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1.
J Comput Chem ; 44(3): 406-421, 2023 01 30.
Article in English | MEDLINE | ID: mdl-35789492

ABSTRACT

Quantum computers are special purpose machines that are expected to be particularly useful in simulating strongly correlated chemical systems. The quantum computer excels at treating a moderate number of orbitals within an active space in a fully quantum mechanical manner. We present a quantum phase estimation calculation on F2 in a (2,2) active space on Rigetti's Aspen-11 QPU. While this is a promising start, it also underlines the need for carefully selecting the orbital spaces treated by the quantum computer. In this work, a scheme for selecting such an active space automatically is described and simulated results obtained using both the quantum phase estimation (QPE) and variational quantum eigensolver (VQE) algorithms are presented and combined with a subtractive method to enable accurate description of the environment. The active occupied space is selected from orbitals localized on the chemically relevant fragment of the molecule, while the corresponding virtual space is chosen based on the magnitude of interactions with the occupied space calculated from perturbation theory. This protocol is then applied to two chemical systems of pharmaceutical relevance: the enzyme [Fe] hydrogenase and the photosenzitizer temoporfin. While the sizes of the active spaces currently amenable to a quantum computational treatment are not enough to demonstrate quantum advantage, the procedure outlined here is applicable to any active space size, including those that are outside the reach of classical computation.


Subject(s)
Computing Methodologies , Quantum Theory , Algorithms , Pharmaceutical Preparations
2.
J Chem Phys ; 158(15)2023 Apr 21.
Article in English | MEDLINE | ID: mdl-37094008

ABSTRACT

In this work, we present a computational approach that is able to incorporate vibrational effects in the computations of magnetic circular dichroism (MCD) spectra. The method combines our previous implementations to model absorption as well as fluorescence and phosphorescence spectra in the framework of excited state dynamics with a new technique to calculate MCD intensities, where molecular orientational averages are treated via semi-numerical quadrature. The implementation relies on a path integral approach that is employed to compute nuclear dynamics under the harmonic oscillator approximation (accounting for the nuclear potential energy surface) together with quasi-degenerate perturbative theory (to include the perturbation of an external magnetic field). We evaluate our implementation with a selected molecular set consisting of five aromatic organic molecules, namely, 1,4-benzoquinone, naphthalene, 2-naphthylamine, 2-naphthaldehyde, and benzene; we also included the MnO4- and the [Co(NH3)6]3+ transition metal complexes. This set is used to validate the ability of the approach to compute MCD A- and B-terms in conjunction with time-dependent density functional theory. The computed intensities are discussed in terms of the overall quality of the electronic structure treatments, vibrational modes, and the quality of the nuclear Hessians. It is shown that in the cases in which the potential energy surface is accurately represented, electric dipole-forbidden transitions are vibrationally activated, producing intensities relative to the dipole-allowed transitions in the same order of magnitude as the experimental measurements.

3.
Phys Chem Chem Phys ; 24(23): 14228-14241, 2022 Jun 15.
Article in English | MEDLINE | ID: mdl-35649286

ABSTRACT

Since the discovery of the peculiar conducting and optical properties of aromatics, many efforts have been made to characterize and predict their phosphorescence. This physical process is exploited in modern Organic Emitting Light Diodes (OLEDs), and it is also one of the processes decreasing the efficiency of Dye-sensitized solar cells (DSSCs). Herein, we propose a computational strategy for the accurate calculation of singlet-triplet gaps of aromatic compounds, which provides results that are in excellent agreement with available experimental data. Our approach relies on the domain-based local pair natural orbital (DLPNO) variant of the "gold standard" CCSD(T) method. The convergence of our results with respect to the key technical parameters of the calculation, such as the basis set used, the approximations employed in the perturbative triples correction, and the dimension of the PNOs space, was thoroughly discussed.

4.
Phys Chem Chem Phys ; 25(1): 684-689, 2022 Dec 21.
Article in English | MEDLINE | ID: mdl-36485073

ABSTRACT

Considering the relevance of room temperature phosphorescent (RTP) materials, we discuss the influence of donor and acceptor groups substituted on to a twisted three-fold symmetric hydrocarbon homotruxene, which presents a persistent RTP, even in the absence of donor or acceptor moieties, under ambient conditions as a result of the twisted π-system. Compared to a fluorine acceptor, a donor methoxy group increases the phosphorescence decay rate in solution, while in the solid-state, molecular aggregation and packing yield a very persistent phosphorescence visible by the eye. The RTP of the intrinsically apolar homotruxene is found to be modulated by polar substituents, whose main impact on the solid-state emission is due to altered packing in the crystal.

