Internal and external heavy-atom effects on phosphorescence radiative lifetimes calculated using a mean-field spin–orbit Hamiltonian

Chalcogen atom effect on the intersystem crossing kinetic constant of oxygen- and sulfur disubstituted heteroporphyrins

The modulation of the photophysical properties of di-substituted porphyrin rings upon the oxygen and sulfur-for-nitrogen replacement has been investigated at density functional theory (DFT) and its time-dependent formulation (TDDFT). The considered properties range from structural behaviors and excitation energies to spin-orbit coupling (SOC) and nonradiative intersystem kinetic constants. Results show that the SOC strongly increase upon chalcogen substitution and, accordingly, the computed nonradiative kinetic constant also indicate an efficient singlet-triplet intersystem crossing in the sulfur containing macrocycle. The presented results indicate an alternative way to properly modulate the porphyrin's crucial properties for their use in photodynamic therapy, without resorting to the use of heavy atoms.

Sulphur- and Selenium-for-Oxygen Replacement as a Strategy to Obtain Dual Type I/Type II Photosensitizers for Photodynamic Therapy

The effect on the photophysical properties of sulfur- and selenium-for-oxygen replacement in the skeleton of the oxo-4-dimethylaminonaphthalimide molecule (DMNP) has been explored at the density functional (DFT) level of theory. Structural parameters, excitation energies, singlet–triplet energy gaps (ΔES-T), and spin–orbit coupling constants (SOC) have been computed. The determined SOCs indicate an enhanced probability of intersystem crossing (ISC) in both the thio- and seleno-derivatives (SDMNP and SeDMNP, respectively) and, consequently, an enhancement of the singlet oxygen quantum yields. Inspection of Type I reactions reveals that the electron transfer mechanisms leading to the generation of superoxide is feasible for all the compounds, suggesting a dual Type I/Type II activity.

On the origin of photodynamic activity of hypericin and its iodine-containing derivatives

The main photophysical properties, useful for establishing whether hypericin in anionic form and some of its derivatives containing heavy atoms such as iodine, can be proposed for their use in photodynamic therapy, were determined using density functional based computations. The results showed that in the anionic form and in the iodinated derivatives, the absorption wavelength undergoes a bathochromic shift, the singlet-triplet energy gap assumes values ​that allow to excite the oxygen molecule from its ground to the excited singlet state, and that the spin-orbit couplings between singlet and triplet states significantly increase.

Chalcogen Effects in the Photophysical Properties of Dimethylamino-1,8-naphthalimide Dyes Revealed by DFT Investigation

Thionation of carbonyl groups of known dyes is a rapidly emerging strategy to propose an advance toward heavy-atom-free photosensitizers to be used in photodynamic therapy (PDT). The sulfur-for-oxygen replacement has recently proved to enhance the singlet oxygen quantum yield of some existing fluorophores and to shift the absorption band at longer wavelengths. Drawing inspiration from this challenging evidence, the effect of both sulfur- and selenium-for-oxygen replacement in the skeleton of the oxo-4-dimethylamino-1,8-naphthalimide molecule (DMN) has been analyzed by means of a DFT study. The thio- and seleno-derivatives (SDMN and SeDMN, respectively) have been shown to offer the possibility to access a multitude of ISC (intersystem crossing) pathways involved in the triplet deactivation mechanisms with a consequent enhancement of the singlet oxygen production, also arising from the change of orbital type involved in the radiationless ¹nπ* → ³ππ* transitions. Moreover, the change in nature from a ¹ππ* to a ¹nπ* observed in the SeDMN has been revealed to be crucial to reach more clinically useful regions of the spectrum suggesting that the selenium-for-oxygen replacement can be proposed as a strategy to achieve more suitable PDT agents while proposing an advance toward heavy-atom-free PSs.

