing (ISC) quantum yields (ΦISC), and triplet excited-state (T1) lifetimes on the microseconds time scale are simultaneously realized. By varying the extent to which the atomic coefficients of heavy metal d orbitals contribute to the one-electron excitation configurations describing the initially prepared singlet and triplet excited-state wave functions, we (i) show that the relative magnitudes of fluorescence (k0F), S1 → S0 nonradiative decay (knr), S1 → T1 ISC (kISC), and T1 → S0 relaxation (kT1→S0) rate constants can be finely tuned in M-(PM')n-M compounds and (ii) demonstrate designs in which the kISC magnitude dominates singlet manifold relaxation dynamics but does not give rise to T1 → S0 conversion dynamics that short-circuit a microseconds time scale triplet lifetime. Notably, the NIR spectral domain absorptivities of M-(PM')n-M chromophores far exceed those of classic coordination complexes and organic materials possessing similarly high yields of triplet-state formation: in contrast to these benchmark materials, this work demonstrates that these M-(PM')n-M systems realize near unit ΦISC at extraordinarily modest S1-T1 energy gaps (∼0.25 eV). This study underscores the photophysical diversity of the M-(PM')n-M platform and presents a new library of long-wavelength absorbers that efficiently populate long-lived T1 states.

Singlet-Triplet Gaps through Incremental Full Configuration Interaction.

The method of increments is herein applied to produce accurate singlet-triplet gaps in a variety of challenging polyatomic systems involving main group elements. This strategy computes incremental Full Configuration Interaction (iFCI) energies for the two spin states in a size-extensive n-body expansion. iFCI avoids exponential costs when n is small and thus is dependent on choice of reference function to maintain good accuracy at polynomial cost. The new algorithm presented in this article therefore employs a high-spin perfect pairing reference to capture the major qualities of the singlet and triplet wave functions at n = 0. Systematic studies will show that singlet-triplet gap predictions approach 1 kcal/mol accuracy at small n (n ≤ 3) compared with available experimental and high-level theoretical values.

Spin-orbit coupling mechanism of singlet oxygen [formula omitted] quenching by solvent vibrations

Degenerate character of the O2(a1Δg) state and of the charge-transfer configurations (CTCs) from solvent to the oxygen open-shell orbitals explains the enhancement of spin-orbit coupling (SOC) which is necessary to overcome spin prohibition during singlet oxygen a1Δg quenching. The former mechanism of non-radiative transition O2(a1Δg)→O2(X3Σg-) based on electronic energy transfer to the solvent vibrational levels (e-v mechanism) is supplemented here by explicit analysis of SOC effects mediated by solvent and O2 vibrations. The SOC matrix element between one component of the initial electronic excited singlet a1Δg state and the final ground triplet X3Σg- state in the oxygen moiety is not equal to zero (as in free O2) in the collision complex with solvent molecule (M) when all possible CTCs of the type O2-…M+ are accounted for. Intermolecular configuration interaction between CTC and locally excited states obeys a simple symmetry selection rule which provides finally the SOC matrix element with a guarantee of large orbital rotation around the molecular oxygen axis creating a torque. The CTCs admixtures into the singlet and triplet wave functions in the collision complex O2…M ensure the SOC enhancement inside the O2 moiety and let the spin-prohibited singlet oxygen a1Δg quenching to become effectively allowed in terms of e-v mechanism. In the new model the solvent is not only a passive “sink” for the singlet oxygen excitation energy but serves as an active perturber of the oxygen open shell and finally – of the whole spin dynamics in the collision system.

Variational Optimization of the Second-Order Density Matrix Corresponding to a Seniority-Zero Configuration Interaction Wave Function.

We perform a direct variational determination of the second-order (two-particle) density matrix corresponding to a many-electron system, under a restricted set of the two-index N-representability P-, Q-, and G-conditions. In addition, we impose a set of necessary constraints that the two-particle density matrix must be derivable from a doubly occupied many-electron wave function, i.e., a singlet wave function for which the Slater determinant decomposition only contains determinants in which spatial orbitals are doubly occupied. We rederive the two-index N-representability conditions first found by Weinhold and Wilson and apply them to various benchmark systems (linear hydrogen chains, He, N2, and CN(-)). This work is motivated by the fact that a doubly occupied many-electron wave function captures in many cases the bulk of the static correlation. Compared to the general case, the structure of doubly occupied two-particle density matrices causes the associate semidefinite program to have a very favorable scaling as L(3), where L is the number of spatial orbitals. Since the doubly occupied Hilbert space depends on the choice of the orbitals, variational calculation steps of the two-particle density matrix are interspersed with orbital-optimization steps (based on Jacobi rotations in the space of the spatial orbitals). We also point to the importance of symmetry breaking of the orbitals when performing calculations in a doubly occupied framework.

Breaking E6 via trinification in F‐theory

We consider E6 GUT model in F‐theory approach where E6 is broken via trinification to the Standard Model (SM) gauge group using non‐abelian fluxes. Including the gauge singlet wave function we found hierarchically small values for both the μ term as well as Dirac neutrino masses.

