Excited State Energy Research Articles

State-Specific Coupled-Cluster Methods for Excited States.

We reexamine ΔCCSD, a state-specific coupled-cluster (CC) with single and double excitations (CCSD) approach that targets excited states through the utilization of non-Aufbau determinants. This methodology is particularly efficient when dealing with doubly excited states, a domain in which the standard equation-of-motion CCSD (EOM-CCSD) formalism falls short. Our goal here to evaluate the effectiveness of ΔCCSD when applied to other types of excited states, comparing its consistency and accuracy with EOM-CCSD. To this end, we report a benchmark on excitation energies computed with the ΔCCSD and EOM-CCSD methods for a set of molecular excited-state energies that encompasses not only doubly excited states but also doublet-doublet transitions and (singlet and triplet) singly excited states of closed-shell systems. In the latter case, we rely on a minimalist version of multireference CC known as the two-determinant CCSD method to compute the excited states. Our data set, consisting of 276 excited states stemming from the quest database [Véril et al., WIREs Comput. Mol. Sci. 2021, 11, e1517], provides a significant base to draw general conclusions concerning the accuracy of ΔCCSD. Except for the doubly excited states, we found that ΔCCSD underperforms EOM-CCSD. For doublet-doublet transitions, the difference between the mean absolute errors (MAEs) of the two methodologies (of 0.10 and 0.07 eV) is less pronounced than that obtained for singly excited states of closed-shell systems (MAEs of 0.15 and 0.08 eV). This discrepancy is largely attributed to a greater number of excited states in the latter set exhibiting multiconfigurational characters, which are more challenging for ΔCCSD. We also found typically small improvements by employing state-specific optimized orbitals.

Boosting Excited-State Energy Transfer by Anchoring Dipole Orientation in Binary Thermally Activated Delayed Fluorescence/J-Aggregate Assemblies.

Förster resonance energy transfer (FRET) has been widely applied in fluorescence imaging, sensing and so on, while developing useful strategy of boosting FRET efficiency becomes a key issue that limits the application. Except optimizing spectral properties, promoting orientation factor (κ2) has been well discussed but rarely utilized for boosting FRET. Herein, we constructed binary nano-assembling of two thermally activated delayed fluorescence (TADF) emitters (2CzPN and DMAC-DPS) with J-type aggregate of cyanine dye (C8S4) as doping films by taking advantage of their electrostatic interactions. Time-resolved spectroscopic measurements indicated that 2CzPN/Cy-J films exhibit an order of magnitude higher kFRET than DMAC-DPS/Cy-J films. Further quantitative analysing on kFRET and kDET indicated higher orientation factor (κ2) in 2CzPN/Cy-J films play a key role for achieving fast kFRET, which was subsequently confirmed by anisotropic measurements. Corresponding DFT/TDDFT calculation revealed strong "two-point" electrostatic anchoring in 2CzPN/Cy-J films that is responsible for highly orientated transitions. We provide a new strategy for boosting FRET in nano-assemblies, which might be inspired for designing FRET-based devices of sensing, imaging and information encryption.

Novel Photocatalyst Based on Through‐Space Charge Transfer Induced Intersystem Crossing Enables Rapid and Efficient Polymerization Under Low‐Power Excitation Light

AbstractCurrently, most photoredox catalysis polymerization systems are limited by high excitation power, long polymerization time, or the requirement of electron donors due to the precise design of efficient photocatalysts still poses a great challenge. Herein, we propose a new approach: the creation of efficient photocatalysts having low ground state oxidation potentials and high excited state energy levels, along with through‐space charge transfer (TSCT) induced intersystem crossing (ISC) properties. A cabazole‐naphthalimide (NI) dyad (NI‐1) characterized by long triplet excited state lifetime (τT=62 μs), satisfactory ISC efficiency (ΦΔ=54.3 %) and powerful reduction capacity [Singlet: E1/2 (PC+1/*PC)=−1.93 eV, Triplet: E1/2 (PC+1/*PC)=−0.84 eV] was obtained. An efficient and rapid polymerization (83 % conversion of 1 mM monomer in 30 s) was observed under the conditions of without electron donor, low excitation power (10 mW cm−2) and low catalyst (NI‐1) loading (<50 μM). In contrast, the conversion rate was lower at 29 % when the reference catalyst (NI‐4) was used for photopolymerization under the same conditions, demonstrating the advantage of the TSCT photocatalyst. Finally, the TSCT material was used as a photocatalyst in practical lithography for the first time, achieving pattern resolutions of up to 10 μm.