Evaluation of two-particle properties within finite-temperature self-consistent one-particle Green's function methods: Theory and application to GW and GF2

One-particle Green's function methods can model molecular and solid spectra at zero or non-zero temperatures. One-particle Green's functions directly provide electronic energies and one-particle properties, such as dipole moment. However, the evaluation of two-particle properties, such as ⟨S²⟩ and ⟨N²⟩, can be challenging because they require a solution of the computationally expensive Bethe-Salpeter equation to find two-particle Green's functions. We demonstrate that the solution of the Bethe-Salpeter equation can be completely avoided. Applying the thermodynamic Hellmann-Feynman theorem to self-consistent one-particle Green's function methods, we derive expressions for two-particle density matrices in a general case and provide explicit expressions for GF2 and GW methods. Such density matrices can be decomposed into an antisymmetrized product of correlated one-electron density matrices and the two-particle electronic cumulant of the density matrix. Cumulant expressions reveal a deviation from ensemble representability for GW, explaining its known deficiencies. We analyze the temperature dependence of ⟨S²⟩ and ⟨N²⟩ for a set of small closed-shell systems. Interestingly, both GF2 and GW show a non-zero spin contamination and a non-zero fluctuation of the number of particles for closed-shell systems at the zero-temperature limit.

Trapping and Releasing of Oxygen in Liquid by Metal-Organic Framework with Light and Heat

Nanoporous materials can adsorb small molecules into their nanospaces. However, the trapping of light gas molecules dissolved in solvents suffers from low concentration and poor adsorption affinity. Here, the reversible trapping and releasing of dissolved oxygen are shown through integrating photosensitization and chemical capturing abilities into a metal-organic framework (MOF), MOMF-1. 9,10-Di(4-pyridyl)anthracene (dpa) ligands in MOMF-1 generates singlet oxygen from triplet oxygen under photoirradiation without additional photosensitizers, and successively reacts with it to produce anthracene endoperoxide, forming MOMF-2, which is proved crystallographically. The reverse reaction also proceeds quantitatively by heating MOMF-2. Moreover, MOMF-1 exhibits excellent water resistance, and completely removes oxygen of ppm order concentrations in water. The new material shown in this report allows controlling of the amount of dissolved oxygen, which can be applicable in various fields relating to numerous oxidation phenomena.

Theoretical investigation on bisarylselanylbenzo-2,1,3-selenadiazoles as potential photosensitizers in photodynamic therapy

Density functional theory and time-dependent (TDDFT) calculations were carried out for recently reported bisarylselanylbenzo-2,1,3-selenadiazoles derivatives capable of producing singlet oxygen (¹O₂) under UV-Vis irradiation. Conformational behaviors, excitation energies, singlet-triplet energy gaps, and spin-orbit coupling constants were evaluated. The conformational analysis evidences that two different conformers have to be taken into consideration to completely describe the photophysical properties of this class of molecules. TDDFT results show that these compounds, though possessing absorption wavelengths that fall in the violet region, are characterized by singlet-triplet energy gaps greater than the energy required to excite the molecular oxygen, thus being able to produce the cytotoxic species, spin-orbit coupling constants large enough to ensure efficient singlet-triplet intersystem spin crossing, and even the highly reactive superoxide anion O₂ ^•(-) by autoionization and subsequent electron transfer to molecular oxygen in its ground state.

Theoretical exploration of the photophysical properties of two-component RuII-porphyrin dyes as promising assemblies for a combined antitumor effect

Due to the extraordinary success of porphyrins in photodynamic therapy (PDT) and Ru compounds as chemotherapeutics, a series of RuII-porphyrin complexes have recently been synthesized and proposed as promising dual-action therapeutic agents. The results of a careful DFT and TDDFT investigation on four mononuclear pyridyl triphenylporphyrin RuII-arene complexes are herein reported and compared with those obtained for the metal-free derivatives. The investigation aims at shedding light on the modulation of the photophysical properties of the light absorber upon metalation and exploring the hydrolysis process of the RuII-moiety in the presence of the bulky porphyrin unit. Type I and Type II photoreactions were analyzed computing absorption spectra, singlet-triplet energy gaps, spin orbit coupling constants and vertical electron affinity (VEA) along with ionization potentials (VIP) for all the investigated compounds, while the chloride/water exchange reaction kinetics were determined by exploring the first and second aquation reactions of the Ru-moiety. Despite the highly similar photophysical properties displayed by the members of this class of compounds, an analysis of the hydrolysis processes in the dark allows to point out an interesting difference related to the type of pyridylporphyrin isomer and could be a preliminary explanation of the greater phototoxicity experimentally found for 3'-pyridyl substituted compounds.

