Lattice Relaxation Effects Research Articles

Effect of trivalent manganese substitution in α-Al2O3 crystal on the absorption spectra based on first-principles calculations

The absorption spectra of α-Al2O3: Mn3+ at low-spin (LS) state have been estimated based on first-principles calculations without referring to any experimental parameter. The effect of lattice relaxation due to the Mn3+ substitution was considered under several computational procedures such as the Shannon’s crystal radii method and the geometry optimization using Cambridge Serial Total Energy Package (CASTEP) code. Two different sizes of model clusters consisting of 7 and 63 atoms were compared. Next, the molecular orbitals (MO) were estimated using the one-electron calculations discrete variational-Xα (DV-Xα) method while the absorption spectra were estimated using the many-electron calculations discrete variational multi-electron (DVME) method. The results show that the lattice-relaxation ratio is about ca. 104.05-106.43% depending on the computational conditions. Due to the Mn-O bond-length elongation, the crystal field splitting (10Dq) decreased ca. 0.24-0.41 eV. Thus, the peak position originating from 3T1 → 3E transition energy shifted toward the lower energy ca. 0.10-0.26 eV. Both of the larger-cluster size and the lattice-relaxation effect decrease the peak energies.

Dynamical Mechanism of Polarons and Bipolarons in Poly(p-Phenylene Vinylene)

Studies on Poly(p-Phenylene Vinylene) (PPV) and derivatives have experienced enormous growth since they were successfully used to fabricate the first efficient prototypes of Polymer Light-Emitting Diodes in the 90s. Despite this rapid progress, understanding the relationship between charge transport and the morphology in these materials remains a challenge. Here, we shed light on the understanding of the transport mechanism of polarons and bipolarons in PPVs by developing a two-dimensional tight-binding approach that includes lattice relaxation effects. Remarkably, the results show that the PPV lattice loses the energy related to its conjugation during time by transferring this amount of energy to electrons. Such a process for energy transfer permits the quasiparticles to overcome the potential barrier imposed by the local lattice deformations, that are formed in the presence of an additional charge and, consequently, their electric field assisted transport takes place. Within the framework of this transport mechanism, a better insight into the origin of the carrier mobility in PPV and derivatives can be achieved and would be a useful guide for improving their chemical structures and morphologies.

Ultrafast direct generation of quasiparticles in graphene nanoribbons

The problem of charge generation at short time scales in organic materials is of crucial importance for optoelectronics. Excluding controversial interpretations, the current state of the art suggests that highly delocalized photoexcitations enable the immediate probability of charge-transfer states within the ultrafast regime (∼ 100 fs). Here, we shed light on this problem by investigating the ultrafast direct generation of quasiparticles in armchair graphene nanoribbons (AGNRs). Through a two-dimensional tight-binding model that includes lattice relaxation effects, the direct creation mechanism of different quasiparticle species is elucidated. Results show that quasiparticles of distinct nature, namely solitons, polarons, and bipolarons, are directly formed in these materials within the ultrafast regime. The creation time for polarons depends on ribbon width and charge density, whereas for solitons and bipolarons only the former property plays a role. Our findings suggest that the creation times of these quasiparticles are quite different among nanoribbon families except under high charge carrier densities. These findings elucidate the assumption in the literature that charge carriers can be directly generated in organic materials within the ultrafast regime.

Realistic microstructure evolution of complex Ta-Nb-Hf-Zr high-entropy alloys by simulation techniques

Over last 15 years high-entropy alloys (HEAs) and complex concentrated alloys (CCAs) have gained much appreciation for their numerous superior properties. In this paper we have shown a novel simulation methodology to realistically predict the nanometer level local structural features of complex Ta0.25Nb0.25Hf0.25Zr0.25 HEA. This involves prediction of the morphology of the short-range clustering (SRCs), their quantitative atomic composition at the nano level and the thermodynamic aspects. An alloy structure model containing 11664 atoms was created and this was subjected to structure evolution at 1800 °C. The structure evolution technique is based on a combined hybrid Monte Carlo and molecular dynamics (MC/MD) approach. The simulated results from this work are further validated against experiments and material characterizations reported in literature and done by high-resolution transmission electron micrograph (HRTEM) for the nano-level microstructure, atom probe tomography (APT) for the local chemical compositions and X-ray diffraction at synchrotron sources for the local lattice relaxation effects. This work qualitatively and quantitatively reproduces the materials characterization results reasonably well from the developed simulation methodologies. The structure evolution methods as described in this work are based on independent computer simulations and does not involve any manual intervention for input based on experiments on evolving SRCs. This work shows the potential of utilizing MC/MD based computational methods to reduce the number of costly experimental characterizations and accelerate the pace for materials development.