Practical consideration on Racah parameter and Tanabe−Sugano diagram analyses for Mn4+ and Cr3+-activated phosphors

The Racah parameters and Tanabe−Sugano (T−S) diagram are widely used as describing the electron−electron repulsion effects within the metal complexes in coordination chemistry. The present study discusses the Racah and related parameters for the Mn4+ and Cr3+-activated phosphors. The main subjects are two-fold: (i) to clarify how different input parameters of the excited-state energies make a difference in the Racah parameters derived from the general model and (ii) to further clarify the differences between the general and our newly proposed models. The three different excited-state energies of (1) the zero-phonon line energy, (2) the photoluminescence (PL) and/or PL excitation (PLE) peak energies, and (3) the Stokes shift-corrected PLE peak energy are considered in (ii). It is shown that the choice of such excited-state energies is of crucial importance for obtaining reliable Racah parameters and T−S diagram. The present analysis of (ii) also suggests our newly proposed model to promise the Racah parameters being satisfied the requirements of B and C to be smaller than and their ratio of C/B being not largely changed from the free-ion values. The lattice temperature effects on the PL and PLE spectral features of the 3d3 ion-activated phosphors are also discussed in detail.

Manipulation of Nonradiative Process Based on the Aggregation Microenvironment to Customize Excited-State Energy Conversion.

ConspectusNonradiative processes with the determined role in excited-state energy conversion, such as internal conversion (IC), vibrational relaxation (VR), intersystem crossing (ISC), and energy or electron transfer (ET or eT), have exerted a crucial effect on biological functions in nature. Inspired by these, nonradiative process manipulation has been extensively utilized to develop organic functional materials in the fields of energy and biomedicine. Therefore, comprehensive knowledge and effective manipulation of sophisticated nonradiative processes for achieving high-efficiency excited-state energy conversion are quintessential. So far, many strategies focused on molecular engineering have demonstrated tremendous potential in manipulating nonradiative processes to tailor excited-state energy conversion. Besides, molecular aggregation considerably affects nonradiative processes due to their ultrasensitivity, thus providing us with another essential approach to manipulating nonradiative processes, such as the famous aggregation-induced emission. However, the weak interactions established upon aggregation, namely, the aggregation microenvironment (AME), possess hierarchical, dynamic, and systemic characteristics and are extremely complicated to elucidate. Revealing the relationship between the AME and nonradiative process and employing it to customize excited-state energy conversion would greatly promote advanced materials in energy utilization, biomedicine, etc., but remain a huge challenge. Our group has devoted much effort to achieving this goal.In this Account, we focus on our recent developments in nonradiative process manipulation based on AME. First, we provide insight into the effect of the AME on nonradiative process in terms of its steric effect and electronic regulation, illustrating the possibility of nonradiative process manipulation through AME modulation. Second, the distinct enhanced steric effect is established by crystallization and heterogeneous polymerization to conduct crystallization-induced reversal from dark to bright excited states and dynamic hardening-triggered nonradiative process suppression for highly efficient luminescence. Meanwhile, promoting the ISC process and stabilizing the triplet state are also manipulated by the crystal and polymer matrix to induce room-temperature phosphorescence. Furthermore, the strategies employed to exploit nonradiative processes for photothermy and photosensitization are reviewed. For photothermal conversion, besides the weakened steric effect with promoted molecular motions, a new strategy involving the introduction of diradicals upon aggregation to narrow the energy band gap and enhance intermolecular interactions is put forward to facilitate IC and VR for high-efficiency photothermal conversion. For photosensitization, both the enhanced steric effect from the rigid matrix and the effective electronic regulation from the electron-rich microenvironment are demonstrated to facilitate ISC, ET, and eT for superior photosensitization. Finally, we explore the existing challenges and future directions of nonradiative process manipulation by AME modulation for customized excited-state energy conversion. We hope that this Account will be of wide interest to readers from different disciplines.