Substituent Effect in the First Excited Triplet State of Monosubstituted Benzenes

The structure of 30 monosubstituted benzenes in the first excited triplet T₁ state was optimized with both unrestricted (U) and restricted open shell (RO) approximations combined with the ωB97XD/aug-cc-pVTZ basis method. The substituents exhibited diverse σ- and π-electron-donating and/or -withdrawing groups. Two different positions of the substituents are observed in the studied compounds in the T₁ state: one distorted from the plane and the other coplanar with a quinoidal ring. The majority of the substituents are π-electron donating in the first group while π-electron withdrawing in the second one. Basically, U- and RO-ωB97XD approximations yield concordant results except for the B-substituents and a few of the planar groups. In the T₁ state, the studied molecules are not aromatic, yet aromaticity estimated using the HOMA (harmonic oscillator model of aromaticity) index increases from ca. -0.2 to ca. 0.4 with substituent distortion, while in the S₁ state, they are only slightly less aromatic than in the ground state (HOMA ≈0.8 vs ≈1.0, respectively). Unexpectedly, the sEDA(T₁) and pEDA(T₁) substituent effect descriptors do not correlate with analogous parameters for the ground and first excited singlet states. This is because in the T₁ state, the geometry of the ring changes dramatically and the sEDA(T₁) and pEDA(T₁) descriptors do not characterize only the functional group but the entire molecule. Thus, they cannot provide useful scales for the substituents in the T₁ states. We found that the spin density in the T₁ states is accumulated at the C_ipso and C_p atoms, and with the substituent deformation angle, it nonlinearly increases at the former while decreases at the latter. It appeared that the gap between singly unoccupied molecular orbital and singly occupied molecular orbital (SUMO-SOMO) is determined by the change of the SOMO energy because the former is essentially constant. For the nonplanar structures, SOMO correlates with the torsion angle of the substituent and the ground-state pEDA(S₀) descriptor of the π-electron-donating substituents ranging from 0.02 to 0.2 e. Finally, shapes of the SOMO-1 instead of SOMO frontier orbitals in the T₁ state somehow resemble the highest occupied molecular orbital ones of the S₀ and S₁ states. For several planar systems, the shape of the U- and RO-density functional theory-calculated SOMO-1 orbitals differs substantially.

General framework for calculating spin-orbit couplings using spinless one-particle density matrices: Theory and application to the equation-of-motion coupled-cluster wave functions

Standard implementations of nonrelativistic excited-state calculations compute only one component of spin multiplets (i.e., M_s = 0 triplets); however, matrix elements for all components are necessary for deriving spin-dependent experimental observables. Wigner-Eckart's theorem allows one to circumvent explicit calculations of all multiplet components. We generate all other spin-orbit matrix elements by applying Wigner-Eckart's theorem to a reduced one-particle transition density matrix computed for a single multiplet component. In addition to computational efficiency, this approach also resolves the phase issue arising within Born-Oppenheimer's separation of nuclear and electronic degrees of freedom. A general formalism and its application to the calculation of spin-orbit couplings using equation-of-motion coupled-cluster wave functions are presented. The two-electron contributions are included via the mean-field spin-orbit treatment. Intrinsic issues of constructing spin-orbit mean-field operators for open-shell references are discussed, and a resolution is proposed. The method is benchmarked by using several radicals and diradicals. The merits of the approach are illustrated by a calculation of the barrier for spin inversion in a high-spin tris(pyrrolylmethyl)amine Fe(II) complex.