Applications of Huang–Rhys theory in semiconductor optical spectroscopy

A brief review of Huang–Rhys theory and Albrechtos theory is provided, and their connection and applications are discussed. The former is a first order perturbative theory on optical transitions intended for applications such as absorption and emission involving localized defect or impurity centers, emphasizing lattice relaxation or mixing of vibrational states due to electron–phonon coupling. The coupling strength is described by the Huang–Rhys factor. The latter theory is a second order perturbative theory on optical transitions intended for Raman scattering, and can in-principle include electron–phonon coupling in both electronic states and vibrational states. These two theories can potentially be connected through the common effect of lattice relaxation – non-orthonormal vibrational states associated with different electronic states. Because of this perceived connection, the latter theory is often used to explain resonant Raman scattering of LO phonons in bulk semiconductors and further used to describe the size dependence of electron–phonon coupling or Huang–Rhys factor in semiconductor nanostructures. Specifically, the A term in Albrechtos theory is often invoked to describe the multi-LO-phonon resonant Raman peaks in both bulk and nanostructured semiconductors in the literature, due to the misconception that a free-exciton could have a strong lattice relaxation. Without lattice relaxation, the A term will give rise to Rayleigh or elastic scattering. Lattice relaxation is only significant for highly localized defect or impurity states, and should be practically zero for either single particle states or free exciton states in a bulk semiconductor or for confined states in a semiconductor nanostructure that is not extremely small.

Phonon characteristics of Si‐doped InAs grown by gas‐source molecular beam epitaxy

AbstractUsing Raman scattering spectroscopy with 514‐ and 633‐nm light sources, we have studied the phonon characteristics of Si‐doped InAs films grown on (100) n‐type InAs by gas‐source molecular beam epitaxy having charge carrier concentration (n) between 2.26 × 1018 and 1.68 × 1020 cm−3. The unscreened longitudinal optical (LO) phonon is observed near ~238 cm−1 along with two plasmon‐LO‐phonon (PLP) coupled L± modes. With increasing n, the L− mode is downshifted from the LO phonon towards the transverse optical mode frequency. This abnormal behavior is ascribed to the large scattering vector and heavy Landau damping. The L+ mode close to the plasma frequency ωP is also detected in samples with n > 1019 cm−3. The observed unscreened LO mode in the forbidden configuration is attributed to the resonance enhanced scattering induced by surface space charge. Reliable values of charge carrier density and mobility are estimated from the simulated shifts of PLP modes in the low Si‐doped InAs films. At higher doping level, a full‐line shape analysis is desired for assessing accurate values of the transport parameters. In Si‐doped InAs, we appraised the existing experimental data of localized vibrational modes (LVMs) from Raman and Fourier transform infrared spectroscopy by exploiting a sophisticated Green's function theory and incorporating lattice relaxation effects around SiIn and SiAs defects for constructing accurate perturbation models. The simulated results of LVMs for several isolated (Td) defects, nearest neighbor pair (C3v), and next‐nearest neighbor complex centers (Cs) are compared, contrasted, and discussed with the experimental data.

Systematic first-principles calculations of charge transfer transitions of trivalent rare earth ions in CaF2

In order to predict the LMCT energies for various trivalent rare earth (RE) ions in CaF2 nonempirically, we performed first-principles calculations using REF85− cluster using the relativistic Discrete Variational Multi-Electron (DVME) method, which is based on the configuration interaction (CI) approach, and constructed the theoretical energy diagram of the RE 4f levels within the band gap. The theoretical Ligand to Metal Charge Transfer (LMCT) energies were overestimated in the case of simple CI calculations. Therefore in order to overcome this problem we considered the configuration-dependent correction (CDC) and the effect of lattice relaxation based on the Shannon's crystal radii. As a result, the quantitative agreement between the theoretical LMCT energies and the experimental ones was greatly improved and the characteristic dependence of the LMCT energies on atomic species was also successfully reproduced without any experimental parameter.