Regioisomerism vs Conformation: Impact of Molecular Design on the Emission Pathway in Organic Light-Emitting Device Emitters.

Despite the design and proposal of several new structural motifs as thermally activated delayed fluorescent (TADF) emitters for organic light-emitting device (OLED) applications, the nature of their interaction with the host matrix in the emissive layer of the device and their influence on observed photophysical outputs remain unclear. To address this issue, we present, for the first time, the use of up to four regioisomers bearing a donor-acceptor-donor electronic structure based on the desymmetrized naphthalene benzimidazole scaffold, equipped with various electron-donating units and possessing distinguished conformational lability. Quantum chemical calculations allow us to identify the most favorable conformations adopted by the electron-rich groups across the entire pool of regioisomers. These conformations were then compared with conformational changes caused by the interaction of the emitter with the Zeonex and 4,4'-bis(N-carbazolyl)-1,1'-biphenyl (CBP) matrices, and the correlation with observed photophysics was monitored by UV-vis absorption and steady-state photoluminescence spectra, combined with time-resolved spectroscopic techniques. Importantly, a CBP matrix was found to have a significant impact on the conformational change of regioisomers, leading to unique TADF emission mechanisms that encompass dual emission and inversion of the singlet-triplet excited-state energies and result in the enhancement of TADF efficiency. As a proof of concept, regioisomers with optimal donor positions were utilized to fabricate an OLED, revealing, with the best-performing dye, an external quantum emission of 11.6%, accompanied by remarkable luminance (28,000 cd/m2). These observations lay the groundwork for a better understanding of the role of the host matrix. In the long term, this new knowledge can lead to predicting the influence of the host matrix and adopting the structure of the emitter in a way that allows the development of highly efficient and efficient OLEDs.

Excited State Dynamics in Unidirectional Photochemical Molecular Motors.

Unidirectional photochemically driven molecular motors (PMMs) convert the energy of absorbed light into continuous rotational motion. As such they are key components in the design of molecular machines. The prototypical and most widely employed class of PMMs is the overcrowded alkenes, where rotational motion is driven by successive photoisomerization and thermal helix inversion steps. The efficiency of such PMMs depends upon the speed of rotation, determined by the rate of ground state thermal helix inversion, and the quantum yield of photoisomerization, which is dependent on the excited state energy landscape. The former has been optimized by synthetic modification across three generations of overcrowded alkene PMMs. These improvements have often been at the expense of photoisomerization yield, where there remains room for improvement. In this perspective we review the application of ultrafast spectroscopy to characterize the excited state dynamics in PMMs. These measurements lead to a general mechanism for all generations of PMMs, involving subpicosecond decay of a Franck-Condon excited state to populate a dark excited state which decays within picoseconds via conical intersections with the electronic ground state. The model is discussed in the context of excited state dynamics calculations. Studies of PMM photochemical dynamics as a function of solvent suggest exploitation of intramolecular charge transfer and solvent polarity as a route to controlling photoisomerization yield. A test of these ideas for a first generation motor reveals a high degree of solvent control over isomerization yield. These results suggest a pathway to fine control over the performance of future PMMs.

Indole-imidazole hybrid Schiff base for the selective detection of the explosive picric acid via fluorescence “turn-off” process: Experimental and theoretical DFT-D3 study

A compound containing a heteroatom and Schiff base, 3-(4,5-Diphenyl-1H-imidazol-2-yl)-1H-indole (INBIL) has been synthesized through the one-pot condensation of indole-3-carbaldehyde with benzil in ethanol and characterized using various analytical parameters like FT-IR, NMR; its thermal and chemical stability also established. The synthesized INBIL showed a 'turn off' luminescent property that has been used to detect picric acid. This luminescent sensor has a broad emission band at 415 nm in acetonitrile due to the conjugation of its double bond. It is worth noting that INBIL can be recycled through TEA treatment. The chemosensor exhibited the highest sensitivity with Ksv = 1.51 × 10−6 M, and a detection limit of 2.91 × 10−7 M, with perfect linearity up to 22 µL. The binding stoichiometry ratio between INBIL and picric acid was predicted to be 1:1 using Job's plot, which was confirmed by 1H NMR analysis. Finally, DFT-D3 calculations were used to calculate the excited molecule's singlet and triplet energy states.