"Through-Space" Relativistic Effects on NMR Chemical Shifts of Pyridinium Halide Ionic Liquids

We have investigated, using two-component relativistic density functional theory (DFT) at ZORA-SO-BP86 and ZORA-SO-PBE0 level, the occurrence of relativistic effects on the ¹ H, ¹³ C, and ¹⁵ N NMR chemical shifts of 1-methylpyridinium halides [MP][X] and 1-butyl-3-methylpyridinium trihalides [BMP][X₃ ] ionic liquids (ILs) (X=Cl, Br, I) as a result of a non-covalent interaction with the heavy anions. Our results indicate a sizeable deshielding effect in ion pairs when the anion is I^- and I₃ ^- . A smaller, though nonzero, effect is observed also with bromine while chlorine based anions do not produce an appreciable relativistic shift. The chemical shift of the carbon atoms of the aromatic ring shows an inverse halogen dependence that has been rationalized based on the little C-2s orbital contribution to the σ-type interaction between the cation and anion. This is the first detailed account and systematic theoretical investigation of a relativistic heavy atom effect on the NMR chemical shifts of light atoms in the absence of covalent bonds. Our work paves the way and suggests the direction for an experimental investigation of such elusive signatures of ion pairing in ILs.

Theoretical insight into joint photodynamic action of a gold(i) complex and a BODIPY chromophore for singlet oxygen generation

Inclusion of a heavy gold atom in a peripheral position of BODIPY is enough to promote ISC.

Photophysical Properties of Nitrated and Halogenated Phosphorus Tritolylcorrole Complexes: Insights from Theory

The photophysical properties of a series of nitrated and halogenated phosphorus tritolylcorrole complexes were studied in dichloromethane solvent by using the density functional theory. Particular emphasis was given to the absorption spectra, the energy gap between the excited singlet and triplet states, and the magnitude of the spin-orbit couplings for a series of possible intersystem crossing channels between those excited states. The proposed study provides a better description of the photophysical properties of these systems while giving insights into their possible use as photosensitizers in photodynamic therapy.

Computational Investigation of the Influence of Halogen Atoms on the Photophysical Properties of Tetraphenylporphyrin and Its Zinc(II) Complexes

How the tetraphenylporphyrin (TPP) and its zinc(II) complexes (ZnTPP) photophysical properties (absorption energies, singlet-triplet energy gap and spin-orbit coupling contributions) can change due to the presence of an increasing number of heavy atoms in their molecular structures has been investigated by means of density functional theory and its time-dependent formulation. Results show that the increase of the atomic mass of the substituted halogen strongly enhances the spin-orbit coupling values, allowing a more efficient singlet-triplet intersystem crossing. Different deactivation channels have been considered and rationalized on the basis of El-Sayed and Kasha rules. Most of the studied compounds possess the appropriate properties to generate cytotoxic singlet molecular oxygen (¹Δ_g) and, consequently, they can be proposed as photosensitizers in photodynamic therapy.

Theoretical Insights into the Switching Off/On of 1 O2 Photosensitization in Chemicontrolled Photodynamic Therapy

Density Functional Theory and time-dependent (TD) DFT calculations were carried out for recently reported 4,4-difluoro-4-bora-3a,4a-diaza-s-indacene (BODIPY)-based photosensitizers (PSs) that could be activated by reactive oxygen species (ROS) to generate ¹ O₂ specifically in target tissues. To assess the applicability of the compounds as activatable PSs (a-PSs) in photodynamic therapy, absorption wavelengths; singlet-triplet energy gaps; and spin-orbit matrix elements for the radiationless transition, S_n →T_m , were investigated. A TD-DFT qualitative analysis indicated that only a Br-substituted BODIPY derivative with the chromanol ring of α-tocopherol linked by methylene functioned as an a-PS. The chromanol ring promotes photoinduced electron transfer to the BODIPY unit that reduces the probability of intersystem crossing and triplet-state population, and can turn off ¹ O₂ photosensitization. Therefore, ¹ O₂ photosensitization can be switched on only in target cells in which the chromanol ring is oxidized by ROS. The oxidation reaction pathways of the most promising derivative, by either ¹ O₂ or cumyloxyl radical as typical ROS, have been examined to reveal that oxidation by the cumyloxyl radical is more effective than that by ¹ O₂ .