5.
J Chem Phys ; 155(10): 104109, 2021 Sep 14.
Article in English | MEDLINE | ID: mdl-34525816

ABSTRACT

In the present work, we describe a more accurate and efficient variant of the chain-of-spheres algorithm (COSX) for exchange matrix computations. Higher accuracy for the numerical integration is obtained with new grids that were developed using global optimization techniques. With our new default grids, the average absolute energy errors are much lower than 0.1 kcal/mol, which is desirable to achieve "chemical accuracy." Although the size of the new grids is increased by roughly a factor of 2.5, the excellent efficiency of the original COSX implementation is still further improved in most cases. The evaluation of the analytic electrostatic potential integrals was significantly accelerated by a new implementation of rolled-out versions of the Dupuis-Rys-King and Head-Gordon-Pople algorithms. Compared to our earlier implementation, a twofold speedup is obtained for the frequently used triple-ζ basis sets, while up to a 16-fold speedup is observed for quadruple-ζ basis sets. These large gains are a consequence of both the more efficient integral evaluation and the intermediate exchange matrix computation in a partially contracted basis when generally contracted shells occur. With our new RIJCOSX implementation, we facilitate accurate self-consistent field (SCF) binding energy calculations on a large supra-molecular complex composed of 320 atoms. The binding-energy errors with respect to the fully analytic results are well below 0.1 kcal/mol for the cc-pV(T/Q)Z basis sets and even smaller than for RIJ with fully analytic exchange. At the same time, our RIJCOSX SCF calculation even with the cc-pVQZ basis and the finest grid is 21 times faster than the fully analytic calculation.

6.
Inorg Chem ; 59(18): 13078-13090, 2020 Sep 21.
Article in English | MEDLINE | ID: mdl-32902965

ABSTRACT

The new luminescent carbonyl compounds [Mn(Oxa-H)(CO)3Br] (1) and [Mn(Oxa-NMe2)(CO)3Br] (2) were synthesized and fully characterized. Complexes 1 and 2 showed CO release under blue light (λ453). Spectroscopic techniques and TD-DFT and SOC-TD-DFT calculations indicated that 1 and 2 release the Oxa-H and Oxa-NMe2 coligands in addition to the carbonyl ligands, increasing the luminescence during photoinduction.

7.
J Biol Inorg Chem ; 24(5): 675-691, 2019 08.
Article in English | MEDLINE | ID: mdl-31267217

ABSTRACT

In this paper, the catalytic effects of aminoguanidine and aminopurine groups in the second sphere of a FeIIIZnII complex that mimics the active site of the metallohydrolase purple acid phosphatase (PAP) are investigated, with a particular view on DNA as substrate. The ligand 3-(((3-((bis(2-(pyridin-2-yl)ethyl)amino)methyl)-2-hydroxy-5-methylbenzyl)(pyridin-2-ylmethyl)amino)meth-yl)-2 hydroxy-5-methylbenzaldehyde-(H2L1bpea) was synthesized and its complex [(OH)FeIII(µ-OH)ZnII(H2O)(L1bpea)](ClO4) was used as a base for comparison with similar complexes previously published in the literature. Subsequent modifications were conducted in the aldehyde group, where aminoguanidine (amig) and aminopurine (apur) were used as side chain derivatives. The complexes [(OH)FeIII(µ-OH)ZnII(H2O)(L1bpea)](ClO4) (1), [(OH)FeIII(µ-OH)ZnII(H2O)(L1bpea-amig)](ClO4) (2) and [(OH)FeIII(µ-OH)ZnII(H2O)(L1bpea-apur)](ClO4) (3) were characterized by spectroscopic methods (infrared, UV-Vis) and ESI-MS spectrometry. Density functional theory (DFT) was also used to better understand the structure of the complexes. The hydrolytic activity of complexes 1, 2 and 3 was analyzed using both the model substrate 2,4-BDNPP (bis-(2,4-dinitrophenyl)phosphate) and DNA. Complexes 2 and 3, containing the derivatized ligands, have a significantly higher association constant (Kassoc≅ 1/KM) for the activated substrate 2,4-BDNPP compared to complex 1. The catalytic efficiency (kcat/KM) is also higher due to hydrogen bonds and/or π-stacking interactions between the substrate and the aminoguanidine or aminopurine groups present in 2 and 3, respectively. In the DNA cleavage assays, all complexes were able to cleave DNA, with 1 and 2 having higher catalytic activity than 3. In addition, when compared to previously analyzed complexes, complex 2 is one of the most active, having a kcat of 0.21 h-1.