Iron(III) Carbene Complexes with Tunable Excited State Energies for Photoredox and Upconversion.

Substituting precious elements in luminophores and photocatalysts by abundant first-row transition metals remains a significant challenge, and iron continues to be particularly attractive owing to its high natural abundance and low cost. Most iron complexes known to date face severe limitations due to undesirably efficient deactivation of luminescent and photoredox-active excited states. Two new iron(III) complexes with structurally simple chelate ligands enable straightforward tuning of ground and excited state properties, contrasting recent examples, in which chemical modification had a minor impact. Crude samples feature two luminescence bands strongly reminiscent of a recent iron(III) complex, in which this observation was attributed to dual luminescence, but in our case, there is clear-cut evidence that the higher-energy luminescence stems from an impurity and only the red photoluminescence from a doublet ligand-to-metal charge transfer (2LMCT) excited state is genuine. Photoinduced oxidative and reductive electron transfer reactions with methyl viologen and 10-methylphenothiazine occur with nearly diffusion-limited kinetics. Photocatalytic reactions not previously reported for this compound class, in particular the C-H arylation of diazonium salts and the aerobic hydroxylation of boronic acids, were achieved with low-energy red light excitation. Doublet-triplet energy transfer (DTET) from the luminescent 2LMCT state to an anthracene annihilator permits the proof of principle for triplet-triplet annihilation upconversion based on a molecular iron photosensitizer. These findings are relevant for the development of iron complexes featuring photophysical and photochemical properties competitive with noble-metal-based compounds.

Effect of Benzo-Annelation on Triplet State Energies in Polycyclic Conjugated Hydrocarbons.

In a series of earlier studies, the effect of benzo-annelation was found to be a useful tool for tuning the aromaticity in polycyclic conjugated compounds to desired level. In this work we studied the (anti)aromaticity of benzo-annelated derivatives of three conjugated hydrocarbons (anthracene, fluoranthene and biphenylene) in their lowest lying singlet (S0) and triplet (T1) states by means of the energy effect (ef), harmonic oscillator model of aromaticity (HOMA), multicentre delocalization indices (MCI), magnetically induced current densities (MICDs) and nucleus independent chemical shifts (NICS). We showed that benzo-annelation is a topology-based effect which can be used to modify the T1 state excitation energies (E(T1)). A quantitative model was established being able to accurately predict the E(T1) based only on the numbers of angularly, linearly and geminally annelated benzene rings. In addition, it was demonstrated that the E(T1) can be directly related to the (anti)aromatic character of the central ring in the studied molecules in their S0 state.

How do spin-scaled double hybrids designed for excitation energies perform for noncovalent excited-state interactions? An investigation on aromatic excimer models.

Time-dependent double hybrids with spin-component or spin-opposite scaling to their second-order perturbative correlation correction have demonstrated competitive robustness in the computation of electronic excitation energies. Some of the most robust are those recently published by our group (M. Casanova-Páez, L. Goerigk, J. Chem. Theory Comput. 2021, 20, 5165). So far, the implementation of these functionals has not allowed correctly calculating their ground-state total energies. Herein, we define their correct spin-scaled ground-state energy expressions which enables us to test our methods on the noncovalent excited-state interaction energies of four aromatic excimers. A range of 22 double hybrids with and without spin scaling are compared to the reasonably accurate wavefunction reference from our previous work (A. C. Hancock, L. Goerigk, RSC Adv. 2023, 13, 35964). The impact of spin scaling is highly dependent on the underlying functional expression, however, the smallest overall errors belong to spin-scaled functionals with range separation: SCS- and SOS- PBEPP86, and SCS-RSX-QIDH. We additionally determine parameters for DFT-D3(BJ)/D4 ground-state dispersion corrections of these functionals, which reduce errors in most cases. We highlight the necessity of dispersion corrections for even the most robust TD-DFT methods but also point out that ground-state based corrections are insufficient to completely capture dispersion effects for excited-state interaction energies.