Excitation energies, singlet–triplet energy gaps, spin–orbit matrix elements and heavy atom effects in BOIMPYs as possible photosensitizers for photodynamic therapy: a computational investigation

Introduction of halogen atoms in different amounts and positions into the BOIMPY skeleton significantly affects its photophysical properties.

Theoretical study on photophysical properties of three high water solubility polypyridyl complexes for two-photon photodynamic therapy

Two-photon photodynamic therapy (TP-PDT) is a very promising treatment that has drawn much attention in recent years due to its ability to penetrate deeper into tissues and minimize the damage to normal cells.

Metal Atom Effect on the Photophysical Properties of Mg(II), Zn(II), Cd(II), and Pd(II) Tetraphenylporphyrin Complexes Proposed as Possible Drugs in Photodynamic Therapy

The effects of Mg, Zn, Cd, and Pd dications on the photophysical properties of the tetraphenylporphyrin ligand have been explored, considering the corresponding complexes and by using the density functional theory and its time-dependent extension. Results show that absorption wavelengths do not change significantly when the metal ion changes contrary to what happens to the singlet–triplet energy gaps (ΔE_S−T) and the spin-orbit matrix elements 〈ΨSn|H^so|ΨTm〉. The most probable intersystem spin crossing (ISC) pathways for the population of the lowest triplet states have been explored. Our findings can contribute to rationalize the available experimental data and promote the potential therapeutic use of these compounds as photosensitizers in photodynamic therapy (PDT).

Theory and Calculation of the Phosphorescence Phenomenon

Phosphorescence is a phenomenon of delayed luminescence that corresponds to the radiative decay of the molecular triplet state. As a general property of molecules, phosphorescence represents a cornerstone problem of chemical physics due to the spin prohibition of the underlying triplet-singlet emission and because its analysis embraces a deep knowledge of electronic molecular structure. Phosphorescence is the simplest physical process which provides an example of spin-forbidden transformation with a characteristic spin selectivity and magnetic field dependence, being the model also for more complicated chemical reactions and for spin catalysis applications. The bridging of the spin prohibition in phosphorescence is commonly analyzed by perturbation theory, which considers the intensity borrowing from spin-allowed electronic transitions. In this review, we highlight the basic theoretical principles and computational aspects for the estimation of various phosphorescence parameters, like intensity, radiative rate constant, lifetime, polarization, zero-field splitting, and spin sublevel population. Qualitative aspects of the phosphorescence phenomenon are discussed in terms of concepts like structure-activity relationships, donor-acceptor interactions, vibronic activity, and the role of spin-orbit coupling under charge-transfer perturbations. We illustrate the theory and principles of computational phosphorescence by highlighting studies of classical examples like molecular nitrogen and oxygen, benzene, naphthalene and their azaderivatives, porphyrins, as well as by reviewing current research on systems like electrophosphorescent transition metal complexes, nucleobases, and amino acids. We furthermore discuss modern studies of phosphorescence that cover topics of applied relevance, like the design of novel photofunctional materials for organic light-emitting diodes (OLEDs), photovoltaic cells, chemical sensors, and bioimaging.

Halogen atom effect on the photophysical properties of substituted aza-BODIPY derivatives

The influence of halogen atom substitution (Br and I), in different amounts and positions in an aza-BODIPY skeleton, on the photophysical properties of some aza-BODIPY derivatives has been investigated by using density functional theory and its time-dependent extension.