Coupled-wire description of the correlated physics in twisted bilayer graphene

Since the discovery of superconductivity and correlated insulator at fractional electron fillings in the twisted bilayer graphene, most theoretical efforts have been focused on describing this system in terms of an effective extended Hubbard model. However, it was recognized that an exact tight binding model on the Moir\'{e} superlattice which captures all the subtleties of the bands can be exceedingly complicated. Here we pursue an alternative coupled wire description of the system based on the observation that the lattice relaxation effect is strong at small twist angle, which substantially enlarges the AB and BA stacking domains. Under an out-of-plane electric field which can have multiple origins, the low energy physics of the system is dominated by interconnected wires with (approximately) gapless $1d$ conducting quantum valley hall domain wall states. We demonstrate that the Coulomb interaction likely renders the wires a $U(2)_2$ $(1+1)d$ conformal field theory with a tunable Luttinger parameter for the charge $U(1)$ sector. Spin triplet and singlet Cooper pair operator both have quasi-long range order in this CFT. The junction between the wires at the AA stacking islands can lead to either a two dimensional superconductor, or an insulator.

Accommodation of a dimer in an Ar-like lattice: exploring the generic structural motifs.

A global optimization strategy is applied to Lennard-Jones models describing the stable trapping sites of a dimer in the face-centered cubic Ar-like lattice. Effective volumes of the trapping sites, quantified as the number of host atoms dislodged from the lattice, are mapped onto the parameter space defined by the strength and range of the dimer interaction potentials. The two models considered differ in the host-guest interaction and give very different maps that reflect the effect of local lattice relaxation. A hierarchical complete-linkage clustering technique is applied to identify generic structural types of the dimer accommodations. The dominant types found and enlisted maintain the symmetry of the isolated dimer and possess high tetrahedral and octahedral symmetry of the host environment with respect to the dimer atoms or center and can be roughly classified as the "whole" or "per atom" dimer accommodations. The results are compared to the analysis of the analogous model for trapped atoms and realistic model for trapped alkaline-earth metal dimers. Implications for matrix isolation spectroscopy are discussed.

Systematic first-principles calculations of charge transfer transitions of transition metal ions (Sc3+, Ti3+, V3+, Cr3+, Mn3+, Fe3+) in α-Al2O3

In order to predict the LMCT energies for various trivalent transition metal (TM) ions in α-Al2O3 nonempirically, we performed first-principles calculations using TMO69− cluster (TM = Sc3+, Ti3+, V3+, Cr3+, Mn3+, Fe3+) using the Discrete Variational Multi-Electron (DVME) method, which is based on the configuration interaction (CI) approach, and constructed the theoretical energy diagram of the TM 3d levels within the band gap. The theoretical Ligand to Metal Charge Transfer (LMCT) energies were overestimated in the case of simple CI calculations. Therefore in order to overcome this problem we considered the configuration-dependent correction (CDC) and the effect of lattice relaxation based on the Shannon's crystal radii. As a result, the quantitative agreement between the theoretical LMCT energies and the experimental ones was greatly improved and the characteristic dependence of the LMCT energies on atomic species was also successfully reproduced without any experimental parameter.

Optical and structural characteristics of Bridgman grown cubic Zn1-xMnxTe alloys

Experimental and theoretical investigations are reported to comprehend the structural and lattice dynamical properties of high quality Bridgman grown zb Zn1-xMnxTe (x ≤ 0.15) crystals. Our detailed far-infrared reflectivity and Raman scattering measurements ascertained atypical “intermediate-phonon-mode” behavior for the alloys. Besides perceiving ZnTe- and zb MnTe-like LO and TO phonons, a weak Mn alloy-disorder mode near ∼205 cm−1 is observed. A classical “Drude-Lorentz” model is used for evaluating the dielectric tensors of ternary alloys to simulate composition dependent reflectivity spectra – providing results in good agreement with the experimental data at near normal incidence. Lattice relaxation effects around MnZn and ZnMn from the synchrotron radiation extended x-ray absorption experiments are meticulously incorporated to help construct the perturbation models for simulating impurity modes using a realistic rigid-ion-model in the frame work of an average t-matrix Greens function theory – reconfirming on much firmer ground – the observed intermediate phonon mode behavior.