Chemiluminescence and electrochemiluminescence of water-soluble iridium(III) complexes containing a tetraethylene-glycol functionalised triazolylpyridine ligand

BackgroundIridium(III) complexes, exhibiting high luminescence quantum yields and a wide range of emission colours, are promising alternatives to tris(2,2ʹ-bipyridine)ruthenium(II) for chemiluminescence (CL) and electrochemiluminescence (ECL) detection. This emerging class of reagent, however, is limited by the poor solubility of many iridium(III) complexes in aqueous solution, and lack of understanding of their remarkably variable selectivities towards different analytes. ResultsSeven [Ir(C^N)2(pt-TEG)]+ complexes, exhibiting a wide range of reduction potentials and emission energies, were examined with six model analytes. For CL, cerium(IV) was used as the oxidant. The alkylamine analytes generally produced greater CL and ECL with the more readily oxidised Ir(III) complexes (C^N = piq, bt, ppy), predominantly through the ‘direct’ pathway requiring oxidation of both metal complex and analyte. Aniline derivatives that did not also contain secondary or tertiary alkylamines elicited CL from the less readily oxidised complexes (C^N = df-ppy-CF3, df-ppy) via energy transfer. The most difficult to oxidise complexes (C^N = df(CF3)-ppy-Me, df(CN)-ppy) gave poor responses due to the limited potential window of the solvent and inefficiency of energy transfer to their high energy excited states. Greater CL and/or ECL intensities were generally obtained for each analyte with at least one Ir(III) complex than with [Ru(bpy)3]2+; superior limits of detection for two analytes were demonstrated. SignificanceThis exploration of CL/ECL in which the properties of luminophore, analyte and oxidant are all varied provides a new understanding of the influence of the metal-complex potentials and excited state energy on the light-producing and quenching pathways, and consequently, their distinct selectivity towards different analytes. These findings will guide the development of water-soluble Ir(III) complexes as CL and ECL reagents.

Fused Azulenyl Squaraine Derivatives Improve Phototheranostics in the Second Near‐Infrared Window by Concentrating Excited State Energy on Non‐Radiative Decay Pathways

AbstractThe second near‐infrared (NIR‐II) theranostics offer new opportunities for precise disease phototheranostic due to the enhanced tissue penetration and higher maximum permissible exposure of NIR‐II light. However, traditional regimens lacking effective NIR‐II absorption and uncontrollable excited‐state energy decay pathways often result in insufficient theranostic outcomes. Herein a phototheranostic nano‐agent (PS‐1 NPs) based on azulenyl squaraine derivatives with a strong NIR‐II absorption band centered at 1092 nm is reported, allowing almost all absorbed excitation energy to dissipate through non‐radiative decay pathways, leading to high photothermal conversion efficiency (90.98 %) and strong photoacoustic response. Both in vitro and in vivo photoacoustic/photothermal therapy results demonstrate enhanced deep tissue cancer theranostic performance of PS‐1 NPs. Even in the 5 mm deep‐seated tumor model, PS‐1 NPs demonstrated a satisfactory anti‐tumor effect in photoacoustic imaging‐guided photothermal therapy. Moreover, for the human extracted tooth root canal infection model, the synergistic outcomes of the photothermal effect of PS‐1 NPs and 0.5 % NaClO solution resulted in therapeutic efficacy comparable to the clinical gold standard irrigation agent 5.25 % NaClO, opening up possibilities for the expansion of NIR‐II theranostic agents in oral medicine.

Fused Azulenyl Squaraine Derivatives Improve Phototheranostics in the Second Near-Infrared Window by Concentrating Excited State Energy on Non-Radiative Decay Pathways.