The unexpected absence of Kondo resonance in the photoemission spectrum of CeAl2

We study the temperature dependent Ce 4f spectral evolution of a well known Kondo system, CeAl2, for a range extending beyond 2 eV below the Fermi level, using photoemission spectroscopy. Interestingly, the spectral evolution is inconsistent with the predictions of the many-body spectral function calculations corresponding to the Kondo resonance interpretation of the screened Ce 4f photoemission features. In order to explain our spectral evolution we propose the phenomenon of collapse of the Kondo singlet wavefunction upon photoelectron kinetic energy measurement. Our proposal suggests that the screened final states in photoemission spectroscopy are not quantum states.

Electron Dynamics of Interatomic Coulombic Decay in Quantum Dots: Singlet Initial State

In this paper we investigated the interatomic Coulombic decay (ICD) of a resonance singlet state in a model potential for two few-electron semiconductor quantum dots (QDs) by means of electron dynamics. We demonstrate that ICD is the major decay process of the resonance for the singlet wave function and compare the total and partial decay widths as a function of the QD separation with that from our previous study on the corresponding triplet states [1].

The electronic structure of Ullman's biradicals: an orthogonal valence bond interpretation

This paper addresses the electronic structure of Ullman's organic biradical, bis(nitronyl) nitroxide, in the frame of ab initio wave function based methods, both using standard (delocalized) molecular orbital methods and a valence bond strategy based on orthogonal localized orbitals. The aim of this study is to clarify the origin of the magnetic coupling of this molecule and to understand the recently observed unexpected behavior of the computed magnetic coupling constant with respect to the use of different theoretical methods. A detailed analysis of the physical effects that govern the correct description of the main characteristics of the electronic structure, in particular the spin density, reveals that the wave functions of the radical fragments are better seen as arising from the interaction of three unpaired electrons and that the intuitive picture of one unpaired electron per fragment is oversimplified and can lead to incorrect results. Furthermore, we establish that both the triplet and the singlet wave functions are well represented by the antisymmetrized product of the two fragment wavefunctions, thus corroborating previous observations concerning the low weight of the ionic structures (hopping of one electron from one fragment to the other) in the biradical singlet wavefunction. The use of the orthogonal valence bond formalism has also allowed us to extract a set of parameters for the fragment (direct exchange, hopping integral, on-site repulsion) which can be used for larger magnetic systems in studies based on model Hamiltonians.

DFT spin–orbit coupling between singlet and triplet excited states: A case of psoralen compounds

We present a computational protocol in which our method is used to compute spin–orbit (SO) matrix elements on time-dependent-density functional theory (TD-DFT). These SO contributions, computed employing our SO program package, MolSOC, have been expressed, in turn, in terms of weighted coefficients and SO matrix elements between singlet and triplet wave functions arising from a given one-electron transition. The protocol has been applied to study psoralen compound and its derivatives obtained from the replacement of one oxygen with sulfur or selenium. The obtained results have been compared with those reported in literature.

Spin-orbit interactions between interchain excitations in conjugated polymers

Motivated by the reported enhanced singlet exciton yield in light-emitting polymers, we investigate spin-orbit coupling between Coulombically bound interchain excitations. We show theoretically that because of the close similarity of the singlet and triplet interchain wave functions, spin-orbit coupling between these states is negligible. Using density matrix renormalization group calculations on model systems, we confirm these theoretical predictions: spin-orbit coupling between interchain states is typically ${10}^{3}--{10}^{4}$ times smaller than between corresponding intramolecular states, being typically ca. $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}\text{ }\text{eV}$ for disordered polymers. We discuss the implication of these results for the possibly enhanced singlet exciton yield in light-emitting polymers.

Phase diagram and single-particle spectrum of CuO2 high-Tc layers: variational cluster approach to the three-band Hubbard model

A detailed numerical study of the three-band Hubbard (3BH) model in the underdoped region is carried out, both in the hole- as well as in the electron-doped case, by means of the variational cluster approach. The phase diagram and the low-energy single-particle spectrum are found to be very similar to recent results for the single-band Hubbard model with next-nearest-neighbor hoppings t′. In particular, we obtain a mixed antiferromagnetic+superconducting phase at low doping with a first-order transition to a pure superconducting phase accompanied by phase separation. Despite the fact that the physically relevant and generally accepted parameters (tpp/tpd, tpd/Δpd) of our 3BH-model are not in the small regime, required for a ‘downward’ projection onto a single-band model, in the single-particle spectrum a clear Zhang–Rice (ZR) singlet band (with a projection on d- and p-orbitals consistent with the phase factor of the ZR singlet wave function) can be seen. It displays an incoherent and a coherent part, in which holes enter upon doping around (π/2, π/2). The latter is very similar to the coherent quasi-particle band crossing the Fermi surface in the t–t′–U single-band model, with generally accepted values of the parameters. Doped electrons go instead into the upper Hubbard band, first filling the regions of the Brillouin zone around (π, 0). This fact can be related to the enhanced robustness of the antiferromagnetic phase as a function of electron doping compared to hole doping.