Spin-Free CC2 Implementation of Induced Transitions between Singlet Ground and Triplet Excited States

In most organic molecules, phosphorescence has its origin in transitions from triplet exited states to the singlet ground state, which are spin-forbidden in nonrelativistic quantum mechanics. A sufficiently accurate description of phosphorescence lifetimes for molecules that contain only light elements can be achieved by treating the spin-orbit coupling (SOC) with perturbation theory (PT). We present an efficient implementation of this approach for the approximate coupled cluster singles and doubles model CC2 in combination with the resolution-of-the-identity approximation for the electron repulsion integrals. The induced oscillator strengths and phosphorescence lifetimes from SOC-PT are computed within the response theory framework. In contrast to previous work, we employ an explicitly spin-coupled basis for singlet and triplet operators. Thereby, a spin-orbital treatment can be entirely avoided for closed-shell molecules. For compounds containing only light elements, the phosphorescence lifetimes obtained with SOC-PT-CC2 are in good agreement with those of exact two-component (X2C) CC2, whereas the calculations are roughly 12 times faster than with X2C. Phosphorescence lifetimes computed for two thioketones with the SOC-PT-CC2 approach agree very well with reference results from experiment and are similar to those obtained with multireference spin-orbit configuration interaction and with X2C-CC2. An application to phosphorescent emitters for metal-free organic light-emitting diodes (OLEDs) with almost 60 atoms and more than 1800 basis functions demonstrates how the approach extends the applicability of coupled cluster methods for studying phosphorescence. The results indicate that other decay channels like vibrational relaxation may become important in such systems if lifetimes are large.

Can Expanded Bacteriochlorins Act as Photosensitizers in Photodynamic Therapy? Good News from Density Functional Theory Computations

The main photophysical properties of a series of expanded bacteriochlorins, recently synthetized, have been investigated by means of DFT and TD-DFT methods. Absorption spectra computed with different exchange-correlation functionals, B3LYP, M06 and ωB97XD, have been compared with the experimental ones. In good agreement, all the considered systems show a maximum absorption wavelength that falls in the therapeutic window (600-800 nm). The obtained singlet-triplet energy gaps are large enough to ensure the production of cytotoxic singlet molecular oxygen. The computed spin-orbit matrix elements suggest a good probability of intersystem spin-crossing between singlet and triplet excited states, since they result to be higher than those computed for 5,10,15,20-tetrakis-(m-hydroxyphenyl)chlorin (Foscan©) already used in the photodynamic therapy (PDT) protocol. Because of the investigated properties, these expanded bacteriochlorins can be proposed as PDT agents.

The heavy atom effect on Zn(ii) phthalocyanine derivatives: a theoretical exploration of the photophysical properties

Absorption electronic spectra, singlet-triplet energy gaps and spin-orbit matrix elements have been computed at DFT and TDDFT levels of theory for a series of substituted Zn(ii)-phthalocyanines (ZnPcs), recently proposed as potential photosensitizers in photodynamic therapy (PDT). Their photophysical properties have been rationalized in the light of the substitution pattern which includes the position, the donor or withdrawing nature, and the relative donating force of peripheral and non-peripheral ligands. Moreover, the effects of heavy substituents on these properties have been investigated by introducing a different number of iodine atoms on the phthalocyanine macrocycle. The results show that the substitution pattern significantly affects the absorption spectra, but just slightly modifies the ΔES-T values. The presence of heavy atoms produces a significant effect on the photophysical properties of the investigated compounds enhancing the spin-orbit coupling (SOC) values.

Luminescent group 12 metal tetracarboxylate networks as probe for metal ions

Hydrothermalin situdecomposition of DMF generated three [NH₂(CH₃)₂]⁺templated anionic zinc and cadmium terphenyl-3,2′′,5′′,3′-tetracarboxylate frameworks, which show tunable luminescence in the presence of metal ions. In particular,1could be a luminescent sensor for selectively detecting traces of Ca²⁺ions at ppm level in a pyridine suspension.