The second near-infrared (NIR-II) theranostics offer new opportunities for precise disease phototheranostic due to the enhanced tissue penetration and higher maximum permissible exposure of NIR-II light. However, traditional regimens lacking effective NIR-II absorption and uncontrollable excited-state energy decay pathways often result in insufficient theranostic outcomes. Herein a phototheranostic nano-agent (PS-1 NPs) based on azulenyl squaraine derivatives with a strong NIR-II absorption band centered at 1092 nm is reported, allowing almost all absorbed excitation energy to dissipate through non-radiative decay pathways, leading to high photothermal conversion efficiency (90.98 %) and strong photoacoustic response. Both in vitro and in vivo photoacoustic/photothermal therapy results demonstrate enhanced deep tissue cancer theranostic performance of PS-1 NPs. Even in the 5 mm deep-seated tumor model, PS-1 NPs demonstrated a satisfactory anti-tumor effect in photoacoustic imaging-guided photothermal therapy. Moreover, for the human extracted tooth root canal infection model, the synergistic outcomes of the photothermal effect of PS-1 NPs and 0.5 % NaClO solution resulted in therapeutic efficacy comparable to the clinical gold standard irrigation agent 5.25 % NaClO, opening up possibilities for the expansion of NIR-II theranostic agents in oral medicine.

Photophysics of a Monoannulated Indigo: Intra- and Intermolecular Charge Transfer.

In the present work, the photoinduced charge-transfer (CT) behavior of 7-phenyl-6H-pyrido[1,2-a:3,4-b']diindole-6,13(12H)-dione (HCB) as a function of solvent polarity is reported by UV-vis absorption, steady-state and time-resolved fluorescence, and quantum chemical calculations. Calculated excited state energies of HCB at the B3PW91/6-31+G* level in vacuo and in solvents fulfill the energy requirements for singlet fission, which is the most promising path for the generation of highly efficient solar cells. The calculated potential energy curve for the compound reveals that the keto form is the predominant form in the ground state. Large bathochromic shifts in fluorescence with decreasing trends of quantum yield and lifetime indicate the occurrence of intramolecular CT from the indole bicycle to the indolinone moiety of HCB in highly polar solvents. The observed quenching of HCB fluorescence in different solvents without altering the spectral shape upon addition of a donor, triethylamine, is attributed to intermolecular CT, and it was examined in terms of the Stern-Volmer kinetics. The thermodynamics of photoinduced CT processes in HCB was analyzed using the measured photophysical data and cyclic voltammetric redox potentials via the Rehm-Weller equation. Analyses with the semiclassical Marcus theory suggest that both the CT processes fall under the Marcus normal region.

The Evolution of 174Yb, 176Hf, 178W and 180Os Isotones

The characteristics of 174Yb, 176Hf, 178W, and 180Os isotones are determined, followed by the calculation of their energy states. The first energy states 𝐸21+ and the ratios of the second excited energy states to the first excited energy states𝑅4/2 = 𝐸41 +/𝐸21+ provide primary information regarding the characteristics of the nuclei at low levels. To know the properties of high-energy states of nuclei, the behavior of the ground states band (GSB) studied by determine the back-bending curves which may occur and determine the change in the moment of inertia 2𝜗/ℏ2 and the rotation energy of gamma emitted at different states 2𝜔2, the E-GOS curve which study the gamma energy emitted from each state 𝐸𝐵🁡nd the behavior of the successive energy states in comparison with those states close to them 𝑟 (𝐼+2🀩 are drawn and studied. The relationship between GSB and NPB (the negative parity band) which give the odd staggering ∆𝐼 = 1 curve of each nucleus have been studied and determine the probability of change of the property of 174Yb, 176Hf, 178W, 180Os isotones. We used all of the information from the previous study to calculate the energy states of GSB using the appropriate equations for the different limits of the interacting boson model IBM-1. The interacting vector boson model IVBM was also utilized to compute the GSB and NPB of the isotones 174Yb, 176Hf, 178W, 180Os. A modification of IVBM was introduced to improve the results of calculations.

Many-Body-Expansion Based on Variational Quantum Eigensolver and Deflation for Dynamical Correlation.