First-Principles Calculations of 4f-5d Transition Energy of Ce3+ in Y(Al1-xGax)5O12

The crystals doped with Ce3+ are utilized as various optical materials such as solid-state lasers, scintillators, and phosphors. Since the 4f-5d transition energy of Ce3+ in crystals strongly depends on the coordination environment, it is important to understand the relationship between the energy levels and the coordination environment for theoretical design of novel optical materials. For this purpose, garnet solid solutions are useful as host crystals since the physical properties can be modified by forming variety of solid-solutions through cation substitution. For example it is known that the 4f-5d transition energy of Ce3+ in Y(Al1-xGax)5O12 increases monotonically as x increases [1]. In this work, in order to investigate the relationship between the 4f-5d transition energy and the coordination environment of Ce3+ in Y(Al1-xGax)5O12, first-principles calculations were performed using the relativistic DV-Xα molecular orbital method [2]. At first YO8 clusters with D2 symmetry were constructed based on the crystal structure of Y(Al1-xGax)5O12 [3,4]. Then Ce was substituted for Y and the Ce-O bond lengths were adjusted based on the Shannon’s crystal radii [5] so as to consider the lattice relaxation effect [6]. In order to produce the effective Madelung potential, point charges were located at the atomic sites outside the cluster. As the exchange-correlation potential, the VWN potential [7] with the relativistic correction [8] was adopted. The 4f-5d transition energy was calculated using the Slater’s transition state method [9]. The calculated results showed that the variations of the average energy and the crystal field splitting of 5d levels of Ce3+ depending on x can be understood by the variations of the bond lengths, they are not monotonic. Although the 4f-5d transition energy is basically determined by these factors, interestingly the resultant theoretical 4f-5d transition energy showed monotonic variation. As a result the experimentally observed increasing tendency of the 4f-5d transition energy for increasing x was well reproduced. [1] P. Dorenbos, J. Lumin., 134, 310 (2013). [2] A. Rosén, D.E. Ellis, H. Adachi, and F.W. Averill, J. Chem. Phys., 65, 3629 (1976). [3] A. Nakatsuka, A. Yoshiasa, and S. Takeno, Acta Crystallogr., B51, 737 (1995). [4] A. Nakatsuka, A. Yoshiasa, and T. Yamanaka, Acta Crystallogr., B55, 266 (1999). [5] R.D. Shannon, Acta Crystallogr., A32, 751 (1976). [6] S. Watanabe, T. Ishii, K. Fujimura, and K. Ogasawara, J. Solid State Chem., 179, 2438 (2006). [7] S. H. Vosko, L. Wilk, and M. Nusair, Can. J. Phys. 58, 1200 (1980). [8] A. H. MacDonald and S. H. Vosko, J. Phys. C12, 2977 (1979). [9] J. C. Slater, Quantum Theory of Molecules and Solids (McGraw-Hill, New York, 1974), Vol. 4.

Dinuclear Cu(I) Complex with Combined Bright TADF and Phosphorescence. Zero-Field Splitting and Spin-Lattice Relaxation Effects of the Triplet State.

The three-fold bridged dinuclear Cu(I) complex Cu2(μ-I)2(1 N- n-butyl-5-diphenyl-phosphino-1,2,4-triazole)3, Cu2I2(P^N)3, shows bright thermally activated delayed fluorescence (TADF) as well as phosphorescence at ambient temperature with a total quantum yield of 85% at an emission decay time of 7 μs. The singlet (S1)-triplet (T1) energy gap is as small as only 430 cm-1 (53 meV). Spin-orbit coupling induces a short-lived phosphorescence with a decay time of 52 μs ( T = 77 K) and a distinct zero-field splitting (ZFS) of T1 into substates by ∼2.5 cm-1 (0.3 meV). Below T ≈ 10 K, effects of spin-lattice relaxation (SLR) are observed and agree with the size of ZFS. According to the combined phosphorescence and TADF, the overall emission decay time is reduced by ∼13% as compared to the TADF-only process. The compound may potentially be applied in solution-processed OLEDs, exploiting both the singlet and triplet harvesting mechanisms.