Subject(s)
Coordination Complexes/chemistry , DNA/chemistry , Ferric Compounds/chemistry , Guanidine/chemistry , Purines/chemistry , Zinc/chemistry , Acid Phosphatase/chemistry , Acid Phosphatase/metabolism , DNA Cleavage , Hydrolysis
8.
J Chem Phys ; 150(21): 214102, 2019 Jun 07.
Article in English | MEDLINE | ID: mdl-31176338

ABSTRACT

In this work, we describe how Resonant Raman (RR) spectra can be predicted with good accuracy using the path integral formulation for the harmonic oscillator, including the Herzberg-Teller and Duschinsky rotation effects. In particular, we will focus on approximations to make these calculations more efficient and expand the current methodology to include overtones and combination bands in the final prediction. After outlining the theory, we explain how it can be made into a black-box method and discuss the approximations that rely on its intrinsic parameters. It is shown that the latter can improve the efficiency by orders of magnitude, without substantial loss in accuracy. We will also show that the predicted RR spectra are in good agreement with experiment for both the intensity and position of spectral peaks, even for higher order vibronic excitations. Thus, the method proposed here can be used as a computational aid to experiments to improve the quality of analysis and theoretical understanding of RR.

9.
Angew Chem Int Ed Engl ; 58(21): 6982-6986, 2019 May 20.
Article in English | MEDLINE | ID: mdl-30908833

ABSTRACT

The dehydrating cyclotrimerization of 1-tetralone in the presence of titanium tetrachloride at high temperatures leads to homotruxene, a nonplanar arene in which the twist angles between its three outer benzene rings and the central benzene are stabilized by ethylene bridges. This non-planar configuration allows for pronounced spin-orbit coupling and a high triplet energy, leading to room-temperature phosphorescence in air with a lifetime of 0.38 s and a quantum yield of 5.6 %, clearly visible to the human eye after switching off the excitation. Triplet-triplet annihilation is found to simultaneously lead to a substantial delayed fluorescence, unprecedented from a pure hydrocarbon at ambient conditions, with a lifetime of 0.11 s.

10.
J Chem Phys ; 148(3): 034104, 2018 Jan 21.
Article in English | MEDLINE | ID: mdl-29352790

ABSTRACT

In this work, we present and implement the theory for calculating fluorescence rates and absorption and emission spectra from first principles, using the path integral approach. We discuss some approximations and modifications to the full set of equations that improve speed and numerical stability for the case when a large number of modes are considered. New methods to approximate the excited state potential energy surface are also discussed and it is shown that for most purposes, these can be used instead of a full geometry optimization to obtain the rates mentioned above. A few examples are presented and the overall performance of the method is discussed. It is shown that the rates and spectra computed in this way are well within the acceptable range of errors and can be used in future predictions, particularly for screening purposes, with the only limitation on size being that of the electronic structure calculation itself.

11.
J Chem Phys ; 149(11): 114108, 2018 Sep 21.
Article in English | MEDLINE | ID: mdl-30243273

ABSTRACT

A spin adapted configuration interaction scheme is proposed for the evaluation of ionization potentials in α high spin open shell reference functions. There are three different ways to remove an electron from such a reference, including the removal of an alpha or a beta electron from doubly occupied or an alpha electron from singly occupied molecular orbitals. Ionization operators are constructed for each of these cases, and the resulting second quantized expressions are implemented using an automated code generator environment. To achieve greater computational efficiency, the virtual space is reduced using an averaged pair natural orbital machinery developed earlier and applied with great success in the calculation of X-ray absorption spectra [D. Manganas et al., J. Chem. Phys. A 122, 1215 (2018)]. Various approximate integral evaluation schemes including the resolution of identity and seminumerical techniques are also invoked to further enhance the computational efficiency. Although the resulting method is not particularly accurate in terms of predicting absolute energy values, with a simple shift in the ionization potentials, it is still possible to use it for the qualitative characterization of the basic features of X-ray photoionization spectra. While satellite intensities cannot be computed with the current method, the inclusion of vibrational effects using a path integral technique allows for the computation of vibrational transitions corresponding to main peaks.