In this work, we utilize the framework of many-body expansion (MBE) to decompose electronic structures into fragments by incrementing virtual orbitals, aiming to accurately solve the ground and excited state energies of each fragment using the variational quantum eigensolver and deflation algorithms. While our approach is primarily based on unitary coupled cluster singles and doubles (UCCSD) and its generalization, we also introduce modifications and approximations to conserve quantum resources in MBE by partially generalizing the UCCSD operator and neglecting the relaxation of the reference states. As a proof of concept, we investigate the potential energy surfaces for the bond-breaking processes of the ground state of two molecules (H2O and N2) and calculate the ground and excited state energies of three molecules (LiH, CH+, and H2O). The results demonstrate that our approach can, in principle, provide reliable descriptions in all the tests including strongly correlated systems when appropriate approximations are chosen. Additionally, we perform model simulations to investigate the impact of shot noise on the total MBE energy and show that precise energy estimation is crucial for lower-order MBE fragments.

Rationale for the extrapolation procedure in selected configuration interaction.

Selected configuration interaction (SCI) methods have emerged as state-of-the-art methodologies for achieving high accuracy and generating benchmark reference data for ground and excited states in small molecular systems. However, their precision relies heavily on extrapolation procedures to produce a final estimate of the exact result. Using the structure of the exact electronic energy landscape, we provide a rationale for the common linear extrapolation of the variational energy as a function of the second-order perturbative correction. In particular, we demonstrate that the energy gap and the coupling between the so-called internal and external spaces are the key factors determining the rate at which the linear regime is reached. Starting from the first principles, we also derive a new non-linear extrapolation formula that improves the post-processing of data generated from SCI methods and can be applied to both ground- and excited-state energies.

Abstract 2372 Increasing Solvent Molecules in an In-Silico Model of Solvated Systems Reduces Gaussian Properties of the Fluctuation of First Excitation State Energy

Abstract 2372 Increasing Solvent Molecules in an In-Silico Model of Solvated Systems Reduces Gaussian Properties of the Fluctuation of First Excitation State Energy

Single-Molecule Magnet Behavior of Confined Dy(III) in a Mixed Heteroatom-Substituted Polyoxotungstate.

Two heteroatom-templated Dy(III)-confined polyoxotungstates [H2N(CH3)2]7Na7[Dy2(H2O)7(W4O9)(HPSeW15O54)(α-SeW9O33)2]·31H2O (1) and [H2N(CH3)2]14K2Na18{[Dy2(H2O)13W14O40]2[α-SeW9O33]4[HPSeW15O54]2}·44H2O (2) were synthesized by a one-pot aqueous reaction and structurally characterized. The most distinctive structural feature of complexes 1 & 2 is the simultaneous presence of both trivacant Keggin [α-SeW9O33]8- and Dawson [HPSeW15O54]10- building blocks containing P(III)-Se(IV) heteroatoms. The trimeric polyanion of 1 can be represented as a fusion of two trivacant Keggin [α-SeW9O33]8- and Dawson [HPSeW15O54]10- building units encapsulating the [Dy2(H2O)7(W4O9)]12+ cluster. On the other hand, hexameric polyoxoanions of 2 are described as four trivacant Keggin [α-SeW9O33]8- and two Dawson [HPSeW15O54]10-, building units anchoring a [Dy4(H2O)26W28O80]20+ cluster. The magnetic investigation revealed the presence of significant magnetic anisotropy and slow relaxation of magnetization behavior for complex 1 with a phenomenological energy barrier, Ueff = 13.58 K in the absence of an external magnetic field, and Ueff = 24.57 K in the presence of a 500 Oe external dc magnetic field. On the other hand, complex 2 favors the QTM relaxation process in the absence of an external magnetic field and shows field-induced slow relaxation of magnetization with Ueff = 11.11 K at 1500 Oe applied dc field. The in-depth analysis of magnetic relaxation dynamics shows that the relaxation process follows the Orbach as well as Raman relaxation pathways. Further, the ab initio calculation of the studied complexes confirms that the highly axial ground and first excited energy states (containing pure highest mJ states) are responsible for the observed single-molecule magnet (SMM) behavior. Remarkably, this is the first example of a mixed heteroatom-based Dy(III)-substituted polyoxotungstate with both trimeric Keggin [α-SeW9O33]8- and Dawson [HPSeW15O54]10- building units showing SMM behavior.