Ab-initio study on the absorption spectrum of color change sapphire based on first-principles calculations with considering lattice relaxation-effect

In this study, we performed an investigation on α-Al2O3: V3+ material, or the so-called color change sapphire, based on first-principles calculations without referring to any experimental parameter. The molecular orbital (MO) structure was estimated by the one-electron MO calculations using the discrete variational-Xα (DV-Xα) method. Next, the absorption spectra were estimated by the many-electron calculations using the discrete variational multi-electron (DVME) method. The effect of lattice relaxation on the crystal structures was estimated based on the first-principles band structure calculations. We performed geometry optimizations on the pure α-Al2O3 and with the impurity V3+ ion using Cambridge Serial Total Energy Package (CASTEP) code. The effect of energy corrections such as configuration dependence correction and correlation correction was also investigated in detail. The results revealed that the structural change on the α-Al2O3: V3+ resulted from the geometry optimization improved the calculated absorption spectra. By a combination of both the lattice relaxation-effect and the energy correction-effect improve the agreement to the experiment fact.

Effect of lattice relaxation on thermal conductivity of fcc-based structures: an efficient procedure of molecular dynamics simulation

This work studied the computational details of the Green–Kubo method with molecular dynamics (MD) simulation for thermal conductivity prediction. In MD thermal conductivity calculation, little consensus has been made about the inclusion of zero-pressure volume relaxation in the isobaric–isothermal (NpT) ensemble, which determines the simulation lattice parameters. Simulations of fcc-based structures with different lattice parameters were performed to calculate lattice thermal conductivities and phonon density of states, and the results were compared to experimental reports and ab initio results to conclude that NpT volume relaxation is crucial for accurate prediction of thermal conductivity. In addition, the relation between thermal conductivity and interatomic potential cutoff distance was also analysed in the context of lattice relaxation. The results suggested that calculated thermal conductivity is strictly dependent on the lattice parameter and essentially independent of the cutoff distance. It was also shown that reducing the cutoff distance can greatly accelerate the thermal conductivity calculation, even without sacrificing the accuracy of thermal conductivity.

Magneto-optical transitions in monolayer molybdenum disulphide on polar substrates

Within the frame of the Huang–Rhys's lattice relaxation model, we theoretically studied the effects of lattice relaxation due to the electrons (holes)-surface optical (SO) phonons coupling on the magneto-optical (MO) transitions in monolayer molybdenum disulphide on three different types of polar substrates. The lattice relaxation resulted in the peak position shifting and the linewidths broadening in MO transitions. The dependences of MO transitions on the magnetic field, temperature and polarization strength of substrates have been discussed in detail. The obtained results may provide a possible method to measure the coupling strength between the electrons (holes) and SO phonons in MO experiments.

First-Principles Calculation on the Emission Energy Level of Ruby Based on DV-Xα Molecular Orbital Method and Ligand Field Theory

The transition metal 3d3 ions activated in various host crystals have been studied in a great number of experiments and calculations. Their energy levels in strong crystal field namely 4A2, 2E, 2T1, 2T2, 4T2, and 4T1a play important roles in the luminescence process. Especially, the transition energy from 2E state to 4A2 state or R-line has been utilized for the emission process. Since the development of ligand field theory (LFT), the first-principles calculations have been helpful to understand the behavior of R-line. In 1982, Ohnishi and Sugano [1] carried out the semi-empirical first-principles calculation based on the discrete variational Xα (DV-Xα) method [2] to estimate the emission energy of ruby (Al2O3 doped with Cr3+) at various bond lengths under Oh symmetry. In their estimation, the barycenter of t 2g 3 configuration was an important parameter to estimate the R-line energy. Although the results are reasonable, the barycenter was defined as the average of only 3 multiplet states i.e. 2E, 2T1, and 2T2 states. However, according to LFT, the t 2g 3 configuration consists of 4 multiplet states not only 2E, 2T1, and 2T2 states but also the ground state, 4A2. Therefore, here we proposed a new calculation formula to improve the accuracy of R-line energy by considering 4 multiplet states such as 4A2, 2E, 2T1, and 2T2 states. Two types of model clusters, non-optimized and optimized model clusters consisting of 63 atoms were used for the calculations. The impurity Cr3+ ion was located at the center of the model clusters. The non-optimized model cluster was constructed based on the experimental crystal structures of α-Al2O3 under pressures with hexagonal A2X3 structure. On the other hand, since the local structure in the actual materials is different from the original ones, the optimized model cluster was constructed to consider the effect of lattice relaxation. It was estimated by performing geometry optimization using the CAmbridge Serial Total Energy package (CASTEP) code [3]. Firstly, the structural optimizations of pure α-Al2O3 crystal under various pressures were carried out and then followed by the geometry optimization of α-Al2O3 crystal doped with Cr3+ ion. The molecular orbitals energies were then estimated by performing one-electron calculations using DV-Xα method for both model clusters. During the calculations, the local C 3 symmetry was maintained to minimize the computational error. Next, the R-line energies were then estimated by two different approaches i.e., (1) based on the approach proposed by Ohnishi’s group and (2) based on LFT. Figure 1 shows the theoretical R-line energies of ruby under pressures calculated using the optimized model clusters. E R1 and E R2 indicate the estimated R-line energies based on the approach proposed by Ohnishi’s group and those based on LFT, respectively. For comparison, the R-line energies of ruby at various Cr-O bond length calculated under Oh symmetry [1] and the experimental R-line energies of ruby under pressures observed within C3 symmetry [4] are shown together in Fig. 1. Our results show that by both approaches, the R-line energies decrease as the applied pressure increases. Accordingly, simple estimation based on one-electron calculations has successfully reproduced the tendency of ruby’s emission energies. Compare to the experimental values, the R-line energies estimated based on Ohnishi’s approach were significantly underestimated. On the other hand, the calculated R-line energies based on LFT improved the accuracy towards the experiment excellently.