12.
Sensors (Basel) ; 18(12)2018 Dec 12.
Article in English | MEDLINE | ID: mdl-30545035

ABSTRACT

A realistic implementation of an all-fiber CO2 sensor, using 74 cm of hollow core photonic crystal fiber (HC-PCF) as the cavity for light/gas interaction, has been implemented. It is based on CO2 absorbance in the 2 µm region. The working range is from 2% to 100% CO2 concentration at 1 atm total pressure and the response time obtained was 10 min. Depending on the concentration level, the sensor operates at one of three different wavelengths (2003.5 nm, 1997.0 nm and 1954.5 nm) to maintain a high sensitivity across all the working range.

13.
Inorg Chem ; 52(7): 3594-6, 2013 Apr 01.
Article in English | MEDLINE | ID: mdl-23496379

ABSTRACT

Herein we describe the synthesis of a new heterodinuclear Fe(III)Cu(II) model complex for the active site of purple acid phosphatases and its binding to a polyamine chain, a model for the amino acid residues around the active site. The properties of these systems and their catalytic activity in the hydrolysis of bis(2,4-dinitrophenyl)phosphate are compared, and conclusions regarding the effects of the second coordination sphere are drawn. The positive effect of the polymeric chain on DNA hydrolysis is also described and discussed.


Subject(s)
Acid Phosphatase/chemistry , Coordination Complexes/chemistry , Coordination Complexes/chemical synthesis , Copper/chemistry , Glycoproteins/chemistry , Iron/chemistry , Plant Proteins/chemistry , Polyamines/chemistry , Amino Acids/chemistry , Biocatalysis , Catalytic Domain , Cations , DNA/chemistry , Hydrolysis , Kinetics , Models, Molecular , Molecular Mimicry
14.
Dalton Trans ; 51(3): 1008-1018, 2022 Jan 17.
Article in English | MEDLINE | ID: mdl-34935838

ABSTRACT

Speeding up the phosphorescence channel in luminescent copper(I) complexes has been extremely challenging due to the copper atoms relatively low spin-orbit coupling constant compared to heavier metals such as iridium. Here, we report the synthesis and characterization of three mononuclear copper(I) complexes with diimines, triphenylphosphine, and iodide ligands to evaluate the effect of the copper-iodide (Cu-I) moiety into the phosphorescence decay pathway. Temperature-dependent photophysical studies revealed combined thermally activated delayed fluorescence and phosphorescence emission, with a phosphorescence decay rate of the order of 104 s-1. Density functional theory calculations indicate very high spin-orbit coupling matrix elements between the low-lying states of these complexes. Compared to the classical [Cu(phen)(POP)]+, our results demonstrate that Cu-I is a versatile moiety to speed up the phosphorescence decay pathway in about one order of magnitude, and it can be prepared by a simplified synthetic route with few synthetic steps. Furthermore, the SOC matrix elements and the phosphorescence decay rates of these complexes are comparable to those of extensively applied coordination complexes based on heavier metals, making them a promising alternative as active layers of organic light-emitting diodes.

15.
Eur J Cardiovasc Prev Rehabil ; 18(2): 233-9, 2011 Apr.
Article in English | MEDLINE | ID: mdl-21450670

ABSTRACT

BACKGROUND: An increase in cardiovascular (CV) disease has been observed in prehypertensive subjects who frequently carry other cardiovascular risk factors. In Brazil, little is known about prehypertension and its association with cardiovascular risk factors. OBJECTIVE: To estimate the association between prehypertension and cardiovascular risk factors in a public primary healthcare programme. METHODS: Associations in this cross-sectional study were estimated on the basis of generalized estimating equations. Results are expressed as odds ratio (OR) or adjusted odds ratio (OR(a)) with 95% confidence interval (CI). RESULTS: The 357 participants were classified as normotensive (64.4%) or prehypertensive (35.6%). In a univariate analysis, prehypertension was statistically associated with male gender, age, table salt use, diabetes, body mass index (BMI), uric acid, and all lipids except high-density lipoprotein cholesterol. When analysis was performed adjusting for gender, age, and table salt use, the association of each metabolic parameter with prehypertension, remained significant for BMI (OR(a) = 1.097; 95% CI 1.035-1.162), triglycerides (OR(a) = 1.008; 95% CI 1.003-1.013), and uric acid (OR(a) = 1.269; 95% CI 1.023- .576). To check for their independence of obesity, associations of triglycerides and uric acid with prehypertension were reanalysed after adjustment for BMI. The association of triglycerides remained statistically significant. A trend of association was present for uric acid. The prevalence of prehypertension paralleled the increase of the number of risk factors. CONCLUSION: Prehypertension in Brazil is associated with well-recognized cardiovascular risk factors even in a continuously monitored population such the one under study. Prehypertension can be a valuable clue to alert health professionals to treat underlying perturbations to prevent overt cardiovascular disease.