The Dalton quantum chemistry program system

Dalton is a powerful general-purpose program system for the study of molecular electronic structure at the Hartree-Fock, Kohn-Sham, multiconfigurational self-consistent-field, Møller-Plesset, configuration-interaction, and coupled-cluster levels of theory. Apart from the total energy, a wide variety of molecular properties may be calculated using these electronic-structure models. Molecular gradients and Hessians are available for geometry optimizations, molecular dynamics, and vibrational studies, whereas magnetic resonance and optical activity can be studied in a gauge-origin-invariant manner. Frequency-dependent molecular properties can be calculated using linear, quadratic, and cubic response theory. A large number of singlet and triplet perturbation operators are available for the study of one-, two-, and three-photon processes. Environmental effects may be included using various dielectric-medium and quantum-mechanics/molecular-mechanics models. Large molecules may be studied using linear-scaling and massively parallel algorithms. Dalton is distributed at no cost from http://www.daltonprogram.org for a number of UNIX platforms.

Bisanthracene bis(dicarboxylic imide)s as potential photosensitizers in photodynamic therapy: a theoretical investigation

The electronic structures and spectroscopic properties of four bisanthracene bis(dicarboxylic imide)s (M1-M4) have been investigated theoretically by using density functional theory (DFT) and its time-dependent extension (TDDFT) in view of their potential use as photosensitizers in photodynamic therapy (PDT). The optimized geometries, electronic absorption transitions, singlet-triplet energy gaps, spin-orbit matrix elements, ionization potentials, and electron affinities have been determined in gas phase and in solvent. Both type I and II PDT mechanisms have been considered. In addition, the variation of a series of relevant properties upon heavy atom substitution (Br and I) have been determined and discussed. Results show that only M4 is able to support the type I reaction, and one of its brominated and iodinated derivatives can produce cytotoxic singlet oxygen (type II reaction).

First-principles calculations of zero-field splitting parameters

In this work, an implementation of an approach to calculate the zero-field splitting (ZFS) constants in the framework of ab initio methods such as complete active space self-consistent field, multireference configuration interaction, or spectroscopy oriented configuration interaction is reported. The spin-orbit coupling (SOC) contribution to ZFSs is computed using an accurate multicenter mean-field approximation for the Breit-Pauli Hamiltonian. The SOC parts of ZFS constants are obtained directly after diagonalization of the SOC operator in the basis of a preselected number of roots of the spin-free Hamiltonian. This corresponds to an infinite order treatment of the SOC in terms of perturbation theory. The spin-spin (SS) part is presently estimated in a mean-field fashion and appears to yield results close to the more complete treatments available in the literature. Test calculations for the first- and second-row atoms as well as first-row transition metal atoms and a set of diatomic molecules show accurate results for the SOC part of ZFSs. SS contributions have been found to be relatively small but not negligible (exceeding 1 cm(-1) for oxygen molecule). At least for the systems studied in this work, it is demonstrated that the presented method provides much more accurate estimations for the SOC part of ZFS constants than the emerging density functional theory approaches.

Importance of direct spin-spin coupling and spin-flip excitations for the zero-field splittings of transition metal complexes: a case study

This work reports the evaluation of several theoretical approaches to the zero-field splitting (ZFS) in transition metal complexes. The experimentally well-known complex [Mn(acac)3] is taken as an example. The direct spin-spin contributions to the ZFS have been calculated on the basis of density functional theory (DFT) or complete active space self-consistent field (CASSCF) wave functions and have been found to be much more important than previously assumed. The contributions of the direct term may exceed approximately 1 cm(-1) in magnitude and therefore cannot be neglected in any treatment that aims at a realistic quantitative modeling of the ZFS. In the DFT framework, two different variants to treat the spin-orbit coupling (SOC) term have been evaluated. The first approach is based on previous work by Pederson, Khanna, and Kortus, and the second is based on a "quasi-restricted" DFT treatment which is rooted in our previous work on ZFS. Both approaches provide very similar results and underestimate the SOC contribution to the ZFS by a factor of 2 or more. The SOC is represented by an accurate multicenter spin-orbit mean-field (SOMF) approximation which is compared to the popular effective DFT potential-derived SOC operator. In addition to the DFT results, direct "infinite order" ab initio calculations of the SOC contribution to the ZFS based on CASSCF wave functions, the spectroscopy-oriented configuration interaction (SORCI), and the difference-dedicated CI (DDCI) approach are reported. In general, the multireference ab initio results provide a more realistic description of the ZFS in [Mn(acac)3]. The conclusions likely carry over to many other systems. This is attributed to the explicit treatment of the multiplet effects which are of dominant importance, since the calculations demonstrate that, even in the high-spin d4 system MnIII, the spin-flip excitations make the largest contribution to the SOC. It is demonstrated that the ab initio methods can be used even for somewhat larger molecules (the present calculations were done with more than 500 basis functions) in a reasonable time frame. Much more economical but still fairly reasonable results have been achieved with the INDO/S treatment based on CASSCF and SOC-CI wave functions.