Deep level defects throughout the bandgap of (010) β-Ga2O3 detected by optically and thermally stimulated defect spectroscopy

Deep level optical spectroscopy (DLOS) and deep level transient spectroscopy (DLTS) measurements performed on Ni/β-Ga2O3 Schottky diodes fabricated on unintentionally doped (010) substrates prepared by edge-defined film-fed growth revealed a rich spectrum of defect states throughout the 4.84 eV bandgap of β-Ga2O3. Five distinct defect states were detected at EC − 0.62 eV, 0.82 eV, 1.00 eV, 2.16 eV, and 4.40 eV. The EC − 0.82 eV and 4.40 eV levels are dominant, with concentrations on the order of 1016 cm−3. The three DLTS-detected traps at EC − 0.62 eV, 0.82 eV, and 1.00 eV are similar to traps reported in Czochralski-grown β-Ga2O3, [K. Irmscher et al., J. Appl. Phys. 110, 063720 (2011)], suggesting possibly common sources. The DLOS-detected states at EC − 2.16 eV and 4.40 eV exhibit significant lattice relaxation effects in their optical transitions associated with strongly bound defects. As a consequence of this study, the Ni/β-Ga2O3 (010) Schottky barrier height was determined to be 1.55 eV, with good consistency achieved between different characterization techniques.

Fabrication and improvement of nanopillar InGaN / GaN light-emitting diodes using nanosphere lithography

Surface-patterning technologies have enabled the improvement of currently existing light-emitting diodes (LEDs) and can be used to overcome the issue of low quantum efficiency of green GaN-based LEDs. We have applied nanosphere lithography to fabricate nanopillars on InGaN/GaN quantum-well LEDs. By etching through the active region, it is possible to improve both the light extraction efficiency and, in addition, the internal quantum efficiency through the effects of lattice strain relaxation. Nanopillars of different sizes are fabricated and analyzed using Raman spectroscopy. We have shown that nanopillar LEDs can be significantly improved by applying a combination of ion-damage curing techniques, including thermal and acidic treatment, and have analyzed their effects using x-ray photoelectron spectroscopy.

Electronic Structure of Muonated Me<sub>4</sub>P[Pd(dmit)<sub>2</sub>]<sub>2 </sub>

Me4P[Pd(dmit)2]2 is an organic magnet that show long range antiferromagnetic ordering as indicated by Muon Spin Rotation measurements. Three muon centers were observed in the material. To determine the muon stopping sites, we have employed the Molecular Orbital Cluster Method to study the electronic structure of muonated Me4P[Pd(dmit)2]2. We used a cluster containing 1 formula unit in our investigations and applied the Density Functional Theory method. Three µ+ centers in the vicinity of three chemically non-equivalent sulfur sites, namely thione, thiol and thiolate were examined. All three µ+ sites were found to be energetically stable. In the pure Me4P[Pd(dmit)2]2 cluster, the spin densities of the doublet state system is spread throughout the entire dimer. Spin density of only about 0.13 is localized around the thiolate moiety. For all three µ+ centers, the lattice relaxation effect is important to stabilize the sites energetically.