Subject(s)
Cardiovascular Diseases/epidemiology , Prehypertension/epidemiology , Primary Health Care , Adult , Alcohol Drinking/epidemiology , Biomarkers/blood , Body Mass Index , Brazil/epidemiology , Cardiovascular Diseases/blood , Cardiovascular Diseases/physiopathology , Cross-Sectional Studies , Diabetes Mellitus/epidemiology , Dyslipidemias/blood , Dyslipidemias/epidemiology , Female , Humans , Hyperuricemia/blood , Hyperuricemia/epidemiology , Lipids/blood , Male , Middle Aged , Obesity/epidemiology , Obesity/physiopathology , Odds Ratio , Prehypertension/blood , Prehypertension/physiopathology , Risk Assessment , Risk Factors , Smoking/epidemiology , Uric Acid/blood , Young Adult
16.
Chem Sci ; 12(8): 2916-2924, 2021 Jan 04.
Article in English | MEDLINE | ID: mdl-34164058

ABSTRACT

Many studies have recently explored a new class of reversible photoswitching compounds named Donor-Acceptor Stenhouse Adducts (DASAs). Upon light irradiation, these systems evolve from a coloured open-chain to a colourless closed-ring form, while the thermal back-reaction occurs at room temperature. In order to fulfill the requirements for different applications, new molecules with specific properties need to be designed. For instance, shifting the activation wavelength towards the red part of the visible spectrum is of relevance to biological applications. By using accurate computational calculations, we have designed new DASAs and predicted some of their photophysical properties. Starting from well-studied donor and acceptor parts, we have shown that small chemical modifications can lead to substantial changes in both photophysical and photoswitching properties of the resulting DASAs. Furthermore, we have also analysed how these substitutions impact the electronic structure of the systems. Finally, some pertinent candidates have been successfully synthesized and their photoswitching properties have been characterized experimentally.

17.
Chem Sci ; 12(45): 15116-15127, 2021 Nov 24.
Article in English | MEDLINE | ID: mdl-34909153

ABSTRACT

Halogenation of a twisted three-fold symmetric hydrocarbon with F, Cl or Br leads to strong modulation of triplet-triplet annihilation and dual phosphorescence, one thermally activated and the other very persistent and visible by eye, with different relative contributions depending on the halide. The room temperature phosphorescence is highly unusual given the absence of lone-pair-contributing heteroatoms. The interplay between the spin-orbit coupling matrix elements and the spatial configuration of the triplet state induces efficient intersystem crossing and thus room temperature phosphorescence even without relying on heteroatomic electron lone pairs. A ninefold increase of the ISC rate after introduction of three bromine atoms is accompanied by a much higher 34-fold increase of phosphorescence rate.