Evaluation of low-scaling methods for calculation of phosphorescence parameters

In order to find a methodology that is a compromise between favorable computational scaling and tolerable errors, a series of nonrelativistic approaches for the calculation of radiative phosphorescence lifetimes are benchmarked against fully relativistic four-component results. The study of the a 3A2-X 1A1 transition intensity in the series of H2CX molecules, where X is a chalcogene atom, X={O,S,Se,Te}, indicates a general good agreement between fully relativistic four-component and nonrelativistic perturbation-theoretical calculations. Among the nonrelativistic approaches, the scaled-charge spin-orbit operator approach is recognized as to provide transition matrix elements that are in good agreement with those obtained with the more elaborate Breit-Pauli and atomic mean field spin-orbit operators. This finding supports phosphorescence calculations using the available linear scaling technology for large complexes and, together with effective-core potentials, large complexes including heavy elements.

A combined experimental and computational investigation of the microscopic external heavy atom effect in van der Waals clusters

We present a combined experimental and computational study of the external heavy atom effect in van der Waals clusters of para-difluorobenzene (pDFB) with rare-gas atoms. Experimentally, clustering with rare-gas atoms is observed to shorten significantly the S1 fluorescence lifetime compared with that of the pDFB monomer, an effect we interpret in terms of an enhancement of the S1-T1 intersystem crossing rate. In order to test the validity of this widely held assumption, we have calculated the S1-T1 spin-orbit coupling matrix elements in the X-pDFB complexes (X=Ne, Ar, Kr) using a multiconfigurational linear response approach.

Response calculations of electronic and vibrational transitions in molecular oxygen induced by interaction with noble gases

The Einstein coefficient for the singlet oxygen emission a1Deltag-->X3Sigmag- at lambda=1270 nm and b1Sigmag+-->X3Sigmag- emission at lambda=750 nm were calculated by quadratic response (QR) multiconfiguration self-consisted field (MCSCF) method for a number of collision complexes O2+M, where M=He, Ne, Ar. Interaction with He clusters was studied in order to simulate cooperative effect of the environment on the oxygen emission. Calculations of the dipole transition moment for the Noxon band, b1Sigmag+-a1Deltag, by linear response (LR) MCSCF method were also performed for a number of collision complexes. Spin-orbit coupling (SOC) between the b1Sigmag+ and X3Sigmag- (MS=0) states does not change much upon collisions, thus the a-X transition borrows intensity mostly from the collision-induced Noxon band b-a. The a-X intensity borrowing from the Schumann-Runge transition is negligible. The calculations show that the b-a and a-X transition probabilities are enhanced approximately by 10(5) and 10(3) times by O2+M collisions. An order of magnitude differences occur for both transitions for noble gases with large difference in polarizability. A strong cooperative effect is obtained when few He atoms perturb the oxygen molecule. Depending on mutual orientation of the partners it can be a complete quenching of the a-->X emission or strong non-additive enhancement. Collision-induced infrared vibrational transitions in a number of molecular oxygen excited states were studied and shown to be state selective.