18.
Inorg Chem ; 49(24): 11421-38, 2010 Dec 20.
Article in English | MEDLINE | ID: mdl-21080710

ABSTRACT

Purple acid phosphatases (PAPs) are a group of metallohydrolases that contain a dinuclear Fe(III)M(II) center (M(II) = Fe, Mn, Zn) in the active site and are able to catalyze the hydrolysis of a variety of phosphoric acid esters. The dinuclear complex [(H(2)O)Fe(III)(µ-OH)Zn(II)(L-H)](ClO(4))(2) (2) with the ligand 2-[N-bis(2-pyridylmethyl)aminomethyl]-4-methyl-6-[N'-(2-pyridylmethyl)(2-hydroxybenzyl) aminomethyl]phenol (H(2)L-H) has recently been prepared and is found to closely mimic the coordination environment of the Fe(III)Zn(II) active site found in red kidney bean PAP (Neves et al. J. Am. Chem. Soc. 2007, 129, 7486). The biomimetic shows significant catalytic activity in hydrolytic reactions. By using a variety of structural, spectroscopic, and computational techniques the electronic structure of the Fe(III) center of this biomimetic complex was determined. In the solid state the electronic ground state reflects the rhombically distorted Fe(III)N(2)O(4) octahedron with a dominant tetragonal compression aligned along the µ-OH-Fe-O(phenolate) direction. To probe the role of the Fe-O(phenolate) bond, the phenolate moiety was modified to contain electron-donating or -withdrawing groups (-CH(3), -H, -Br, -NO(2)) in the 5-position. The effects of the substituents on the electronic properties of the biomimetic complexes were studied with a range of experimental and computational techniques. This study establishes benchmarks against accurate crystallographic structural information using spectroscopic techniques that are not restricted to single crystals. Kinetic studies on the hydrolysis reaction revealed that the phosphodiesterase activity increases in the order -NO(2) ←Br ←H ←CH(3) when 2,4-bis(dinitrophenyl)phosphate (2,4-bdnpp) was used as substrate, and a linear free energy relationship is found when log(k(cat)/k(0)) is plotted against the Hammett parameter σ. However, nuclease activity measurements in the cleavage of double stranded DNA showed that the complexes containing the electron-withdrawing -NO(2) and electron-donating -CH(3) groups are the most active while the cytotoxic activity of the biomimetics on leukemia and lung tumoral cells is highest for complexes with electron-donating groups.


Subject(s)
Acid Phosphatase/metabolism , Biomimetic Materials/metabolism , DNA Cleavage , Ferric Compounds/metabolism , Glycoproteins/metabolism , Organometallic Compounds/metabolism , Pyridines/metabolism , Zinc/metabolism , Acid Phosphatase/chemistry , Biomimetic Materials/chemistry , Cell Line, Tumor , Cell Survival/physiology , Circular Dichroism , Crystallography, X-Ray , Electron Spin Resonance Spectroscopy , Ferric Compounds/chemistry , Glycoproteins/chemistry , Humans , Kinetics , Models, Molecular , Organometallic Compounds/chemistry , Pyridines/chemistry , Zinc/chemistry
19.
Front Chem ; 8: 360, 2020.
Article in English | MEDLINE | ID: mdl-32478032

ABSTRACT

Herein, we report the synthesis and characterization of fluorophores containing a 2,1,3-benzoxadiazole unit associated with a π-conjugated system (D-π-A-π-D). These new fluorophores in solution exhibited an absorption maximum at around ~419 nm (visible region), as expected for electronic transitions of the π-π* type (ε ~2.7 × 107 L mol-1 cm-1), and strong solvent-dependent fluorescence emission (ΦFL ~0.5) located in the bluish-green region. The Stokes' shift of these compounds is ca. 3,779 cm-1, which was attributed to an intramolecular charge transfer (ICT) state. In CHCl3 solution, the compounds exhibited longer and shorter lifetimes, which was attributed to the emission of monomeric and aggregated molecules, respectively. Density functional theory was used to model the electronic structure of the compounds 9a-d in their excited and ground electronic states. The simulated emission spectra are consistent with the experimental results, with different solvents leading to a shift in the emission peak and the attribution of a π-π* state with the characteristics of a charge transfer excitation. The thermal properties were analyzed by thermogravimetric analysis, and a high maximum degradation rate occurred at around 300°C. Electrochemical studies were also performed in order to determine the band gaps of the molecules. The electrochemical band gaps (2.48-2.70 eV) showed strong correlations with the optical band gaps (2.64-2.67 eV).

20.
J Chem Theory Comput ; 15(3): 1896-1904, 2019 Mar 12.
Article in English | MEDLINE | ID: mdl-30721046

ABSTRACT

In this work, we present a general method for predicting phosphorescence rates and spectra for molecules using time-dependent density functional theory (TD-DFT) and a path integral approach for the dynamics that relies on the harmonic oscillator approximation for the nuclear movement. We first discuss the theory involved in including spin-orbit coupling (SOC) among singlet and triplet excited states and then how to compute the corrected transition dipole moments and phosphorescence rates. We investigate the dependence of these rates on some TD-DFT parameters, such as the nature of the functional, the number of roots, and the Tamm-Dancoff approximation. After that, we evaluate the effect of different SOC integral schemes and show that our best method is applicable to a large number of systems with different excited state characters.

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